Copyright )J? CO^i << COPYRIGHT DEPOSm J ELEMENTS OF HEAT- POWER ENGINEERING ,v- BY C: F. HIRSHFELD, M.M.E. Professor of Power Engineering, Sibley College, Cornell University, Ithaca, N.Y. AND WM. N. BARNARD, M.E. Professor of Steam Engineering, Sibley College, Cornell University, Ithaca, N.Y. SECOND EDITION, REVISED ^ TOTAL ISSUE FOUR THOUSAND NEW YORK JOHN WILEY & SONS, Inc. London: CHAPMAN & HALL, Limited 1915 4^ .^ Vi A Copyright, 1912, 1915 BY C. F. HIRSHFELD AND W. N. BARNARD Stanbopc iptess r. H. GILSON COMPAMT BOSTON, V.S.A. OCT I 1915 CU4in55 V_ PREFACE In preparing this textbook the Authors have attempted to include in a single volume not only the elementary thermo- dynamic theory of gases and vapors and of their cycles, but also the consideration of the sources of heat, the methods of making it available for useful purposes, its utilization in the various types of heat-driven prime movers and "their auxiliary apparatus, together with a discussion of the fundamental theory, the ideal and actual performance and the practical considerations con- nected with such apparatus. The book is prepared primarily for the use of students in Mechanical Engineering in their junior and senior years, after they have completed college courses in physics, chemistry, analytical and applied mechanics and empir- ical machine design. The text is supposed to be supplemented by lectures, lantern slides, a study of trade catalogues and collateral reading; and, as it is prepared primarily for students who will have separate courses in mechanical laboratory practice and in the economic problems connected with heat-power engineering, but little relating to these branches is given. A large part of the material contained in the following pages has been used during the last four years, first in pamphlet and later in book form, as a text in the junior and senior courses in Sibley College, Cornell University. It has been revised from time to time as the necessity became apparent, and now the original matter has been practically rewritten, rearranged and considerably amplified for the present book. To add to its convenience and value as a textbook in recita- tion courses, all sections are numbered, the sub-paragraphs are lettered, and sample problems are given in the Appendix. Undoubtedly errors of various kinds will be discovered, and in order that they may be eliminated it is hoped that they will be brought to the attention of the Authors, who will also welcome any other suggestions for the improvement of the book. iV PREFACE The Authors express grateful acknowledgment of their in- debtedness to Professor A. W. Smith, Director of Sibley College, for many helpful suggestions and criticisms during the inception and progress of this work, and to Assistant Professor EUenwood who prepared a large number of the appended problems. They desire to extend their thanks to Professor Lionel S. Marks and to Dr. Harvey N. Davis, and their publishers, Longmans, Green & Co., for permission to use an abstract of their steam tables, and to Professor Cecil H. Peabody and John Wiley and Sons for permission to use a reduced and modified drawing based on the former's temperature-entropy chart. Thanks are also due the following members of the Sibley Col- lege instructing staff for valuable assistance: Messrs. H. M. Parmley, T. C. Ulbricht, and R. Matthews; and to F. A. Burr, formerly Assistant Professor in the College. July I, 19 1 2. PREFACE TO SECOND EDITION Since the appearance of the First Edition of this book, Pro- fessor EUenwood has published some very valuable and extensive steam charts which have a much wider field of application and greater accuracy than have any of the Mollier Charts that have appeared. The present edition includes a discussion of these important new charts and to the Appendix has been added a small two page EUenwood chart redrawn from the original ones, covering twelve pages. The other changes in this edition consist of a number of minor corrections and a few additions. The authors desire to express to Professor EUenwood their appreciation of the privilege of introducing the new charts; and they desire to thank him and also Professor Matthews and Mr. C. H. Berry for many valuable suggestions. August I, 1915. CONTENTS, PAGE 1. Introductory xv CHAPTER I. — Heat i 2. Heat a Form of Energy, 3. Unit of Heat Energy. 4. Solar Heat. 5. Heat from Mechanical Energy. 6. Heat from Electrical Energy. 7. Heat from Chemical Combination. CHAPTER II. — Elementary Laws of Heat Energy 6 8. Conservation of Energy. 9. Ideal Mechanisms. 10. The Second Law of Thermodynamics. 11. Distribution of Associated Heat Energy. 12. Specific Heat. 13. Total Associated Heat. CHAPTER III. — The Heat-power Plant 16 14. General. 15. The Steam-power Plant. 16. The Producer Gas- power Plant. 17. Analogy. 18. Further Study. CHAPTER IV. — The Laws of Gases 28 19. States of Aggregation of Substances. 20. The Ideal Laws of Condi- tion of Gases. 21. The Specific Heats of Ideal Gases. 22. Constant- volume Specific Heat of Ideal Gas. 23. Constant-pressure Specific Heat. 24. The Ratio 7. 25. Table of Gas Constants. CHAPTER V. — Expansions and Compressions of Gases 43 26. Volume Changes. 27. Isobaric Changes of Gases. 28. Isovolumic Changes of Gases. 29. Isothermal Changes of Gases. 30. Adia- batic Volume Changes of Gases. 31. General Expression for Volume Changes. 32. Construction of Lines Representing Volume Changes. CHAPTER VI. — Reversibility 59 33. Definition. 34. Some Reversible Processes. 35. Some Irreversible Processes. CHAPTER VII. — Entropy 65 36. Explanatory. 37. Definition. 38. Entropy Changes for Reversible Processes with Ideal Gases. 39. Sign of Entropy Changes during Reversible Processes. 40. Reversible Isobarics of Gases. 41. Revers- ible Isovolumics of Gases. 42. Reversible Isothermals of Gases. 43. Reversible Adiabatics of Gases. 44. Irreversible Adiabatic Proc- esses of Ideal Gas, and the Corresponding Entropy Changes. 45. En- tropy Changes Independent of Path. 46. Temperature-entropy Diagrams. vi CONTENTS PAGB CHAPTER VIII. — Gas Cycles 76 47. Definition of a Cycle. 48. Diagram of a Cycle. 49, The Carnot Cycle for Gases. 50. All Reversible Engines Have the Same Efficiency as the Carnot Engine. 51. Comparison of Carnot Engine and Real Engine. 52. T. o o O «N M Ti- O >o i^ OD'O fO Ot CN On CN 00 M O M H o o o o o o o rfOO o o O f>. ■* o H o o t~ H O t-^ r-vo mD M oi, H 00 r— H lo rooo o M t^ o O o 00 t^oo O Ommo.OOO 00 rt" lO lO f^ VO O t^MD CS • 't O o o IT) lO ^ o O o o o o o o o o o o o o o o o o o u CO 00 Mo mno t- h ro OnnO r^ m On OnOO !>• lO t-» ro NO OnnO no rONO O COH On'^CnOOOnhi On On O <^ . (N M . O NO NO HI t-- HI O < SgOQ i^ Vh O ^ 5 W 4 N THE LAWS OF GASES 41 CO MD O vO C^ CO o 100 10 M ■^ O 10 CO M . CN r-^ H M M CO cn O U c/5- O t-». O lO ro OOOiOQ'^toc^ O MD"^ 0\c0000\00 Tf VOM3 COCOCO-^C^-^-^ 0\ t^ On 1000 \ PQ S.2 V U -"J O O Ot re tH tn^i > 00 «, O) ^ in M ^ to 00 00 NO 00 MD H t^O 8 CN C) H On t^ VO '^ H to On to 00 On t-* On 00 CN H -d- '^ T^ t^ 01 M 00 W rt OnOO ,_, O) H 00 00 to CO cq I^ On M H *-• M M H M C^ CN 00 VO CO -O" o 00 O to CO o 10 O O 00 O 00 On OnOO CN M o gives a graph less steep than the isothermal and that any equa- tion with w > 1 < 00 gives one steeper than the isothermal are very useful and should be memorized. The idea of steepness in this statement is important, as in general one curve cannot be said to lie above or below another. For example, if the curves in Fig. 10 are continued as compres- sions, to the left from the point A, their relations as to vertical position are reversed. Fig. Volumes lo. — Showing Effect of Value of n in Equation PV^ = Const. 32. Construction of Lines Representing Volume Changes. (a) In dealing with heat engines it is frequently necessary to construct the lines representing graphically the changes already discussed and others of similar character. This can always be done by substituting assumed volumes or assumed pressures in the equation for the type under consideration, solving for the other quantity and plotting the resulting points. The curve joining these points is the graph sought. An exponential form of equation involves the use of logarithms and in some cases the calculations become a little more troublesome. It is therefore convenient to know graphical methods of de~ termining directly the curves representing the various changes. Graphical Construction of Curve PV = Constant. (b) In Fig. II, with coordinates P and V as before, let it be desired to draw an equilateral hyperbola through point A. For doing this two methods will be given. First Method: — Draw through the point A horizontal and vertical lines ppi and z^iz^/; next, from the origin O draw any number of rays (such as Od) EXPANSIONS AND COMPRESSIONS OF GASES 55 to intersect these lines (as at a and b) ; then horizontal and ver- tical lines drawn through these points of intersection will meet at points (such as B) on the desired curve. For expansion from point A, the rays fall below A ; for compression, they fall above. Second Method: — Through A, Fig. 12, draw any number of Figs. II and 12. — Construction of Curve PV = Constant on PV-Chart. lines, as bbi, cci, etc.; make biB = Ab, CiC = Ac and so on then the points A, B, C, etc., will be on the desired curve. Construction of Curve PV" = Const, by Using Logarithmic Cross-Section Paper. (c) The equation PV"^ = K = const., if solved by logarithms, takes the form log P = — n log V + log K. Then letting y = log P, X =^ log F, and k = log K, the last equation may be re- written y = — nx -{- k. This is the equation of a straight line with negative slope n and 3;-intercept k. It is shown in Fig. 13 by KS, drawn to the ordinary uniform scales Ox and O7. The abscissa of any point A on KS, measured on the scale Ox, gives the logarithm of the value of V represented; its ordinate on scale Oy is the logarithm of the value of P. If now new scales L^ and Lp are constructed in such a manner that the lengths 1-2 and 1-3, etc., represent the logarithms of 2, 3, etc., — as is done on the scale of the slide rule, — then these logarithmic scales may be used for reading directly the numerical values of P and V corresponding to points on KS. To the scale Lp, the 3'-intercept of this line is the constant K, and to the uniform scale the slope is n. Since the values of P and V 56 HEAT-POWER ENGINEERING Ov Lp 10 -| 10 2 1 ■1 — p 9 8 K A: 7 \ \, 5 \ i 3 2 - 1 - a\ \ \ \ s Fig. 13. — Logarithmic Chart. 10 may be read directly on the logarithmic scales, the uniform scales are not usually given on charts of this character. Any straight line can be lo- cated on the logarithmic chart if the PV values for two points are known; or if one point and the slope n are given; but in the latter case it must be remembered that the slope is laid off using the uniform scale. For one of the points it is sometimes conven- ient to use the 3;-intercept, K. After the line has been drawn the simultaneous values of P and F may be read, and these may then be used in drawing the P V curve on ordinary cross-section paper. The chart in Fig. 13 is arranged for numbers between i and 10, but it may be used for numbers between .1 and i, between 10 and 100, 100 and 1000, and so on, by merely changing the scales to suit. When a wider range of numbers is under considera- tion (as from .1 to 100) a " checkerboard " composed of several similar logarithmic charts may be used. Thus in Fig. 14, let each of the squares contain such a chart and let the one surrounded by heavy lines correspond to Fig. 13, with KS reproduced. In the lower tier of charts the ordinates are for numbers from .1 to i, in the middle tier they are from i to 10, and in the upper from 10 to 100. The abscissas for the vertical columns progress, from left to right, by multiples of ten also. The coordinates of a point anywhere on the checkerboard can Fig. 14. Checkerboard of Logarithmic Charts. EXPANSIONS AND COMPRESSIONS OF GASES 57 be read directly on the proper scales. For example, point B has coordinates P= 25 and V= .35; for point C the value of P is .14 and F is 13. As all the squares are cross-ruled the same, and differ only as to scales (and that by multiples of 10), it is evident that if S'T' is drawn in the central chart in a position similar to that of ST in the square below, it can be used in place of the latter line provided points on it are read to a scale jo that used for KS. Similarly, T"U', K'Q', and Q^'M' may be drawn to correspond to TU, KQ, and QM respectively, and may be used instead of them with proper change in scale. Thus a single logarithmic chart may be used in place of the checkerboard. Obviously, when the curve crosses a horizontal boundary line the scale of ordinates changes; and when it crosses a vertical boundary the scale of abscissas changes. U n = I, as in the case of the equilateral hyperbola, the slope of the line is — 45°. If the exponent is greater than i, the slope is steeper, and vice versa. 58 HEAT-POWER ENGINEERING O 0) d U 3 > u a e o U >> 1 ^ < 1—1 1 rH 1 1— 1 ^ o 1 > 1 1 1 1 1 ' 8 ^ 1 8 ~f= f^ Rh 0=^ < ^ < ^ + + + + + + + ^^ ^_^ i-^ o 4-3 E^^ ^ . »<. ^^-s s* bjo hAi > w Is . 4-> 1 b + 1 + + + c sga G cu 4J < a cs a T 7 u T 7 e ^^1^^ ^ ^ ^ fC c ^ ^ ^ fo ^ ^ ^ E^ rH| ^ 'HI se a ;3 ^1^^ ^^K fCK t:!^: ^x ^n^: ® E^^K "o 1:^ ^ tT tei fcT ft^ ^ ^ ^ ^ > '-J II II II II II II II II II II s £ ^ > tr >- tT >^ ^ > ^ > -^'i pC ^1> E^l^" t:;i>~ t^lt-^ f."|>^ s E.^i> ^ E.1> 1^ f^ a: ^ < ^ fc ^ ^. •vi •*^ ■** ^ ^H "«o c^ ■> . .^ ^ 'cd +-» ^CJ C2 2^ 03 3 i 1^ S §d o3 C "" o 2 >'^ MS MO 5 ^ r •^ CO 1— 1 1 -i-j l-H o c cu OH U 03 --2 3 ^< CHAPTER VI. REVERSIBILITY.* 33. Definition, (a) Processes, or series of changes, which may be made to occur with materials and their associated energies are broadly divided into two kinds: 1. Irreversible processes, and 2. Reversible processes. An Irreversible Process is one which affects the participating materials and energies in such a way that after its total or partial completion it would be impossible to return those mate- rials and energies to initial conditions, without leaving changes in other materials and their associated energies. All the actual processes with which the engineer has to deal are of this character. It is, however, possible to imagine some of these processes as taking place under ideal conditions in such a way that after their completion everything can be again returned to starting condi- tions without leaving changes in anything, even though it be entirely extraneous to the system under investigation. Such ideal changes are called Reversible Processes. (b) A good mechanical example of a reversible change is furnished by a pendulum swinging on a frictionless support and in a perfect vacuum. Each cycle of the pendulum is accom- panied by a change of kinetic to potential energy, and then a reversal of this process so as to bring everything concerned to exactly the conditions pertaining at the start. This, then, is a process which may be said to be by nature reversible. A real pendulum can never reproduce this ideal process exactly, because of friction at the support and more or less friction in the enveloping medium. These resistances change some of the kinetic energy of the pendulum into heat which in the usual case leaves the system by radiation. Thus, the end of each cycle finds the pendulum system poorer in energy by the amount * The study of this chapter may be deferred until Section 49 (h) is reached- 59 6o HEAT-POWER ENGINEERING of heat which has been lost; and surrounding materials must of course have gained a corresponding amount of energy. The real process does not therefore fulfill the requirements of a reversible process.* (c) It will be observed from the preceding paragraph that the ideally reversible process becomes imperfectly reversible as soon as losses are assumed to occur. Although the process could never be performed in reality without such losses, this does not in- validate the determination of the laws of the ideal pendulum, — laws which are very valuable for investigations of a certain type. Since a reduction of losses in a real process of this character will cause the process to approach the ideal reversible one more closely, it is evident that the reversible process and the laws derived for it may be regarded as the ideal limiting case of the real process and of the laws governing it. This applies to processes of a certain character only. (d) There are many other processes of such character that no assumptions of ideal mechanisms and no reasonable assump- tions as to the elimination of losses can reduce them to limiting reversible processes, as was done in the case of the pendulum. Such processes are the irreversible ones, examples of which will be given later. (e) In the investigation of certain thermodynamic trans- formations accompanying pressure, volume, and temperature changes, it is often possible and desirable to assume all losses absent so that the process may be considered reversible. The assumptions as to the elimination of loss must be reasonable ones, however, — those not involving changes in the intrinsic character of the process. Thus it is permissible to assume that there is an absence of friction, and that one may use a material which does not conduct heat, as was done in previous chapters; but an assumption that there is no internal heat energy lost when a gas does work by expanding adiabatically behind a piston would have been unreasonable, as it would have been absolutely con- trary to the intrinsic character of the process. * The process might still be considered reversible if there was any way of gather- ing up the energy lost as heat, converting all of it into mechanical form, and return- ing this to the pendulum. But, even assuming that the heat could all be caught, the second law of thermodynamics states that it cannot all be again converted into the mechanical form, and the statement made above must therefore be correct. REVERSIBILITY 6 1 The study of an ideal reversible process in lieu of a real im- perfectly reversible one greatly simplifies problems and makes possible the development of laws which would otherwise be obtainable only with great difficulty. (f) For thermodynamic purposes a reversible process may be defined as follows : A thermo dynamically reversible process is one involving heat and mechanical energy transformations which are of such character that, after completion, they can be carried through in the opposite sense, without resulting in any changes in anything extraneous to the system under consideration. The practical application of this simple definition is often confusing. There are certain processes which are obviously reversible in this sense and certain others which are as obviously irreversible; but there are also many about which a decision is difficult. A few reversible and irreversible thermodynamic processes are given in the succeeding sections. 34. Some Reversible Processes, (a) A good example of an ideal thermodynamically reversible process is as follows: Imagine a perfect gas inclosed in a cylinder made of material that will neither absorb nor conduct heat and let it be fitted with a friction- less piston of the same material. If the gas expands it must do so adiabatically, since the heat insulation is assumed to be perfect. The temperature will drop, the volume will increase, and work will be done in driving the piston outward against what- ever resistance is offered : — for instance, the raising of a weight. If, after the piston has reached a certain point, the work which has been done by the gas is returned to drive the piston back to its original position — for instance, by the dropping of the lifted weight, — the gas will be compressed adiabatically to its original condition and, in the ideal case, nothing in the universe need have been changed by the process. Such a process is thermodynamically reversible. It is evi- dently ideal and can only be approximated in real cases, for every material known absorbs and conducts heat, and no piston can be frictionless.* * It is really necessary to further stipulate that the expansion and compression of the gas in this process take place at infinitely slow rates, to make it perfectly reversible in theory. This is necessary in order to exclude any degree of what is termed " free expansion," an irreversible phenomenon which will be treated in a later paragraph. 62 HEAT-POWER ENGINEERING • r (b) Again, imagine a body which is at a certain temperature, and is so arranged that the withdrawal of heat from it does not change its temperature. The steam in a boiler is a body of material approximating this conception. If a confined body of gas is kept in contact with this source of heat, or hot body, — as in a steam- jacketed cylinder made of perfectly conducting material, — and if it is allowed to expand and do external work, such as driving out a piston against resistance, the expansion must be isothermal. During the process heat will be drawn from the hot body and appear as mechanical energy to do external work. This work may be returned by compressing the gas isothermally and restoring the resulting heat to its original source. The ideal process is thermodynamically reversible, but practically some heat must have been radiated and some lost as friction, so that the reversibility is, as before, ideal only. (c) A reconsideration of the simple ideal expansions discussed in Chapter V will now show that all of these may be made reversible processes. 35. Some Irreversible Processes, (a) One of the best ex- amples of an intrinsically irreversible process is furnished by the passage of heat from one body to another which is at a lower temperature. Consider two bodies at different temperatures brought into contact and thermally isolated from the rest of the universe. Experience shows that the colder body will receive heat from that having the higher temperature, and that this proc- ess will continue until the two temperatures become the same; also it shows that certain physical changes will accompany this passage of heat. Thus there may be a change of state, as would be the case, for instance, if the colder body is ice at the melting point; or again, there may be simply changes in volume accompanying the doing of external work. No matter what the conditions, no method has yet been devised to reverse this process thermodynamically; that is, to make heat flow from the previously cool body to the other so as to leave them at different temperatures, return them to the initial physical conditions, and leave no change in anything else. The process is then irreversible by definition. (b) Another example of an intrinsically irreversible process is the free expansion of a perfect gas similar to that which occurs REVERSIBILITY ^ 63 in Joule's experiment.* Imagine two vessels of equal size joined by a pipe containing a valve, ail made of non-heat-con- ducting material. Imagine further that one vessel contains a quantity of perfect gas at some given pressure and temperature and that the other vessel is absolutely empty. If the valve in the connecting pipe is opened, the gas will rush from the high- pressure vessel into the other one and ultimately both will contain the same quantity of gas at the same pressure and temperature. To make this possible, the gas originally contained in one vessel must have expanded until its volume became suffi- cient to fill the two. Since the volume occupied by the gas is now greater than before, the pressure must be lower unless the temperature has risen, and it will be found that this has not occurred. Further, since the vessels and connecting pipe are nonconducting, and since the system is so arranged that no disturbance of surrounding media can be caused, it follows that there can have been no loss of heat energy by the gas. The heat energy associated with the system must therefore he the same before and after the change. Since, however, as was shown in connection with the specific heat of gases, the intrinsic heat energy of a perfect gas is always the same at the same temperature, it follows that the temperature of the gas must he the same when filling two vessels as when filling one. To make this process reversible, it must be possible to com- press the gas again into one vessel, keep the temperature the same, and have no change in anything outside the system of two vessels and contained gas. This is impossible, as work would have to be done upon the gas to compress it, and there would then either be a rise in temperature or the heat of compression would have to be absorbed by some body outside the system. This heat, though equal to the work of compression, could not be returned to the engine, or device doing that work, as an equivalent of the work done. This is so because (according to the Second Law of Thermodynamics) no engine could deliver in mechanical form all the heat supplied it. Obviously the process is intrinsically irreversible because it is impossible to imagine its thermodynamic reversal even with ideal mechanism. * This is not to be confused with Joule's experiment for the determination of the mechanical equivalent of heat. 64 HEAT-POWER ENGINEERING (c) The process of free expansion is one of the most interest- ing and is worthy of more detailed study. What really happens is best considered in two parts. The gas in the high-pressure vessel begins to expand as soon as the valve in the connecting pipe is opened, and it acquires a high velocity with rapid drop of pressure as it flows into the empty vessel. The kinetic energy associated with this velocity must come from the intrinsic heat energy possessed by the gas. The expansion is in reality adiabatic, and the intrinsic heat energy, which during expansion behind a piston would have been converted into mechanical work, is here converted into the kinetic energy acquired by the gas itself. The temperature of the gas drops just as in the other adiabatic expansions already considered; thus, the material entering the empty vessel has the low temperature which corresponds to the low pressure and is deducible directly from the law of adiabatic expansion. Considering next the receiving vessel, — the gas with low pressure and temperature enters with high velocity but imme- diately becomes churned up, impinges on the walls, etc., and slowly comes to rest. The energy originally possessed by virtue of its velocity cannot be destroyed, but is reconverted into heat. It is absorbed as sensible heat by the gas and raises its tempera- ture. Given sufficient time, equilibrium will, be established between the material in the two vessels, and then the gas, with the same stock of heat as before, will have returned to the tem- perature it had initially.* * The importance of the footnote on page 6i can now be appreciated. If gas, expanding adiabatically behind a piston, is allowed to acquire an appreciable velocity, some of the heat energy which has previously been assumed as doing external work will be used to impart this velocity to the gaseous molecules. In just so far as this occurs the process will be irreversible. In all real piston engines the velocity acquired is so small that the heat thus used is negligible. Hence no attention is ever given the phenomenon from this viewpoint, and it need not be considered in discussing the elementary cycles in the following chapters. ^-^ CHAPTER VII. ENTROPY. 36. Explanatory. In the more advanced discussions of ther- modynamic theory a certain property of substances, know as their " Entropy " (represented by 0), is found to be of great importance. The solution of most, if not all, engineering prob- lems involving thermodynamic changes can be obtained with- out employing entropy; but its use enables scientists to draw certain sweeping conclusions with regard to natural phenomena, — conclusions which would otherwise be difficult to formulate, and which materially assist in developing the laws governing thermo- dynamic transformations. The consideration of entropy also serves the useful purpose of giving the engineer a broader view- point with regard to the processes he makes use of. For these reasons it is introduced here. 37. Definition, (a) It has been seen that it is impossible to measure the absolute amount of associated heat energy ((2), and that all cases can be analyzed when the discussion is limited to changes of energy {dQ, 8Q, or AQ). Later it will be shown that entropy is a similar function ; therefore the treatment will be limited to entropy changes {d(f), 8(f>, A0), rather than to consider the absolute amount. (b) To a student unable to distinguish between heat and cold and not familiar with the phenomena accompanying tempera- ture changes, it would be very difficult to convey a conception of what a temperature change really is. Probably the best definition would be the mathematical one 8T = -~^ which would be unsatisfactory and troublesome to the student until, by experience, he became familiar with the phenomena accompany- ing changes in temperature. The same difficulty occurs in attempting to define any unfamiliar physical quantity or prop- erty, and applies equally well to entropy. Hence, the best 65 66 HEAT-POWER ENGINEERING that can be done at present is to give a mathematical definition of entropy and rely on the experience and familiarity, which will come from the solution and discussion of problems involving its use, to give a more or less concrete conception of the physical meaning and properties. (c) The Mathematical Expression for an Infinitesimal Change of Entropy is ^^ dS + dl+APdV , , d(l> = Y ' ^53) in which the numerator indicates the summation of the in- finitesimal changes indicated, T = absolute temperature of material during these infinites- imal changes, and A = 1/778, introduced to keep all terms in numerator in same units. A finite change of entropy will then be 1 ^^ = j. T — (54) It is often convenient to first evaluate per pound and then for the weight concerned. If A0i is for unit weight, A<3!)R. = TFA01 (55) (d) It will be observed during the further development of thermodynamic phenomena that all those processes which occur " naturally," i.e., spontaneously, are accompanied by an increase of entropy. Any process which results in a decrease of entropy must be forced in some way, and is in that sense " unnatural." Hence it may be said that the entropy of every substance tends to increase. A somewhat analogous, though not a parallel, case may be cited from mechanics. It is well known that the potential energy of mechanical systems always tends to decrease, for there is a tendency for the centers of i^ass of all terrestial bodies to approach the earth's center as closely as conditioils will permit. Given a mechanical system, in which processes result- ing in change of the position of the center of gravity can take place, that change will occur which will make the potential energy of the system least, unless external forces impose a different behavior. ENTROPY 67 38. Entropy Changes for Reversible Processes with Ideal Gases, (a) It was mentioned (in Section 34c) that the ideal expansions considered in Chap. V may be made reversible proc- esses; and a further consideration will show that in every such case the external work, dE^ can be represented sls AP dV. Further study will show that for all reversible processes APdV = dE and A C P dV = AE. Then, since dl = o for an ideal gas, the numerator of Eq. (53) becomes dS -{- dE = dQ. And the infinitesimal entropy change experienced by an ideal gas, during a reversible process, is then ^^dS + dE^dQ (^^^ The finite change is ^-£f <"> or, if dQ be assumed to refer to unit weight, see Eq. (55), A0,r = w£^ (58) (b) It must be noted that the last three equations are proved only for reversible processes, and for the present they will be considered as apphcable only to ideal gas. They may be used for finding the entropy change experienced by a given weight of ideal gas which, while expanding behind a piston, is undergoing one of the reversible processes, such as those de- scribed in Chapter V; they are not applicable for determining the entropy change when a given weight of gas experiences an irreversible process, such as the free expansion of Joule's experi- ment. Section 35 (b). In such cases the entropy change must be determined in other ways which will be presented later. 39. Sign of Entropy Changes during Reversible Processes. (a) The integration of Eq. (57) between the limits i and 2 for any assumed process will result in a difference of two quantities ; thus the sign of the right-hand member will depend upon which of these quantities is the larger. The sign of this number indi- cates whether the process in question will increase or decrease the entropy of the material. 68 HEAT-POWER ENGINEERING (b) A reversible increase of heat energy would give a positive value for the right-hand member of the equation, — a positive value of A0, — and this corresponds to an increase of entropy. (c) A reversible rejection of heat results in a negative value of A0, indicating a decrease of entropy. (d) Eq. (57) would show no change of entropy for any revers- ible process involving no change of associated heat, but this could only be true of an adiabatic process (in which dQ = o, see Section 30 (a) ). An ideal gas, therefore, experiences no change of entropy during a reversible adiabatic process. (e) Although it is the entropy change which is really con- sidered in thermodynamic calculations in which entropy is con- cerned, yet engineers are accustomed to speak of the " total entropy " of the substance for the particular conditions of tem- perature, pressure, and volume pertaining. They do this because they have by common consent agreed that the entropy of materials shall be measured above a certain arbitrarily chosen datum, which is taken as zero for convenience. Thus the term " total entropy " (0) refers to the total entropy change ex- perienced by the material in passing reversibly from the arbi- trarily chosen datum to the conditions in question. As the entropy difference (02 — i) is dealt with, any~ datum whatever may be selected provided the same one is used for both of the entropy quantities, 02 and 0i. 40. Entropy Changes during Reversible Isobarics of Gases. In Eq. (56) the numerator of the right-hand member can be replaced by the product of specific heat into an infinitesimal temperature change, thus for unit weight d,^§^^., ...... (59) the symbol C representing the proper specific heat for the par- ticular change under consideration. For a change at constant pressure C becomes Cp and the differential equation for entropy change, per unit weight, is -a£ff, or A During an isothermal change the temperature is constant by definition; that is, T in Eq. (56) is the same for each of the differ- ential heat changes dQ. Then T * It is usually more convenient to use logio instead of logg. As loge = 2.302 logio, Eq. (6ic) may be written A = Cp X 2.302 logio (T2/T1). The other logarithmic equations which are to follow may be similarly transformed. 70 HEAT-POWER ENGINEERING becomes A0 = (0. - 0x) = ^^^^ (64) Thus, for isothermal changes, since {Q2 — Qi) = AQ, A* = f. (65) The entropy change will obviously have the same sign as AQ, indicating increase of entropy with increase of associated heat and decrease of entropy with decrease of associated heat. 43. Entropy Changes during Reversible Adiabatics of Gases. An adiabatic change being one which occurs under conditions of heat insulation, that is, one during which heat energy is neither given to nor abstracted from the substance, it follows that dQ = o, and therefore J0 = ^ = o.. (66) Thus during a reversible adiabatic change there is no entropy change, just as during an isothermal process there is no tem- perature change. Reversible adiabatics are therefore often called Isentropics, and these two terms may be used interchangeably. 44. Irreversible Adiabatic Processes of Ideal Gas, and the Corresponding Entropy Changes, (a) Besides the reversible adiabatic expansion already discussed, there are an unlimited number of adiabatic processes which are irreversible. These are thermodynamic processes which ideal gas undergoes when confined in vessels which are nonconducting as regards heat, that is, in those which neither permit the gas to receive nor to surrender any heat through the surrounding walls. Of the processes which are strictly adiabatic, those which arfe isentropic are the only ones that are reversible. (b) As an example of an irreversible adiabatic change of ideal gas, assume the process similar to the free expansion of Joule's experiment, discussed in Section 35 (b). During such a process, the entropy change experienced by unit weight of gas cannot be found by Eqs. (56) and (57), as they apply only to reversible processes. An attempt to use them would give the zero entropy ENTROPY 71 change that was obtained in Section 43, which is very far from being correct, as the next paragraph will show. (c) Recourse must then be had to the original definition, Eq. (53), which may be rewritten as d(j) = ^ [-A^r-. ..... (a) In the process under discussion there can be no change in the sensible heat because the temperature of the gas is the same after as before the change, and dl is of course zero for ideal gas. Hence dS -{- dl = b and Eq. (a) becomes dcf> = A-Y- (b) The PVT changes in a unit weight of ideal gas are represented by the expression —j^ = R. Thus P = RT/V dV and PdV = RT — This value of PdY may now be substituted in Eq. (b), which then becomes ,^ ,RTdY ,RdY dcf> = A-jr Y=^-y-' Integrating this between the limits i and 2 gives the true entropy change, per pound of material, A /2 dV R^=AR{\0geV2-l0geYl). • . (c) As the volume V2 occupied when the gas fills the two vessels is greater than the volume Vi which it had when confined in one of them, the process, as shown by Eq. (c), must result in an increase of entropy despite the fact that the conditions are adiabatic. This is quite different from the zero value obtained by applying the equation for reversible changes in which A PdV = dE. This emphasizes the statement already given that only reversible adiabatics are isentropic processes. (d) The free expansion of a gas may be called a '' natural " process. It was seen to be accompanied by an increase in 72 HEAT-POWER ENGINEERING entropy of the materials concerned. A similar increase also occurs with all other natural processes, such as the flow of heat from a higher temperature bod}^ to one at lower temperature. Thus the entropy of all substances always tends to increase. These facts will become more apparent as the subject is developed. 45. Entropy Changes Independent of Path, (a) The in- tegration of Eq. (54) results in a difference in two quantities, the values of which depend merely on the conditions of the substance before and after the change. Evidently, then, the entropy change is in no way dependent on the method of changing from the one set of conditions to the other. Thus the entropy change experienced by a material in passing from some definite set of conditions i to another definite set 2 will always be the same, no matter what path is pursued on the graphical repre- sentation of the process. (b) This fact is often of great importance, as the entropy change experienced by a substance when undergoing any very complicated set of changes can be determined by finding the entropy change accompanying any simple change, or group of changes, which will carry the body from the same initial to the same final conditions. It is, however, very essential to make sure that the final conditions are the same in both cases, as mistakes are easily made in just this point. 46. Temperature-Entropy Diagrams, (a) Just as pressure- volume diagrams are useful as a means of graphically represent- ing certain changes, so diagrams with absolute temperature plotted vertically and entropy change plotted horizontally are capable of visualizing some very important transformations. They are known as T(/)-diagrams. There is a peculiarity about the plotting of diagrams with temperature and entropy coordinates, to which attention should be called. In the PV-diagram the intersection of the coordi- nate axes represents zero pressure and zero volume, and this is possible because both absolute pressure and absolute volume can be determined. In the T^-diagrams, however, although absolute temperature can be determined inferentially, as pre- viously shown on p. 30, the absolute quantity of entropy is inde- terminate like the absolute quantity of associated heat. As already shown, the equations give change of entropy, Acf), and not ENTROPY 73 absolute quantity of entropy, . It is this A<^ which is used in plotting. The abscissas thus represent entropies of a substance above some conveniently chosen datum, such as that at 32° F. (b) In Fig. 15, the point A represents the temperature- entropy conditions of a substance as Ti^i. This means that at temperature Ti the entropy of the substance is <^i, above what- D / B G A X EH 1 £ ^ •ft s 1 Ti, and A(2 = (22 ~ & = f Tdcf>. . . (67) The last term of this equation is, however, the mathematical expression for the area under a curve drawn to 7"0-co6rdinates. It therefore follows that area on the T(i>-diagram represents heat change during reversible processes, and inspection of the graphs already given will show that area under a line traced from left to right represents heat given to a substance, while area under a line from right to left represents heat abstracted from a substance. One of the great conveniences resulting from the use of the T0-diagram in engineering may now be seen. The PV-diagram shows by the area beneath the expansion line the total external work associated with a process; while, for reversible processes at least, the T0-diagram shows by the area beneath the corre- sponding line the change of total associated heat occurring during the same processes. The engineer is thus enabled to quickly solve many problems by simple inspection of these two dia- grams, and can avoid the necessity of making long mathematical calculations with the ever-present possibility of error. It may be objected that it involves more work and time to construct the necessary diagrams than it would to make the ENTROPY 75 calculations direct. It will, however, be discovered in a later chapter that certain standard diagrams can be constructed for the solution of by far the larger class of problems in which the conception of entropy change is particularly helpful. These diagrams, once constructed, can be used indefinitely without further calculation. , /-^ CHAPTER VIII. GAS x:ycles. 47. Definition of a Cycle, (a) As already stated, man re- quires far more energy than his body can supply, and this energy is obtained from Nature's stores. Energy as used by the engi- neer is always associated with some substance, body, or " sys- tem ": kinetic energy with moving masses; potential mechanical energy with masses by virtue of position; heat, sensible or latent, with solids, liquids, or gases. (b) When energy is used for the doing of work the material with which it is associated is called the working substance. Thus in a hydraulic power plant, water is the working substance; gas is the working substance in a gas engine ; and water is the working substance in a steam engine. (c) If a given quantity of a working substance, with its asso- ciated energy, be used so as to obtain all the work possible under given circumstances, the same amount of work cannot be again obtained under the same circumstances unless the substance is first returned to its initial condition. Thus a pound of water falling a given distance will develop a certain amount of work, and that work will be the greatest obtainable under the circum- stances when the water falls to the lowest possible point. To again develop the same amount of work with the same pound of water, it must first be raised to the height from which it origi- nally fell. Or similarly, if one pound of gas does work by ex- panding adiabatically from a temperature Ti to a temperature T2, which is the lowest possible under the conditions, it cannot again do the same amount of work in the same way until its temperature is again raised to the initial value Ti. (d) In order to deliver work continuously as is generally required, there are obviously only two possible methods of operation: either (i) the working substance must be periodically returned to initial conditions, or (2) new quantities of working 76 GAS CYCLES 77 substance must be supplied at regular intervals. The latter is the simpler and is often used, but it is not Nature's method. If man usfes falling water to develop power and allows the water to run to waste at the lower level, Nature immediately begins to lift it by evaporation, so that sooner or later it will be again available. If man burns carbon in air, getting hot CO2 and N2, and then, after obtaining work by lowering the temperature, discharges the gas as useless. Nature through the agency of plant growth decomposes the cold CO2 into C and O2 so that they can again be combined to evolve the same amount of heat energy as before. Thus without man's agency all working substances periodically return to the same starting conditions, that is, pass through cycles. A cycle is any series of operations which periodically brings the working substance back to initial conditions. It is customary to speak of Open and Closed Cycles, but there are really no open cycles in engineering. If the engineer carries a working substance through any series of changes which does not return it to initial conditions, Nature kindly closes the cycle for him. (e) One difficulty here confronts the beginner: Experience shows that it requires at least as much energy to pump water between levels as can be obtained from it in flowing down again ; this being true, how is man to obtain available work from a substance if equal work has to be returned to raise the material to starting conditions? There are two solutions which amount to the same thing in the end: 1 . Allow Nature to do the pumping, as in the case of the water- fall; or 2. Imitate Nature in finding some way of pumping that does not require the return of the identical energy which has been obtained from the cycle. When a heat engine is used heat energy is available but mechani- cal energy is sought. Most of the methods in use for returning the working substance to initial conditions in such cases depend upon the use of a small amount of the generated mechanical energy and a large amount of the available heat energy for this purpose; or they employ some group of processes which are the substantial equivalent of this. 78 HEAT-POWER ENGINEERING 48. Diagram of a Cycle. (a) Cycles are conveniently rep- resented diagrammatically, as has already been done for pres- sure-volume changes or temperature-entropy changes. The coordinates used are generally either P V, or T the cold body the same quantity of heat that this latter received from the engine ; it will require for its operation the same quafitity of mechanical energy that was delivered by the engine; and it will discharge to the hot body the sum of the two energies, — that is, an amount of heat equal to that which the engine removed from the hot body. If the two pieces of apparatus can be con- nected so that the engine drives the pump, a device results which, theoretically devoid of friction and radiation losses, can go on moving forever, though delivering no useful work. This is what was called in Section 9 perpetual motion of the third type, which, though conceivable, cannot be materialized. 50. All reversible engines have the same efficiency as the Carnot engine when working between the same temperature limits. 86 HEAT-POWER ENGINEERING There are many possible types of reversible and irreversible ideal engines. It will now be proved that, when working between the same temperature limits, — i.e., receiving heat from a hot body at the same temperature as that supplying the Carnot engine and rejecting heat to a cold body at the same tempera- ture as that used with the Carnot engine, — (i) no engine what- ever can have higher efficiency than the Carnot engine and (2) the efficiency of all reversible engines equals the efficiency of the Carnot engine. To prove (i): Assume that any engine, A, is more efficient than the Carnot engine, C. Obviously A could deliver more mechanical energy than could C, although receiving the same amount of heat; and the heat rejected by A to the cold body would evidently be less than that delivered by C by an amount equal to the difference between the quantities of mechanical energy delivered by A and C* Let A J operating as an engine, drive C reversed, that is. as a heat pump. This is shown diagrammatically in Fig. 20, in Fig. 20. — Heat Flow Diagram to show that no engine can have a greater efficiency than the Carnot. which the width of stream is supposed to be a measure of the energy flow. From the combination there would result an excess of mechanical energy A£2 which could be used outside * Because heat received = heat discharged + mechanical energy delivered. With the left member of the equation constant, neither term of the right member can vary except at the expense of the other. GAS CYCLES 87 the system. This excess mechanical energy would be exactly equal to the only heat supplied the system, that is, to AE2 given by the cold body. Therefore the combination could continuously convert into mechanical energy all the heat supplied it; but this would be Perpetual Motion of the Second Type, and is contrary to human experience as expressed in the Second Law of Thermo- dynamics. Since the assumption that A is more efficient than C results in this impossibility, it follows that that assumption must be incorrect, and that no heat engine, reversible or irrevers- ible, can have an efficiency greater than that of the Garnot engine. Hence statement (i) is correct. To prove (2), that if the engine A is reversible it must have the same efficiency as the reversible Carnot engine C working between the same temperature limits, imagine it to have an efficiency less than that of C* Being reversible, it can be used as a heat pump driven by C. Then, if the pump can be less efficient than the engine, perpetual motion of the second type again appears. Hence, neither engine can be more efficient than the other, so the efficiencies of all reversible engines working between the same temperature limits must be the same, which proves (2). 51. Comparision of Carnot Engine and Real Engine. The Carnot engine as described above is evidently only an ideal mechanism, for the material assumed for the parts does not exist and a perfect apparatus could not be constructed. It is possible, however, to approach such ideals and they may there- fore be regarded as limiting cases for actual constructions. Comparing the real engines with the Carnot as a standard gives a measure of the perfection of attainment. In any actual engine, the piston, which itself meets with frictional resistance, is connected to a friction-burdened mech- anism. In the real engine, provision must also be made for storing part of the energy delivered during the expansion, to be returned for the compression of the working substance, and this storage and return always involves waste. In the reciprocating engine, for instance, this energy-storing device is usually a fly- wheel, and some of the energy stored is lost in friction and windage. * It has already been proved that its efficiency cannot be greater than that of C SS HEAT-POWER ENGINEERING Obviously there must be the following losses in any real engine: 1. Some of the heat received from the hot body must be lost as heat through conduction and radiation by the material of the engine. 2. Some of the mechanical energy delivered to the piston must be lost by friction in the mechanism of the engine. 3. Some of the energy stored for compressing the working sub- stance must be lost by friction during its storage and its return. Recalling the meanings of the three types of perpetual motion (page 7) , it is evident — (a) That no ideal engine can give perpetual motion of the first or second type; (b) That any ideal reversible engine combined with another 0} similar character can give perpetual motion of the third type only; but (c) That no real engine can give perpetual motion of any of the three types. 52. T0-Diagram of Carnot Cycle, (a) The Carnot cycle, being made up of two reversible isothermals and two reversible adiabatics, must be represented by a rectangle when drawn to T0 coordinates. Such a diagram is given in Fig. 21, in which the horizontal lines ab and cd represent the reversible isothermal reception and rejection of heat and the vertical lines be and da show the reversible adiabatic changes. The corresponding corners of the cycle are for convenience lettered the same as in Fig. 18. (b) Since for reversible changes with ideal gases, AQ = r Td the area abef under the isothermal expansion ab represents heat A(2i received from the hot body, and the area cefd is similarly proportional to heat A(22 rejected to the cold body during the isothermal comp>ression cd. The difference abed is the area of the cycle and represents heat converted into work. Then A(2i = Ti{d) = T2 {(t>h ~ a) and AQl - Aft _ Ti (0, - 0a) - T2 (cf>b - (f>a) Ef. AQl Ti (05 - 0a) ^ — -, as before. GAS CYCLES 89 53. Criterion of Maximum Efficiency may have the maximum possible efficiency That an ideal engine T, when re- ceiving heat from a body at temperature Ti and rejecting heat to a body at temperature T2, it is necessary that — (i) All heat received from the hot body be taken when the working substance has the same temperature as that body; and (2) All the heat rejected, to the cold body be given it when the working material has the same temperature as that body. This is easily proved from the T(/)-diagram, Fig. 21. Im- agine heat to be received re- versibly along some such line as d' a' b, with the tempera- ture of the working substance varying from Td' to Ti. Obvi- ously less heat is received than if the reception had been iso- thermal, because the area fd' a' be { = fabe — ac^V) is less than the area fabe. The work done is also less because the area dd'a'bcd ( = dabc — ad' a') is less than dabc. But since the area ad'a' is lost in both — T<^-Diagram of Carnot Cycle. cases, and since the (smaller) area representing work is affected more than the (larger) area representing heat received, it follows that a'bcdd' abed , „ „, ^ ^ , A similar proof would show that the rejection of heat along a line such as b'c' also gives a cycle which is less efficient than that with isothermal heat rejection.* * Confusion is sometimes caused by the apparent contradiction of these state- ments and those given as propositions (i) and (2) in Section 50. It should, how- ever be noted that a very distinct limitation is put upon the reversible engines considered in that section. They receive all their heat at temperature Ti from the hot body in reversible fashion and reject reversibly to a cold body at temperature T2. On the other hand, engines receiving heat along such a line as d'a', Fig. 21, could only do so reversibly by employing a string of hot bodies with temperatures 90 HEAT-POWER ENGINEERING 54. The Constant- Volume Regenerative or Stirling Cycle, (a) In this cycle, which is drawn to PV-co6rdinates in Fig. 22, the gas receives heat from the hot body and rejects heat to the cold body along the iso- thermals ab and cd exactly as in the case of the Carnot engine. The two adiabatics of this latter case are, however, replaced by the two constant volume lines be and da. The line be is supposed to be obtained by allowing the working substance to reject heat to a body so arranged that it stores that heat in such a manner that (i) each part of the body is always at the same temperature as the contiguous gas, (2) the temperature of each part remains constant, and (3) each in- crement of heat after storing is maintained at the temperature of reception. The line da is supposed to be obtained by the return of the stored heat to the gas by a reversal of this a i s \ d 1 Volumes Fig. 22. — PV-Dia- gram of Constant-Vol- ume Regenerative operation. Cycle. Air as work- (^) q^^^^ ^ j^eat storing and restoring body ing substance. Same pressure range as in Fig. 18. is known as a Regenerator and in its perfect state is of course purely ideal. It may be ap- proximated, however, by a long pipe of heat- insulating material filled with wire gauze or equivalent, and with temperature Ti at one end and T2 at the other. As hot gas flows through in the direction T1T2 it will impart heat to the walls and filling at a progressively decreasing temperature and give the change be; while da may be obtained by causing gas to flow through the regenerator in the opposite direction. The Mechanism of the Stirling Engine. (c) The machinery necessary for the carrying out of such a cycle is shown in Fig. 23. The cylinders, Y and Fi, and the hot and cold bodies, U and X, are similar to those used in the Carnot engine. The tube R is the regenerator just described and its varying from Td' to Ta by infinitesimal elements, so that the gas might without sensible error be said to receive each element of heat when at the same temperature as the body supplying it. This is distinctly contrary to the assumptions of Section 50 as reiterated above. GAS CYCLES 91 1 1 1 1 1 1 1 1 1 i j 1 1 1 1 1 1 1 1 R J j Fig. 23. — Machinery of Constant- Volume Regenerative Cycle. contained volume is assumed to be negligible compared with that of either cylinder. Imagine the piston in Fi at the bottom of the cylinder and that in Y at the top, as the result of the expansion ab, Fig. 22. Y is then filled with a gas with conditions shown at b. Now drive the right piston down, thus forcing the gas through the regen- erator, and allow the left piston to rise at just the rate necessary to keep constant the total volume of the gas. During this process the regenerator will absorb heat and its temperature will grade from Th at the right to Tc at the left. When the piston in Y has reached the bottom of its stroke all the gas will be in Fi, the piston in the latter will be at the top of the stroke, and the constant-volume line be will have been produced. Now hold the right piston sta- tionary, bring the cold body up to cylinder Fi and force the pis- ton into this cylinder, until the volume occupied by the gas is that shown at^, in Fig. 22. This will produce the isothermal com- pression. Free the piston in F, continue the downward motion of that in Fi until it reaches the bottom of its cylinder, and simul- taneously allow the right piston to rise as much as is necessary to keep the volume constant. This will give the line da of the dia- gram, and the gas in passing through the regenerator will rise in temperature from Td ( = Tc) to Ta{= Tb). Finally fix the left pis- ton in its position, bring the hot body up to cylinder F, and allow the gas to expand isothermally from a to b, completing the cycle. Work Obtained per Unit Weight of Gas by Use of Constant- Volume Regenerative Cycle. (d) The work theoretically available from an engine using this cycle can be found, as in the case of the Carnot engine (see Section 49 (d), by summing up the quantities of work done during each process of the cycle. This is done in the following tabulation in which the letters in the first column refer to Fig. 22. It is evident from the figure that, as before, the ratios of expansion and compression are equal. Thus, using unit weight, 92 HEAT-POWER ENGINEERING Line. Process. Work Done /Ft.-Lbs.\ \Lb.-Gas/ • ab be cd da Isothermal Expansion Isovolumic Change Isothermal Compression Isovolumic Change + RTi loge r - RT2 loge r' Net work per cycle = RTi loge r — RT2 loge r', and since r = /, = (T,- T,) RXoger ft.-lbs. ... (73) Thus ^ {T,-T,) RXoger 778 (74) Efficiency of the Constant-Volume Regenerative Engine. (e) With an ideal regenerator the isovolumic processes be and da would he thermodynamically reversible, and the isothermal compression and expansion, as in the Carnot engine, are also reversible. The cycle as a whole must then be reversible, and therefore its efficiency must equal the efficiency of the Carnot cycle. This may be proved as follows: (f) With unit weight of gas, the heat received from the hot body may be called Aft, and as before it must equal ^^ • The heat rejected to the cold body is similarly Aft and is equal to RJ\Aog^ ^ RTAog^ 778 778 ' The external work done, or the mechanical energy made available, must equal the difference between the work done by the gas during the isothermal expansion and the work done upon it during the isothermal compression, hence it must be 778 AE = RTi loge r- RT2 loge r. Then the efficiency is Aft - Aft _ RT^ loge r - RT^ loge r ^ T.-T^ RTi loge r since r is equal to /. Ef (75) Aft RTi log, r Ti There is often difficulty at first in realizing that this cycle, which has the same efficiency as the Carnot cycle, fulfills the criterion of maximum efficiency stated in Section 53. Careful study will show, however, that the statements in that section apply only to heat transfers between the working substance and GAS CYCLES 93 bodies external to the actual engine — i.e., the hot and cold bodies. The heat given up or received by the gas during the constant-volume changes, i.e., Cv(Ti— T2), is really stored and restored reversibly and does not enter or leave the system. T0-Diagram of Constant-Volume Regenerative Cycle. (g) Fig. 24 shows the T0-diagram of this cycle as abed super- imposed upon that of the Carnot cycle ahe'd\ For convenience a J" .c^ 1 vo^^ y ^ c ^ > >^ <^^ d ^^^ _^ y — *. c d' b' 1 a Entropy Fig. 24. — T0-Diagfam of Constant-Volume Regenerative Cycle. Same temperature range as in Figs. 18 and 21. in comparison the two cycles are drawn for the same temperature range. The lines be and da are obtained from Eq. (63) and are evi- dently parallel curves. The areas be^e and ad'd are, therefore, equal, hence abed must equal abe'd'. Each of these areas, how- ever, represents the heat converted into mechanical energy. The heat supplied in each case is shown by the area under ab. There- fore, the heat supplied in each cycle being the same, and the work done being the same, the efficiencies are equal. 55. The Constant-Pressure Regenerative, or Ericsson, Cycle. The PV-diagram for this cycle, shown in Fig. 25, differs from the cycle last considered only in the fact that the regenerator proc- esses are carried on at constant pressure instead of at constant 94 HEAT-POWER ENGINEERING volume. The same mechanism may be used as in the last case, and the cycle, being reversible, must have the same efficiency. The T \ \b C "Volumes Fig. 25. — PV-Dia- gram of Constant Pres- sure Regenerative Cy- cle. Air as working substance. Same vol- ume range as in Fig. 22. two adiabatics be and da and two constant volume lines ab and ed. Heat is received from the hot body along the line ab, the pressure and temper- ature rising while the volume remains con- stant. Heat is rejected to the cold body along the line ed, the pressure and temperature dropping while the volume remains constant. (b) The reception of heat is irreversi- volumes ble, since the temperature of the hot Fig. 26. — PV-Diagram of body is at least as high as that which Otto Cycle. Air as working the gas attains when reaching condition substance. Conditions at h b, and therefore must be higher than same as those at a in Fig. 18 ,1 , r .1 1 • ^1 ^- and lowest pressure same as that of the gas durmg the entire recep- . ^, ^ ^ ** . ^ m that case. tion of heat A(2i. The same is true for the rejection of heat along ed, the cold body having a tempera- ture at least as low as that of the gas at d. This case is the first one cited in Section 35 as a process intrinsically irreversible. This eyele is not only irreversible, but, as is evident, it does not fulfill the criterion for maximum efficiency (Section 53), and h \ V a ^ I \j N I GAS CYCLES 95 hence has an efficiency lower than that of the cycles previously described. It is, however, the only one of the four gas cycles so far considered which is of any great practical importance. Mechanical Energy Obtained per Unit Weight of Gas Operating in Otto Cycle. (c) The following tabulation gives the mechanical energy changes for each line per unit weight of gas: Line. Type of Change. Work in Ft. -lbs. Done by Gas. ab Constant- Volume Pressure Rise be Adiabatic Expansion R{n-Tc) T-l - cd Constant- Volume Pressure Drop o da Adiabatic Compression R(Ta-Td) y -1 The summation of the last column gives the net work per cycle per unit weight of gas, as Network = R FromEq. (33), R (n-To- Ta+ Td) ft.-lbs. is equal to Kv, giving (76) 7-1 Network = 778 AE = K, {U - Tc - Ta + Td). . (77) (d) This same result could have been obtained more briefly as follows: The mechanical energy obtained must equal AQi — AQ2, when measured in heat units; that is, AE = AQi — Aft. Since the heat changes take place at constant volume, AQi = C„ in - To) and Aft = C. (^ - Td), hence, in ft. lb. units, 778 AE = Kv in - To) - K, (Tc - Td) = KAn-Ta-Tc+Td) which is the same as Eq. (77). 96 HEAT-POWER ENGINEERING Efficiency of Otto Cycle. ' (e) Writing j^r ^^E ^ A(2i-AQ2 '^^' A(2i A(2i and substituting in the last form gives CAn- Ta)-CATc- Ta) Ef.= CATi = 1-^ ^ (78) This expression can be further transformed and simplified so that important conclusions can be easily deduced. Since the curves he and da are adiabatics, Eq. (51) gives Since Va = Vb and Vc = Vd (^ and therefore Tc Td J Tc — Td Td /_ X -7f^ = — and -^ 7^ = T^ • . . • (79) J-h J- a J-h ~ J a J a Substituting from this in (78) gives L T, £/. = 1-^ = ^V^. .... (80) and Ej. = 1 -(^y ' (81} Thus it is evident — (i) That the efficiency of this cycle is independent of the upper temperature, but depends only upon the temperature range of adiabatic compression. (2) That with the same value of P^, the less the volume of one pound of gas at the end of compression the higher the efficiency. (3) That with the same temperature Td, the higher the tein- perature at the end of compression the higher the efficiency. Eq. (81) shows that the efficiency of the cycle may vary with different real gaseous working substances because the value of 7, as shown in Table I, is not the same for different gases. This is in marked contrast to the cycles previously considered, where the efficiency could be expressed entirely in terms of the tem- GAS CYCLES 97 peratures of the hot and cold bodies, and where the efficiency was independent of the individual characteristics of the gaseous working substances. Writing the Carnot efficiency T,- T, and the Otto efficiency Ta- T, Ti 1 — inspection shows that for the same upper and lower tempera- tures the Otto efficiency must be the smaller, as Ta must be less than Ti. T<|> -Diagram of Otto Cycle. (f) In reality the T0-diagram of this cycle cannot be drawn by the same means that was used in the preceding cases, for the reason that in Chapter VII the equation A(j) = j —^ was proved for reversible processes only, whereas two processes in this cycle are irreversible (see(b)). It is possible, however, to draw a T-diagram for this case by making use of the fact that the entropy change accompanying an alteration from any given condition to another must always he the same, no matter how the change from the first state to the second occurs. To find the entropy changes occurring as the gas receives heat along the line ab in Fig. 27, it is then only necessary to discover some Entropy Fig. 27. — T = Cv loge T and by the use of this equation the T(^-diagram can be drawn as in Fig. 27. The diagram in this figure shows the same changes as are represented by PV-co6rdinates in Fig. 26. The dotted rectangle is the Carnot cycle originally given in Fig. 21. 57. The Constant-Pressure Heat-Addition, Brayton, or Joule Cycle, (a) This cycle, like the last, is an irreversible one in the thermodynamic sense, but it is impor- tant because of its practical application to certain purposes which will be con- sidered later. It is now necessary to derive the type equations for the cycle, as has been done in the preceding cases. Fig. 28 shows the Joule cycle drawn to PV- coordinates. Starting at a, heat is added to the working substance by the hot body, volumes and temperature increasing at constant pressure, until the point b is reached. Obviously the tem- perature Ti, of the hot body, must be at least as high as that of the gas at &, and therefore higher than that of the gas at a. The heat addition is there- fore irreversible. From b the gas expands adiabatically to c, then rejects heat irreversibly, main- taining constant pressure until the vol- ume Vd is reached, and is then compressed adiabatically to a, completing the cycle. Volumes Fig. 28. — PV-Diagram of Joule Cycle. Air as working substance. Adiabatic expan- sion with same pressure range as in Fig, 26. GAS CYCLES 99 Mechanical Energy Obtained per Unit Weight of Gas Operating in Joule Cycle. (b) As before, the useful effect per unit weight of gas can be found by tabulation. Thus: Line. ab be cd da Type. Constant-Pressure Expansion Adiabatic Expansion Constant-Pressure Compression Adiabatic Compression Mechanical Energy (Ft.-lbs.) Made Available. + Pa(V6-Va) Pbyb-PcVc + 7- 1 - Pc (Vo -Vd) PaVa- PdVd The summation of the last column gives for the cycle Net Work = Pa (Vb - Ya) + P5V5 - PcYc 7- 1 - Pc (Ve - Vd) - P<^^<^~^J^^ ft.-lbs. (82) (c) This expression could be simplified, but it is hardly worth while, as a shorter one can be obtained more easily in the follow- ing manner. Writing available mechanical energy, or work done, as AE = (A(2i - A(22) B.t.u., it follows from the character of the lines ah and cd that AE = CAn- Ta)-CATc- To) = Cp in - Ta- Tc+Td) B.t.u. . . (83) and 778 AE = K^n - Ta) - K^ {Tc - Td) = Kp(Tb- Ta- Tc+ Ta) ft.-lbs. . (84) lOO HEAT-POWER ENGINEERING (d) Since Efficiency of Joule Cycle. A(3i - AQ2 Ef. it must be in this case, £/• = Cp {Tb A(2i To) -CATc- T,) To) = 1 - ^ -^' (85) lb — J^ a This can be further simplified by using Eq. (52). From this 7-1 7-1 then, since Tb \Pb) and Ta ^ (PA ^ Ta \Pj Pc. Pa = Pb and Pd Tb Ta Tb Substituting this in Eq. (85) gives t I \ V^ r, t \ N P^ d £/. = !- r- (86) a result similar to that obtained for the Otto cycle. The last equation can, by simple sub- stitution, also be written £/. = !- V, (87) which is likewise similar to the corre- sponding form for the Otto cycle. T0 -Diagram of Joule Cycle. (e) By replacing the irreversible iso- barics by equivalent reversible proces- voiumes ggg^ ^]^g T(/)-diagram to represent this Fig. 29. — PV-Diagram of ^ycle can be constructed, as was done Diesel Cycle^ Air as working ^^^ ^^^ ^^^^ , ^^^ ^^ ^j^.^ diagram is of little practical value it will be omitted. substance. The lines he and cd coincide with the lines sim ilarly lettered in Fig. 26. 58. The Diesel Cycle, (a) This cycle, drawn to PV-coordi- nates, is shown in Fig. 29. The heat is added from the hot body GAS CYCLES lOl during the constant-pressure expansion ab, and then the gas ex- pands adiabatically from b to c. Heat is discharged to the cold body while the pressure of the working substance decreases from c to d a.t constant volume. The cycle is closed by the adiabatic compression da. The Diesel cycle is irreversible for the same reasons that the Otto and Joule cycles are. Mechanical Energy Obtained per Unit Weight of Gas Operating in Diesel Cycle. (b) As before, the amount of mechanical energy made avail- able can be found by tabulating: mne. Character. Work (Ft. -Lbs.) Done by Unit Weight Gas. ah he cd da Constant-Pressure Expansion Adiabatic Expansion Constant- Volume Pressure Drop Adiabatic Compression + Pa {Vb - Va) 1 PbYb-PcYc y - 1 PaVa - PdVd 7- 1 The summation of the last column gives for the cycle Net Work = 778 A£ = P„ (V6 - VJ + Pa^a - PdY d^ld ft.-lbs. .. . . (88) (c) This expression need not be simplified, since, as in previous cases, there is a more convenient way of finding a short ex- pression for the work done. Writing A£ = (A(2i - Aft) B.t.u., it follows that, in the case of the Diesel cycle, AE = C An- Ta) - a (Tc-Td) B.t.u. . . (89) and 778 AE=.KAn- To) -K,{T,- Ta) ft.-lbs. (90) I02 HEAT-POWER ENGINEERING (d) Writing Efficiency of Diesel Cycle. AQi - A(32 £/. = AQi the efficiency in this case must be J,, Cp ( n - Ta)-CATc-T,) Ej. = Cp(Tb — To) Cv Tc — Td (91) ^6 — Taj LT This has the same form as Eq. (85), for the efficiency of the Joule cycle, with the exception of the introduction of 1/7. It should, however, be noted that the temperature term is not numerically the same in both cases, on account of the difference in the shape of the two cycles. (e) By substituting reversible processes for the irreversible ones, a T0-diagram equivalent to this cycle can be constructed. GAS CYCLES — TABLE III CYCLE 1 WORK-FT.LBS. PER LB. OF GAS. EFFICIENCY NAME PV-DIAGRAM GENERAL Any Number W. of Processes ^m Enclosing = Area Enclosed (A) = AQiX Eff.x778. =778 AE =778(AQ,-AQ2) =Ilesult -4- Effort =(AQ,-AQo)4-AQi CARNOT T rsothermals y^ Afiiahatics = CT-T2)Rloger Tj Ti / STIRLING k n" Isof hernials ^ and I2* Isovoluraics (( (( ERICSSON T Isothermals tf- ana To Isobarics ( ( ( ( OTTO ^ Adiabatics ^(jr Isovolumics = K,(T,-T-T,+TJ BRAYTON OR JOULE «J> Adiabat'ics a ^ Isobarics =Kp(TrTrT,+T^) (S DIESEL ah Adiabatics ^ c Isobaric and d Isovolumic =k/Vt;)-k„(vt^) -1 V .''<'-^ .J CHAPTER IX. VAPORS. 59. Vapors and Gases. When materials change from the liquid* to the gaseous state they do not immediately reach the condition in which their behavior even approximately obeys the laws of ideal gases. It is customary to designate materials as Vapors when in this intermediate condition. It will appear later that when strictly interpreted the term vapor will apply to many of the materials with which the engineer deals and which he is accustomed to call gases. 60. Formation of Vapor, (a) When a liquid is heated under constant pressure its temperature will first rise until it reaches a certain temperature which is dependent upon the pressure under which it exists; after which further addition ^oi heat will cause some of the material to change physical state at constant tem- perature, this temperature being the one fixed by the pressure existing. The amount of material that has changed state will increase as this further addition of heat progresses, and if sufficient heat is added all the liquid present will thus change its state. The material formed during this change of state is called a vapor. (b) Considering the process for the first time, one would recognize two possible methods of formation of vapors, and without previous knowledge would not be able to decide be- tween them. Thus: (i) The liquid as a whole might gradually change from liquid to vapor, all of it being at any one time in exactly the same con- dition of transformation. Or, (2) Parts of the liquid might progressively change to vapor as the necessary heat became available, leaving the remainder still in the form of liquid. Usually vaporization occurs by method (2), and as heat is added more and more vapor appears at the expense of liquid. * Or directly from the solid, as in "sublimation." 103 I04 HEAT-POWER ENGINEERING Thus when one-fourth of the total heat necessary for complete vaporization is added one-fourth of the liquid will be vaporized, and so on until vaporization is complete. (c) In the sections which follow the generation of vapor may be conveniently studied by imagining the process carried out in the device illustrated in Fig. 30. It consists of a vertical cylinder with closed end down, containing a friction- less piston of given weight, — all being placed under a bell jar in which a per- fect vacuum is maintained. Assume now that one pound of liq- uid is inclosed in the cylinder beneath the piston. The total pressure on the upper surface of this liquid will be that due to the weight of the piston, and since it is evenly distributed over b^:^^^^^^^:^dMM$^M^^WI ^^ ^^ the entire surface it may be desig- nated as P pounds per square foot of surface. Any liquid may be used and, in general, may have any tem- perature between that of solidification and that of vaporization at the chosen pressure. It is, however, customary to assume the temperature at a convenient value dependent on the physical characteristics of the liquid dealt with. In the case of water, and of all other liquids for which such a temperature is at all convenient, the engineer is accustomed to refer all vaporization phenomena to a datum temperature of 32° F. As this is the melting temperature of ice under ordi- nary conditions, it is readily checked and is hence a very satis- factory standard. To make the results of the process under consideration con- form to the engineering reality, the liquid beneath* the piston, in Fig. 30, will be assumed at 32° F. Fig. 30. 61. Heat of the Liquid, (a) If heat is added to the liquid beneath the piston in Fig. 30, the temperature will rise and, in the case of water, at the approximate rate of 1° F. for each B.t.u., since the specific heat of water at constant pressure is approxi- mately I. In any case the rise will take place at the rate of VAPORS 105 1° F. for each addition of heat equal to Cp, the constant-pressure specific heat of the liquid dealt with. This will continue until a temperature is reached at which vaporization begins. This tem- perature will depend upon the value of the pressure, and in any case has to be determined by experiment. Thus with water at atmospheric pressure (equal to 14.7 pounds per square inch, or 14.7 X 144 = 21 16.8 pounds per square foot), the tem- perature will be 212° F. ; while for a pressure of 100 pounds per square inch (equal to 100 X 144 = 14,400 pounds per square foot) the temperature will be about 327° F. These various tem- peratures are called the Temperatures of Vaporization and will be designated by the symbols tv and T^ respectively for Fahr. and Absolute temperatures. When it is necessary to indicate a particular temperature, the corresponding pressure in pounds per square inch will follow the subscript v; thus, the tempera- ture Fahr. of vaporization at atmospheric pressure would be tvu.7 or temperature absolute Tyi^.T. (b) The heat added during the process of raising the tempera- ture from 32°, or other datum level, to the temperature of vapor- ization is called the Heat of the Liquid and is designated by q. Obviously it has a different value for every different pressure and it is customary to tabulate these values with others in so- called Vapor Tables. In general -/ CpdT, (92) the integration being performed between the datum tempera- ture as the lower limit and the temperature corresponding to the pressure in question as the upper limit. If the specific heat of water were exactly equal to unity at all temperatures, the value oif q for this material for any temperature or pressure of vaporization could be found from the equation q = tv-32; (93) and since these values vary but slightly from those determined by experiment, this equation is often used by engineers. For accurate work the experimentally determined values given in the steam tables should be used. (c) Eq. (93) could not be used, even as an approximation, with any liquid other than water, since it depends upon the assumption that the specific heat of the liquid is invariably I06 HEAT-POWER ENGINEERING equal to unity. If, as before, the specific heats of Hquids at con- stant pressure are designated by Cp, and if they are assumed con- stant over the ranges of temperature considered, the equation q= Cpiiv- 32) (94) may be used in determining the heat of the Uquid for any tem- perature or pressure of vaporization. Note that there are Hquids which vaporize at ordinary pressures below the temperature of 32° F. In such cases a datum temperature lower than 32° may be taken from which the heat of the liquid is calculated. This necessitates a different form of equation. In its most general expression this would become a = CATv- To) ^ . (95) where Tq stands for any arbitrarily chosen datum. 62. Latent Heat of Vaporization, (a) Consider now the pound of liquid which has been raised to the temperature t^. With further addition of heat vaporization occurs. The marked char- acteristics of vaporization under the assumed conditions are (i) the very great increase of volume at constant temperature and pressure, (2) the change of the physical state of the material from liquid to vapor, and (3) the enormous quantity of heat absorbed. (b) The process carried out in the apparatus of Fig. 30 would result in driving up the piston to some higher position in the cylinder, against the pressure exerted by that piston on the upper surface of the vapor. Evidently, here, force would act through distance and therefore external work would be done. This work could not be done without a supply of energy, and, since heat energy is the only form supplied during the process, it follows that at least some of this heat must have been used for the doing of the external work-. Let F be used to designate the area of the piston face in square feet, and L the number of feet the piston is moved during the vaporization of the entire pound of liquid under consideration. Then the foot-pounds of external work done per unit weight are 778 AE = (PF) L, which, rearranged, becomes y 778 AE = P (FL) = P (V2 - Fi), . . . (96) VAPORS 107 where Vi represents the volume occupied by the liquid and V2 that occupied by the vapor. It is customary to designate the increase of volume (V2 — Vi) by the letter u, hence the external work done, in foot-pounds, is 778 AE = Pw, (96a) and its value in thermal units can be found by dividing Pu by 778. Representing — ^ by A, the expression for the B.t.u. of heat used in the doing of external work becomes A£ = APu ....... (97) This quantity is called the External Latent Heat of Vaporiza- tion. It has a different value for every different pressure at which vaporization takes place, and these values are tabulated in the Vapor Tables already mentioned. It is very necessary to observe that the term external '^latent heat " is a misnomer. The heat used for the doing of external work does not exist as heat energy in the vapor, for, during the process of vaporization, it is changed into mechanical energy which is extraneous to the vapor itself. The case is somewhat similar to isothermal expansion of a gas. This heat is con- verted into mechanical energy as rapidly as received. Hence, in a piston engine, the external latent heat may be considered as external work delivered by the piston rod. If the energy after reception can be said to be " latent," it must be latent mechani- cal energy and not latent heat energy. It is stored, if stored at all, in the piston or other similar part of the apparatus, and is in no sense in the vapor. (c) Experiment shows that the heat used during the process of vaporization is not all accounted for by the external latent heat. Inspection of Eq. (i), AQ = AS + AI -}- AE, suggests the reason. In this case AQ represents the heat added to vaporize the liquid. As the temperature does not change during vaporization, no heat can be used as sensible heat, hence A5 = o; but some of it may be used for the doing of internal work, A/. In fact the striking change of properties during this process could not occur without a very great readjustment within the material. The part of AQ which does not become Io8 HEAT-POWER ENGINEERING external latent heat is supposed to be used for doing this internal work, and is therefore called the Internal Latent Heat. It is designated by the symbol p and is tabulated in the Vapor Tables. Recent work has led to the conclusion that liquid water is a more complex material than was originally supposed. It seems probable that instead of being simply a collection of molecules with formula H2O it is really a mixture of at least three different kinds of molecules, H2O, (H20)2 and (H20)3. It also seems prob- able that during the formation of vapor some of the more com- plex molecules break up into simpler form. If this is so, a possible use of at least part of the Internal Latent Heat in the case of water becomes evident since it would be used for break- ing up the complex molecules. " Internal '• latent heat would then be a correct name to apply to this part of the heat as it is latent within the substance, though there is room for argu- ment as to whether it is latent as heat. (d) The sum of the two latent heats, p and APu, is called the Total Latent Heat of Vaporization, and is designated in the tables by r. Thus r = p + APu 63. Total Heat per Pound of Vapor, (a) Using symbols, the total heat, above the arbitrarily chosen datum temperature, per pound of vapor at any pressure P, is the sum of the sensible heat, the internal latent heat, and the external latent heat; thus it is qp- + Pp + {APu) J, = qp-\-rp, . . . . (98) and calling this X gives K = Qp + rp, . . . . . . (99) which is also given in the tables. (b) Had the addition of heat in the process under considera- tion ceased before the entire pound of liquid had been vapor- ized, the cylinder would have contained both vapor and liquid at the same temperature. Representing by y the fraction of the total pound vaporized, the " heat of the vapor " * present must be A(2' = yqp -\- ypp + y (APu)p * The expression "heat of" will hereafter be used to designate the quantity- necessary to bring the material in question to the condition under consideration, either from liquid at datum temperature or from liquid at the temperature of vaporization. The context will indicate which is referred to in any case. VAPORS 109 and that of the remaining liquid must be AC' = ii-y) gp, hence the total heat of the material in the cylinder is Aftp = A(3' + AQ'' = qp-h yPp-\- y {APu)p .... (ico) = 2p + y^py (looa) which will be equal to Eq. (98) when y = 1, that is, when the entire pound has been vaporized. 64. Saturated Vapor, (a) The process assumed in the pre- vious sections is really more or less idealized. In real cases, such as that taking place in the steam boiler, the vaporization does not progress so quiescently that the vapor separates en- tirely from the liquid and collects above it in the simple fashion already described. Instead, the formation of vapor is gen- erally more or less violent, and, in separating from the body of the liquid, the vapor carries with it small drops of that liquid still unvaporized but mechanically entrained. These may often be carried great distances by a stream of vapor, and their sepa- ration from that vapor frequently presents considerable diffi- culty. (b) Such mixtures of vapors and liquids are called Wet Vapors, to indicate the presence of the liquid; and when the entrained moisture has been entirely eliminated the material is called Dry Vapor. Since, under the conditions assumed in connection with Fig. 30, the liquid must all be raised to the temperature of vaporization before any of it can be converted into vapor at the same temperature, it follows that the vapor and liquid in such a wet mixture are in thermal equilibrium; that is, if there is any tendency for heat transfer from liquid to vapor, there is an equal tendency towards transfer in the opposite direction. With no heat lost to surrounding materials, such a mixture would main- tain a constant composition indefinitely. Vapor when in thermal equilibrium with its liquid is called Saturated Vapor. It is termed Wet Saturated Vapor, or simply Wet Vapor, if containing entrained liquid and Dry and Saturated Vapor, or simply Dry Saturated Vapor, if free from moisture in suspension. no HEAT-POWER ENGINEERING. (c) At different pressures the quantity of heat necessary to maintain material in the condition of dry saturated vapor has different values, being greater the higher the pressure. Abstrac- tion of heat without change of pressure (and therefore without change of temperature) will cause partial or total condensation, but any vapor remaining will still be saturated vapor exactly like that which existed before condensation occurred. There- fore saturated vapor may be described as vapor so near the point of liquefaction that the removal of the slightest quantity of heat will produce partial condensation. Or (see following paragraphs) it may be described as vapor in which the maximum number of molecules, consistent with the maintenance of a vapo- rous state at the given pressure, exist in a given space. 65. Quality, (a) Practically all saturated vapors in actual use contain some entrained moisture, and it is often necessary to express just how much of each pound of such a mixture is liquid and how much is vapor. This is done by using the fraction representing the proportion of mixture which is really saturated vapor. This fraction is denoted by x, and is called the Quality Factor, or Quality of the vapor or mixture. Thus if X is i, or 75 per cent, it means that three-quarters of every pound of mixture is vapor and the other quarter is liquid. The quality of the mixture would then be said to be 75 per cent. (b) The heat content above datum temperature of such a mixture could obviously be found by putting x in place of y in Eq. (100), since, so far as associated heat is concerned, it makes no difference whether the vapor and liquid are separated or intimately mixed. For wet vapor of quality x, the total heat above datum temperature is then ^Qxp = qp -{• xpp -\- X {APu)p == qp -j- xTp. . (lOl) 66. Superheated Vapor, (a) Having converted an entire pound of liquid into dry and saturated vapor in the apparatus of Fig. 30, its condition may be further modified if the addition of heat is still continued. Experiment shows that this further addition causes the temperature of the vapor to rise above that which existed during vaporization. This process is known as superheating, that is, raising above the saturation temperature corresponding to the existing pressure. The material formed is VAPORS III called Superheated Vapor, and it becomes more and more like an ideal gas as its temperature is raised at constant pressure. Thus it increases in volume with the addition of heat, and a given space must hold fewer and fewer molecules as the rise of temper- ature continues. (b) To make the meaning of the term " saturated " clearer, imagine a superheated vapor to be cooled, at constant pressure, by the removal of heat. As temperature decreases the vol- ume also becomes less, and any given space holds more and more molecules until the temperature of vaporization is reached, at which point the material is reduced to the saturated condi- tion. There is then, in a given space, the maximum number of molecules which can exist as vapor under the conditions obtain- ing; and further removal of heat would allow some of these to collect and form molecules of liquid, — that is, it would cause partial condensation. The material remaining uncondensed would still be saturated vapor, and with further removal of heat more and more of it would condense until finally all would be- come liquid, if the removal of heat were continued sufficiently far. 67. Heat per Pound of Superheated Vapor. The amount of heat added during superheating at constant pressure, to any temperature Tg, as described above, depends upon two things, — on the degree of superheat, which will be called D and equals {Tg — Tv), and on the specific heat Cp of the vapor. Then the heat added during superheating would be given by the following equation if Cp happened to be a constant: AQd = CpD : (102) The total heat (above datum temperature) of one pound of superheated * vapor would be AQs= qp-i- Pp-i- {APu)p-{- CpD . . . (103) = qp -\- rp -\- CpD = \p -\- CpD. . . (103a) * Recent experiment has shown that liquid water can exist for a considerable length of time within a mass of superheated steam, despite the fact that the two are not in thermal equilibrium. This fact must sometimes be taken into account in dealing with superheated steam in practical problems, when sufi&cient time does not elapse to establish thermal equilibrium. The heat per pound of such a mixture would be _ Qxs = qp + xrp + xCpD. 112 HEAT-POWER ENGINEERING 68. Diagram of Heat Changes during Vaporization, (a) The heat changes associated with the process of vaporization can all be graphically represented, as in Fig. 31, by plotting temperature as ordinates and heat added as abscissas. The figure is for water, but a similar diagram could be drawn for any material whose physical constants are sufficiently well known. ,a. <- h\^~ -XtdO-- -H I '/ 150 Lbs. Sq. In. C3y b J 70 ." " " ' 30 " " " 1 ';-&- 10 " -Xio- — ----- c — ^ / 400 600 800 1000 Heat.Added- B.T.U. Fig. 31. — TQ-Diagram for Vapor Phenomena. The line ahcd shows the relation of temperature to heat added while one pound of water under 10 pounds pressure is first heated from 32° F. to vaporization temperature (line ah) , is then completely vaporized (line be), and finally is superheated through a limited range (line cd). The lines abiCidi, aZ>2t2^, etc., show the same things for the other pressures indicated. (b) A diagram drawn to a sufficiently large scale would show the line abbs, and lines cd, cidi, etc., as slightly curved because of the variation in the value of the specific heat of liquid water and of the specific heat, Cp, -of superheated water vapor. In draw- ing Fig. 31 an average specific heat was used for the liquid and an average over each temperature range cd, Cidi, .etc., for the superheated vapor. The latter accounts for the slight differ- ences in slope of the superheating lines. (c) The diagram shows how great an amount of heat is absorbed during the process of vaporization as compared with that used in bringing the liquid to the temperature of vaporiza- tion, or with that used in superheating. This is of great im- portance in heat engineering and will be fully considered later. Two other facts of importance are made evident by the dia- VAPORS 113 gram: One is the small change of total heat, X, for a wide pressure range, as is seen by comparing the abscissas of c, Ci, etc.; and the other is the decrease of the total latent heat of vaporization, r, as the pressure rises. (d) This figure also shows the temperature changes and heat given up when superheated vapor at any of the given pressures is cooled to the saturated condition, then is condensed, and the resulting liquid cooled to 32° F. The engineer must often con- sider changes in this direction. 69. Vapor Tables. Since the various values of q, p, APu, r, and X are very frequently used by engineers and scientists, they are recorded, as already intimated, in the so-called Vapor Tables. There is of course a table for each material dealt with, so that it is customary to speak of " Steam Tables," " Ammonia Tables," " Carbon Dioxide Tables," etc. The various values of each quantity are usually tabulated in vertical columns, the first two columns giving pressures and corresponding temperatures of vaporization, and the succeeding columns giving the corresponding values of the various heat quantities. Certain other columns are usually added containing such values as the volume occupied by a pound of liquid and by a pound of dry and saturated vapor. See tables in Appendix. 70. Saturation Curve, (a) Experiment shows that just as the saturated vapor of a given material at any particular tem- perature always exerts the same definite pressure, so also does one pound of dry saturated vapor at any temperature always occupy a definite volume. This latter is called the Specific Volume and is tabulated in the vapor tables. If the specific volumes are plotted against the corresponding pressures, the locus of the points is a PV-diagram similar to Fig. 32, which like the last is drawn for water vapor. (b) This curve, called the Saturation Curve, may be very useful. If one pound of material at a given pressure has a volume rep- resented by a point which falls to the left of the saturation curve, the material must be wet vapor; but if the point falls to the right of that curve, the material must be superheated vapor. In the case of most engineering materials, the volume occupied by one pound of liquid is negligible as compared with that of one pound of vapor. In the case of water, the volume increases 114 HEAT-POWER ENGINEERING nearly 1700 times when changing from liquid to dry saturated vapor under atmospheric pressure. If the volume of the liquid present be neglected, steam of 50 per cent quality would occupy 0.5 the volume it would if dry and saturated, and steam of 75 per cent quality would have 0.75 of the volume of dry saturated steam, and so on. It follows that, if one pound of mixture is found to occupy a volume ab, Fig. 32, at the pressure indicated, it must have a \ a -^-V >, i Wet Region "~ Specific Volumes Fig. 32. — Saturation Curve for Water Vapor. quality oi x = — , if the volume of the water present is neglected. The case of superheated steam will be considered later, after the discussion of the experimental results. The area to the left of the saturation curve might be called the region of wet saturated vapor; and the area to the right, the region of superheated vapor. The curve itself would then repre- sent the boundary between the two, thus emphasizing the fact that dry saturated vapor is a unique condition at each pressure. (c) Because of the resemblance of the saturation curve to an expansion curve there is a tendency to regard it as represent- ing a possible expansion of vapor, that is, as an increase of volume during which the vapor remains dry and saturated throughout the entire process. Such an expansion might be obtained under very forced conditions, but normally no such process could be made to occur. It is then best to regard this VAPORS 115 curve only as a boundary line between two fields and not as the graph of a process. 71. Defining Conditions for Saturated Vapors. In dealing with ideal gases the variables to be considered are pressure, temperature, and volume. They are so interrelated that fixing any two determines the third. In the case of dry saturated vapors, however, the pressure, temperature, and volume are so related that the fixing of one determines the other two. This is not true of wet saturated vapors nor of superheated vapors. In the case of wet saturated vapors, the fixing of temperature determines the pressure, and vice versa, but the quality must be known in order to determine the volume occupied. Superheated vapors are more or less like gases, and in general the fixing of any two of the variables determines the third. 72. Evaporation, (a) There is sometimes difficulty in harmo- nizing the phenomena of vaporization, just described, with what is commonly known as evaporation. There is no real difference in the phenomena, vaporization as so far considered being only a limiting case of evaporation. (b) In what follows it will be of material assistance if it is remembered that the so-called temperature of vaporization at any pressure is really the temperature of saturated vapor (wet or dry) at that pressure. Thus the pressure exerted by a saturated vapor is determined by the temperature of the space the vapor occupies, and the pressure corresponding to any temperature can be found in the vapor table for the material. (c) Experiment shows that when the surface of a liquid is ex- posed to a space which is not already filled with the saturated vapor of that liquid, vapor is generated until the space is filled with such saturated vapor, unless the liquid present is insufficient in amount. Of course vaporization ceases if the liquid is exhausted. If the condition of equilibrium is reached, the saturated vapor must exert the pressure corresponding to the temperature of the space occupied. Until this equilibrium is attained, any vapor present must be superheated vapor because the number of mole- cules in a given space Is less than, would be the case if the space were filled with saturated vapor. Superheated vapor, however, Il6 HEAT-POWER ENGINEERING exerts a pressure less than that exerted by saturated vapor at the same temperature. It follows that the pressure under which the liquid changes to vapor must constantly increase until a maximum is reached, when the space becomes filled with saturated vapor. After that, there can be no further change in the relative quantities of liquid and vapor present unless temperature changes. (d) Since heat is required to change a liquid to a vapor, a supply of heat must be obtained from some source to cause " evaporation." If heat is not supplied from external sources, it is taken from the liquid and surrounding matter; hence the sensation of cold when alcohol, or other volatile liquid, is quickly evaporated from the skin. The actual amount of heat necessary for evaporation may be found by considering the process after equilibrium is attained. Every pound of dry saturated vapor must have associated with it the total heat X corresponding to the existing pressure and temperature. (e) Usually the space into which the vapor passes contains other material beside the vapor; for example, some air is almost always present. Dalton's law states that each constituent of such mixtures behaves as though the others were not present. There- fore, the phenomenon is not in any way complicated by the presence of any number of other vapors and gases. The evapo- ration goes on until the space is filled with the saturated vapor of the liquid in question, and only then is equilibrium reached. The vapor will then have all the properties given numerically in its vapor table opposite the existing temperature. The reason for calling vaporization as first considered a limit- ing case of what is generally known as evaporation should now be evident. The apparatus used in explanation was so arranged that the space available automatically increased as saturated vapor became available to fill it. This was done for simplicity and because of the close resemblance to the process taking place in the steam boiler, from which the vapor is withdrawn as rapidly as it is generated. Note that the final conditions are the same in either case. A certain space is filled with saturated vapor of a given material, and what is true of that vapor in one case is true in the other. When a space is . thus filled with the saturated vapor of a VAPORS 117 material, it is said to be saturated with that vapor or with respect to that vapor. Because of a peculiar construction of this ex- pression an incorrect idea has become fixed in engineering language. It is usual to speak of air saturated with water vapor, whereas the real meaning is that a space occupied by air is also occupied by saturated water vapor. (f) Dalton's law is sometimes called the Law of Partial Pres- sures. From the previous statement of this law it is evident (i) that when several gases and vapors occupy a space in common, each behaves as though the others were absent, and (2) the pressures upon the walls enclosing the space, or at any point within the space, must be the sum of the pressures exerted by all the constituents of the mixture. This pressure is called the total pressure of the mixture, while the pressures due to each of the constituents are- called partial pressures. If each constituent may be considered as obeying the laws of ideal gases, the same is true of the mixture. The pressure in the vessel, then, would be the total pressure, the volume would be that occupied by the mixture, and the temperature would be that of the mixture, which temperature must be the same for all constituents. When some of the constituents of such a mixture are satu- rated vapors, the perfect gas laws cannot ordinarily be used if great accuracy is desired. When, however, the quantity of such vapors is small as compared with that of the gases present, the error resulting from the use of the gas laws is small, and for the sake of simplicity those laws are generally used and the error is neglected. 73. Boiling. Heat is often added to a liquid at such a rate and in such a way that the temperature of one part becomes higher than the temperature of adjacent parts; that is, local heating takes place. This is the result when the local addition of heat exceeds the rate of heat conduction through the material. Such heating raises the temperature locally to that of vaporiza- tion corresponding to the pressure, after which further addi- tion of heat would cause local vaporization; that is, a small amount of the liquid inclosed within the rest would be converted into vapor and appear as a bubble. The pressure at any point within a liquid at rest must be that Il8 HEAT-POWER ENGINEERING due to the static head of the hquid above that point plus the pressure due to any material resting upon the surface. Therefore, the bubble of vapor would be formed under that pressure and, during formation, would have to displace the column, or " piston," of water above it against that pressure. The bubble, being less dense than the surrounding liquid, would rise, but if the temperature of the liquid encountered was lower than its own it might entirely condense before reaching the surface. This process continued long enough would bring all the liquid approximately to the same temperature, after which the vapor bubbles could travel upward through the liquid and escape as vapor from the surface. Liquid is said to be in a state of ebullition or to be boiling when it is in such a state that bubbles of vapor formed within its mass pass up and out through its surface. From what has preceded it can be seen that this process will occur when the body of water is at such a temperature that the pressure of its saturated vapor is equal to that upon its surface. This is sometimes given as a definition of boiling temperature. 74. Temperature -Entropy Changes of Vapors, (a) All the processes described in connection with the formation of vapor are thermodynamically reversible; hence for vapors, just as was done for gases in Section 38 (a), dE may be substituted for APdV in the general Eq. (53) defining an infinitesimal entropy change. Then for such a change in a unit weight of vapor the expression becomes j^ dS-\-dI + dE , , d = ^ — — , (104) or d4> =-^, (105) and for a finite change h4> = £^ ...... (106) These expressions may be used for determining the entropy changes for unit weight of any vapor when undergoing any reversible processes. (b) The reversible temperature-entropy changes occurring during the vaporization of water at several different pressures are shown graphically in the T^-diagram given in Fig. 33. VAPORS 119 During the heating of the liquid at constant pressure the specific heat Cp, or heat required per pound per degree, may be either variable or constant. The equation for the lines ab, abi, ab2, etc., for the entropy change experienced by the liquid. 60.0 dOO ¥ \ \ /\ h bJ Yz V i k 2 ^800 / 150 Lbs \eo — -V M / 70 Lbs. \1 % 1"' faoo iOO a 30 Lbs \(>. ^^ / > 10 Lbs. Saturation Line-^^ / 0.6 1.2 0.8 1.0 Entropy Fig- 33. — T0-Diagram for Water and Water Vapor. called briefly the entropy of the liquid, must be the same as Eq. (61) and is A0Z -/ 'C^dT (107) or Acf>i = Cp\0ge*-7f?. ..... (108) This last equation can be_used even if the specific heat is not a constant, by interpreting Cp as the mean value over the given temperature range. (c) The process of vaporization is a constant-temperature or isothermal one; here, following Eq. (65), the entropy change experienced by the material during vaporization, called briefly the entropy of vaporization, is evidently A(f)y='^^=— (109) where Tv is the temperature of vaporization. (d) During superheating of the vapor at constant pressure the specific heat may be either variable or constant, and, parallel- ing Eq. (61), the entropy change, called briefly entropy of super- heating, is (no) ■-~L A4>D = '^'CpdT * It is usually more convenient to use logio instead of loge. Since logg = 2.302 logio, Eq. (108) maybe written A0z = Cp X 2.302 logio (T2/T1). The other logarithmic equations which are to follow may be similarly transformed. Then 1 20 HEAT-POWER ENGINEERING oi" A , 7^ 1 Ts -TT ^ Tv -\- D , V A0i) = Cplogc ^ = Cp logc — If. — , . . . (iioa) where Cp is the mean specific heat, D is the temperature in- crease above the saturation temperature, Tv, and Ts = Tv -\- D. (e) Summing up these results gives the total entropy change experienced by the material when transformed at constant pressure from liquid at datum temperature to superheated vapor at temperature {tv + D). This, which is briefly called the total entropy of superheated vapor, is A03 = A0i -f A0V + A0i) (ill) ^^^ = 1 -^ + r. + l-^ • • ^"^^ = Cp loge ^ + ^ + Cp loge -^^ , . (l 12a) i -i V J^ V in which To is the datum temperature, Tv is the temperature of saturation, and Ts(= T^ -\- D) is that of the superheated steam when the amount of superheat is D degrees. (f) If vaporization ceases before the entire pound of material has been vaporized, only a part, xr, of the total latent heat of vaporization, r, will have been added. The entropy change experienced by the material in coming to the condition of wet saturated vapor with quality x would then be A0;, = ^(i>l + xA0« (113) ^ CpXoge Tf- + TfT (114) When X becomes unity, — that is, when vaporization is just complete, — there is dry saturated vapor, and this equation becomes A0,a = A0Z + A0^ (115) — T r = Cpl0ge-;r^ + ^. .... (116) The points e, ^i, ^2, etc., in Fig. 33, show the entropy change for different pressures as determined by Eq. (114) when x = 0.75. Obviously the distances he, biCi, etc., must be 0.75 of the dis- tances be, biCi, etc. This diagram then furnishes a means of determining quality in a manner similar to that used in the case of the saturation curve. Fig. 32, but is not subject to the ap- proximation there necessary. / 0^ 'v^*^ Y-. VAPORS I2l 75. Continuity of the Liquid and Gaseous States. . (a) It has been stated, in Chapter IV, that no real gases obey exactly the laws of ideal ones, but that it may be assumed without great error that those real gases which are farthest removed from the conditions of liquefaction do obey these laws. This assumption, however, is not justified at very low temperatures or very high pressures. The study of materials in the liquid and gaseous spates shows clearly that these states are in the nature of limiting conditions to gradual physical changes. This may be presented by means of Fig. 34. It should be clearly understood how- ever that this figure is qualitatively but not quanti- tatively correct; that is, it is not drawn to scale, nor does it exactly represent the be- havior of any real material. It does, however, show the nature of the changes under consideration for all known materials. (b) The diagram is for unit weight of material on pressure- volume coordinates, and each of the heavy lines is an isothermal. Starting with the lowest line of the series, the point a represents the volume occupied by unit weight of liquid at temperature T and at the pressure shown. If the pressure is decreased while the temperature is maintained constant, the volume of the liquid will increase until the point h is reached.* At this point the pressure, volume, and temperature are such that any further change can only be a progressive vaporization at constant pres- sure, as shown by line he (since the temperature is constant) with increase of volume from h to c\ that is, the material is at the Specific Volumes Fig. 34. — Isothermals of Material in Liquid^ Vaporous and Gaseous States. * The increase of volume has been much magnified in the figure to emphasize the phenomenon. 122 HEAT-POWER ENGINEERING point of vaporization for temperature T. At c the material has become fully vaporized, and hence is dry saturated vapor. A further decrease of pressure at constant temperature will cause it to become superheated and to behave somewhat like an ideal gas. The volume will then increase almost inversely with the pressure, bringing the material to the conditions d along the curve cd. Starting from ai, with the material in liquid form at a tem- perature Ti > T, a. similar process carries the material isother- mally to di. The same statements can be made for all other starting points at different temperatures up to some such value as Ts, when the process will be that shown by the curve azb^ds. In this case the points b^ and Cs have become coincident, the liquid, if it is such, having the same volume at pressure Pbs as does its vapor. At higher temperatures, such as T4 and T^, the material begins as a gas and the -isothermals become more and more nearly rectangular hyperbolas (PV = const), as they are drawn for higher and higher temperatures. Reversing the process, a gaseous material compressed iso- thermally from d^ conditions will remain gaseous no matter how high the pressure is carried. A gaseous material compressed isothermally from di will, however, begin to condense at Ci and will continue to liquefy with further compression until it all becomes liquid at bi. (c) If ds is chosen as the point to begin isothermal compression, it is obvious that the material after passing bz must be on the boundary between the liquid and gaseous states; that is, the pressure, volume, and temperature conditions for the two states are the same and the material may be considered a liquid or a gas, or both. The conditions at &3 are called critical conditions, that is, critical volume, critical pressure, and critical temperature. The critical temperature of gaseous material is usually defined as the temperature above which liquefaction is impossible by any increase of pressure. The truth of this definition is evident from the diagram; no isothermal of higher temperature than a^b^dz could cross the latter and so enter the liquid region. (d) In the figure the hatched area with the lines running upward from left to right represents the region in which the VAPORS 123 material must be liquid. That is, when any point representing the pressure and volume of the substance falls within this region, the material must be in the liquid state. Similarly, the part hatched downward from left to right represents the region of superheated vapor, and that crosshatched in both directions represents the region of liquid mixed with its saturated vapor. The part not hatched represents the region in which the material cannot be liquefied by change of pressure. This is now commonly called the region of the gaseous state. A gas may then be defined as a material above the critical temperature, and a vapor as material which, while resembling a gas, is below the critical temperature. It must not be inferred that material above its critical tem- perature sensibly obeys the laws of ideal gases. It must be far removed on the temperature scale before this occurs. The isothermal T^ shows this. Note in the figure that the curve bze is the saturation curve, a part of which was drawn for water vapor in Fig. 32. (e) This diagram, Fig. 34, is useful for determining the be- havior of material when subjected to volume, pressure, and temperature changes. Material in the gas state, as at / for in- stance, can be liquefied by lowering temperature and decreasing volume while the pressure is maintained constant, as along the line fg. Or it can be brought to the condition of wet vapor by lowering pressure, volume, and temperature according to some curve fh. Similarly, increasing the temperature and pressure of a superheated vapor at constant volume (line kl) results in carrying it into the gas field. (f) At the critical temperature the latent heat of vaporiza- tion, r, becomes zero; that is, no internal and no external work of measurable magnitude is done, as the material passes from just above to just below the point ^3 on the isothermal T3. In- spection of the Steam Tables in the Appendix will show the way in which the latent heat of vaporization of water vapor gradually decreases from large values at low temperatures to a value of zero at the critical temperature. 76. Van der Waals' Equation for Real Gases, (a) Obviously any gas is really only a very attenuated liquid, differing in its properties from the liquid because its molecules are much farther 124 HEAT-POWER ENGINEERING apart, and possibly of simpler structure. If this is true, it ought to be possible to write laws of condition which would fit the same material in either the liquid or the gaseous form. Several attempts have been made to do this, and one in particular is of great interest. It is due to Van der Waals and was developed by modifying Boyle's law to take account of two assumed facts. These are: (i) The space filled by a gas is partly occupied by the mole- cules of that gas, and it is only the space between the molecules which obeys Boyle's law. (2) In no real gas are the molecules far enough apart to be absolutely independent of one another; certain intermolecular forces still exist. These decrease the total volume occupied or make the gas behave as though subjected to a pressure greater than the real external pressure. The law in mathematical form is (-+^) (V — b) = Constant, or (p+§i))=RT^' • (117) in which a and b are constants, differing with the kind of gas. (b) This equation can be rearranged to read v-v^(f:+6)+v|-J = o,. . . (118) a cubic equation in terms of the specific volume V. Then for a given temperature and pressure there must be three values of V which satisfy the equation. If the curves obtained by substituting in the equation are drawn for constant temperatures, they resemble the lines abed, etc., in Fig. 34, except that the horizontal lines be, etc., are re- placed by the dotted curves shown. If the equation is really true, the process of vaporization must be more complicated than at first appears. The fact that the phenomena corresponding to part of the curve from b downward and from e upward can be realized experimentally gives evidence in support of this law. The condition of the material thus carried into the dotted position of the curve is, however, very unstable, and the sub- VAPORS 125 stance suddenly assumes the condition shown by the horizontal line if disturbed. (c) The critical point may now be said to be the point at which all three roots of the equation coincide or at which one is real and two are imaginary. (d) The equation of Van der Waals, though better than that of Boyle, does not fully express the truth. If it did, it would hold for material in the solid as well as in the liquid state. It really recognizes no such condition as solid. If it did, its graph, continued far enough back in the direction dcba, would show another jog similar to but shorter than cb, representing the con- stant-pressure, constant- temperature change from liquid to solid. This it does not do, and hence it is imperfect. (e) The phenomenon of zero volume at absolute zero tem- perature can now be explained. According to the simplest kinetic theory of gases, the temperature is supposed to be a measure of the translational energy of the molecules, and the pressure is the result of the bombardment of containing walls by the rapidly moving molecules. Assuming, with Van der Waals, that the volume to which the ideal laws refer is not the total volume occupied by the gas, but equals that volume corrected for the volume of the molecules present, the limiting case of the ideal laws is easily explained. When absolute zero of temperature is reached the molecules of a gas must be assumed to be devoid of translational motion and in such positions that the volume referred to above has become zero. Then as the molecules at rest could not bombard sur- rounding surfaces the pressure would also be zero. This equation of Van der Waals is in general only of theoretical interest to the engineer. Seldom does the accuracy required in engineering calculations warrant the use of such refinement. It is introduced here only to give a possible simple explanation, though an incomplete one, of what otherwise seems very in- definite, and to furnish a more complete view of the continuity of the liquid and gaseous states. CHAPTER X. PROPERTIES OF STEAM. 77. Steam or Water Vapor. (a) All that has just been said about the formation and the properties of vapors in general applies, of course, to the case of water vapor or steam. This vapor is usually generated in a boiler in which the pres- sure is maintained substantially constant by the withdrawal of some of the steam as rapidly as more vapor is generated. This withdrawal occurs ordinarily through the steam pipe, at other times through the safety valve. The water when pumped into the boiler is under the pressure existing in that vessel. Thus the application of heat causes the temperature of the liquid to rise under constant-pressure conditions. This increase of course ceases when the temperature of vaporization, correspond- ing to the pressure, is reached. Since the heat is added at con- stant pressure, 2 would be computed from Eq. (94), using the mean specific heat at constant pressure for Cp. (b) The further addition of heat to this water causes the formation of vapor, or steam. Associated with this process there is great increase in volume and the absorption of large amounts of heat. In discussing the general case, in connection with Fig. 30, it was considered that the external latent heat expended in connection with the volume-increase was utilized in lifting a weight, thus doing work in overcoming the action of gravity. In the case under consideration, when steam is supplied to a piston engine, the external latent heat is expended in displacing the piston against resistance, thus doing external work equal to APu per pound of material and making available increased volume of steam space in the cylinder as rapidly as the vapor is generated. It is true that engines of this type ordinarily take steam intermittently from the boiler, hence the steam pressure witl>in that vessel would fluctuate slightly on this account, even if other causes of fluctuation could be eliminated. In such cases the mean pressure is the one commonly used. 126 PROPERTIES OF STEAM 127 It is not only true in the case of the piston engine but also in all other cases, that the withdrawal of steam from the boiler is accompanied by the doing of external work, equal to APu per pound of material, although just how this energy is expended is not always clear to the beginner. The rest of the heat utilized in the process of vaporization is the " internal latent heat," p, expended in causing the molecular rearrangement accompanying the change from water to steam. (c) In many instances a portion of the steam pipe is modified in form and subjected to heat in such manner that it becomes what is termed a " Superheater," in which the steam becomes superheated by the reception of more heat, as it passes through, on its way to the engine or other device which is being supplied. During this superheating the steam is under constant pressure, hence in using Eq. (102) to determine the heat added the mean specific heat at constant pressure Cp should be introduced. 78. Sources of Data. The different related properties of dry saturated steam are tabulated in Steam Tables such as that given in the Appendix. Some of the properties are determined directly by experiment and others are derived quantities which are found by computations involving the experimentally de- termined data. Many different Steam Tables have appeared, and all except the most recent ones were based on Regnault's experiments, published in 1847. These older tables, while thus based on the same data, depart somewhat from one another in the values tabulated, the disagreement arising from differences in inter- preting the data and in choosing values of Joule's equivalent, absolute zero, specific heat of liquid, etc. In spite of their differences and errors, these steam tables are still sufficiently accurate for most engineering calculations; and ordinarily the results of investigation which involved their use may be compared with those based on the later tables, without introducing serious errors. The recent rapid increase in the use of superheated steam has led to many attempts to determine accurately the different values of the specific heats of this material under various con- ditions. This has revived interest in the properties of saturated steam, with the result that in 1909 new and more accurate Steam 128 HEAT-POWER ENGINEERING Tables appeared in book-form, one by Peabody, and another by Marks and Davis. Both books, besides giving tables for the properties of dry saturated steam, contain elaborate tables giving the entropy and other properties of superheated steam, and other auxiliary tables, together with certain charts which are useful to the engineer. For the mechanical equivalent of i B.t.u., Peabody uses 778 foot-pounds and M. & D. use 777.52. For the absolute zero the former uses 491.5° F. below freezing; the latter 491.64. Peabody uses for the B.t.u. the heat required to raise one pound of water from 62° to 63° F.; whereas M. & D. use the ''mean B.t.u." defined in Section 3.* The values chosen for the specific heats of water also vary slightly. However, the differences mentioned are so small as to be negligible for engineering purposes. The discussion of how tables may be made will now be taken up very briefly. For a more thorough treatment and for references to the sources of data the student is referred to the books just mentioned.! 79. Properties of Dry Saturated Steam. The properties given in the Steam Table in the Appendix are the corresponding values of (a) Pressure and Temperature ; (b) Heat of the Liquid ; (c) Total Heat of Steam; (d) Latent Heat of Vaporization; (e) External Latent Heat; (f) Internal Latent Heat; (g) Entropies of Water, Vaporization, and Total; and (h) Specific Volumes. ' The properties are tabulated for one pound of material, the pressures are in pounds per square inch absolute, and the heat quantities and entropies (excepting those for vaporization) are measured above 32° F. Temperatures and Pressures. (a) It has been seen that saturated vapor has a definite tem- perature corresponding to each pressure at which the vaporiza- tion occurs. The variation of temperature with pressure of water vapor has been determined experimentally and is shown graphically in Fig. 35, to two different pressure scales. It is important to note the shape of this curve, especially the rapid rise * The mean B.t.u. is about ^Iq larger than that measured at 62°. t Also see Trans. A. S. M. E., Vols. 29 to 33, for papers, discussions, and refer- ences to sources. PROPERTIES OF STEAM 129 dp of pressure, or increase in the slope -77 with elevation of tem- perature in the upper region. The TP relations can also be « 250 P 200 B "500 / / ^ / 1 A 4 r innn 1/ dp / / / / / dt / _^ y ^.-' ^^' 100 200 300 400 500 600 700 •Temperatures Deg.Pahr. Fig. 35. — PT Relations for Steam. expressed algebraically by formulas* which are rather compli- cated. These need not be given here, however. Heat of Liquid (2). (b) The heat of the liquid is the amount added to water at 32 degrees in order to bring it to the temperature of vaporiza- tion. Its amount is computed by using Eq. (92) and integrating between the temperatures of freezing and of vaporization, thus: Cpdt = I Cpd T, 32 t7492 (119) where Cp is the constant-pressure specific heat of the liquid, which in the case of water varies with the temperature. The progressive values of Cp have been found by several experimenters with results that are not absolutely in accord. The curve in Fig. 36 represents an interpolation between the several data. The right member of Eq. (119) will be recognized as the ex- pression for the area below the Cp curve, and lying between the ordinates at 32 degrees and ty. This area can be found by planimeter or other method of integration. *See "The Pressure-Temperature Relations of Saturated Steam," by Prof. Lionel S. Marks. Trans. A. S. M. E., Vol. i2>- I30 HEAT-POWER ENGINEERING If Cp is the Mean Specific Heat for the temperature range d — {tv — 32), between limits 32 degrees and tv, then 2 = Cp (^ - 32) =^ Cp X (^ (120) Cp is obviously the mean height of the part of the Cp-curve lying between the temperature limits under consideration. a.i8 % 1.08 1.06 1.02 1.01 1.00 .99 / 1 / Water / / / / V / / / \ y k ^ /^ ^•^ —-""'^ 100 200 300 400 500 Temperatures Deg. Fahr. 700 Fig. 36. — Progressive Values of Specific Heat, Cp, of Water. Hereafter the instantaneous, or the progressive, values of Cp (that is, those corresponding to one degree rise at different tem- peratures) will be called the progressive specific heats to dis- tinguish them from the mean values. For many purposes, especially at low temperature, it is sufficiently accurate to assume Cp = i, then g = (/ — 32). In computing the values of g for the steam tables, however, it is necessary to employ the greatest accuracy. In Fig. 31, the curve ab^ shows approximately how g varies with U. If Cp is taken as unity, this curve becomes a straight line. Total Heat of Steam (X). (c) This is the amount of heat required to raise one pound of water from 32 degrees to the temperature of vaporization, then to separate the constituent particles during the formation of PROPERTIES OF STEAM 13 1 steam, and to do the external work accompanying the increase in volume. The values of X have been determined for a number of pressures by various experimenters. By plotting the most trustworthy data on cross-section paper, with X and temperature as coordi- nates. Dr. H. N. Davis obtained a curve which is generally regarded as giving the most reliable values of this quantity. The portion of the curve lying between 212 degrees and 400 degrees is represented by the equation X = 1150.3 + 0.3745 (/.- 212) - 0.00055 (iv- 212)2. (121) Regnault's formula for total heat, which was generally em- ployed before 1909, is accurate enough for ordinary engineering purposes and is much simpler than Davis'. It is X = 1091.7 + 0.305 {tv- 32). ... (122) Note that this quantity increases with the temperature, but at a very slow rate. This is shown in Fig. 31, by the abscissas of points c, Ci, C2, etc. The higher the pressure the less rapid is the rate of increase. Latent Heat of Vaporization (r). (d) Having obtained the total heat X and the heat of the liquid q, the latent heat of vaporization may be found from r = \- q (123) If the specific heat of water is taken as unity, q = (/„ — 32) ; and if this is subtracted from Eq. (122), Regnault's approxi- mate equation for the latent heat of vaporization is obtained. This is r = 1091.7 - 0.695 (/r, - 32) (124) In Fig. 31, the values of r for different temperatures and pres- sures are shown by the distances be, ^2^2, bsCs, etc. The latent heat decreases with rise in temperature, and becomes zero at the critical temperature. At atmospheric pressure r is 970,* and this figure should be remembered, as it is used frequently in engineering computations. * The old value is 966. 132 HEAT-POWER ENGINEERING The External Latent Heat (AE). . (e) The external latent heat AE expended in displacing the surrounding media can be computed from the equation AE = ^^l^= 144 Apu = A Pu, . . . (125) in which A = — -^ p is the pressure in pounds per square inch, P is the pressure in pounds per square foot, and u is the increase in volume during vaporization. How u may be determined will be explained in (h) of this section. The value of APu is rela- tively small and varies from about 61 B.t.u. at one pound pressure to about 85 B.t.u. at 400 pounds. The Internal Latent Heat (p). (f ) The internal latent heat expended in producing- the molec- ular rearrangement may be obtained by subtracting the external latent heat from the total. Thus p = r —APu. . (126) Entropies (A). (g) The values tabulated are per pound of steam. The entropy of the liquid may be found from A(f>i = / ^=CA -TfT (127) J 492 ^ J 492 ■* As the heat of the liquid, Cp I dT, is measured above the freez- ing point of water, it follows that the corresponding entropy must also be calculated above the same datum, that is, 492° F. absolute. The integration of Eq. (127) gives for the entropy of water, A(A, = Cplog.^, (128) in which Tv is the saturation temperature for the pressure under consideration and Cp is the mean specific heat of water for the temperature range from 32 degrees to tv, as found from Fig. 36 in the manner described in Section 79 (b). The entropy of vaporization (A^,,) may be found from Eq. PROPERTIES OF STEAM 133 (109) by substituting the values of Tv and r corresponding to the pressure under consideration. The total entropy (A0sa) of one pound of dry saturated steam above 32 degrees is ^i-{- ^(t>v- Specific Volume (V). (h) This is the number of cubic feet occupied by one pound of steam. It varies with the pressure and is equal to the sum of the original volume of the pound of water (0.017 =t cu. ft.)* and u, the increase in volume during vaporization. Thus, V = w + 0.017 zb cu. ft (129) The value of u can be obtained from what is known as Clapey- ron's equation, t' \dt) cu. ft. (130) Here (-77) is the slope of the pressure-temperature curve (see Fig. 35, in which -^ = Tfi' ^^^ '"^^ ^^ found either graphically or mathematically. The following is a rather crude way of deriving Clapeyron's equation: On a PV-diagram, Fig. 37, starting at A with one Fig. 37- Fig. 38. pound of water already at the boiling point (pressure P, and absolute temperature T), let sufficient heat be added to cause complete vaporization, the increase in volume being u] then let there be a slight drop in pressure dP, next let there be a de- * The volume of a pound of water varies from 0.016 to 0.018 cubic feet within the ordinary range of temperatures. 134 HEAT-POWER ENGINEERING crease in volume at the uniform pressure (P — dP) until all of the steam is condensed to water at the corresponding boiling point; and finally bring the water up to its original temperature to complete the cycle. Evidently the work done, as shown by the area of the figure, is u . dP foot-pounds, which in B.t.u. is u • dP , s (a) dE = 77^ On the T<^-diagram, Fig. 38, let the same cycle be shown. Starting at A with water at the boiling temperature T, let heat, r, be added to vaporize the water. This is accompanied by an increase in entropy of amount ^. Next let there be a temper- ature drop dT (corresponding to dP), and then let the steam be condensed at constant temperature (2" — dT), corresponding to (P — dP), to water at the boiling point. Upon returning the water to its original condition the cycle is completed and the work done in B.t.u., as shown by the area surrounded, is dE = (j^dT. (b) Evidently equations (a) and (b) both represent the same amount of work. Hence, — ^ =(-7p]dTj solving which for w results in Clapeyron's equation. The Specific Density. (i) The specific density or weight of one cubic foot of steam is equal to f-j. As this is merely the reciprocal of the specific volume, it is not given in the Steam Table in the Appendix. Properties of Steam at High Pressures: (j) Above 250 pounds per square inch (400° F.) the properties of steam have not been determined with great accuracy, so that the values given in the tables above this pressure are not very trustworthy. More accurate values are, however, not available at present. It will be noticed that the latent heat decreases as the tem- perature increases until it becomes zero at the critical tempera- PROPERTIES OF STEAM 135 ture of about 706° F.,* corresponding to a pressure of about 3200 pounds per square inch. 80. Properties of Superheated Steam, (a) Specific Heat at Constant Pressure. In dealing with superheated steam the engineer ordinarily uses only the specific heat at constant pres- sure. For ideal gases it has been shown that Cp is independent of temperature and pressure, and that it is sensibly so for most real gases within ordinary ranges. For superheated steam, however, it cannot be considered constant at the temperatures used in engineering, for the material is always far below the critical conditions, and though approximating the behavior of a gas it varies greatly from the laws for perfect gases. Several experimenters have recently determined values of Cp for steam over wide temperature and pressure ranges. Among these the results of Knoblauch and Jakob are generally con- sidered the most trustworthy, and were used both by Peabody > .7 1 Super heated Steam 1 / /I / \\ \ ^X ^0 ^ ii v^ . ^ + A(2i) = X + C;A . . . . (132) The Entropy of Superheated Steam. (d) The entropy above saturation temperature Tv is A) P X / 1 50,300,000 „ \ . . [ , \, 0.0833J, . . . .(133) in which Vs is in cubic feet, T is the absolute temperature of the superheated steam in Fahr. degrees, and p is in pounds per square inch. A simpler formula and one that is nearly as accurate is given by Tumlirz. It is, for p in pounds per square inch, T Ys = 0.5962 - - 0.256, ..... (134) and for P in pounds per square foot, ¥3 = 85.86-^-0.256 (135) 81. Temperature-Entropy Chart for Water and Steam. (a) Diagrams drawn with T^-coordinates are of great con- venience in solving many problems involving the use of steam. Especially are they valuable when reversible adiabatic changes and associated heat changes are considered, for with these co- ordinates, the former are straight lines and the latter are areas. The Ti and U used in plot- ting the W-curve can be obtained directly from it. In general the heat used during a reversible process to pro- duce a r<^-change is Fig. 41. — T<^-Diagram for Water Vapor. AQ -i: Td(i>. The right side of this equation is of the form / y dx, which is the mathematical expression for an area, and which here represents the heat quantities AQ. As dx in this case is dcf), which is measured above 32° F., the heat represented by the area must be that above 32° F. also ; and a,s y = T (abs) these areas must extend down to absolute zero of temperature, that is, to the (^-axis. From this it is seen that the heat of the liquid above 32° F. is represented by the area under the W-curve, extending to the T and axes, such as area OAB(f)i, in Fig. 41. PROPERTIES OF STEAM 1 39 The W-curve has Httle curvature. If it is considered straight (involving small error for ordinary ranges) , it is seen that the area under that line is the product of A^^ by the mean temperature X±49L:thatis, 2 q = A(l>i ^^^(approx.) (136) Substituting g. = {T — 492), which would be its value when C = 1, gives the following approximate equation for the entropy of water : ■ ^^^^ ^rV.nf^ (approx.), . . . (137) I +492 which is convenient for rough computations, as it does not involve the use of tables. Saturation Curve, or S-curve. (c) The entropy of dry saturated steam is, from Eq. (115), Acpsa = Ai + ^/^, the values of all quantities in which are given in the steam tables. In Fig. 41, the abscissa TB is A0i for the temperature T; so if 5 C is made equal to the corresponding value of A^^, the point C must fall on the Saturation Curve. The locus of a series of points plotted in this manner for different temperatures is the S-curve. Evi- dently this curve is the graph of Eq. (115). The area of the rectangle below the line BC \s Acf>,XT = YXT = r, and hence is the latent heat of vaporization. Then the total heat of the steam, X, is given by the area below ABC, since this latter represents r + g. Constant-Quality Curves, or X-curves. Xf (d) The equation of these curves is A-Diagram Showing X-Curves. Y? ) , thus locating the state point at D for the temperature T. The locus of points similarly plotted for different temperatures is the Curve of Constant Quality. A series of such curves is shown in Fig. 42 (a). Since BC = ^ and BD = ^' it follows BD that -^ = X. This relation suggests another and simpler method of plotting points to determine the X-curve: In the figure draw the hori- zontal intercepts BC, BiCi, etc., between the W-curve and the S-curve, and on them locate the points D, Di, etc., in such positions that ^7:; = J ^ = etc. = x. Then the locus of these X)C -oiCi points, D, Di, etc., is the curve desired. The heat used in vaporizing x parts of a pound of steam at temperature T is shown by the area below BD^ Fig. 42, since (xt\ -^J X T = xr. The total heat in the mixture of steam and water is given by the area below ABD, for this area equals xr -\- q. Constant-Volume Curves, or V-curves. (e) At any temperature T, Fig. 43, the change in entropy from B to C during complete vaporization is accompanied by an increase, equal to u, in the volume of the working substance. If at the same temperature only part of the unit weight — occupying the volume V — is in the vaporous form, it is evident PROPERTIES OF STEAM 141 that the quality of the steam must he x = '- — —. By maintaining V constant in this equation and substituting values of u corresponding to different temperatures, the way x varies with T during an isovolumic change can be determined. Then the V-curve can be plotted either by using the quality or by making BD ^ {V - 0.017) ^lA _ (F- 0.017) BC u ' BiCi Ui ' The same curve can be obtained by graphical construction in the following manner: In Fig. 43 lay off a V-axis opposite to the T-axis, thus forming a V(/)-quadrant in which volumes are laid off downward. Directly below B drop an ordinate ab for the corresponding volume of the material. This is the volume of the water at temperature T, or 0.017 =b cubic feet. Directly below C lay off the volume corresponding to that point, thus locating c. The value in this case is V, the specific volume of the steam. Then the straight line be joining these points shows the uniform increase of the volume and entropy during the process of vaporization of one pound of working substance at the temperature T. In like manner similar Vaa can be obtained from the tables. __ A difficulty arises in selecting the proper value of Cp, because the mean specific heat is dependent on D, which is initially unknown. Hence it is necessary to adopt the " cut and try method." That is, a trial value of Cp is assumed and D is com- puted; then the value of Cp corresponding to the pressure and to D is obtained from the curves, and if it is the same as the trial value the assumption was correct; but if there is much difference, a new value must be assumed and the process must be repeated. Constant-Pressure Curves, or P-curves. (h) For saturated steam the P-curves are isothermals; for superheated steam' they are not. In the latter case, the rela- tion between Ai, and p can be read directly, while q is given by the area below the curve. For a point on the saturation line the values of r», A0,a, X, V, and p can be read at once. If the point is in the Region of Superheat, T, A(^«, A^^a, P, and AQ can be read directly; the increase in temperature above saturation is D = T — Tv] the B.t.u. superheat, A(2^, is given either by an area, or by (AQ — X) ; and the entropy of super- heat A(/)^ is (A<^s — A0sa). If any expansion line is drawn on the chart, all of the above- mentioned quantities can be read for each point on the line. If the lines inclosing a cycle are drawn, the work done per cycle is of course given by the area surrounded. It is important to note that the quantities given by the Q-curves are values of {xr + q), not (xp + q), and contain the external work of vaporization (xAPu). * A larger and more accurate T), quality (x), superheat {D) and entropy (0). (b) For any state point on the chart one may read directly the values of p, x or D, xV or Vs, A '^^ which V may be obtained from the Steam Tables. VOLUME CHANGES OF VAPORS I49 Work during Isobaric or Isothermal Changes of Saturated Vapors. (d) The External Latent Heat of vaporization is that part of the total heat which does the external work accompanying the increase of volume; it must therefore be equivalent to the ex- ternal work done. Hence in vaporizing to quality x, per pound of material, ^E = X' APu B.t.u (142) and 778 b.E-^ x^Pu ft.-lbs. ..... (143) This work is shown in Fig. 46 by the area below ah' . For the case in which x = i.oo, it is the area below ab. With change of quality from Xi to X2 the work done is, AE = {x2— Xi) APu B.t.u. . . . (144) and 778 AE = (x2- Xi) Pz^ ft.-lbs (145) 85. Constant-Pressure Volume Changes of Superheated Vapors, (a) Starting from the point h in Figs. 46 and 47, the dry and saturated vapor may be made to still further expand at constant pressure to some point Ci by superheating, that is, by raising the temperature above that corresponding to saturation at that pressure. The further this expansion continues the more nearly the behavior resembles that of a gas, and there is no theoretical limit to such expansion, as there was in the case of the saturated vapor. Equation of Isobaric Change of Superheated Vapor. (b) The equation in terms of P and V must be the same as that already developed for gases and saturated vapors, namely, PYQ = P = Constant. Heat Change during Isobaric Changes of Superheated Vapor. (c) As the temperature must be raised at constant pressure in order to increase the volume, or lowered at constant pressure to reduce the volume, it follows that a quantity of heat equal to the specific heat at constant pressure, Cp, must be added or abstracted per degree change. Then for heat added above saturation /»2 AQd= / CpdT, 150 HEAT-POWER ENGINEERING or, using the mean specific heat Cp for the temperature range D measured from the temperature of saturation, AQd= CpD (146) In Fig. 47 this is shown by the area below bci for a case in which the heat change is reversible. For an isobaric change from superheat temperature Di to D2 AQ = (CpD\ - {CpD\ (147) This is equivalent to AQ = Cp {D2 — Di) = C'p {T2 — Ti), where C^p is the mean specific heat for the temperature range involved. In Fig. 47 this heat change is shown for reversible conditions by the area below C1C2. The foregoing equations giving the heat change are not sufficient for use in engineering problems as they generally occur. It is usually not only necessary to know the range of superheat, but also the volume change accompanying it. In the case of gases, this can be found from the Law of Charles, but superheated vapors as generally treated in engineering are not far enough removed from the condition of saturation to even sensibly obey that law. It is possible to find this volume change for superheated water vapor by using the approximate equation of Tumlirz pre- viously given as Eq. (134). Writing this for volumes Vi and V2 and then dividing gives, for pressures in pounds per square inch, Vi ^ Ti - 0.4293 Pi V2 r2- 0.4293 ^ ^^^ Since p2 = pi during an isobaric change, this equation reduces to the form Vi _ Ti — Constant , . V2 ~ T2 - Constant' ^^49) in which the constant has a different value for every pressure. The effect of this corrective constant becomes less with in- crease of temperature or decrease of pressure, and there is an accompanying closer approach of the equation to that of Charles' Law and a closer resemblance of the superheated vapor to an ideal gas. VOLUME CHANGES OF VAPORS 151 Work during Isobaric Changes of Superheated Vapor. (d) During an isobaric change with one pound of any work- ing material the work is 778 AE = P (V2 - Vi) ft.-lbs., . . . (150) which was first developed in the case of gases as Eq. (24). If, in Fig. 46, the expansion is from Ci to C2, the work done is given by the area below C1C2. 86. Isothermal-Volume Changes of Superheated Vapors. (a) These must in a general way resemble the isothermal changes of gases, since superheated vapors approximate the gaseous conditions. The exact behavior of any particular vapor under these conditions must, however, be determined by experi- ment. For superheated water vapor the necessary information can be obtained from the approximate equation of Tumlirz. Equation of Isothermal Change of Superheated Water Vapor. (b) Rearranging the Tumlirz equation (134) and maintaining T constant gives the following for isothermal changes for this material, for p in pounds per square inch, pV + 0.256 p = 0.5962 T = Constant, . . (151) and from Eq. (135), for P in pounds per square /oo/, PV + 0.256 P = 85.86 T = Constant. . . (152) Comparing this latter with the Eq. (14) for gases, namely, PV = RT, it is evident that it differs only In the addition of a second term (0.256 P) in the first member. Obviously the smaller the numerical value of the pressure the smaller will be this cor- rective factor and the more nearly will the vapor obey the ideal gas law. If Eqs. (151) and (152) be divided by P, it becomes apparent that the greater the numerical value of T the smaller will be the effect of the corrective factor and therefore the more nearly will the material approach the condition of an ideal gas. Work during Isothermal Changes of Superheated Vapor. (c) The work done by an expanding vapor, as well as gas, is given in all cases by the expression first developed as Eq. (41), 778 A£ = r^'p^F ft.-lbs. JVx 152 HEAT-POWER ENGINEERING However, in order to perform the integration in any case, it is necessary to know the relation between P and F, and this is a matter for experimental determination. The relation given by the equation of Tumlirz, Eq. (135), may be used for superheated water vapor. From this equation, p^ 85-86 r V + 0.256' which value may be substituted in the type integral, and the integration performed, giving per pound of water vapor '^^ dV 778 A£ = 85.86 r f '^ Jvi V + 0.256 = 85.86 riog 4; + ^;g ft-ibs. (153) Eq. (43b), for work during isothermal changes of gases, may be written 778 A£ = (PiVilog. ^y^T \oge ^ . Comparing Eq. (153) with this, it again appears that the higher the temperature and the lower the pressure the more nearly do the equations developed for superheated water vapor approach those for the behavior of gases, and by analogy the same must be true of the behavior of all superheated vapors. If, in Fig. 46, the isothermal expansion is from ^2 to d, the work is represented by the area below C2d. Heat Change during Isothermal Changes of Superheated Vapors. (d) Applying Eq. (i), A(2 = A5 + A/ + AE, to this case, it is evident that the term A^* must be zero, since temperature does not change; but A/ must have some value other than zero, since the materials cannot be said to even sensibly approach the condition of ideal gases. The term AE must also have a value other than zero if work is to be done by or upon the superheated vapor. For any case AE can be readily found, but AI is more difficult to evaluate, and any equation for the value of AQ which could be developed would necessarily be a very cumbersome one. VOLUME CHANGES OF VAPORS 1 53 (e) Fortunately the T^-diagram offers a simple means of deter- mining AQ, since this quantity is represented by an area on that diagram, when the change is reversible. Assume for instance that it is desired to find the heat required when one pound of water vapor is expanded iso thermally and reversibly from a pressure Pi and a temperature T2 above satu- ration temperature T^^, to a lower pressure P3. It is only necessary to draw the horizontal line C2d in Fig. 47, between the two pressure lines and at the desired temperature, and then determine the area under C2d. Fig. 47 is only a special case of Plate I of the Appendix, and in practice the latter would be used. (f) Note that the heat added to, or subtracted from, super- heated steam isothermally is not equal to the difference in total heats, since the isothermal of superheated vapors is not a constant-pressure line. In the case of reversible isothermal expansion this heat is equal to P X A0, both of which quan- tities can be obtained from the Mollier or EUenwood Charts given in the Appendix. 87. Adiabatic Changes of Saturated Vapors, (a) With the exception of problems involving the flow of vapors in which the material is accelerated as a whole, the adiabatic changes of vapors which are considered by the engineer are thermodynamically reversible in the ideal case. In the following paragraphs only these reversible processes will be considered, leaving the more complicated irreversible processes for later development. Since reversible adiabatic changes are also isen tropic ones, their graph on the T0-diagram must be a vertical line. This offers a very easy means of studying these changes in every case where there are sufficient experimental data for the drawing of this diagram. (b) The diagram in Fig. 48 is developed from the T0-dia- gram for water vapor with the lines of constant quality shown — originally given in Fig. 42 (a) and Plate I. To this have been added vertical lines representing reversible adiabatic expansions starting at each 20 per cent of quality at the pressure Pi. The diagram shows that when the initial quality is high (point a in Fig. 48) the quality of water vapor must decrease as the expansion progresses, and when the initial quality is low (point b) it must iri^ 154 HEAT-POWER ENGINEERING crease during expansion. Near the middle of the diagram, that is, with initial quality near 50 per cent, x remains nearly con- M 20^ ^j^^ mfo mfo 100 /» guality d 6 5)5 i \a ^ iC e j w 1 \^ 1 \^ j 1 \ %. 7 / 1 1 \cJ 7 / 1 1 1 I |1 [ \ / / ■ 1 ! \ 1 \ 100 5« ' /• i i 1 1 0^ 20i> 4Qi 50 1 \ ( 80^ Quafily Entropy- Fig: 48.- — T<^-Diagram for Water Vapor. stant during the entire expansion. This is not necessarily a property of all vapors, as it depends on the relation between the various heat quantities and is thus a matter for experimental determination. This is well shown by considering the case of Ether Vapor. The T0-diagram for this material is given in Fig. 49, As in the Q Charts. Work Done during Adiabatic Changes of Saturated Vapors. (g) Since all the work done during such an expansion must be obtained at the expense of intrinsic heat energy, and since no heat energy is used for other purposes, it follows that if (xr + 2 — xAPu)i = {xp + q)i represent the intrinsic heat energy before an adiabatic change and {xr -{- q — xAPu)2 = (xp + 2)2, the intrinsic heat energy after such a change, the External Work Done is AE = (xr -\- q — xAPu)i — {xr -\- q — xAPu)^ . (157) = fepi + 2l) - (^2P2 + 22) (158) In using this equation the initial conditions are known: x^ is obtained from Eq. 154, and p2 and 22 are found from the Vapor Tables for pressure p2. (h) If the PV-diagram, Fig. 50, be for one pound of steam, then when the point h is reached the heat-energy {xAPu)i has been abstracted from the steam and absorbed by displacing a piston or surrounding media against resistance. Thus there re- main {xp 4- 2)1 heat units with which to begin the adiabatic ex- pansion. At point c, there are {xp + 2)2 heat units left in the steam, and the quantity {xAPu)2. would not appear unless either by compression or some equivalent process the volume of the steam is contracted isobarically an amount X2U2 to the volume of the liquid, as shown at d. VOLUME CHANGES OF VAPORS 157 The area below ah is {xAPu)i B.t.u.; the area below he shows the work done, or heat utilized during adiabatic expansion alone, Volumes Entropy Fig. 50. — PV-Diagram, Fig. 51.- T0-Diagram. and is [{xp + 2)1 — {xp + 2)2] B.t.u.; the area below cd is {xAPu)2 B.t.u. (i) On the T(/)- diagram, Fig. 51, the areas below lines such as oah represent {xr + g) quantities which include the external latent heat of vaporization. From these quantities must be de- ducted the appropriate values oi xAPu"^ to obtain the heat in the steam during an isentropic process. (Note that in the Tv)2- .... (159) (A(^s)i can be computed from Eq. 138, (A0;)2 and (A0^)2, in the case of water vapor, can be obtained directly from the Steam Tables. If the expansion takes place entirely in the Region of Super- heat, the final temperature T2 = (Tv -\- D)2 can be found from (A0.)i = (a0,„ + Cp loge ^^ ^ ^ )^ . . . (160) Here Cp is the mean specific heat for the temperature range A = (T — r^)2 and T^^ .is the temperature of vaporization at the terminal pressure. External Work Done during Adiabatic Changes of Superheated Vapors. (c) As in other cases of adiabatic changes, the external work done during this reversible adiabatic change is equal to the intrinsic heat change. During a constant-pressure change from liquid at the temperature of vaporization to superheated vapor, the external work per pound is / AEp = AP(Y;- 0.017) B.t.u., a/ . . (161) where Vs is the specific volume of the superheated steam from Eq. (134) ; hence the external work done, if the steam remains in the superheated state throughout the isentropic expansion, is A£, = X+ rCpdT- AEp]-\\+ rCpdT-AEp] (162) L *Jtv Ji L ^tv J2 = [X -t- CpD-AEpl -[\-\-ClD -AE,]2, .... (163) in which A is found from Eq. (160) VOLUME CHANGES OF VAPORS 1 59 If vapor initially superheated is expanded to wetness with quality X2, the external work done is A£,. = [X + CpZ) - A£Ji - [:x:p + g]2, . . . (164) in which X2 is found from Eq. (159). On the PV-diagram this work is represented by the area below the expansion line. In using either the T<^, MoUier, or Ellen- wood diagrams, to obtain the work done during isentropic ex- pansion alone, it is necessary to deduct the AJ5p quantities (and the APu quantities if entering the saturation region) from the heat values found. 89. Constant-Volume Changes of Saturated Vapors, (a) If a saturated vapor is to change pressure at constant volume, there must be a quality change, because the same weight of material • in the form of vapor cannot occupy a given space at two differ- ent temperatures. During a pressure drop there is a tendency for saturated vapor to increase in volume, hence if the volume is maintained constant there must be a decrease of quality ; that is, condensation must take place. The reverse is of course true for a pressure rise. Equation of Constant-Volume Change of Saturated Vapor. (b) As in previous cases, the equation of a constant-volume change is, in terms of pressure and volume, V = Constant. Heat Change during Constant-Volume Change of Saturated Vapor. (c) It was shown in Section 70 that the quality of saturated vapor could be found by dividing the volume occupied per pound of mixed vapor and liquid by the specific volume corresponding to the pressure existing. By using this method the quality changes which occur during a constant- volume change of saturated vapor may be found, and when the quality at any pressure is known the intrinsic heat for that state may be determined. 90. Constant-Volume Changes of Superheated Vapors. (a) When a superheated vapor changes pressure at a constant volume, there must be a temperature change similar, but not equal, to that occurring in the case of an ideal gas undergoing / l6o HEAT-POWER ENGINEERING the same sort of change. The equation of Tumlirz, Eq. (134), may be used to find the temperature of water vapor correspond- ing to any pressure and volume, and hence such changes (01 their equivalents, if irreversible) can be plotted to PV or T<^ coordinates. Equation of Constant- Volume Changes of Superheated Vapors. (b) As in all other cases, the equation in terms of PV coordi- nates is V = Constant. Heat Change during Constant-Volume Change of Superheated Vapor. (c) Since the temperature and pressure can be found for any point in a constant-volume pressure change of superheated vapor, the intrinsic heat can also be found for every point. The difference between the intrinsic heats at beginning and end of the constant volume change must be the amount of heat added to, or subtracted from, the steam. CHAPTER XII. VAPOR CYCLES. 91. Carnot Cycle with Dry Saturated Steam, (a) The Carnot cycle may be carried out with a saturated vapor of any kind in the same apparatus as was assumed in Section 49 and shown in Fig. 17. For simphcity assume the cyHnder to contain unit weight of water at the temperature Ti. Then the volume occu- pied by the liquid, inclosed by the cylinder head, cylinder walls, and piston, will be that of unit weight of water at temperature Ti and corresponding pressure. This is plotted as the point a on the PV-diagram, in Fig. 52, with volume greatly exaggerated. If heat is added to the liquid from the hot body U and the piston is allowed to move out at just the proper rate to maintain a constant pressure on the working substance, vaporization will occur at constant pressure and therefore at constant temperature. The volume would consequently in- crease isothermally, or the process would be an isothermal ex- pansion. When vaporization is complete the volume attained will be the specific volume, V^, of water vapor at temperature Ti and corresponding pressure. The isothermal expansion will then be represented by the constant pressure line ah. If now the nonconducting cylinder cover Z is applied and the piston allowed to continue its outward motion, the expansion of the vapor must be adiabatic. The actual shape of the line representing such expansion will be given approximately by PV^ = Constant, and is represented by the curve he, on which c is a point where the temperature has reached that of the cold body, T2. If now Z is replaced by the cold body and the piston is forced inward, condensation must occur, the heat liberated being ab- sorbed by the cold body. Condensation, like evaporation, is a change at constant temperature and constant pressure, and hence is represented by a horizontal line from c toward the left. 161 l62 HEAT-POWER ENGINEERING To complete a Carnot cycle, it is necessary to stop the process of condensation when the volume has decreased to some value Fd, so chosen that the final adiabatic compression will bring the material back to the liquid form with conditions Ti, Pa, and Va. a b \ \ \ \ \ % Car aot 1 ^1 :> S% \ X ^^^ \. ^^^ ^^ ^] ~~"~~- d c Volumes Fig. 52. — PV-Diagram for Carnot Cycle with Dry Saturated Water Vapor at 6. (b) The T0-diagram of the cycle is drawn in Fig. 53, on which the water curve and saturation curve are indicated by dotted lines. This diagram is lettered to correspond with Fig. 52. It shows how the quality of the steam must decrease during the adiabatic expansion be, and how by stopping the condensation, or iso- thermal compression, at the proper point, d, it is possible to return the material to the liquid condition at temperature Ti by adiabatic compression da. Note that the T (^-diagrams for the Carnot cycle for vapor and gas are identical, but that this is not true for the PV-diagrams because of the difference in the properties of the materials. Work per Pound of Dry Saturated Water Vapor Operating in Carnot Cycle. (c) The work done per cycle can be obtained in several ways, two of which will be considered. They are practically the same as those previously used for gas cycles. (d) The first method is to take the algebraic sum of the quan- tities of work done during the several processes of the cycle. VAPOR CYCLES 163 Pi (i) The work during the isothermal expansion equals — ^ (V& — Va) B.t.u., and (2) that during the isothermal compression similarly equals -^ (Vc - Vd) B.t.u. (3) The work during adiabatic ex- pansion must be, as shown in Eq. (158), the difference between the quantities of intrinsic heat energy above 32° F. at the be- ginning and end of the process; that is, (qb + pb) — {^c + Xcpc)- (4) Similarly, the work during adiabatic compression is Qa — (qd + Xdpd). The values of the qualities Xc and Xd can be found from the constant-entropy equation (154) or from either a Ti h il 1 Cai not ^1 \5 TO / T2 9 c s 1 Entropy Changes Fig^ 23 , — T<^-Diagram for Camot Cycle with Dry Saturated Water Vapor at b. of the entropy diagrams ; hence in any problem all the terms are known and the total work done during the cycle equals the algebraic sum of the four expressions. (e) The second method and more direct one is to subtract from the total heat supplied the total heat rejected; the differ- ence must be the heat converted into work, and must be rep- resented by the area within the four lines of the cycle. The heat supplied during the isothermal expansion is n, the latent heat of vaporization of the material at the temperature Ti. The heat rejected is the part of the latent heat liberated during the partial condensation and is (xcr2 — ^^^2) = n {xc — Xd) , in which Xc and Xd are determined from the constant-entropy equation* (154) or from either of the entropy diagrams. The * Just as Xc is the quahty at the end of adiabatic expansion be, so xd may be considered as the quahty at the end of an adiabatic expansion ad. The constant- entropy equation is apphed to the Hne be to find Xc and to the Hne ad to find xd-. 1 64 HEAT-POWER ENGINEERING external work done must then be, when the steam is dry and saturated at the beginning of expansion, AE = AQi - Aft = ri-r2 (Xc - xa) B.t.u. . . (165) and 778 AE = 778 [n - r2 {xc - Xd)] ft.-lbs (166) The expression numbered (165) is really obvious from the T0-diagram drawn in Fig. 53. (f ) From Fig. 53 it is also seen that A£= (ri- r2)A0. =(ri- Ta)^. . . (167) i 1 The last form is the simpler in use. In it the expression — ^-^ is the efficiency Efc of the cycle, as will be shown next, hence ,^^. 0;i/^ AE^riXEfc (168) Efficiency of the Carnot Cycle Using Dry Saturated Water Vapor as a Working Substance. (g) The efficiency must of course equal the ratio of the work done per cycle to the heat supplied per cycle; hence from Eq. (165) n — Ti {Xc — Xd) 'Efe = ri A more convenient expression can be found directly from the T0-diagram. (h) Remembering that area under the line ab in Fig. 53 repre- sents heat supplied from the hot body, and that the area of the cycle represents heat converted into work, it is evident that j,r ■ T, (A05 - A0a) - T2 (A0, - Ac/,,) ri- T2 ... ^^' = ^ r,(A0.-Ac/>.) = ^V~' • ^'^^^ which is the same as the expression for efficiency of the Carnot engine using gas as a working substance. (i) The Carnot cycle, consisting as it does of two reversible isothermals crossed by two reversible adiabatics, must have identical T0-diagrams for all working substances. Since the development just given depends only on this diagram and not VAPOR CYCLES i6s upon the properties of the material, it follows that the expression T, must give the efficiency of the Carnot cycle operating with any working substance. 92. The Carnot Cycle with Any Vapor, (a) The case just con- sidered, in which the working vapor is brought to the dry satu- rated condition before adiabatic expansion begins, is the simplest possible case as far as the expressions for heat and work are con- cerned. But adiabatic expansion might begin with the liquid only partly vaporized by isothermal expansion; that is, with a quality, Xh, at the top of the adiabatic. Or, the vapor might be superheated before adiabatic expansion begins. Further, a mate- rial like ether, with properties markedly different from steam, and with different behavior during adiabatic expansion, might be used. In any case T —T Efc = Ti (170) and AE = AQiXEfe, (171) where Aft is the heat added at constant temperature Ti to the liquid previously raised to that temperature. For steam initially dry and saturated, AQi = n . . For steam initially wet, AQi = xin . (172) (173) 1 \ Ti / 1 1 1 1 t Q Ti \/ 1 1 \ 1 Carnot \ 1 1 / 1 To \ \ \ 2 \ \ 1 ^ia^i-^ 1 (Fig. 54. Entropies •T^-Diagram for Carnot Cycle with Superheated Steam, (b) For steam at pressure P, Fig. 54, superheated to temper- ature Ti, AQi is given by the area below ah. In the figure PP i66 HEAT-POWER ENGINEERING is the constant-pressure curve through b and A(j>8a is the entropy of saturation at this pressure. Evidently Aft = ri + 7\ iAcf>sa' - A0,a, + A0z,O n + Ti{Acf>sa' - Asa, + C/ log, T/ + D (174) (175) where the subscript 1 refers to the values corresponding to Ti and the primed quantities are those referring to the pressure at the point b: hence ri does not correspond to pressure P. (c) In Pig. 55 are shown PV- and T^-diagrams of Carnot cycles illustrating different possibilities when saturated and c / 1 1 1 d I bi \b Ti k T2 Ci ^ (/~i\ Steam Wet at 6l and ^^^ Diy at 6 To ^ \ steam Superheated Through- out Expansion fi-om bi to Cj a b 1 ""^ Ml . d T2 G Cl X 6 5, Ti ^ / / / d 1 \ T2 G Oi' (T^\ Superheated Steam at 61 ^ ^ ' Expanded to Wetness at Cl Ts Cl T„ G y y a ' Ti ,/ / 1. d Ta 'G-L <^ f^\ EtherYapor-Dryat 6 becomes Superheated during Expansion bc Fig. 55. — Carnot Cydes for Vapors — Various Possibilities. superheated vapor are used as working substances. The bold lines represent the isothermal reception and rejection of heat. In the PV-diagram these are horizontal only when the vapor is saturated. Figs. 55 (a), (b), and (c) are for steam, and in each VAPOR CYCLES 167 case abed is the diagram which is obtained with dry saturated vapor at b. Fig. 55 (d) is for ether. 93. Clausius Cycle with Dry Saturated Water Vapor, (a) This cycle is often called the Rankine cycle, but as another cycle which is universally known by this latter name must also be considered, the name of Clausius will be used in this book to designate the cycle at present under consideration. As shown in the PV-diagram, Fig. 56, it consists of two constant-pressure b \ \ ^ Clausi us ^i\ 1? V ^^^^ ■^■-■>.^. a d ' Volumes Fig^ ^6_ — PV-Diagram for Clausius Cycle with Dry Saturated Water Vapor at c. lines be and da joined by an adiabatic cd and what is practically a constant- volume line ab. The apparatus of Fig. 17 used in developing the Carnot cycle can also be used for the ideal Clausius cycle. The volume plotted at b is that of unit weight of water just ready to vaporize, corresponding to a of the Carnot cycle shown in Fig. 52. The addition of the latent heat of vaporization, n, causes the material to expand at constant pressure until it occupies the specific volume Vc at c. This quantity of heat, as before, comes from the hot body at temperature Ti. The adiabatic expansion is exactly like that of the Carnot cycle and is produced in exactly the same way. The constant-pressure decrease of volume starts exactly like the similar line in the other cycle, but condensation is carried to completion by the removal of heat equal to Xdr2. The volume 1 68 HEAT-POWER ENGINEERING Va is then the volume of unit weight of water at the temperature of vaporization corresponding to the lower pressure P^. The heat given up during this condensation is received by the cold body at the constant temperature T2. The line ab which takes the place of the adiabatic compression of Carnot represents the heating of the liquid from temperature T2 to the higher value Ti, while the pressure rises from Pa to Pb. There will be a very small volume change in the liquid during this process, but it is so small in comparison with the other volume changes in the cycle that it may be neglected and the process considered as a constant-volume pressure rise. (b) The Td- A4>a) (178) Since (A0c - Ah) = Aa = A^^^, Eq.(i78) may be written AE =\Cp(T,- T2)+TiAct>,^l -{T2(Act>,a,-Acj>i,)\ (179) A more useful formula, which may also be written from in- spection of the T(/)-diagram, is AE = ^iTi-T2)-{-qi-q2-T2{Ai^-Acl>i,), . (180) -t 1 all quantities in which may be obtained directly from the Steam Tables. lyo HEAT-POWER ENGINEERING Efficiency of the Clausius Cycle with Dry Saturated Water Vapor at the Point c. (d) To find this item, it is only necessary to divide the work done, Eq. (177), by the heat suppUed; then AE ^Xi Ef. q2 — Xdr2 0.2 = 1 Xdr2 (I8i) (182) Xi - 02 (e) This form is not readily comparable with the expression for the Carnot efficiency, and although the fact is already known that the Clausius efficiency must be lower than the other because of the addition of heat below maximum temperature, it is of interest to derive an expression which will show this difference. This can be done by using Eq. (178) in obtaining the efficiency expression, thus, AE C^Ti- n) + Ti (A0, - A06) - T2 (Aw- Ad - A(f>a) Mb) Cj,{Ti-T2) + Ti{Acl>c-Aclyt) Aft A(2i The Carnot efficiency written in similar form is = 1 Ef. =1 Ti = 1 Aft Aft (183) (184) (185) In Eqs. (184) and (185), the magnitude of the last term deter- mines the value of the efficiency in each case, but inspection of the expressions as they stand does not show which of the last terms is the greater. If Fig. 57, which shows [the two cycles superposed, is consulted, the interpretation of the last terms is much simplified.* It is evident from the figure that the heat supplied during the Clausius cycle, equal to the area under ahc, is greater than that * In the strict interpretation of Fig. 57, the line ah is not the irreversible line of the Clausius cycle, but represents a reversible process which would give the same P, V, T conditions as the other, as mentioned before in connection with Fig. S1^ VAPOR CYCLES 171 I r. supplied during the Carnot cycle by the triangular area abdu plus the area below adi. The heat rejected is, however, greater by the area below adi. Therefore in the case of the Clausius cycle the heat rejected is increased in greater proportion than the heat received, and the fraction -^ for this cycle must be greater than for the Carnot, and hence the efficiency is less. ArZ 94- The Clausius Cycle in General, (a) As in the case of the ^/^arnot cycle, it is possible to imagine a Clausius cycle developed b Ci c 1 1 \ a c U d ' / q\ steam Wet at C 1 and Dry at C f^\ Steam Supei-heated Through- out Expansiott ftomCi to d\ (h\ Superheated Steam at Ci Expanded to Wetness at dl f/J\ Ether Vaper- Dry at C Becomes Superheated During Expansion cd Fig. 58. — Clausius Cycles — Various Possibilities. with the vapor of any material in either the saturated or super- heated condition. The general equations for the Clausius cycle will be given in the latter part of this section. Some of the possible cases are shown in Fig. 58, in which the heavy lines in all instances represent constant pressures. A word of explanation will probably help to make the con- struction of the diagrams in Fig. 58 clearer. In the Carnot cycle the upper and lower lines are defined as isothermals, while in the 172 HEAT-POWER ENGINEERING Clausius cycle they are lines of constant pressure. For saturated vapors the two are the same, but for superheated vapors the two cycles present very different phenomena. The isobars give " horns " (at Ci) in the T0-diagrams when in the superheated region, the height of these being determined directly by the de- gree of superheat. (b) Another interesting difference results from the character- istics of ^this constant-pressure line. In the Clausius cycle the temperature rises during superheating, while in the Carnot it remains constant and the pressure drops. In the case of the former cycle, then, the hot body must have a temperature at least equal to that reached at the end of the superheating process and therefore higher than that of the working substance during the entire reception of heat. For this case, then, all the heat is received irreversibly. (c) It thus develops that for all Clausius cycles the heat re- ceived along the line ah is received irreversibly, the hot body having a temperature at least as high as T^j and for Clausius cycles in which superheating takes place, all the heat is received irreversibly, because the hot body must have a temperature at least as high as that attained by superheating. This cycle when using superheated vapor therefore departs still further from the criterion for maximum efficiency, and must have a theoretical efficiency lower than that of the same cycle with saturated vapor having the same maximum temperature. This conclusion is the more interesting because, notwithstanding the lower theoretical efficiency, real engines operating on this cycle obtain their highest commercial efficiency with superheated vapor. The reason for this will be brought out in a later chapter. (d) For the Clausius cycle with the adiabatic expansion start- ing with wet steam, with quality Xi, and J- 1 AE r2(Ai + xA0, + A4>D)d = {Acf>i + xA0, + A<^z>)c, . . (188) or, VAPOR CYCLES 173 {A(f)l + xA(f>v + Cp loge -^ — j >c (189) If the steam is initially superheated Xc = 1; if wet, the entropy of superheat {A4)d)c disappears. Should the value of Xd found be greater than i.oo, it indicates that the steam is still super- heated, then Dd should be determined, using xa = 1.* Having determined xa (or Dd), the work may be found from AE = (2 + xr + C^D), - to + xr + CpD)d. . (190) Also, the work may be found from AE = AQ, - AQ2, ..... (191) in which the values of AQi and Aft, the heat supplied and the heat rejected, are equal respectively to the heat above 32° F., at the beginning and end of the isentropic expansion, and may be read directly from the Q-curves on the T "^v. ■•-— — _ _ __ h a d • -"— c Volumes Fig. 62. — Cycle with Rectangular PV-Diagram. composed of two constant-pressure lines joined by two lines of constant volume, as shown in the PV-diagram, Fig. 62, and in the T0-diagram, Fig. 63. The diagrams show this cycle superimposed upon a Clauslus h / \ \ / y ^ 1 l\ 1 \ 1 V / y y 1 \ \ \ i V I L X 1 \ \ 1 \ ri s ^ Entropies Fig. ti. — T^-Diagram for Rectangular PV Cycle. cycle so chosen that the same weight of working substance is used in each. It is evident that the Clausius cycle will require a much larger cylinder than the cycle under consideration, but the work per cycle will also be much greater per pound of vapor. VAPOR CYCLES 1 79 The T0-diagram shows that the heat absorbed is the same with both cycles, namely, the area beneath the line abc. The work done is, however, greater with the Clausius cycle than with the rectangular PV cycle, as is shown by the inclosed areas of the diagrams. It follows that the efficiency of the cycle with rec- tangular PV-diagram must be less than that of the Clausius cycle. The Rankine cycle for the same heat input evidently gives an amount of external work intermediate between that obtained with the Clausius cycle and that obtained with the cycle under consideration, and must therefore have an inter- mediate efficiency. The rectangular PV-diagram may be looked upon as a limiting case of the Rankine cycle, the Clausius cycle being the other limit.. Work per Pound of Dry Saturated Steam Used. (b) From Fig. 62 it is apparent that A£ = A (Pi - P2)u (201) Efficiency of the Cycle Using Dry Saturated Steam. (c) The heat received is the same as that in the Clausius cycle. Hence ^, AE A (Pi - P2)u , . ^f' = TTT = k T^ • ... (202) ^ AQi (Xi -52) 98. The Rectangular PV Cycle in General. In any case AE = A (Pi - P2) XcU, (203) where XcU = (xV — 0.017)0 if the steam is wet, or = (Vs — 0.017)0 if superheated. V5 can be found from Eq. (134). The general expression for the efficiency is Ef. = ^ . . . . (204) (g + xr H- CpD)c — 22 For method of using EUenwood's Charts for solving the Rec- tangular PV cycle see the middle of 96(d). h CHAPTER XIII. POWER, EFFICIENCY, AND PERFORMANCE. Certain general definitions which are necessary in the con- sideration of real engines are collected in this chapter. They will be discussed here very briefly; most of them will be con- sidered more fully in later chapters and some belong more prop- erly to the province of Experimental Engineering. 99. Power, (a) In English-speaking countries, the foot- pound (ft. -lb.) is the unit of work generally used by engineers. The unit of power, or unit of the " rate" of doing work, is the horse power (h.p.) ; it equals the power equivalent to the doing of 33,000 foot-pounds of work per minute. Then the horse power developed by any apparatus is . . _ Total ft.-lhs. of work developed per min. . . •P- ~ "~ 33,000 • ^^^^^ The heat equivalent of one horse power is "Z "x 000 One h.p. = = 42.42 B.t.u. per min. . . (206) (b) If work is done for one hour at the rate of one horse power, the total work done is called one horse-power hour (h.p. -hr.). Then, oneh.p.-hr. = 33,000 X 60 = 1,980,000 ft.-lbs. . (207) 1,980,000 778 = 2545 B.t.u (208) 100. Distinction between Real and Ideal Engines. In con- sidering the ideal or thermodynamic engine in preceding chap- ters, a working substance was assumed to pass through cycles within a closed cylinder, and it was found that a certain amount of work, A£, would be delivered to the piston during each cycle. The material of the cylinder and piston was assumed to have certain properties which no available material really has. The cylinder and piston were assumed to neither absorb nor conduct 180 POWER, EFFICIENCY, AND PERFORMANCE l8l heat. The piston was supposed to be without leakage and friction; and any other necessary mechanism of the engine was assumed frictionless. These conditions cannot be reaUzed in practice. Therefore, the action of a real engine must differ con- siderably from the conceived action of an ideal engine. Losses in real heat engines may be classified as follows: (i) Cycle loss, — for even with the ideal cycle only part of the heat supplied can be converted into work. (2) Cylinder losses, or those which occur within the real cylinder because the ideal cycle is not perfectly produced. These losses reduce the work actually delivered to the piston by the working substance. (3) Friction losses, occurring in the mechanism used in the transmission of work between the piston face and the place of utilization. loi. The Indicator. The work actually performed on the piston by the working substance in the cylinder of the real engine and the pressure-volume changes that actually occur within the cylinder can be determined by using the in- strument called the " Indica- tor," which can be made to draw the PV-diagram for the changes actually occurring. The comparison of such a dia- gram with the ideal one aids in determining the cylinder losses. This instrument is shown in Fig. 64. A card is mounted on the outside of a metallic cylinder which is caused to oscillate in unison with the motion of the engine piston. A pencil, which may be pressed against this card, is actuated by a small, spring-balanced piston subjected to the same pressure as the engine piston. Thus the card movement is proportional to the volume dis- placed by the engine piston, while the pencil movement is pro- Fig. 64. l82 HEAT-POWER ENGINEERING portional to the pressure which actuates the piston. The pencil movement is at right angles to the card movement, and hence a pressure-volume diagram with rectangular coordinates, such as abcde in Fig. 65, is drawn. If the card cylinder oscillates under the pencil while the indicator piston is disconnected from the engine cylinder and subjected to atmospheric pressure, a horizontal line, called the atmospheric line, will be drawn. latinos. Pres. | ^ Zero Abs. Pres. — ^ i ^ Y Clearance -Piston-rDisplaceTnent- 102. The Indicator Diagram, (a.) In the pressure- volume diagram drawn by the indicator, as in the PV-diagrams pre- viously considered, the inclosed area represents the work done upon the engine piston by the working substance during the cycle. (b) The Pressure Scale, Sp, or pressure per inch of ordinate, equals the pressure in pounds per square inch of piston area corresponding to one inch -90 s movement of the pencil paral- Jj [!^ ^ lei to the pressure axis. This is also called the '' Spring Scale." The datum of absolute pres- sures is a horizontal line, 00 in Fig. 65, drawn at a distance below the atmospheric line, A A , equal to the atmospheric pressure as measured on the pressure scale. Thus for any point, the absolute intensity of pressure per square inch of piston area = (ordinate above 00) X Sp] similarly, the pressure above atmospheric = (ordinate above A A) X Sp. The latter pressure is usually called the " gauge pressure.'' (c) The Volume Scale, Sv, is the displacement, in cubic feet per square inch of piston, represented by one inch of abscissa. The datum of total volumes is a vertical line, YY in Fig. 65, located to the left of ^ a at a distance representing, to scale, the " clearance volume " or space in the cylinder occupied by the working substance when the piston is at the beginning of its stroke. Thus for any point on the diagram, the total volume of working substance in the cylinder equals Sv X (abscissa from YY) , and the volume displaced by the piston is Sv X (ab- scissa from Aa). Fig. 65. POWER, EFFICIENCY, AND PERFORMANCE 183 (d) The Scale of Work, Sw, corresponding to one square inch of area of the diagram = Sw = Sp X Sv foot-pounds per square inch of piston area. The work done by the working substance upon the total piston area, as represented by the area of the diagram, is called the Indicated Work. Thus the i.w. = (area of diagram) X (area of piston) X Sw. The corresponding rate of doing indicated work is expressed in terms of horse power; ijt is called the Indicated Horse Power (i.h.p.) and is computed by using Eq. (205). (e) Consider Fig. 65 as an actual diagram taken from an engine. From the point a the engine piston moved out until the point c was reached. By virtue of the property of the PV-diagram, the area between the lines abc and 00 represents the work done upon the piston by the expanding working substance. This work may be computed by multiplying the average pressure on the face of the piston of the engine by the piston's move- ment. To find the average pressure per square inch of piston, divide the square inches of area between abc and the pressure datum 00 by the length A A in inches and multiply this average height by Sp. Multiplying this mean intensity of pressure by the area of the piston in square inches and by the length of stroke of the piston in feet gives the work done during the out stroke of the piston. (f) Similarly, the area under the line cde represents the work done by the piston upon the working substance during the return stroke, and the mean ordinate of this area multiplied by Sp gives the average intensity of pressure against which the engine piston moved during this stroke. This, multipHed by the area of the piston in square inches and by the stroke of the piston in feet, gives the work in foot-pounds done by the piston on the working substance during the return stroke. (g) The useful work deUvered to the piston during one cycle equals the difference between the work done upon it on the out stroke and that done by it on the working substance during the return stroke. The amount of work actually accomplished would have been the same if the difference between these two average pressures had acted upon the piston during one stroke only. The value of this difference is, however, given by dividing the area abcde by 184 HEAT-POWER ENGINEERING the length of the diagram and multiplying by Sp. This is known as the mean effective pressure (m.e.p.), and is defined as the pressure which, operating on the face of the piston during one stroke, would do the same amount of work as is actually done per cycle by the variable pressure really acting. (h) In terms of the mean effective pressure, which will here- after be designated by pm, the work done upon the piston by the working substance, per cycle, is Work = pm' a • L ft. -lbs., .... (209) in which a represents the area of the engine piston in square inches and L is the stroke in feet. If there are n cycles per minute, the work per minute will be n times the work per cycle, and the indicated horse power of the engine will be . , pmLan . . i.h.p. =- (210) 33,000 (i) Eq. (210) can be used to determine the diameter of cylinder needed to develop any i.h.p., provided the m.e.p., the length of stroke, and the number of cycles per minute are known. Thus the effective area of the piston must be a = 33,000 i.h.p. ^ pmLn from which the piston diameter follows. 103. Methods of Determining the Area of an Indicator Diagram, (a) The area of an indicator diagram can be deter- mined (i) by placing transparent " cross-section paper" over the diagram and counting the squares surrounded; (2) by using some such form of mechanical integrating instrument as the '' planimeter;" (3) by applying the '' method of ordinates;" or (4) by using some integration rule such as the " Trapezoidal Rule " * and '' Simpson's One- third Rule." t (b) One form of planimeter is shown in Fig. 66. It consists of two arms jointed together, one terminating in a " fixed point " which is a stationary pivot, while the other carries a " tracing point." The third support for the instrument is a point of the *For this rule see Kent's " Pocket Book." t See Church's " Notes on Mechanics " or Kent's " Pocket Book," published by John Wiley & Sons. POWER, EFFICIENCY, AND PERFORMANCE 185 'Joint rim of a graduated wheel or " record roller." If the record wheel is set at zero and the tracing point is moved clockwise around the outline of the diagram and is re- turned to its original position, the area of the figure is given by the reading of the record wheel. The theory and use of planimeters is treated in books on Experimental Engi- neering.* The mean ordinate is found by dividing the area by the length of dia- gram, and the m.e.p. is the product of the mean ordinate and the pressure scale. (c) In the method of ordinate s, the length of the diagram is divided into a number of equal parts, with interval Ax as in Fig. 67, and ordinates are drawn, as I, 2, 3, etc., in the figure. Central intermediate ordinates are then drawn and the intercepts yi, y^, 3/3, etc., are scaled and used as the mean heights of the elementary areas between ordinates. The area of the dia- gram is approximately A = ^y Y. Ax, and ^FixedToinfr Fig. 66. Tracing Point A£C the mean ordinate is yr. ^y Fig. 67. (no. of ordinates) This method is not strictly correct, for the middle intercepts are not necessarily the mean heights of the elementary areas. These mean heights can be found quite accu- rately by the method shown in Fig. 68. Here lines AB and CD (not necessarily horizontal) are so drawn that areas ai and 02 are equal and that bi =1)2. Then the distance y between the centers of these lines is the true mean height. The equality be- tween areas ai and a^ and between hi and 62 can be estimated very accurately by eye. 104. Delivered Power, (a) In Section 100 it was stated that only a part of the net work done on the piston by the working substance is delivered by the engine, as there is a friction loss in the moving parts. The power which actually is made available by the engine is variously called the * See Carpenter and Diederich's John Wiley & Sons. Experimental Engineering," published by 1 86 HEA T-POWER ENGINEERING delivered horse power (d.h.p.). the brake horse power (b.h.p.), and the effective horse power (e.h.p.). The difference between the indicated horse power and the delivered horse power is a measure of the power lost in friction, and is called the friction horse power (f.h.p.). Then f.h.p. = i.h.p. — d.h.p (212) The indicated horse power can be determined by means of the indicator, and hence, if either the friction horse power or the delivered horse power can be measured, all three of the quanti- ties of Eq. (212) become known. (b) The direct measurement of the friction horse power is usually impossible, but several approximate methods are used. One scheme depends upon the assumption that the power con- sumed in engine friction is constant for all values of delivered power. This assumption is not accurate, but may be used for approximation. Assuming it true, the indicated horse power obtained when the ^engine is running at speed with no external load, that is, when all the indicated power is applied to overcome friction, may be taken as a measure of the friction horse power. Sometimes it is possible to drive an engine at its normal speed, from some external source of power, such as an electric motor or a shaft. When this can be done, and when the power thus con- sumed can be measured, it furnishes an approximate determina- tion of the friction horse power. However, it is necessary to make the same assumption as in the previous case. The usual method is to determine the delivered horse power experimentally and to calculate the friction horse power by Eq. (212). The delivered horse power may be measured by the use of a prony brake or similar absorption or transmission dynamometer ; hence the term " brake horse power." For large engines ab- sorption dynamometers become elaborate and expensive and are seldom used except in special cases. 105. Efficiencies, (a) Efficiency is the ratio of result to effort. For the heat engine there are several such ratios, which depend upon the meanings given to the terms " result " and " effort." They are useful in comparing performances of dif- ferent engines, in locating losses, and in showing opportunities for improvement. Unfortunately, there is lack of uniformity in the POWER, EFFICIENCY, AND PERFORMANCE 187 names applied to the various efficiencies, and in some cases the same term has been used for entirely different ratios. In the fol- lowing discussion the names which are apparently the most suit- able have been adopted. Fig. 69 is a diagram showing the energy stream. Here, as in Fig. 3, the width of stream shows the amount of energy still available for doing external work. As the stream progresses losses occur, as shown by the offshoots, and less energy remains Fig. 69. available for doing external work. The several efficiencies, which will now be considered, may be studied in connection with this figure, and the relation between the various ones will be made clearer by referring to the figure as the discussion pro- gresses. (b) Camot Efficiency. It has been shown that the efficiency of the Carnot cycle, and of all other reversible cycles, is the theoretical maximum with any given temperature limits. It is an ideal efficiency, but is impossible of attainment in any real case. Its value regardless of the kind of working substance is 77/. -t 1 — 72 / X ^fo = — Y^ — (^^^) In Fig. 69, XZ represents the heat supplied and XY that which would be delivered as external work if the Carnot cycle XY were followed ; hence the Carnot Efficiency is Efc — tf^ • 1 88 HEAT-POWER ENGINEERING (c) Cycle Efficiency. In all real engines the working sub- stance in its action approximates one of the theoretical cycles already developed. Each of these cycles was shown to have in- herent thermodynamic loss and a theoretical efficiency less than unity. This efficiency will hereafter be called the Cycle Effi- AB * ciency, CEf. It is shown in Fig. 69 by the ratio -r-^- For example, if a steam engine is assumed to follow the ideal Clausius cycle, the Cycle Efficiency is given by Eq. (192), and the work, AEi, per pound of material by Eqs. (188) to (191). In Fig. 69, AB represents AEi. No real engine actually attains the efficiency of its theoretical cycle because of unpreventable losses, but the Cycle Efficiency represents the best result attainable with the cycle in an engine having no extra-thermodynamic losses. (d) Relative Efficiency. It would seem that the engineer should be able to design and construct engines to operate with the Carnot and other reversible cycles, and thus approximate the ideal efficiency. However, practical reasons generally compel the use of engines approximating theoretical cycles that are thermodynamically less efficient. This reduces the possible efficiency even before the practical losses are considered. A measure of this reduction is obtained by dividing the Cycle Efficiency of the engine considered by the Carnot Efficiency. The quotient will be called the Relative Efficiency, REf, and is ^£/ = ^ (214) Referring to Fig. 69, it is evident that AB XY ^-'-rnhm- _ Work done by cycle under consideration Work done by Carnot cycle (e) Indicated or Cylinder Efficiency. In actual engines, as stated, the work done upon the piston by the working substance is of course always less than the theoretical quantity; that is, * Note that any engine operating on a cycle which is theoretically reversible will have a Cycle Efficiency equal to the Carnot Efficiency (as in (b)). In other cases the amount by which the CEf falls short of Efc indicates the theoretical disadvan- tage of the irreversible cycle. POWER, EFFICIENCY, AND PERFORMANCE 189 It is less than the product of the Cycle Efficiency by the heat supplied. The ratio of work actually done to work theoretically possible measures the perfection of design, construction, and operation of the cylinder, piston, and valves. This ratio, which will be called either the Indicated or the Cylinder Efficiency,* lEf, can be expressed in several ways as follows : TTPf — ^^^^ of actual indicator diagram . , Area of theoretical PV-diagram * ' * * ^ Indicated work per pound of working substance . (215b) 778 AE (for corresponding theoretical cycle) Heat utilized per pound of working substance AE (for corresponding theoretical cycle) I.h.p. Theoretical horse power (215c) (2i5d) In the energy stream shown in Fig. 69, DE represents the indi- cated work and AB the theoretical work. Evidently the Cylin- der Efficiency is ^^^ AB DF For example, if, in the case of the steam engine previously cited, the work per pound of steam shown by the actual indicator diagram is AE\ and if AEi is the work with the Clausius cycle, AE' then the lEf = -—=r , and DE in Fig. 69 represents AE\ AiLi (f) Mechanical Efficiency. The ratio of work delivered by the engine to work received by the piston (equal to the ratio of delivered power to indicated power) is called the Mechanical Efficiency, MEf. Thus ^^/ = Sf • (-^) This fraction gives the proportion of the power received by the piston which actually becomes available as mechanical power for the consumer. The loss is a mechanical one due to friction of the mechanism. * This is also often called the " Potential Efficiency on the i.h.p.", and the " thei?- mal efficiency ratio." igo HEAT-POWER ENGINEERING In Fig. 69, JK represents the energy delivered by the engine, and DE, or JL, shows the indicated work done on the piston; hence the mechanical efficiency is -jy • J l-j (g) Thermal Efficiency on the I.h.p. The ratio of indicated work done {GH in Fig. 69) to heat supplied in the working sub- stance {XZ or GI) is useful in showing the combined efficiency of the cycle and the cylinder with appurtenances. It will be called the Thermal Efficiency on the i.h.p., abbreviated TIEf, and is rr.TT^r Indicated work in B.t.u. , . TIEf = Y^ — 7 7T-3 F— T— . . . (217) Heat supplied to cylmder Obviously, this efficiency equals the product of the Cycle Effi- ciency by the Indicated Efficiency, that is, TIEf = CEf X lEf (218) The TIEf is shown in Fig. 69 by the ratio -^ ' (h) Thermal Efficiency on the Brake or Delivered Power. The ratio of delivered work {PQ in Fig. 69) to the heat supplied the engine will be called the Thermal Efficiency on the Brake or Delivered Power, TDEf. Thus TTt'Rf — ^^^^ delivered in B.t.u. , , Heat supplied cylinder Also, it is evident that TDEf = TIEf X MEf (220) PQ The TDEf is shown in Fig. 69 by the ratio -^z^- (i) The Overall Efficiency of the Engine. The true efficiency of the engine as a whole, compared with the ideal or thermody- namic engine with the same cycle, will be called the Overall Efficiency, OEf. This takes account of both the cylinder and the mechanical losses.* Hence OEf = IEfxMEf (221) MN ■ MN The OEf is shown in Fig. 69 by the ratio -j^ , or -^^ • A study of Fig. 69 shows that all of these efficiencies follow one another in logical order, and that each has a definite bearing upon the analysis of the performance of real engines. * This is also called the '' Potential Efficiency on the d.h.p." POWER, EFFICIENCY, AND PERFORMANCE 191 106. Engine Performance, (a) The relative performance of two heat engines can be determined by comparison of the amounts of heat used to produce a given amount of work. The unit of work usually adopted for comparison . is either the indicated horse-power hour or the delivered horse-power hour. Thus the Rate of Heat Consumption may be defined as B.t.u. required per B.t.u. , B.t.u. , horse-power hour, that is, .-j , — or the ^-j -. — , as the case ^ i.h.p.-hr. d.h.p.-hr. may be. (b) If the amount of working substance used per hour is weighed and if the h.p. is determined, then the weight of mate- rial per h.p.-hr. can be computed. Evidently, if l^i, or Wd, is the weight of working substance per h.p.-hr., and if AQ is the heat per pound of material, then . ^•^•^' =WiXAQ, (222) 1. h.p.-hr. ^ dlS^.^'^^x^e (223) Since the equivalent of one h.p.-hr. is 2545 B.t.u., and since the Thermal Efficiency is the ratio of the work actually done to the heat supplied, it is evident that B.t.u. ^ 2545 ^ h.p.-hr. TIEf, or TDEf, as the case may be • • v 4; If several engines use working substances of the same kind with the same heat content per pound, the relative performances can be found by comparing the Rates of Consumption of Work- ing Substance (i.e., pounds per i.h.p.-hr. or per d.h.p.-hr.). These values are known as Engine Economies. Further, if unit weights of these working substances receive their store of heat from equal weights of fuel, the Rates of Fuel Consumption (pounds per i.h.p.-hr. or d.h.p.-hr.) may be used for comparison. (c) Graphical representations of engine performances are often very useful. They may be based upon the scheme shown in Fig. 70, which applies to an impossible machine supposed to con- vert into mechanical energy all of the heat supplied it ; — thus it is the case with efficiency of 100 per cent. Since 2545 B.t.u. are equivalent to one h.p.-hr., and since in this case the efficiency is the same at all rates of power develop- 192 HEAT-POWER ENGINEERING ment, that Is, at all " loads," the curve showing the Rate of Heat Consumption, or R-curve, is a horizontal line with ordinate 2545 B.t.u., as shown in the figure. The scale for this line is at the right. The Total Heat Consumption per hour at any load is the pro- duct of the horse power and the corresponding rate. Thus the curve showing the Total Con- sumption, or the TC-curve, re- sults from plotting the products of corresponding abscissas and ordinates of the R-curve. Since 250,000 ■3 << / ^ 1 'I ^ / Rat / / R ^^ /id /dx i Horse Power 2545 42000 200 300 Fig. 70. the latter is a horizontal line in this case, the corresponding TC-curve must be a straight line passing through the origin and with slope corresponding to the rate. The scale for this curve is given at the left of the figure. (d) When the B.t.u. per pound of working substance remains constant, it is sometimes convenient to construct curves similar to those in Fig. 70 but for the consumption of the working sub- stance instead of B.t.u. Thus the R-curve would represent the Rate of Consumption of Working Substance (as pounds of steam per h.p.-hr., or cubic feet of gas per d. h.p.-hr., etc.), and the TC-curve would represent the total consumption of working sub- stance (as total weight of steam or cubic feet of gas per hour) . Sometimes similar curves are drawn to represent the rate and total consumption of fuel used (as pounds of coal per h.p.-hr., and total weight per hour). (e) According to assumption the efficiency of this impossible device is constant, and if the efficiency line were drawn it would be horizontal at a height corresponding to 100 per cent. Even in the best theoretical cycles, that is, the Carnot, and the other reversible ones, the work performed is very much less than the mechanical equivalent of the heat supplied, and the efficiency is always much less than unity. (f) In the real engine the efficiency, and hence the rate, instead of being constant, varies characteristically with the load ; thus, instead of being straight, as in Fig. 70, the lines representing the efficiency and rate may be curved, as is shown for one real POWER, EFFICIENCY, AND PERFORMANCE 193 ,.>'t / / q_ ^ / / 1 100 H 200 Horse Power Fig. 71. engine in Fig. 71. Further, the TC-curve will not pass through the origin of coordinates, but will have a positive intercept on the Y-axis, as shown in Fig. 71. This is because there is a heat loss when the external load equals zero; for, even when an engine is running without delivering power, there is heat lost in radiation and conduction and in overcoming fric- tion, and if the engine is motionless at the operating temperature, there is still the loss due to radiation and conduction. (g) The ordinate scales in Fig. 71, as in the case of Fig. 70, may be made to read in thermal units, pounds of working substance or pounds of fuel. The ratios of the number 2545 to the different ordinates of the heat-rate curve evidently give values of the Thermal Effi- ciencies at different loads, as shown by the curve Rf in Fig. 71. This curve will give either the TIEj or the TDEf, according to the basis used in determining the R-curve. Also, the Thermal Efficiencies are given by the ratios of ordinates in Fig. 70 to the corresponding ones in Fig. 71. Similar comparisons between the curves for any theoretical cycle with those for the Carnot cycle will give the Relative Efficiencies for the former. (h) In Fig. 71 a dotted line is drawn from the origin tangent to the TC-curve. The point of tangency, Z, determines the abscissa, or horse-power output, at which the efficiency is maxi- mum and the rate minimum. Evidently, the best economy is obtained when the engine develops this power, and, other things being equal, an engine should be of such size as to operate most of the time at or near this load. If the engine normally fur- nishes more or less than this power, it is either too large or too small from the standpoint of economy only. It will appear later, however, that many other considerations enter into the choice of size of engine best suited for a given set of conditions. CHAPTER XIV. THE THEORETICAL STEAM ENGINE. 107. General, (a) In the actual steam engine only a por- tion of the heat supplied in generating the steam is converted into useful work. This portion at maximum is only about 25 per cent and ordinarily is from 5 to 12 per cent. All the rest jof the heat, from 75 to 95 per cent, is lost, and represents a pro- portionate waste of fuel and of money spent for it. It is very important for one who is to be connected with steam engineering to understand why this great loss occurs and how it can be minimized. (b) The greater part of the heat loss would occur even in the theoretically perfect engine, — because of imperfections inherent in the ideal cycle; and the exact extent of the loss in this case can be readily computed. The further losses that occur in the actual engine are due to physical imperfections; and their amounts can be determined experimentally, while their causes and proportionate distribution can be studied by comparing the actual cycle with the ideal. Many of the losses can be determined by comparing the actual cycle with the ideal ones, — the Carnot, Clausius, and Rankine. 108. The Carnot Cycle and the Steam Engine, (a) As the Carnot cycle (Section 91) gives the greatest possible efficiency, it would seem to be the most desirable cycle to use in any type of engine. Heretofore, in discussing this cycle, it was assumed that all operations were performed within a single nonconducting cyl- inder, to the end of which could be '^attached the hot body, or the cold body, or the nonconducting head, as required during the cycle. While such an arrangement is conceivable, it cannot be realized materially, and to obtain an apparatus of practical value it is necessary that some parts of the cycle shall be per- 194 THE THEORETICAL STEAM ENGINE 195 formed outside of the cylinder. In this latter case, however, the result will be the same, provided the cycle is carried through in the same manner as before. Thus the cycle may be per- formed in the following apparatus: (b) Let the cylinder, the cylinder end, and the piston be per- fectly nonconducting, and let the cylinder end be permanently attached. Then, instead of a hot body, let there be a pipe with a valve (" Steam Valve ") connecting the cylinder to a boiler which will supply steam (heat) at the constant temperature Ti, corresponding to pressure pi] and in place of the cold body let there be another pipe with a valve ('' Exhaust Valve ") con- necting the cylinder to the condenser, in which the temperature is maintained constantly at 72, corresponding to the exhaust pressure p2. Such an arrangement, with the addition of a feed pump to return the condensate from the condenser to the boiler, completes the apparatus, which contains the simple elements of a steam power plant. (c) In performing the Carnot cycle, note that (see Section 53) : (i) All heat from the external source must be received at the constant temperature Ti of the source. (2) All heat discharged to the cold body must be rejected at the constant temperature J2 of the cold body. Hence: (3) Before heat is received at the upper temperature Ti, the working substance must be brought to that temperature with- out receiving heat energy from the outside ; so it must be done by adiabatic compression from T2 to Ti, and (4) Before heat is rejected, the temperature must be lowered from Ti to T2 without losing heat as such to the outside; so this must be accomplished by adiabatic expansion. Referring to Fig. J2 (a) for the PV-diagram and to Fig. 72 (b) for the T («) 'Ch (6) {0) ume. PV-diagram, as shown by cl in Fig. 77. The percentage of '' clearance volume " as com- pared with the piston displacement, or volume displaced by the piston per stroke, is from 2 to 15 per cent in practice.* * The term " clearance " is used rather loosely as applying either to the linear or volumetric quantity, but the kind of cleararfice meant is usually apparent from the context. Fig. 77. 204 HEAT-POWER ENGINEERING (b) The clearance theoretically influences the amount of steam heat consumed per unit output of work. If the engine operates with a theoretical PV-diagram of rectangular form, Fig. 77 (a), the clearance space must be filled with steam each cycle, before the piston starts, and as nearly all of this steam is exhausted with that which performs the work, it theoretically represents a direct waste, the percentage of waste being equal to the per- centage of clearance volume. (c) If the cycle is that shown in Fig. 77 (&), a still greater pro- portion of the steam heat is wasted because of the clearance space; for in this case the clearance volume is greater in pro- portion to the total volume of steam admitted than in the pre- ceding instance. (d) If the cycle followed is that shown in Fig. 77 (c), in which there is adiabatic compression along ab, there is theoretically no loss due to the clearance ; for at each stroke the weight of steam entrapped at a and compressed along ab can be considered, dur- ing expansion, as following back along ba, just as if this amount of steam were separated from the rest by a flexible diaphragm and were compressed and expanded adiabatically without being exhausted from the cylinder. (e) If the compression is not carried to the initial pressure, but is along some line ka in Fig. 78, the case is intermediate ^\ ^N^^ between (c) and (d). If, in addition, the > 1 — :--^di expansion is incomplete, terminating at some point d in Fig. 78, the clearance loss is theoretically a minimum when com- pression is carried to a point somewhat below b* (f) In the actual case there are certain influences to be dis- cussed later, which modify the theoretical effect of compression. Whether or not compression in the actual engine, improves the steam consumption is still a matter of discussion. The influence is so small that the effect is difficult to determine experimentally. 113. Cushion Steam and Cylinder Feed, (a) It is sometimes convenient to consider the weight of working substance present in an engine cylinder as composed of two parts, namely, that Fig. 78. * See Heck's " Steam Engine," Vol. I, p. 97. i THE THEORETICAL STEAM ENGINE 205 entrapped during compression and that fed from the boiler during each cycle. (b) The steam entrapped during compression is called the " cushion steam.'* It is difficult to determine its quality through- out compression, but it is customary to assume it dry when com- pression begins. Since almost immediately after release the steam pressure drops to the back pressure, there is but little steam in the cylinder soon after the beginning of the back stroke. That part subsequently trapped in the clearance and compressed is subject to the higher temperature of the cylinder walls throughout nearly the whole of the return ^^§- 79- stroke, hence must be practically dry when compression begins. With this assumption, the weight of the cushion steam at k, Fig. 79, can be computed from V wic = Vk-^Yk, (226) in which Vk can be scaled from, diagram and V^ is the specific volume, as given in the Steam Tables, for the pressure p2 existing. If the same weight of steam is raised to the initial pressure pi and is maintained dry and saturated, it will occupy the volume Vb' =WkXYi, (227) where Vi is the specific volume at the initial pressure pi. The volume Vb is shown by the abscissa at the point b' in Fig. 79, in which b'k is the saturation curve for a weight of steam equal to Wk. Evidently when the valve opens to admit steam to the cylinder this weight Wk is already present, and it occupies the volume Vb as soon as its pressure is raised to that of the entering steam. (c) The steam that is supplied to the cylinder from the boiler at every cycle is called the " cylinder feed" (w/). The cylinder feed may be determined by finding the weight of steam delivered to the engine in a given time and dividing this by the correspond- ing number of cycles. If the boiler, without loss, furnishes to the engine all the steam it generates, the weight of steam supplied is equal to the weight of water fed to the boiler in the given time. If a surface con- denser is used, Wf can be determined from the weight of the 2o6 HEAT-POWER ENGINEERING Steam condensed in the given time, provided there is no leakage in the condenser. In Fig. 79 the volume of the cylinder feed is shown by the distance b^c. It would be represented by be only in case the compression terminated at point b. (d) The total weight (w) of steam in the cylinder during expansion is evidently made up of the cylinder feed (w/) and the cushion steam (wk) ; thus w = w/ + Wk. Its theoretical volume at the time of cut-off, if it is dry and saturated, is Fc =10X^0, where Vc is the specific volume of the steam at the cut-off pressure. 114. Saturation and Quality Curves, (a) If the weight of steam (w) present in the cylinder is considered to be dry and saturated, it occupies at any time a volume Va = wV, where V is the specific volume for the pressure under consideration-. By plotting on the PV-diagram the values of Vs for different pres- sures, a Saturation Curve is obtained. Such a curve is shown by cs in Fig. 80, and is of value in determining the quality of steam at different points during expansion (Section 70). For example, in Fig. 80, in which the expansion line cd is adiabatic, the quality AC of steam at any point C is x = ~a~^' ^^^ ^^^^ "wetness factor" is (b) If qualities are determined for several points along the expansion line and are plotted as ordinates on the corresponding volumes, as in the upper part of Fig. 80, a Curve of Qualities is obtained, which shows how X varies during the expansion. The quality curve in this case shows the condensation that takes place in order to make heat available for doing external work during the adiabatic expansion. In the figure the steam is assumed to be dry and saturated at c, hence the saturation curve must pass through that point. Quality curves for any other kind of ex- pansion line can be found in the same AC way; thus, if c'y is the line, the quality at C ^^ ^-^, if the weight of material present is the same as before. 100 f, •^^, iJ'-tv Xc ^ b C c\ j a ^-. > e V Fig. 80. THE THEORETICAL STEAM ENGINE. 207 » (c) Should the expansion Hne cross the saturation curve, as in Fig. 81, the quality ratio would be greater than 100 per cent, which would indicate that the steam becomes superheated during expansion. If the weight {w) of steam is known, the specific volume of the super- heated material follows from V = — , in w which V is the volume scaled on the dia- gram. Then the absolute temperature of the steam may be computed by solving Tumlirz's Eq. (134). Thus T = p (V -\- 0.256) -^ 0.5962, in which p is the absolute pressure in pounds per square inch. By sub- tracting from T the absolute temperature of saturation at the pressure p the degrees of superheat D can be found. (d) On page 156 it was shown that under certain conditions the adiabatic expansion of wet steam can be represented quite accurately by PV"^ = const., where n has different values which depend on the quality x at the beginning of expansion. The re- lation between n and x was given in Eq. (156), thus the initial quality can be determined if n is known. The value of n in any case can be found in several ways, but probably the most convenient method is to replot the expansion curve using loga- rithmic coordinates, in which case n is the slope of the expansion line (page 55). With the quality and volume known at the be- ginning of expansion, the corresponding weight of steam in the cylinder and the water rate can be determined readily. if CHAPTER XV. ACTION OF STEAM IN REAL ENGINES. 115. Cylinder and Thermal Efficiencies of the Steam Engine. (General.) (a) The actual behavior of the steam in a cyhnder is quite different from the theoretical, because of modifications of the ideal cycle, heat interchanges between the steam and the cylinder walls, and leakage of valves, piston, etc. The greater the per- fection attained in the design, construction, and operation of the engine, cylinder, piston, valves, etc., the closer will the actual behavior approach the ideal. The measure of this perfection is given by the indicated or cylinder efficiency (lEf), Section 105 (e), which can be computed by Eq. (215), or by the following: _ Actual B.t.u. of indicated work per lb. of steam _ Hi . . Theoretical B.t.u of work with Clausius cycle AE _ B.t.u. equivalent of 1 i.h.p.-hr. _ 2545 , . Heat available per i.h.p.-hr. Wi AE _ Theoretical lbs. of steam per h.p.-hr. _ W / q \ Actual lbs. of steam per i.h.p.-hr. Wi' In which AE = B.t.u. work with Clausius cycle per lb. of steam. Hi = Actual B.t.u. indicated work per lb. of steam = -^^• W = Pounds of steam theoretically needed per i.h.p.-hr. with Clausius cycle = 2545 -^ AE. Wi = Pounds of steam actually used per i.h.p.-hr.- as found by weighing the water used. (b) The cylinder efficiencies of steam engines and turbines range from 40 per cent to 80 per cent, and in one exceptional case 88.2 per cent was attained. The reasons for the differences occurring between the real cycle and the Clausius, and for the losses which they represent, and the methods of reducing these losses, will be discussed in the succeeding sections. 208 ACTION OF STEAM IN REAL ENGINES. 209 If the same Clausius cycle is followed by two reciprocating steam engines, or by a reciprocating engine and a steam turbine, the ratio of the consumptions of steam, or heat, per i.h.p.-hr. of the two engines is equal to the inverse ratio of the cylinder efficiencies. If the theoretical cycles are not the same, such a comparison should not be made. (c) It is at times necessary to predict the performance of a new engine, or turbine, when operating under certain definite conditions. In such cases the B.t.u. of work, AE, done by the Clausius cycle, per pound of steam, can be obtained from Eqs. (188) and (191), or from the MoUier or EUenwood diagrams in the Appendix; then if the proper value of the Cylinder Efficiency (/£/) can be found, from data relating to similar engines oper- ating under like conditions, the probable number of heat units that will be converted into work per pound of steam is, from Eq. (228a), Hi = AEX lEf, (229) and, from Eq. (228b), the probable steam consumption per i.h.p.-hr. is T7i = 2545 ^ (A£ X /£/) (230) (d) The Thermal Efficiency on the i.h.p. (TIEf), Section 105 (g), is the ratio of the indicated work to the heat supplied for doing this work; it is therefore a measure of combined efficiency of the cycle and of the cylinder with its appurtenances. The engine cannot use heat that is of temperature lower than that of the exhaust steam T2* and, theoretically at least, the heat remaining in the condensate can be returned to the boiler with the feed water; hence the heat of the liquid below this lower temperature is not chargeable against the engine, when considered by itself and not in connection with the power plant as a whole. Therefore, TTT7f — ^•l-'^-'i'''^dicated work per lb. of steam . . Heat supplied above T2 per lb. of steam Hi (Aft - 52) 2545 (231b) (231c) Wi{AQ,-q2) * Proc. Inst. C. E. (British), Vol. CXXXIV; and Trans. A. S. M. E., Vol. XXIV, pp. 716 and 755 2IO HEAT-POWER ENGINEERING Where Hi = B.t.u. of actual indicated work per pound of steam = 2545 -r- Wi= AEX lEf (232) AQi =(xr + q + CpD)i. . (233) g2 = heat of liquid above 32 degrees when at the tem- perature r2* of the exhaust steam. Wi = Pounds of steam actually used per i.h.p.-hr. as found by weighing the water used. The value of TIEf varies with the kind of engine and condi- tions of operation, and ranges in practice from 5 per cent to 25.05 per cent, this latter value being the maximum yet recorded. In the case of a new engine, the probable performance may be computed, if the value of TIEf for similar engines and conditions are known, by using the following equations, derived from Eq. (216) : jYi = 2545 -^ 5 (A(2i - 52) X TIEfl . . (234) Hi = (Aft - 52) X TIEf. ..... (235) (e) The Mechanical Efficiency (MEf) of the steam engine mechanism varies from 85 to 97 per cent. (f) The measure of the combination of the efficiencies of the cycle, cylinder, and engine mechanism is the Thermal Effi- ciency on the d.h.p. (TDEf), Section 105 (h). The TDEf can be computed from Eqs, (219) and (220). Since it is the ratio of the B.t.u. of work delivered, to the heat supplied in doing that work, 2=;a=; ^''^f- w.m-,.) ' • • • • ^^''^ in which Wd is the weight of working substance supplied to the engine per d.h.p.-hr,, and AQi is the heat per pound as given by Eq. (233), and $2 is the heat of the liquid at exhaust tempera- ture T2. The TDEf is from 85 to 97 per cent of the TIEf, the ratio being equal to the mechanical efficiency. The probable performance of an engine on the basis of de- livered power may be estimated by using the following equations, Wa = 2545 -^ 5(A(2i -52) X TDEf I = Wi -i- MEf (237) ^""^ Ha = TDEf{AQ,-q,), . (238) where Ha is the B.t.u. of work delivered per pound of steam. * Proc. Inst. C. E. (British), Vol. CXXXIV; and Trans. A. S. M. E., Vol. XXIV, pp. 716 and 755. ACTION OF STEAM IN REAL ENGINES 2II (g) The measure of the performance of the engine as a whole as compared with the ideal engine following the Clausius cycle is given by the Overall Efficiency (OEf). This is the combined efficiency of cylinder and mechanism, hence OEf = lEf X MEf as in Eq. (221). Since it is the ratio of work actually delivered to that which would be delivered by the ideal engine, in which Wd is the weight of steam actually used per d.h.p.-hr., and AE is work theoretically obtainable per pound of steam fol- lowing the Clausius cycle. AE can be computed by using Eqs. (188) to (191). The overall efficiency of steam engines is from 35 to 78 per cent. The probable performance of the steam engine, based on the delivered output, can be estimated from Wd = 2545 - (AE X OEf) (240) and Hd= AEX OEf . (241) 116. Actual Behavior of Steam in an Engine Cylinder, (a) The materials with which the steam comes in contact in the engines previously considered have been assumed to be perfect nonconductors of heat; but materials actually used are good heat conductors, and this modifies the behavior of steam in real engines. (b) The steam on its way from boiler to engine gives up to the pipe a part of its heat, which is lost by conduction, radiation, and convection. Because of this, the steam arrives at the engine with quality or superheat reduced. There is another loss due to the drop in pressure necessary to cause the steam to flow from the boiler to the engine against resistances due to friction of the pipe and inertia of the steam itself.* (c) At the engine the steam on its way to the cylinder passes through a " Throttle Valve." If this valve is only partly open, the steam is " Throttled " or " Wire-drawn,'* with an accom- panying drop in pressure. These changes take place with such *This kind of loss will be considered later in the chapter on flow of steam through pipes. 212 HEAT-POWER ENGINEERING great rapidity and within such small space that little heat loss to the outside can occur, but as there is an increase in the veloc- ity of the steam there is a small amount of heat expended in im- parting kinetic energy. This, however, returns as heat when the velocity is reduced in the engine. The heat lost while the pressure is decreased is so small as to be negligible, hence the process may be considered one in which the total associated heat remains constant. The throttling increases the quality (or superheat), the value of which can readily be found by follow- ing along the proper constant-heat line either on the Mollier diagram or on the T0-diagram, from the point for the initial condition to that for the lower pressure (or temperature). A further wire-drawing takes place, with a similar effect on the condition of the steam, while the steam passes the more or less restricted opening of the admission valve on its way to the cylinder. (d) When the steam enters the clearance space in the cylinder, it comes in contact with surfaces that were cooled during the period of exhaust of the preceding cycle. In the resulting inter- change of heat, the temperature of the clearance walls is raised, and ordinarily from lO to 40 per cent of the steam is con- densed. The corresponding de- crease in the quality of the steam is shown by the inclina- tion of the quality curve Xibi in Fig. 82. As the piston recedes during admission {be), an increasing amount of the cylinder wall is exposed to the entering steam and further condensation takes place (as shown by the slope of hiCi) until, at the point of cut-off, from 20 to 50 per cent of the steam has usually been condensed. Next to the heat loss inherent in the theoretical cycle, this Initial Condensation, as it is called, causes the largest loss that ordinarily occurs in the steam engine and is therefore the one most desirable to minimize. (e) During admission the pressure is decreased by the wire- drawing of the steam while passing the admission valve and Fig. 82. ACTION OF STEAM IN REAL ENGINES 213 while flowing through the passages to the cylinder. This causes small loss of heat but decreases availability. It improves the quality or superheat of the entering steam somewhat and may reduce the initial condensation a very slight amount. The decrease of pressure by wire-drawing and the effect of con- densation during admission are shown by the downward slope of the admission line, he. (f) After cut-off (c), the condensation continues, until expan- sion has reached a point (/) where the temperature of the steam equals the mean temperature of the exposed cylinder walls. The accompanying change in quality is shown by the curve Citi. With further expansion the average quality of steam increases; steam is still condensed on the surfaces newly un- covered by the continued motion of the piston, but the heat thus absorbed by the cooler portion of the cylinder wall is less than that given up, to evaporate moisture, by the rest of the wall which is at relatively higher temperature. The increase in quality is shown by hvi. Of course, the condensation during expansion is not all due to the influence of the cylinder walls, for heat must be used in performing the external work, as was shown in Section 114 (b). The quality curve Cihri, for the period of expansion, is readily obtainable after the saturation curve has been drawn for the total weight of mixture in the cylinder; but that part of the quality curve which relates to admission {xihiCi) is indeter- minate and is therefore shown dotted in the figure. (g) Theoretically, expansion should be continued to the point d on the back pressure line; therefore, in the actual case there is a loss due to incomplete expansion,* measured by the area rde* During release {re) the' steam is dried to some extent by the heat that is given up by the cylinder wall to the steam, which is now at a low temperature, and also by the heat released from the steam itself while decreasing in pressure. (h) During exhaust {ek) the confining walls are cooled by the outflowing steam, and by the evaporation of the film of moisture on the walls. The greater the amount of moisture, within limits, the cooler will the walls become and the greater will be the amount of steam condensed during admission in the *See Section iii. 214 HEAT-POWER ENGINEERING iy next stroke. The exhaust pressure, or back pressure, is some- what higher than the theoretical because of the resistance to steam flow offered by the valve opening and passages, by the inertia of the steam itself, and because of the evaporation of moisture. (i) During compression the quality of the steam is indeter- minate. It is usually assumed, however, that the steam is dry at the beginning of compression, and this is accurate enough for most practical purposes because of the small weight of steam involved. During the first part of compression the steam will probably be slightly superheated owing to the reception of heat from the hotter walls of the cylinder. If the compression is high, the temperature from compression may rise PJJ^^X above that of the cylinder walls, in which case \ ^^ condensation will follow. Further compression ] '■ ' of the now saturated steam will be at constant ig- 3; pressure, and on the PV-diagram the line be- comes horizontal, thus forming the " hook " as in Fig. 83.* (j) The cycle is further influenced by the leakage of steam past the valves and around the piston, which would modify the actual -diagram. (k) The loss of heat from the cylinder walls by radiation, conduction, and convection lowers the mean temperature of the walls and adds slightly to the condensation. 117. Diagrammatic Representation of the Heat Interchange in the Cylinder, (a) In the PV-diagram, Fig. 84 (a), the point Fig. 84. C represents the total charge of steam and water in the cylinder, considered raised to the initial pressure and in a dry saturated condition. CC is an adiabatic expansion line drawn through *A somewhat similar hook occurs when there is leakage past the piston or valve. ACTION OF STEAM IN REAL ENGINES 215 this point, and fCC'g is the Clausius diagram which this charge should theoretically give. The actual diagram (omitting com- pression and clearance) is fbcreg. If through c the adiabatic C1C2 is drawn, then fciC2g is the Clausius diagram for the vapor actually present at cut-off. Thus the loss of area from initial condensation is seen to be CiCC'c2, and that due to wire drawing is bcci. That the expansion line from c to t has greater slope than CC2 shows that the condensation takes place more rapidly than it would with adiabatic expansion. At /the temperature of the steam is the same as that of the cylinder walls, and from / to r reevaporation takes place, as shown by the expansion line being more nearly horizontal than the adiabatic. The loss due to early release is shown by the area rde, in which rd is an adiabatic line. (b) The diagram for the compression of the cushion steam is shown separately in Fig. 84 (b) by gkaai ; and above it is the area aiabf for admission at constant volume. By subtracting Fig. 84 (b) from Fig. 84 (a) the net diagram is obtained, as in Fig. 84 (c). (c) The use of a T^-Diagram to represent the heat inter- changes occurring in the cylinder is more or less conventional and is only partly correct from the theoretical standpoint. In f-' -ft" n r \ (6) Fig. 85. (<=) Fig. 85, which is lettered to correspond with Fig. 84, fCC'g is the Clausius diagram for the total weight of charge used per cycle; fbcreg conventionally represents the actual diagram, neg- lecting clearance and compression ; and fciCig is the Clausius cycle for the vapor actually present at the time of cut-off. The loss of heat to the cylinder wall due to initial condensation is given by area below CiC down to the 0-axis; but as that part below c^C could not be utilized, the net loss of area from this cause is CiCC'c2. The wire-drawing loss is represented 2l6 HEAT-POWER ENGINEERING approximately* by the area bcci. That heat is lost to the cylinder wall after cut-off is shown by the sloping of the expan- sion line ct to the left of the adiabatic cc2, which indicates that the quality decreases more rapidly than it would with adiabatic expansion. At t condensation ceases; and from t to r reevapo- ration takes place, accompanied by an increase in the quality. The loss due to early release is represented approximately by the area erd. (d) The T0-diagram for compression of the small weight of cushion steam is shown in Fig. 85 (b) by the negative area kacig drawn to the same scale as before, except that the width has been reduced in proportion to the weight of working substance involved. Here it is assumed that the steam is dry at the be- ginning of compression, in which case the saturation curve S would pass through the point k. The heat lost to the cylinder walls during compression is shown by the area under ka, and the qualities during compression can be readily determined in the usual manner on such diagrams. In Fig. 85 (c) the intercepts between a^g and ak are the same as those between the similar lines in Fig. 85 (b) ; ab is the line for the constant volume during admission (corresponding to ab in Fig. 84) , and fbcreg is the same as in Fig. 85 (a) . The area abcrek evidently approximately represents the work done during the actual cycle. (e) Obviously, cr is the only part of the diagram that shows the true behavior of all the steam used per cycle; for, during the other parts of the cycle, only a part of the steam is within the cylinder. As the T ACTION OF STEAM IN REAL ENGINES 223 Between r and k, the steam for a while does work, as shown by ^r on the indicator diagram; afterwards work is done upon it, as shown by Ae. At r the heat in the steam is Hr (from Eq. (247)), and at k there is left in the steam Hk = Wk{p -\- g)k, since Xk is taken as unity. Hence the heat interchange during exhaust is Le = (Br - Hk) - (K, + K2) - {Ar " Ae), • (251) in which positive and negative results have the same meanings as explained in connection with Eq. (246). (g) If the steam is exhausted to the atmosphere, the heat discharged is indeterminate. An approximation can be made if the mean quality of the exhaust steam is known, but it cannot be computed accurately because the weight, pressure, and quality of steam are variable throughout the exhaust period. (h) During compression the change of associated heat is (Hk - Ha), in which Hk=wk{p + q)k (252) ^""^ Ha=Wkixp+q)a (253) The work actually done upon the steam per cycle is shown by Ak' Hence the heat interchange during compression is Lk = Hk - Ha + Ak, (254) in which the sign of Lk has the same meaning as before. (i) Ideally, the heat given to the cylinder walls should equal that given up by them to the steam. Actually, in the case of an ordinary engine, the heat given up is less than that received, and this is because of conduction and radiation. Evidently, the conduction and radiation loss in B.t.u. per cycle is ' R=La + Lc-^Lr-{-Lk. . . . (255) (j) If the steam is initially superheated, the analysis would be carried through in a manner similar to that just given. If the engine is steam- jacketed (Section 129), or is a compound engine with reheating receivers (Section 130), account must be taken of the heat furnished by the jacket steam. '^, 120. Experimental Determination of the Actual Performance of Steam Engines, (a) The indicated horse power of an engine can be determined from the indicator diagram, if the diameter 224 HEAT-POWER ENGINEERING of cylinder, length of stroke, and r.p.m. of the engine are known. The delivered horse power can be measured by a Prony brake or other form of dynamometer and in other ways which need not be considered here. The mechanical efficiency of the engine and power lost in engine friction can then be calculated. The total amount of steam used per hour may be determined by weighing the water pumped to the boiler which supplies the engine, making proper allowance for loss or withdrawal of working substance between the pump and the engine; or it may be found by weighing the condensate, if a surface conden- ser is used, and making correction for leakage. The weight of steam used per h.p.-hr., or Water Rate, can then be obtained as in Section io6. (b) If these measurements are made for a range of loads on the engine, the resulting data can be used in plotting curves of Total Consumption of Steam (TC) and of Rate of Consumption (R), as in Fig. 71. These curves show the performance of the engine under all conditions of loading, and determine the power output at which the engine operates most economically. The curve of total consumption is usually nearly straight. If the abscissas are d. h.p.-hr., the Y-intercept shows the steam used in overcoming the friction of the engine alone. (c) If two engines receive steam of the same pressure and quality, their relative performance is shown by comparing their Water Rates. In other cases the only true measure of econ- omy is on the basis of heat used per unit of power, and in order to determine the heat in the steam as it enters the engine the quality, or superheat, must be known. The quality of the steam can be determined by using instru- ments which will be described in the next section. 121. Steam Calorimeters.* (a) The apparatus used to de- termine the quality of steam is called a " steam calorimeter." There are several kinds of calorimeters, which will be considered very briefly. The Barrel Calorimeter. (b) If into a barrel containing water, of known weight (W) and temperature (^1), a sample of the steam is piped, and con- * For more detailed discussion see Carpenter and Diederichs' " Experimental Engineering," published by John Wiley & Sons. ACTION OF STEAM IN REAL ENGINES 225 densed, and if the increase {w) in weight of water and the result- ing temperature (^2) are measured simultaneously, there are suf- ficient data for determining the quality of the sample of steam, provided the steam pressure is known. The heat given up by the steam is ^Q^ = w\xr-\-q- fe- 32°)} and that received by water is AQ2 = W{h-k), assuming Cp of the liquid as unity. Evidently AQi = A(22, from which the quality is found to be W{h-ti)-w{q-\-2>2-h) X = wr (256) Correction should also be made for conduction and radiation losses in accurate work. a I The Separating Calorimeter. (c) In using the Separating Calorimeter (Fig. 89), a sample of steam is first led to the sepa- rating chamber C, where the moisture is thrown out and collected (the amount w being shown by the gauge glass G), then the resulting dry steam passes into the jacket / and out through the orifice to a can of water in which it is condensed and its weight W determined. Using simultaneous values of w and W, the quality evidently is W ..... (257) X = w-\-W The Throttling Calorimeter. (d) In this case a sample of wet steam is passed through the device shown in Fig. 90, and is superheated by being throttled through the valve V while expanding into the cup C, where the pressure is low. This pressure is usually nearly atmospheric when high-pressure steam is being sampled. If the sample of steam is at pressure near or below that of the atmosphere, the cup may be connected with a condenser to obtain a sufficiently low pressure therein. The temperature ts of the superheated steam in this cup C is 226 HEAT-POWER ENGINEERING measured by the thermometer T; and the degrees of superheat D are found by subtracting from 4 the saturation temperature ^2 corresponding to the cup pressure shown by the manometer. The expansion through the valve causes the jet of steam to acquire a high velocity at that point, hence some of the associated heat is converted into kinetic energy. In the cup, the velocity of steam is reduced and this kinetic energy is reconverted into associated heat. If the velocity in the cup, where the tempera- ture ts is measured, is the same as that in the main steam pipe (which is usually approximately true), and if there are no radia- Exhaust Steam Fig. 90. tion or conduction losses (and these are usually almost negligible), the associated heat is the same before and after the steam passes the expansion valve. Before throttling, the amount of heat per pound is AQi = Xin + qi ; afterward, it is AQ2 = X2 + Cp (D) = X2 + 0.48* (ts - 12). Then since A(2i = A(22, ' the qualitv is found to be X2+o.48*fe-^)-gi * For cup pressures other than atmospheric substitute the proper value of Cp for 0.48. Xl (258) ACTION OF STEAM IN REAL ENGINES 227 The Electric Calorimeter. (e) In using this calorimeter the sample of wet steam is dried by letting it flow over coils of wire which are heated by an elec- tric current, the energy input being measured by a wattmeter. The watts are gradually increased until a value E is reached at which the thermometer in the calorimeter outlet starts to rise, which is supposed to show that all moisture has been dried by the heat from the coils, by expending an amount of heat corre- sponding to E. If the quantity of mixture {w) flowing through the calorimeter in a given time is weighed, or otherwise deter- mined, the heat Qi) added to dry one pound of the steam can be computed from the electrical input. Then r — h , ■ ^=-^7- (259) The Degrees of Superheat. (f) This is determined by subtracting the saturation tempera- ture, for the existing pressure (as shown by a pressure gauge), from the actual temperature of the steam, as shown by a ther- mometer placed in the steam. 122. Weight of Steam Accounted for by the Indicator Diagram, (a) Not only is it possible to draw a theoretical PV- diagram for a given weight of steam per cycle, as has already been done, but obviously, if a diagram is given and the scale of volumes is known, it is possible to determine the theoretical weight of steam that the given cycle would use. This not only applies to theoretical diagrams, but also to actual ones. The theoretical weight of dry steam per actual cycle can be found in exactly the same way as for the theoretical cycle. The ratio of what is called the '' Steam Accounted for by the Diagram," " Indicated Steam Consumption," or " Diagram Steam," to the steam actually used by the engines is useful in showing the per- fection of performance within an engine cylinder. This ratio can be easily obtained, and the difference between the weight of dry steam actually used and the theoretical is the amount liquefied by cylinder condensation. In the actual case it is convenient to consider the working sub- stance within the cylinder as a mixture of dry steam and water. The indicator diagram shows the behavior of the vapor only. 228 HEAT-POWER ENGINEERING (b) Suppose the clearance line and zero-pressure line, that is, the PV-axes, have been drawn on an actual diagram, Fig. 91. Then let Vz be the volume as scaled "'^___^ I to some point z on the expansion ^ ^^\i ^^^^' between cut-off and release^ , .a ^\^^^ and let Yz be the specific volume at |\ ^^ ^^^ corresponding pressure. Then 1 _> ,^ the total indicated weight of dry -1 ^ [—rr vapor in the cylinder at that time is I, 1 ^ V r- ' ' Vz Fig. 91. Wz = ^. , . (260) Similarly, at any point k on the compression line the weight of dry " cushion " steam is Wk =~, ...... . (261) Vk in which Vk is the actual volume as scaled to point k and Yk is the specific volume for that pressure. Subtracting the cushion steam from the total in the cylinder gives the indicated cylinder feed (w/) per cycle; thus w/ = (Wz — Wk) = ;(^ — ^ (262) As the quality changes during expansion and compression, the value of w/ will depend on the locations of points z and k. It is customary to take z either near the beginning or near the end of expansion, and k is usually assumed near the beginning of compression. (c) Now let yc = clearance volume -^ piston displacement per stroke = -y in Fig. 91 yz = fraction of stroke completed corresponding to any point on the diagram fyj* a = area of piston in square inches. pm = m.e.p. - L = stroke in feet. n = number of cycles per minute. Then the piston displacement in cubic feet per stroke isf j ACTION OF STEAM IN REAL ENGINES 229 and the volume of vapor when any fraction jz of the stroke is completed is Substituting this and a similar value for the volume Vk in Eq. (262) gives for the number of pounds of Indicated Cylinder Feed, per cycle, Multiplying this by (60 X n) cycles per hour and dividing by {— ), gives the number of pounds of steam per i.h.p.-hr., or " Diagram Water Rate," as If points z and k are taken at the same pressure level, p, then Y^ = Yk = Yp and ^^ = r¥^ ^3^. + yc) - {jk + yc)\ =^^^iy^ - y^)- (265) If the pressure is taken as that at the end of compression, then yk = o and "^^-S^.'^y- (^^^> (d) If W = Xi X cylinder feed, represents the dry steam actually supplied per i.h.p.-hr. and Wd is the indicated water rate corresponding to the point z located at the cut-off, the " Cylinder Condensation," or weight of steam condensed by the cylinder walls and that lost by leakage, is approximately (W — Wd) per i.h.p.-hr.; and the proportion of the whole that is condensed, or '* Condensation Fraction," is CF=(W-Wd)-^W (267) If the Condensation Fraction, or " Per cent Cylinder Con- densation," is known for a certain type of engine under certain operating conditions, then, in considering a prospective engine of this class, the probable water rate under the same conditions can be estimated by dividing the theoretical diagram water rate, found from the probable diagram, by (1 — CF). CHAPTER XVI. METHODS OF DECREASING CYLINDER CONDENSATION. 123. Condensation and Leakage, (a) It has already been shown that the cyhnder condensation causes the largest loss in the steam engine, with the exception of that inherent in the theoretical cycle. Condensation is evidently dependent on, but not necessarily proportional to, (i) the ratio between the condensing surface (5), to which the steam is exposed, and the volume of steam used per cycle; (2) the temperature differ- ence {T) between the entering steam and the surfaces; and (3) the time (/) of exposure, which is inversely proportional to the number (n) of cycles (i.e., to -1. For computing the probable steam consumption many formulas have been proposed in- volving functions of S, T, t, or - , and numerical coefficients determined from experimental data. Such formulas are suffi- ciently accurate for ordinary purposes, when there is no leakage past piston and valves.* (b) Unfortunately, while it is possible to determine experi- mentally whether or not leakage does occur, the amount of leakage per cycle cannot be closely evaluated ; thus it is impossible to separate the loss due to leakage from that due to condensa- tion. Hence cylinder condensation and leakage must be con- sidered together. Formulas for cylinder condensation should be derived from a study of data from engines that are known to have little or no leakage. Unfortunately, most of the data available are from engines which were not tested for tightness of valves and pistons and hence are unsuitable for the purpose. 124. Size and Proportions of Cylinder, (a) The size of cylinder has an important influence on the cylinder condensa- tion. It can be shown by computation that large cylinders * For formulas and data see Heck's " Steam Engine," and Thurston's "Manual of the Steam Engine." 230 \ METHODS OF DECREASING CYLINDER CONDENSATION 231 have a smaller ratio of surface to volume inclosed than have small cylinders of the same proportions. It is therefore to be expected that large engines will have less cylinder condensation and consequently will give better economy than small ones; and that is actually the case. Very small engines may use twice as much as, or even more, steam per i.h.p.-hr. than very large ones of the same proportions and same conditions of operation. (b) The amount of surface in the clearance space (including that of the steam passages between valves and cylinder) has a predominating influence on the amount of cylinder condensa- tion that takes place; for, just after admission, the piston is moving so slowly that the time of exposure of the steam to these surfaces is comparatively long, hence the amount of condensation that occurs is large. Probably the greater part of the cylinder condensation occurs in the clearance space. The cylinder passages and clearance space should therefore be designed to present the minimum amount of surface consistent with the other considerations involved. (c) The cylinder condensation is also dependent on the length of stroke of the engine. If long and short cylinders are of the same diameter and have their passages and clearance space identically the same, and cut-off steam at the same per cent of stroke, obviously the ratio of clearance surface to the total surface exposed per stroke of the engine is smaller in the long- stroke engine than in the one with shorter stroke. Neglecting the time element, the long-stroke engine should give better economy than the short-stroke one; and in general that is the case, though this is in part due, to the fact that the long-stroke engines are usually also larger, have cylinders that are better designed, and have better valve gear than those with shorter stroke. The time element may have an important influence, however; for example, due to the fact that most of the condensation occurs in the clearance space and because of the shorter time of exposure, some of the short-stroke " high-speed " Corliss engines give as good or even better economy than the long-stroke low- speed Corliss engines. (d) In many engines the exhaust steam flows over the outer surface of the cylinder wall, on its way to the exhaust pipe. 232 HEAT-POWER ENGINEERING Because of the high velocity of flow, this steam carries away heat more rapidly than would stagnant air in contact with the same surface. This lowers the mean temperature of the cylinder walls and increases the cylinder condensation. In the better designed engines the exhaust steam is not brought in contact with the cylinder walls after it leaves the exhaust valve. Dry Steam Mixture II.. la 10 -3 + -^\xei 30 iO 50 ^ Cutoff 125. Influence of Point of Cut-off. (a) As most of the cylinder condensation occurs in the clearance space, the later the cut-off (or the greater the vol- ume of steam admitted per cycle), the less will be the percentage of steam condensed, although the amount may be greater. ^ (i) The percentage of steam not condensed is shown in Fig. 92 (a),* by the or- dinates, the abscissas being percent- age of stroke at cut-off. (2) The work theoretically done per pound of steam decreases as the cut-off is advanced in the stroke (because of the reduction of expansion), hence the theoretical steam consumption per unit of work is greater the later the cut-off occurs, as shown by the ordinates of the curve in Fig. 92 {h) . (3) Evidently, dividing the theo- retical water rate per h.p.-hr.. Fig. 92 (6), by the percentage of steam not condensed. Fig. 92 (a), will give the true consumption at the various cut-offs. The values of the actual "water rate," ob- tained in this way, are shown by the lower curve in Fig. 92 (c). Similar " water-rate " curves can be drawn by using data obtained by direct engine test, in which the water per i. h.p.-hr. is measured with engine operating under different loads (i.e., different cut-offs). Usually the water rates are plotted with respect to power output instead of cut-offs. (b) Inspection of the water-rate curve makes it evident that, * This is for large four-valve engines having little leakage. See " Engine Tests," by G. H. Barrus. 30 40 50 J^ so arranged that, as the valve moves to . ^If'^— ^ the right in the figure, the edge / opens simultaneously with the main steam edge y. The exhaust is single-ported. Considering the valve as moving to the right, the phases of opening of the steam edge are: (i) ''Double-ported'' action while edges / and y open at the same rate. This continues until the auxiliary port a is wide open. (2) With movement continuing, Fig. 152 (&), the opening at y increases but that through a remains constant, ^ (a) ^ £ (b) Fig. 152. — Allen Valve. 290 HEAT-POWER ENGINEERING i.e., the opening is ''single-ported plus a constant.^' This con- tinues until a' in Fig. 152 (c) becomes throttled by the exhaust edge of the valve seat. (3) As the opening at a' is then decreasing (as the valve continues to the right) at the same rate as that at edge y is increasing, the effective area: .remains " constant.'' (4) If the movement is sufficient to completely close a', the valve becomes " single-ported.'' Now if the valve returns to the left to close, the effective openings will decrease in the reverse order. The openings of the steam edge of an ordinary valve are shown by the sectioned part above the steam-lap line of the elliptical diagram in Fig. 139. This is also shown (somewhat distorted) by the light line in Fig- 153- The heavy lines in this figure show the character p. ^ "of the openings when an Allen valve, like that just described, is used. Note that the smaller openings are affected more than the larger ones. Piston valves similarly arranged have been used (Armington- Sims valve). (e) The Sweet Valve shown in Fig. 154 is another valve hav- ing an auxiliary port. This valve is a rectangular piston valve which slides be'tween the valve seat and a "balance plate," which latter is supported by distance pieces so as to just clear the valve. The face of the balance plate is similar to the face of the valve seat. All sliding surfaces are scraped to give sufficient clearance for free movement of valve but not enough to permit of appreciable leakage of steam. The valve has separate auxiliary ports a at each end, which causes double- ported action through at least part of the opening of the valve. Referring to Fig. 155, it is seen that as the valve moves to the right the phases of opening of the steam edge are the same as those of the Allen valve; thus there is (i) " double opening," with y and /opening together; (2) "single-ported plus a constant," when / becomes greater than a; (3) " constant," when a is being closed by the exhaust edge of the valve seat at same rate that y is opening; and (4) " single-ported," when a is entirely closed by THE VALVE GEARS OF STEAM ENGINES 291 the exhaust edge. The areas during closure decrease in the reverse order. The auxiliary port, or another one, may be so arranged as to assist during the exhaust. (f) A combination of the Allen and Sweet arrangements gives quadruple openings (Woodbury valve) , and there are many Ea- Fig. 154. — Cylinder with Sweet Valve. Fig. 155. Other forms of such valves. For further discussion see text- books on Valve Gears. (g) Valve Friction is undesirable, not only because of the waste of power it causes, but because it may disturb the action of the governor, if one is used. The whole back of the simple D- valve is subject to full steam pressure, while the larger part of the under side is exposed to the exhaust pressure. The un- balanced pressure causes excessive wear and friction loss at the rubbing surfaces. To reduce this unbalanced pressure, various schemes of " balancing " are used. The simplest is the use of •292 HEAT-POWER ENGINEERING a piston valve which is perfectly balanced except for its weight. The Sweet type of valve is practically the equivalent of the piston valve in this respect. Some valves have " balance or equilibrium rings " on their backs (like that shown in Fig. 156) so arranged that the area within the ring is subject to exhaust pressure and is about equal to the area subjected to exhaust pressure on the under side. However, in such cases there should always be enough unbalanced pres- sure to maintain steam-tightness between valve and seat. (h) In case there should be entrapped in the cylinder a quantity of water more than sufficient to fill the clearance space, some part of the engine would break dur- ing compression unless some means of relief were provided. Sometimes "Relief Valves," which are somewhat similar to boiler safety valves, are attached to the cylinder ends. Sometimes the slide valve itself offers this relief; for example, the simple slide valve, with or without balance rings, and valves (like the Sweet) with pressure plates can lift from their seats and thus give relief. In such cases there should be springs or other devices to return the valve and bal- ance ring, or plate, to its proper position after the cylinder has been relieved of the water. Piston valves offer no such relief themselves, and engines with this type of valve should be pro- vided with special relief valves or other similar device. Fig. 156. — Valve with Balance Ring. 157. Valve Gears for High-Speed Engines, (a) The high- speed engine was briefly described on page 245. It is fitted with a "shaft governor," which controls the point of cut-off by vary- ing the position of the eccentric with respect to the crank. (b) Simple engines of this type usually have cut-off occur at about one- fourth stroke when operating under " normal load." The " range of cut-off " is generally from zero to five-eighths or three-fourths stroke, and the " range of load " is from "friction load " to 50 or even 100 per cent overload. It was shown on page 288 that if a simple slide valve is used to give cut-off as early as one-fourth stroke, certain features will THE VALVE GEARS OF STEAM ENGINES 293 be introduced which are undesirable in the ordinary case. Two of these are early release and early compression. (c) It so happens, however, that these phenomena are de- sirable in a high-speed engine. The early release is advanta- geous, as it allows more perfect drop to back pressure in the short time available. The early compression assists in causing a gradual absorption of the inertia forces; and an excessive ter- minal pressure can be prevented by increasing the ratio between clearance volume and piston displacement. With a given clearance volume and piston area, this ratio can be made large by using a short stroke, and with high rotative speed a short stroke is desirable in order to keep the piston speed down to safe limits; hence what are faults in the ordinary case make the short-stroke high-speed engine possible. (d) The excessive size of the valve-gear parts, which ordinarily occurs when a valve is designed for an early cut-off, as was shown in Section 155, may be overcome by increasing the length of port, which calls for a narrower valve opening and a cor- responding reduction of the laps, travel, and size'^f the eccen- tric; and these in turn are accompanied by a decrease in the friction and wear of the valve gear. The greater length of port may be obtained by using a wide valve, a piston valve, or a multiported valve. With the type of valve gear which is used on this class of engine, the travel of the valve varies with the cut-offs, and the earlier the cut-offs the more restricted are the openings of the valve. The valves may be designed to have open- ings ample for the latest cut-offs, and to have auxiliary ports added in such a manner as to assist during the early openings only, and to have little or no effect on the wider openings. Examples of these various types of valves have already been given. Sometimes special arrangements of linkage are employed to give wide openings with small travel, as in the case of the "High-Speed Corliss " engine to be considered later. (e) The friction of the valve is undesirable, not only because it decreases the mechanical efficiency of the engine and causes ivear, but also because it disturbs the action of the shaft gover- nor. This latter is especially true if the governor is of the Inertia type. The governor is also affected by the inertia of 294 HEAT-POWER ENGINEERING the valve gear ; hence high-speed engines use valves that are balanced and are of light weight. (f) In Fig. 157, which is a diagram of positions, i~j is one path, with respect to crank OP, over which the eccentric might be shifted by a shaft governor in adjusting the cut-off to meet the power demanded of the engine. When, in Fig. 157 (a), the eccentric is at i (with throw O-i and angle of advance 0:1) the cut-off is at about three-fourths stroke, for when the eccentric has rotated in the direction of the arrow to Ci (displacement Stvolje ■> Fig. 157. — Diagram of Positions. equal to steam lap) the crank pin is at Ci; when, in Fig, 157 (b), the eccentric is at 2 (with throw O-2 and angle of advance 0:2) the cut-off is about one-half stroke, for when the eccentric is at C2 the crank pin is at G; and when the eccentric is at J, diametrically opposite the crank, the cut-off is at C3. In this case the path i-j is so selected that it will coincide with Lai when the crank is in position OAi; hence the crank-pin positions (Ai, A2, and ^3) for the admissions corresponding to all cut-offs will coincide, that is, the admission is constant. With crank at OP, the horizontal distance between the eccen- tric and the steam-lap line aiCi is the lead. From the figure it is seen that Lead2 is less than Leadi, and that as the eccentric is shifted to give earlier cut-off the lead becomes less. The figure also shows that when the eccentric throw is O-i the maximum valve opening is LMi, when the throw is O-2 the maximum opening is LM2, and with 0-j this opening is L-j. Thus the maximum openings decrease as the cut-off is made to THE VALVE GEARS OF STEAM ENGINES 295 occur earlier. The valves are therefore usually designed to have proper opening at latest cut-off when operating as a single- ported valve and to be multiported when early cut-offs occur. If the exhaust-lap line is added to the diagram of positions, Fig. 157, and the crank positions are determined for exhaust events corresponding to the different points of cut-off, it will be found that as cut-off is made to occur earlier the release and compression are also made earlier. Thus with early cut-off Fig. 158. Fig. 159- there is greater compression than with late cut-off. Fig. 158 shows how these events vary and affect the form of the ideal indicator diagram, and Fig. 159 is an actual diagram obtained from a high-speed engine. From the foregoing it is seen that the following general state- ment can be made: As the eccentric is shifted from the outer to the inner position, cut-off, release, and compression are made to occur earlier and the maximum opening is decreased. I Fig. 160. Paths of Swinging Eccentric. Fig. 161. Instead of shifting the eccentric over a straight path, it can be swung about a pivot in the governor case or flywheel. When an inertia governor (Fig. 130) is used with external valve, the eccen- tric center will be moved over a circular path, as in Fig. 160, with 296 HEAT-POWER ENGINEERING pivot opposite the crank. When the ordinary centrifugal gover- nor is used, the eccentric may be pivoted on either side of the shaft with respect to crank, hence its path may be that in Fig. 160 or that in Fig. 161. These curved paths approximate the straight one in Fig. 157. The admission will vary as the eccen- tric position is changed, and the character of the variation depends on the curvature of the path. (g) The various valve-gear diagrams can be constructed in the usual manner, taking each position of the eccentric inde- Fig. 162. — Valve Diagrams for Variable Eccentric Valve Gear. pendently. The diagrams for the different eccentric positions may be drawn separately, but usually they are superimposed on one another, as in Fig. 162, which corresponds to Fig. 160. (h) At any one cut-off the valve events can be equalized in the manner mentioned in Section 151 (b). In some cases it is THE VALVE GEARS OF STEAM ENGINES 297 possible to approximate the equalization in all positions of the eccentric by using a special arrangement of rocker arm or guide for the eccentric-rod pin. 158. General Characteristics of Independent Cut-off Gears. (a) If an engine operates at a constant speed, as most engines do, it is desirable to have the admission, compression, and release remain constant, no matter how the cut-off varies. It has been seen that the simple valve with shifting eccentric does not give this desired constancy of all these events, nor does it give suf- ficient opening and sharp closure when cut-off is early in the stroke. If, however, instead of a single valve, two or more are used, with two independent sets of valve gear, it is possible to avoid some or all of these difftculties. Owing to the complications and extra expense involved with such arrangements, they are not often used on the small high-speed types of engines. They are quite common on larger and longer stroke, medium speed engines. (b) In general the gear having the two valves may be ar- ranged in either of two ways: (i) Each valve may control one pair of conjugate events; thus, one valve, having a fixed eccen- tric, may operate the release and compression, while the other valve takes care of the admission and cut-off, the latter event being changed by shifting the eccentric by a shaft governor, as in the case of the valve gear used on high-speed engines. In this case, separate valve diagrams would be drawn for each pair of conjugate events; that for the steam events would be con- structed the same as for the simple-shifting eccentric gear ; that for the exhaust events would be constructed the same as for any case in which the crank positions for the opening and clos- ing of the exhaust edge are given, together with the maximum width of opening desired. This arrangement will not be con- sidered further. (2) In the other arrangement of the gear, one valve, which will be termed the main valve, controls the admis- sion, compression, and release, and is driven by a fixed eccentric (" main eccentric "). The other valve operates the cut-off only, and will be called the cut-off valve. It is an intercepting valve, being located between the main valve and the source of steam supply. It may slide on a separate valve seat, or it may ride on the back of the main valve, in which case it is called a " riding " cut-off valve. 298 HEAT-POWER ENGINEERING The variation in cut-off may be accomplished in three ways: (a) by changing the lap of the cut-off valve, (b) by changing the position of the cut-off eccentric with respect to the crank, and (c) by a combination of (a) and (b). The range of cut-off on medium-speed engines is usually from zero to five-eighths or three-fourths stroke. Under normal load simple engines usually cut-off at about one-fourth stroke. (c) In all the gears having a cut-off valve of the intercepting type, the main valve or valves (operated by the main eccentric) control the admission, release, and compression. Referring to Fig. 144 it is seen that the line OQ bisects the angle formed between OR and OK produced; hence, in order to determine [the proportions of the main valve and its eccentric, proceed as follows: The two conjugate events (R and K), which can be decided upon initially, fix the angle of advance of the main eccentric, for, in the Bilgram diagram. Fig. 163, OQi must bisect the angle Diagram of openings Fig. 163. Fig. 164. between R and K (produced). After drawing the lead line L, and the arc W for maximum opening, the steam lap is determined by drawing the lap circle tangent to W and L in the figure, the center, Q, being on OQi. Having located Q, the exhaust-lap cir- cles can then be drawn. The diagram is now complete and all dimensions for the valve and eccentric have been found. The cut-off of the main valve is unimportant, provided it is at least as great as the latest given by the cut-off valve. Compression, of course, can be equalized by using unequal exhaust laps. The diagram of openings of the main valve, which is that part of the elliptical diagram which lies above the steam lap, S.L., (for the H.E. of the valve), is shown in Fig. 164. (d) In all valve gears in which there is a separate cut-off THE VALVE GEARS OF STEAM ENGINES 299 valve it is necessary that this valve open before the main valve does, as the latter controls the admission. To provide for this, it is necessary in many instances to have negative lap on the cut-off valve and large angle of advance, a', of the cut-off eccentric {a may even be greater than 180 degrees in some instances). In the general case the constructions of the various valve diagrams for negative lap and large angle of advance are identical ZEUNER BILQRAM Fig. 165. with those previously described; in each case the angle of ad- vance is located in exactly the same manner, and the negative lap is laid off opposite the positive lap; the openings are then equal to the displacement plus the negative lap, and the closures equal the displacement minus this lap. With negative lap the valve when central is open, hence closure must occur after the central position has been passed, and opening takes place before that position is reached. Figs. 165 (b) to .(e) show the various valve diagrams for angle of advance greater than 90 degrees, and Fig. 165 (a) gives the actual position of the eccentric with 300 HEAT-POWER ENGINEERING respect to the crank when the latter is on dead center. The lengths of the section lines show the widths of valve openings. The generating point in the elliptical diagram will move around the ellipse in a counter-clockwise direction if the angle of advance is greater than 90 degrees, as it is in Fig. 165. As before, the part of the elliptical diagram lying above the steam- lap line constitutes a diagram of openings. The cut-offs at one point in the stroke can be equalized by using unequal laps. (e) Referring to Fig. 165 (e), it is seen that the cut-off can be varied either (i) by altering the size of the lap circle (which may even be made positive), or (2) by changing the angle of advance, a'. Both methods are used in practice. A shaft governor may be used to automatically change the angle of advance by turning the cut-off eccentric about the center of the shaft on which it is loosely mounted. 159. Independent Cut-off Valve with Stationary Seat. Fig. 166 shows diagrammatically an arrangement with cut-off valve C riding on an independent valve seat between the main valve M and the steam pipe. The main valve is driven by a fixed eccentric. It controls the admission, re- lease, and compression, and is designed in the manner outlined in Section 158 (c). The cut-off valve is driven by an inde- pendent eccentric and controls only the one event. The cut-off can be changed in either of two ways already mentioned. Case I. — The lap of the cut-off valve may be altered by any of the following methods: (i) The valve may be in two parts, mounted on the valve stem with R.H. and L.H. threads respectively. By turning the stem, the distance between the ends, and consequently the laps, can be varied. With this arrangement, as in Fig. 167, the ad- justment is made by hand, and the point of cut-off for the setting can be read on the indicator, which is moved by a nonrotating nut on the valve stem. It is difficult to arrange a governor to make the adjustment with this arrangement, as several revolutions of the valve stem are required to accomplish the full range of cut-off. THE VALVE GEARS OF STEAM ENGINES 301 -Indicator Sqnare.Nut R.H. Tha. st,.' i ,, ^ /L.H. -Thd. Fig. 167. (2) Fig. 168 shows the back of another arrangement in which the edges of the valve and ports are obUque. On the back of the valve is a rack with which a pinion, on the valve stem, engages. By turning the stem the valve may be raised or lowered (as viewed in the figure), thus changing the distance be- tween its edge and that of the port. ]^ Va:lve »I -Neg. Lap Fig. 168. Fig. 169. (3) Fig- 169 shows a somewhat similar arrangement, except that the valve face and seat are cylindrical surfaces. The valve is fastened to the stem, so that by turning the latter the lap is changed. The arrangements shown in Figs. 168 and 169 can be controlled by a fly-ball governor, which can be connected to an arm on the valve stem. Case II. — The angle of advance may be changed, as in Fig. 170, in which M is the main eccentric, o, J and f are the positions of the cut-off eccentric for those cut-offs, X is the " range angle ** through which the governor has to turn the eccentric on the shaft, ao' is the maximum angle of advance of the cut-off eccentric, and aa' is that for three-fourths cut-ofT. Fig. 171 shows for this case the diagram of openings of the cut-off valve (dotted lines) superimposed on that for the main valve (heavy lines), and the sectioning shows the effective open- ing from the time of admission of the main valve to the closure of the cut-off valve at one-fourth stroke. - The arrangement of valves shown in Fig. 166 is not satisfac- tory, as with early cut-offs the space beyond the end of the main 302 HEAT-POWER ENGINEERING Fig. 170. DIAGRAM OF OPENINGS Fig. 171. valve is clearance space during the part of the expansion preced- ing the closure of the main valve. 160. Riding Cut-off Valves, (a) Instead of having a separate seat for the cut-off valve, this valve may ride directly on the back of the main valve (or within it, if piston valves are used) and perform its functions with respect to a port in that valve. There are several such arrangements possible. One, the Buckeye Gear, is in effect the exact equivalent of the arrangement de- scribed as Case II above. The arrangement of valves in this gear is given in Fig. 172, both valves being shown central with' respect to the ports. The , ^SieamXap {gjtliaustXap^ik^ |_>n^Neg. CO. Lap^ Cylmder Fig. 172. cut-off valve has negative lap equal to the amount it is open in the figure with respect to the main valve. The main valve is a box filled with live steam, practically a reciprocating steam chest. It is an " internal " valve, taking steam from the inside and exhausting at the ends. The cut-off valve rides inside the THE VALVE GEARS OF STEAM ENGINES 303 main valve and is "external"; its negative lap is of constant amount. Its valve stem passes through that for the main valve, the latter being hollow. The main valve is driven by a fixed eccentric, and controls admission, release, and compression. The cut-off valve is driven by an eccentric which is controlled by a shaft governor which turns the eccentric about the center of the shaft, thus varying the angle of advance, a', as in Fig. 170. (b) The arrangement of the rockers which guide the eccentric- rod ends is shown in Fig. 173. The main rocker ab is pivoted at b Fig. 173. to the frame of the engine. The cut-off rocker cd is pivoted at its middle e to the middle of the main rocker. With this special arrangement of rockers, it is seen that the displacement (5) of the center of the cut-off valve with respect to the center of the main valve is given by the distance between a and c, which is the same as that between b and d. Evidently, then, the motion of the cut-off valve with respect to the main valve is the same as that of c with respect to a, or opposite to that of d with re- spect to b. Since & is a fixed point, it follows that the motion of the cut-off valve with respect to the main valve is the same as that of a simple valve with respect to a fixed seat. The distance the cut-off valve travels with respect to the main valve remains constant, no matter how the cut-off and phase relations of the two valves are altered by changing the angle of advance of the cut-off eccentric. Thus this arrangement is equivalent to Case II of Section 159, but avoids its faults. (c) In other " riding cut-off " gears, this peculiar arrange- ment of rockers of the Buckeye gear is not used, but both valves receive motion direct from their respective eccentrics. The general arrangement of the valves is shown in Fig. 174, in which both valves are external. The main valve has a false 304 HEAT-POWER ENGINEERING end B, the only purpose of which is to provide an edge F, with respect to which the cut-off valve opens or closes. Each valve is driven by its own eccentric, the location of which is shown in Steam Lap Fig. 174. Crank | tt|;>^^'~Maiii Ecc. cb /j^-Main EcC. FT* ^C.O.-Ecc. kW Rp Relative Ecc. Fig. 175. Fig. 175. The main valve controls the admission, release, and compression, and is designed as in (c) of Section 158. To analyze the action of the cut-off valve, its motion with respect to the main valve must be considered. (d) As the crank revolves, not only do the eccentrics rotate about the center of the shaft, but they rotate about each other. That this last statement is true can be seen by turning Fig. 175 about 0, and it will be noticed that, at the same time, the cut-off eccentric rotates about the main eccentric and in the same direction as that in which the crank turns. Evidently, then, the motion of the cut-off valve with respect to the main valve is produced by the rotation of the cut-off eccentric about the main eccentric; hence, this motion is equivalent to that which a simple valve would have, with respect to a fixed seat, if driven by an eccen- tric having throw equal to the distance between the eccentric centers (Fig. 175) and with angle of advance equal to 6. This imaginary eccentric will be called the " relative eccentric " R. Thus, to analyze the action of the cut-off valve with respect to the main valve (its moving seat), the position of the relative eccentric must first be determined, after which the valve diagrams would be constructed in the usual manner, but using the throw and angle of advance of this eccentric. (e) The Meyer Valve Gear has the same arrangement of valves as that shown in Fig 174. The cut-off eccentric usually has a 90-degree angle of advance, that is, it is located opposite the crank. The cut-off is varied by changing the lap of the valve by the method shown in Fig. 167. (f) The Russell Valve Gear is similar in character to Figs. 174 and 175, but the cut-off is altered by changing the position THE VALVE GEARS OF STEAM ENGINES 305 of the cut-off eccentric. This adjustment is made by a shaft governor which turns the eccentric on the shaft to vary the angle of advance. Fig. 176. Fig. 177. The valves are shown in Figs. 176 and 177. The main valve operates the admission only. The exhaust is controlled by sepa- rate triple-ported valves of the Corliss type shown in Fig. 177, 3o6 HEAT-POWER ENGINEERING The cut-off valve is made triple-ported, as is its seat on the back of the main valve. The arrangement of eccentrics is similar to that shown in Fig. 170. (g) The Mclntosh-Seymour Gear has separate main, cut-off, and exhaust valves, of the "gridiron" type, working across the cylinder, as shown in the section in Fig. 178. These six ^alve. Fig. 178. valves are driven by arrangements of rockers and toggles in the linkage, which distort the movements, so that after the valves are closed they have little motion; hence the friction and wear are reduced to a minimum. The main valve receives its motion from a fixed eccentric, and the cut-off valve is driven by an eccentric which is turned about the shaft by a shaft governor to adjust the cut-off. Fig. 100 (p. 247) shows the general arrangement of the valve gear and the rocker shafts, which latter are given an oscillatory motion by the eccentrics acting through bell cranks. The arrangement of eccentrics is similar to Fig. 170. Fig. 179. Fig. 180. Fig. 179 is the distorted elliptical diagram for the main valve, with the opening diagram shown by bold lines. Superimposed on TEE VALVE GEARS OF STEAM ENGINES 307 the latter are lines showing the closure of the cut-off valve. Fig. 180 gives the distorted elliptical diagram for the exhaust valve. It is seen that the valve movements after closure are much less than with ordinary valve gears. (h) There are many other possible arrangements of riding cut-off gears, a great number of which are in actual use. 161. Gears with Oscillating Valves, (a) Instead of having the slide valve flat, it may have a curved face, as in Fig. 181, in which case the valve oscillates about center 0'. The displace- ment X of the eccentric-rod pin U from the Y-axis is always equal to that of the eccentric with respect to the vertical axis through the shaft. This valve is substantially equivalent to the ordinary flat D- valve, and would be designed or analyzed in Fig. 181. — Oscillating Valve. Fig. 182. the same manner, using the same valve diagrams. These dia- grams show the true positions of the crank for all events; but the laps, displacements, and openings are chordal, that is, would be measured as chords instead of as arcs. (b) This arrangement of valve introduces very long steam passages, extending from the center to the ends of the cylinder, and this is not conducive to economical performance, as has already been seen. (c) A better arrangement is one in which there are four oscillating valves, as in Fig. 182, each of which performs the single function of one of the four edges of the single valve. In the figure the outer edges of the two upper valves control the steam events, and the inner edges of the lower valves operate the exhaust events. The other edges of the valves perform no function. The chordal laps would be the same as in the case of the single valve of Fig. 181. The valves shown in Fig. 182 are of the " Corliss " type. With this arrangement the steam and exhaust passages are very short and direct, thus the clearance volume and surfaces are relatively small. 3o8 HEAT-POWER ENGINEERING (d) All four valves may be driven by the single variable eccen- tric with shaft governor, as is common with high-speed engines. It is better, however, to connect the steam valves in this manner, and to drive the exhaust valves by a separate fixed eccentric, so that release and compression will remain constant. (e) One fault of most valve gears is that the valve has large movement after it has closed. To reduce wear and friction, the movement should cease as soon as the overlapping is sufficient to prevent leakage. Also, it is desirable to have more rapid imovement of the valve after it opens than is obtained with the Imagrinary Eqaiva;lent Eccentric Closed , N^ O^ii Open Closed Fig. 183. simple gear. Both results can be effected by using links and rockers so arranged as to give the valve the desired motion. One such arrangement is shown in the upper right-hand corner of Fig. 183. Engines using this type of gear may be called High- Speed Corliss Valve Engines, or positive cut-off Corliss engines. (f) At the left of Fig. 183, the edge s of the steam valve is shown even with the port edge with which it opens or closes. Let g' be the desired (small) angular movement after closure, and /' be the (large) angle after opening. The steam arm „ (292) p^, = \p,{^±^)-p,\^K, . (293) in which i^T is a factor introduced to correct for the loss due to the omission of the toe of the H.P.-diagram. It ranges from 0.9 to i.o, the latter value being for the complete expansion in the high-pressure cylinder. Substituting for pmH and pmR in Eq. (291) and solving for pji, results in the following expression for the receiver pressure which will give the desired distribution of work: (f ) With p^ known the ratio of expansion in the low-pressure cylinder can then be found. Since ^l = ?7^ = T^ (see Fig. 215) and since pD pi rrp Vc pD it follows that (I) rT. (295) Pn. V (g) This analytical method not only applies to two-stage compound engines but also to multiple-expansion engines having any number of expansion cylinders. Thus, if the work is equally distributed among x cylinders (for example, rx: = 3 in Fig. 216), the work in the first cylinder is 1/x th of the total. Then the pressure {pn^ in the first ^^' ^^ receiver can be found from Eq. (294), with x substituted for n. The second cylincier receives steam at this same receiver pres- \ 336 HEAT-POWER ENGINEERING sure ipRi) ; and this cylinder and the succeeding ones can be considered as constituting another engine with initial pressure equal to pR^ and with (x — 1) cylinders. This engine will do (x — 1) parts of the work of the whole engine, and this second cylinder (considered now as a high-pressure cylinder) will do 7 -rth of this work. Then the pressure (pR.) in the second [x — I) receiver can be found by again using Eq. (294) with (x — 1) sub- stituted for n and by making such other changes as will be apparent. Pressures in succeeding receivers (if any) can be found in like manner. (h) In a triple-expansion engine, after the ratio R of low- pressure cylinder to high-pressure and ratio Rm of LP. to H.P. have been selected, it is evident (since Vl= Fjyi^ and Vi=VhRih) that the cylinder ratio Rli of L.P. to I. P. is Rli = ^ = ^. ..... (296) (i) Following (f) of this section, the ratio of expansion in the low-pressure cylinder is -{^h •- (^97) Also, by analogy, r^ = {'t—j^t^i in which rrp^ is the total expansion in the intermediate-pressure and the low-pressure cylinders com- fpR \ bined. After rL is known, r^^ can be computed from r-^^ = r^, ( — -M- Then by comparison with Eq. (290) it is seen that the ratio of expansion in the intermediate- pressure cylinder is The ratios of expansion in a quadruple-expansion engine would be determined in a similar manner. 170. Cylinder and Expansion Ratios Used in Multiple-Ex- pansion Engines, (a) In general the greater the total range of pressures in the engine the larger should be the cylinder ratio and the expansion ratio. Thus high-pressure engines have rL CONVENTIONAL INDICATOR DIAGRAM 337 larger ratios than low-pressure engines, and those condensing have greater ratios than those which operate noncondensing. Practice varies widely and only the average values can be given here. (b) Modern compound engines usually operate with steam pressures between 125 pounds and 150 pounds gauge. In many instances, however, much higher and lower values have been used. Stationary engines of this type usually have cut-offs in the high-pressure cylinders between 0.25 and 0.4 of the stroke under normal load. With late cut-ofT a smaller engine can be used for a given power than with early cut-off; but the conse- quent saving in " first cost " of engine may be more than balanced by loss in efficiency and greater cost of operation. Cylinder ratios customarily used are about as follows: CYLINDER RATIOS FOR COMPOUND ENGINES. Cylinder ratio 2^ 3^ 4 4I Gauge pressure, noncondensing 100 120 Gauge pressure, condensing 100 120 150 Dividing the cylinder, ratio by the H.P. cut-off fraction (0.25 to 0.4) gives the total ratio of expansion. What the best cyl- inder and expansion ratios are, is still under discussion. Some advocate cylinder ratios even as large as 6 or 7 and remarkable economies have been obtained with such.* (c) The ratio of expansion is sometimes fixed by first assum- ing the pressure drop at release. If this drop is added to the L.P. exhaust pressure, the pressure {p^ in Fig. 215) at release is obtained. Then, considering the expansion to be hyperbolic, the total ratio of expansion on the conventional diagram is Pd which is approximated more or less closely in the actual case. If the expansion ratio (rn) in the high-pressure cylinder is then selected, the cylinder ratio is R = 'f (300) *r =6.25 Cross Compound Corliss. Am. Electrician, June, 1903. vt = 7-3 Fleming Four-valve. Trans. A. S. M. E., Vol. XXV, page 212. I'T = 6 .4 Tandem Compound Corliss — Barrus' Engine Tests, page 185. r-f = 6.2 Edison Waterside Station, New York. Power, July, 1904, page 424. Also see papers in Trans. A. S. M. E, 338 HEAT-POWER ENGINEERING After the receiver pressure, which will give the proper distri- bution of work between the cylinders, has been determined, the drop in pressure at H.P. release should be checked. (d) Modern triple-expansion engines usually operate with steam pressures from 150 pounds to 180 pounds gauge or even higher. The pressure at L.P. release in condensing marine en- gines is commonly about 15 pounds per square inch absolute under normal load, and in stationary engines it is about half this value. As before, the total expansion ratio (r^) can be found approx- imately by dividing the initial pressure by the L.P. release pres- sure (considering the expansion to be hyperbolic) ; or it can be obtained from economy curves of similar engines operating under similar conditions, when ratios have been used as abscissas. The H.P. cut-off in marine engines is usually from 0.55 to 0.7 of the stroke and in stationary engines is much earlier. The H.P. expansion ratio (rn) is the reciprocal of this cut-ofT ratio (neglecting clearance). With r^ and th known, the volume ratio of high-pressure to low-pressure cylinder is R = — . If the strokes are equal, as is almost invariably the case, the ratio of piston areas will be the same as the volume ratio. If the conventional diagrams of the various cylinders have sharp toes, the work will be equally distributed among the cylin- ders if the cylinder volumes (or piston areas) are such that TT T — = y (in which the letters refer to the high-, intermediate, and low-pressure cylinder volumes, or areas). In such a case the intermediate cylinder volume (or piston area) is found from / = Vi7x L. In the actual case, because of departure of the real indicator diagrams from the theoretical and because of cylinder conden- sation, cushion steam, etc., the intermediate-pressure cylinder is made a little smaller than this equation would give. Seaton* states that in marine practice the intermediate cylinder volume (or piston area) is about as given by the following equation : ^ = — y:\ — ^^^^^ * Seaton's "Manual of Marine Engineering"; or Seaton and Rounthwaite's "Pocket Book of Marine Engineering." CONVENTIONAL INDICATOR DIAGRAM 339 Marine triple-expansion engines are proportioned about as follows : Initial pressure, abs 165 175 195 Ratio I to H 2 . 33 2.4 2.54 Ratio L to fl" 6.6 7.0 7.8 Total expansion ratio 11. 11. 7 13. (e) Quadruple-expansion engines usually operate with pressures from 175 to 225 pounds gauge. The L.P. terminal pressures and H,P. cut-off percentages are about the same as for triple- expansion engines. Thus the total expansion ratios are some- what larger than in the latter engines. If the ratios of adjacent cylinders are made equal, then H~ h~ h~ ^' in which /i and 1 2 refer to the first and second intermediate cylinders. From which it follows that Ii = R.H (302) I2 = RJi = R.'H (303) L = RJ2 = R.'H (304) Hence the ratio of adjacent cylinders (assuming -73. known) is ^-V^|. (305) or the ratio of low-pressure to high-pressure cylinder (assuming Rx known) is R = ^=^RJ' (306) After Rx, H, and L are known, /i and 1 2 follow from Eqs. (302), (303). These values of /i and I2 should be reduced some- what, for the same reasons that were given in the case of the triple-expansion engine. In quadruple-expansion marine engines the cylinders are about in the following proportions: — i : 1.8 : 3.6 : 7.8. A study* of 14 different quadruple-expansion engines, with pressures about * H. H. Suplee. Trans. A. S. M. E., Vol. X, page 583. 340 HEAT-POWER ENGINEERING 1 80 pounds per square inch, showed the average cylinder propor- tions to be 1 : 2 : 3.78 : 7.70; or nearly i : 2 : 4 : 8.* 171. The Theoretical Indicator Diagram of Multiple-Expan- sion Engines with Clearance. In the foregoing discussion clearance was neglected. If clearance is considered, the results will be changed somewhat. In such cases the analytical method is a little complicated, hence the graphical method is generally the best one to use. This method needs no explanation. In the theoretical cards of a compound engine with clearance, as shown in Fig. 217, ^1 h z- ^- ^H-H / < It r-X:^^ Fig. 217. the total ratio of expansion is Tt Ll+CIl the H.P. ratio of expansion is rn = Lh + CIh Ih + CIh ' the cylinder ratio is R = Lh' and the H.P. and L.P. cut-off ratios are respectively-^^ and -^r— - I^H J-^L 172. Effects of Changing the Cut-offs in the Respective Cylinders of Multiple-Expansion Engines, (a) In " regulating " the engine to make the power output equal to the demand, the steam distribution to the cylinders can be varied in several ways. (b) It has already been shown that the effect of making the L.P. cut-off occur later in the stroke (other things remaining the same) is (i) to lower the receiver pressure, (2) to increase the H.P. work, (3) to decrease the L.P. work; and vice versa. But (4) such change does not affect the total work of the engine if the toes of the diagrams are not lost, hence the engine cannot be regulated by changing merely the L.P. cut-off. (c) If the L.P. cut-off is fixed, and the H.P. cut-off is made to * For data relating to multiple-expansion marine engines, see Seaton's " Manual of Marine Engineering," Robertson's "Translation of Bauer's Marine Engines and Boilers." For all types of multiple-expansion engines, see Heck's "The Steam Engine," Vol. II, pages 506-9, and Gebhardt's "Steam Power Plant Engineering." CONVENTIONAL INDICATOR DIAGRAM 341 occur later, there results (i) an increase in the receiver pressure (Fig. 218), (2) a greater increase in the L.P. work than in the H.P. work. Making H.P. cut-off occur earlier produces the reverse effects. Com- pound engines can be regulated by having an automatic governor control only the cut-off in the high-pressure cylinder. But in such case, if there is much change in the load on the engine, the L.P. cut-off should be ad- justed by hand to equalize the distribution of the load between the cylinders. (d) If the initial, receiver, and exhaust pressure lines on a PV-diagram for a compound engine are extended from one hy- perbolic expansion line to another, as from cD to c'D' in Fig. 219 (a), it will be found (i) that the expansion ratios in the cylinders Fig. 218. p, b c\ \^ \ \ W p. a c\ \d'. B c\ ^k^ A d^ ^"--..D 4 n Fig. 219. remain unchanged; and that, in consequence, (2) the propor- tionate distribution of work between the cylinders also remains the same. In Fig. 219 (b) it is seen that the high and low cylinder volumes (Vh and Vl) are such that the expansion lines cd and CD in the two cylinders are complete and continuous. If the cylinder volumes are related thus, and if the cut-offs are advanced pro- portionately (so that c'd^ a.nd CD' in Fig. 219 (6) are on the same hyperbola), the distribution of work can be shown to be in the same proportion as in the case of complete expansion just dis- cussed; and further (from this), that (3) the toe areas {Xh and Xl) lost will be in this same proportion. These same state- ments are also true in case the cut-offs are decreased propor- tionately as in Fig. 220. In this figure, however, it is seen that the diagrams have '' loops " Xr and Xl, which represent nega- ■ ■\ O 342 HEAT-POWER ENGINEERING tive work. Evidently the cut-off should not be earlier than c, if good economy is important. With such arrangement the automa.tic governor can be made to change the cut-off equally in the two cylinders and the proper balance of work will be always auto- matically maintained. The tandem com- pound engine in Fig. 107 is an example of this case. If the L.P. toe loss is greater than the similar H.P. loss, it can be shown that to maintain the same relative balance of power between the cylinders, the L.P. cut-off must vary more rapidly than the H.P. cut-off; thus as the power is in- creased the receiver pressure must be raised. (e) If the cut-offs (or expansion ratios) in the two cylinders remain constant, the power of the engine may be decreased by throttling the steam, and in this case the distribution of power between the cylinders remains in substantially the same proportion. That this is true may be seen from inspec- tion of Eq. (294), in which pR is seen to be practically propor- tional to pi (since all other quantities are constants in this case, except the ratio P2/P1, which is so small a quantity that its change is negligible). This shows that the effect of throt- tling is substantially equivalent to changing the pressure scale of the diagram. (f) Because of the effect of clearance, " wire drawing," cyl- inder condensation, etc., the real diagrams differ greatly from the theoretical ones, hence the conclu- sions just given can be used only in a very general sense in actual cases. 173. Theoretical PV-Diagrams of a Tandem Compound Engine with Receiver of Finite Volume, and having Clearance, (a) Fig. ^^* ^^^* 221 shows the PV-diagrams for a tandem compound engine which has clearance volume and finite receiver volume. The CONVENTIONAL INDICATOR DIAGRAM 343 abscissas of both the H.P. and L.P. diagrams are the strokes (same for both cyHnders). OF is the hne of absolute zero for volumes in the low-pressure cylinder, and oy is the similar line for the high-pressure cylinder. In the latter cylinder abc is the admission line, cd is the expansion line (with respect to axes oy and oO), ddi is the drop in pressure when the H.P. steam is released to the receiver, diei is the period when the high-pres- sure cylinder is exhausting into the receiver alone, and eief'is- the period during which the high-pressure cylinder is exhausting into both the receiver and the low-pressure cylinder; fg shows the period when the high-pressure cylinder is exhausting into the receiver, after cut-off has taken place (at C) in the low-pressure cylinder; and ga is the compression into the H.P. clearance space (and is therefore asymptotic to oy). Evidently if O'Y^ is drawn to the right of oy at a distance {Vr) equal to the receiver volume (measured to the same scale that is used for the H.P. volumes) , fg will be a hyperbola with axes 0' F' and O'O. Dur- ing the period ef of the H.P. exhaust the low-pressure cylinder is receiving steam along the coincident line BC. After L.P. cut-off at C, the steam in the low-pressure cylinder expands according to CD, is exhausted along DEF, compressed along FA, and admitted along ABC from the high-pressure cylinder and from the receiver. Evidently CD and FA are hyperbolas with respect to axes Oo and OY. (b) These diagrams can also be constructed by the method given in the next section. 174. Theoretical PV-Diagrams of a Cross Compound Engine with Receiver of Finite Volume, and having Clearance, (a) In Fig. 222 (a) the H.P. and L.P. diagrams of opposite strokes are shown with true volumes as abscissas, and with the clearance and receiver volumes in proper proportion and relation for a single-acting cross compound engine with L.P. cut-off less than one-half stroke. It will be seen that the arrangement of dia- grams is similar to that in Fig. 212 {d), but with clearance and receiver volumes added. If the points in the stroke at which the valve events occur are known, the lines ahcd and EFA are easily drawn, but the points on the H.P. exhaust line and L.P. admission line are harder to find. The method of determining these will now be considered. 344 HEAT-POWER ENGINEERING (b) It will be convenient to have an auxiliary diagram, such as Fig. 222 (5), called a steam-distribution chart, which will / Y Fig. 2 2 2. show for each crank angle (ordinate) the volumes (abscissas) of steam in both the cylinders and in the receiver. If the motion of the piston is harmonic (as it is approximately) , the curves of CONVENTIONAL INDICATOR DIAGRAM 345 volumes displaced by the pistons are of course sinusoids, and can be easily constructed in the manner shown in the lower part of the figure. In the case under consideration, as the cranks are at right angles these sinusoids must differ in phase by 90°. The clearance lines {oy' and OY') are added to the chart; thus the distance from a point on a sinusoid to the clearance line gives the volume of steam in the cylinder for the corre- sponding crank angle. The percentages of stroke for all '' valve events " are sup- posed to be known, thus the abscissas of all events can be laid off on the PV-diagrams in Fig. 222 (a). Lines ahcd and EFA can be drawn at once, and efgha and BBiC can be drawn ten- tatively to show roughly the general shape of the diagrams. The exact lines will be found later. Then on the sinusoids, in Fig. 222 (6), the points for the valve events can be found by projecting downward from the PV-diagrams, or may be located more accurately by using the crank angles corresponding to the valve events. The points thus found are lettered the same as the corresponding points on the PV-diagrams, but are primed. (c) From h^ to c' in Fig. 222 {h) is H.P. admission, and from c to d' is H.P. expansion, with volumes varying according to the heavy abscissas to the right of the sinusoid between these points. The product PV is constant during this expansion (and its value can be found since Pc and Vc are known), hence the " PV-quantity " {PV)c may be taken as representing the whole process of expansion. Evidently the following broad statement can be made: General Proposition A: Between valve events (not neces- sarily in the same cylinders) controlling the weight of steam involved, the " PV-quantity " is constant; and when its value is known the expansion curve can be constructed. Thus, in this instance, dividing the PV-quantity {PV)c by different values of V gives the pressures to be used in plotting the expansion curves cd. (d) At d (and d') the steam with PV-quantity equal to {PV)c is released from the high-pressure cylinder and mixes with the receiver steam which has a PV-value equal to mn(PV)g, in which m and n are unknown coefficients, the value of which will be determined later. In such cases the following assumption is made : 346 HEAT-POWER ENGINEERING General Proposition B: The PV -quantity resulting from a mixture is [PF]. = S(PF) (307) Thus, after point e is passed [PV]e = {PV)c + mn [PV],, . . . (308) from which lPV]e can be found when mn [PV]g has been deter- mined, since (PV)c is already known. (e) The L.P. compression occurs from 7^ to ^ (and F' to A') with PV-quantity constant and equal to (PV)f, — the value of which can be easily found, since Pp and Vf, are given, — and with volumes varying as shown by the heavy dotted abscissas to the left of sinusoidal arc F'A\ At A (and at A^ and /) this L.P. cushion steam mi^jes with that in the receiver and high- pressure cylinder; hence the PV- value of the mixture is, from Proposition B, [^FL = [PF]e + (PF)f (309) Thus during phase gh and BBi the pressures may be found by dividing [PV]g by the volumes which are shown by the dotted abscissas between arcs g%' and A^B/. (f) After the H.P. exhaust valve has closed at h there remain in the receiver and low-pressure cylinder n parts of the steam that has been represented by [PF]^, and the rest, (i — n) parts, is used for compression in the high-pressure cylinder. Between Bi and C (and B/ and CO the PV-quantity of the steam in the low-pressure cylinder and receiver is n [PV]g in accordance with the following assumption : General Proposition C: If a weight of steam, having a cer- tain PV-quantity, is divided without change in pressure, the PV- quantity of the part is the same fraction of the original PV-quantity that its weight is of the original weight. For example, if one-half the steam involved is left in the cylinder and receiver, when the H.P. exhaust closure occurs at h or Bi (h^ or J5/), then'n = |, and the PV-quantity of this remaining steam has the value J [PFJ^,. Thus, between points Bi and C the PV-value is n [PV]g and the volumes are shown by the abscissas to the left of the sinusoidal arc between points Bi and C\ After the L.P. valve has cut off at C (and C') there are left in the receiver m parts of the steam which was represented by n [PV]g] hence, this receiver steam has a PV-value of mn lPV]g, CONVENTIONAL INDICATOR DIAGRAM 347 which continues constant until point a in the next cycle is reached. (g) In the simultaneous equations (308) and (309) all quan- tities are either known or can be determinable directly, except the bracketed quantities [PV]e and [PF]^; but these latter can be found by elimination. When these are known, the PV-diagrams can easily be completed. (h) If the engine is double-acting, and if it has equal PV-dia- grams at both ends of the cylinders, the solution of only one end is necessary. But if the diagrams are not equal, it is necessary to draw the steam-distribution chart for both ends of the cylinders. Then there will be four unknown PV-quantities, but there will be the following four simultaneous equations, from which the unknowns can be determined: \PVl = {PV), + m'n' [PV]', . . . (310) [PV], = [PV]e + {PV)f . . . . (311) [PV]\ = {PV)'c + mn [PV], . . . (312) [PF]', = [PF]'. + (PF)'p .... (313) in which the primed quantities are those for the cylinder ends not considered in the previous discussion. I Fig. 223. — Effect of Early Release (i) In the foregoing it has been assumed that release and admission occur at the ends of the stroke. If the engine is double-sicting and if the steam is released before the end of the stroke in the high-pressure cylinder, the L.P. admission line will suddenly rise, in case the L.P. cut-off has not already occurred; for this release suddenly increases the steam pressure in the re- ceiver from which steam is still being supplied to one end of the low-pressure cylinder. This is shown in Fig. 223, from which it 348 HEAT-POWER ENGINEERING is seen that, when the steam is released at di, there is a drop of pressure in the high-pressure cyhnder accompanied by a simul-. taneous rise at X in the low-pressure cylinder, until the pres- sures at X' and d\ are equal. This case can be analyzed by the method already given. (j) The case with cut-off later than half-stroke is somewhat similar to that discussed in (i) of this section and is illustrated in Fig. 224. Even if the H.P. release occurs at the end of the stroke (at di), there will be the sudden rise XX' on the L.P. admission line, as the low-pressure cylinder has not previously Fig. 224. — Low-pressure Cut-off later than Half-stroke. been cut off from the receiver. From X' to cut-off at C the low- pressure cylinder continues to receive steam from the receiver, while simultaneously the high-pressure cylinder is discharging steam into the receiver according to line ei^/. Evidently the pressures at points ei and X' are equal ; and the same is true of points ei and C. This case can be analyzed with the aid of a steam-distribution chart, in the same manner as that which has just been discussed in connection with the other cases. 175. Theoretical PV-Diagrams of Multiple-Expansion En- gines with Finite Receiver and Clearance Volumes, with Any Number of Cylinders and with Any Angles between Cranks (General Case). The methods just discussed in connection with the construction of PV-diagrams for compound engines can be extended to this perfectly general case. It is assumed that the initial and exhaust pressures are known, together with the vol- ume ratios of cylinders, receivers, and clearances, and that the CONVENTIONAL INDICATOR DIAGRAM 349 percentages of stroke (or crank angles) of the various valve events are given. The procedure is as follows: (i) Draw the cylinder, clearance, and receiver volumes in proper relative positions on the PV-diagrams. (2) Sketch as much of the H.P. and L.P. PV-diagrams as can be done initially. (3) Draw the sinusoids on the steam-distribution chart in a proper phase relation (considering the crank angles and '' se- quence " of cranks); locate the valve events; and by a system of section lining show the volumes connected between events (remembering that these volumes are not necessarily confined to those in one cylinder). (4) On the distribution chart: — (a) give the PV-quantities initially known, such as {PV)c and {PV)f in the previous cases; {h) in accordance with General Proposition C state the PV- quantities resulting from a separation of volumes (when not accompanied by change in pressure) as fractional parts of the quantity which is divided, as mn {PV)g', and (c) in accordance with General Proposition B, write equations for the PV-quan- tities resulting from mixtures. (5) Obtain the values of the fractional coefficients, m, n, etc. (6) Find the unknown PV-quantities by solving the simul- taneous equations, of which there should be the same number as there are unknowns. (7) Complete the construction of the PV-diagram, which can be done now that the PV-quantities are all known. The heavy lines in Fig. 225 show the PV-diagrams for a triple-expansion engine. The in- dividual diagrams were first ob- tained in the manner just outlined and then were combined with respect to a common axis of volumes as shown in this figure. 176. The Actual Combined In- dicator Diagrams of Multiple- Expansion Engines, (a) In Fig. 225 it is seen that the theoretical PV-diagrams (in heavy lines) overlap, that their expansion Fig. 225. 350 HEAT-POWER ENGINEERING lines do not fall on the same hyperbola, and that the sum of their areas is much less than that of the simple diagram abode. The overlapping parts of the diagrams do not occur simultaneously. The lack of continuity of the expansion lines is largely due to the difference in the amounts of cushion steam in the various cylinders; it is also due to the sloping and irregu- larity of the LP. and L.P. admission lines, and to earliness of the LP. and L.P. cut-offs compared with that in the high- pressure cylinder. The ratio of the sum of areas H, I, and L to area ahcde is the theoretical diagram factor in this case, and it is evidently much less than unity. (b) The actual indicator diagrams depart considerably from the theoretical. This is partly because of wire drawing during flow of steam through valves, receivers, and piping, partly be- cause of condensation or reevaporation in cylinders, receiver, and piping, partly from radiation and similar losses, partly be- cause the real expansion line is not hyperbolic, and may also be partly due to the withdrawal of the condensate collecting in " separating " receivers. In Fig. 225 the probable diagrams are shown dotted. (c) Given the actual indicator cards obtained from the en- &' s ■J — ' — ' — I Fig. 226. gine, as h and / in Fig. 226, they can be readily " combined," as shown by H and L, if the cylinder and clearance volumes are known. CONVENTIONAL INDICATOR DIAGRAM 351 The areas of diagrams H and L can then be found and the *' referred m.e.p." determined in the usual manner. After this, the actual diagram factor can be obtained by getting the ratio of these quantities to the area of the conven- tional diagram.* (d) On Fig. 226 the saturation curves, SS and 5'5', have been drawn. As the weights of cushion steam in the two cyl- inders are not the same, and because the condensate has been removed from the receiver in this case, there are unequal weights of steam in the two cylinders during the respective expansions, consequently saturation line S'S' lies to the left of SS. Fig. 226 also shows the quality curves xn and Xi, which are obtained, after the saturation lines have been drawn, by the same method that was described for simple engines. 176A. Clajrton^s Analysis of Expansion Lines, (a) By re- plotting indicator cards on logarithmic coordinates Clayton f has determined the expansion coefficients n for many engines. He found that such expansion lines were substantially straight (except when modified by leakage or faulty indicator practice which, if present, were revealed by the curvature); that the points of cut-off and other valve events could be accurately determined; and that, as in the ideal case (see (d), page 207), there appeared to be a definite relation between the quality {xc) at cut-off and the exponent of expansion {n) for each type of engine and condition of operation. For a Corliss non-condensing engine, without leakage, he found Xe = 1.245 w - 0.576 (313a) There was some variation with change of speed and pressure; but cylinder size and point of cut-off had little influence. Having determined n for the engine Xc can be computed, after which the water rate can be found. With the logarithmic coordinates the clearance volume can be determined quite closely, when there are no abnormal dis- turbances, by finding the origin which will give a straight line. * There are several diflferent kinds of diagram factors, each of which may be used to best advantage for some particular purpose. When the engine is consid- ered by itself, the definition previously used in the text is the one most commonly given. The A. S. M. E. Report of Committee on Standardizing Engine Tests defines the card factor in such manner as to include the cyUnder-feed losses be- tween engine and boiler. See Trans. A. S. M. E., Vol. XXIV, page 751. t Trans. A. S. M. E. 34, p. 17. Bulletin 58 and 65, U. of 111. Exp. Sta. CHAPTER XXI. PERFORMANCE OF STEAM ENGINES. 177. Steam Consumption, (a) Steam engines are governed by (i) throttling the steam, (2) by varying the cut-off, and (3) by combining (i) and (2). When the engine is governed by throttling (the cut-off re- maining constant), the available energy A£ per pound of steam theoretically decreases as the pressure is reduced. This is shown in the MoUier diagram, Fig. 227. Starting with initial pressure pu the associated heat A(2i, and back MOLLiER CHART prcssurc ph, thc available energy is AEi. In throttling to pressure p2 the associated heat remains unchanged, but the available energy per pound ^ is reduced to AE2, and consequently Fig. 227. more steam, in the ratio — ^r |, must be used to develop one i.h.p.-hour. Evidently the actual throt- tling engine gives the best economy only under maximum load, hence the water-rate curve will resemble cd in Fig. 228. It is found that with this type of governing, the curve of total consumption {ah) is practically a straight line, and this relation is commonly called Willans' Law. When two points on this line, or one point and the slope, are given, the line can at once be drawn. Then dividing ordinates by corresponding abscissas gives the simultaneous values of the water rate, and these values can be used for plotting the water curve. With greater ratio of expansion, less steam is used for a given output, hence for such cases the curves a'b^ and c'd' in Fig. 228 would lie below the others. (b) When the engine is governed by varying the cut-off, the water-rate curve resembles efg in Fig. 229, the reasons for which were made clear in Section 125. To this figure has been added 352 PERFORMANCE OF STEAM ENGINES 353 the curve cd of Fig. 228, the point d of course coinciding with g. Thus It Is seen that cut-off governing gives better results than throttle governing except at the maximum load. The product of abscissas by ordlnates gives the total steam consumption, plotting which gives the curved line hij as the Curve of Total Water Consumption for cut-off governing. Evi- dently point i, where a line drawn from becomes tangent to hij, determines the abscissa for the lowest water rate, for that point has the smallest ratio of ordinate to abscissa. (c) The y intercept Oy of the T.C. curve represents the weight of steam used when no I.h.p. Is being developed. It Is the weight which furnishes heat equivalent to the losses from condensation, leakage, and radiation. Curves similar to Figs. 228 and 229 might have B.t.u. as ordl- nates; and m.e.p's, cut-offs, ratios of expansion, or d.h.p's may be Fig, 228. used as abscissas. When abscissas are d.h.p., then the y Inter- cept represents the consumption due to engine friction In addi- tion to the other losses mentioned In the preceding paragraph. (d) If, in Fig. 229, 00' is the i.h.p. used in overcoming the engine friction, then O'Y' is the axis from which the d.h.p. are measured. If the engine friction Is assumed constant for all loads (which is not strictly true), the curve TC In the figure, with origin at 0', gives the total consumption for the d.h.p. de- veloped. The curve efg' of water rate per d.h.p. -hour will of course lie above efg, and the lowest point f will lie farther from than /. Evidently, on the basis of delivered power, the best economy In this case occurs when the i.h.p. equals Ok' (corre- sponding to a d.h.p. of O'k'), and this should be the power which the engine normally develops (" Normal Power ") if steam econ- omy is of prime Importance. This should then be the '' rated » 354 HEAT-POWER ENGINEERING power," or power at which the engine is rated to operate nor- mally. When the i.h.p. developed is either more or less than this, the engine has poorer economy. (e) The load factor is the ratio of the actual load to the rated load. There are instantaneous load factors, and average load factors. For best steam economy the load factor should be unity; and, since it is better to overload than to underload a steam engine (see Fig. 229), a load factor a certain amount above unity is preferable to one the same amount below. There are, however, other considerations which may make it financially more profitable to rate the engine at output other than that giving best steam economy, and to operate with some load factor other than unity. In many instances, the average load factor of the power plant as a whole is low, but in such cases it is customary, when pos- sible, to have several engines and to place in operation such a number as will cause those in service to operate under the most economical conditions; that is, the load factors of the individual engines are maintained near unity. The instantaneous load factor may vary widely, as in a street- railroad power plant, and the fluctuations may be of such rapid character as to prohibit changing the number of engines. In such a case a small average load factor may be unavoidable. . (f) Curves of steam consumption for an engine are useful in determining the best conditions of operation for that particular engine and for comparing it with others that operate under similar conditions. When the conditions are widely different the water rates should not be compared directly. To reduce water rates to a comparable basis, when the differ- ence in conditions of operation is not great, the following cor- rections may be made : * 0.4 to 0.6 per cent per i inch change in vacuum (between 25 and 28 inches). I per cent per 8 to 11 degrees of superheat (at from 50 to 100 degrees). 0.1 to 0.2 per cent per pound of initial pressure. I per cent per i per cent of moisture. The only true comparison is on the basis of B.t.u. per h.p. per unit of time (minute) or on the basis of thermal efficiency * Moyer's Steam Turbines, page 288: — Wiley & Sons. PERFORMANCE OF STEAM ENGINES 35S .9 .^ 'So So < < < < ^ t^ ,n "CJ, <=* '^ C! •1^0 -d'T japunAQ }J5 ^ ; ti fo o ( .a > '^ ■In rt 2 1 B^. U) W ii''^ ^ § yu,-^ lo'Si ^ W •ftrt ^: To ^"^L H > a yl f^U <1 «^ H w ^w - . ,« < .ti fe H hJ Ph CW N ►^ H t" ^.Rit:i •Xonapigg IBUiianx 12 fo (^ T o o t »^ M o ro Ov 9 ^ S5 ^ 'S'id ti^ N i ??" l^ '^N iR '^R o o t^ < 0\ N • I t^ 5o >o o 00 ^ o S ^ 25 ^ ^ N ^ ^ o ■* ^ ^ •* 00 •t t>- ^ fO HI •* tr> ^ t> o JunoH •d'n-i J9d uiB9q.g Ajq JO spunojj -STUipV l-'B :^'B9qj9(Ing O ro t^ ^^ if O n' ^ •J9;B^ p99^ JO sjn% -BJ9dtU9X •sqv -sqq '9JUSS9JcJ •93nBQ -sqq '9JnSS9Jj£ 6 a a -p -u +j < < < U9MO(J 9SJOH ?^ ^ ? CMCDOabOCM nJ>rt>rt>cS> cwiaboabooM om P^ < 6 a 5 ^ ^ M (0 ^ 6 1 51 ?.v> cr y -J;^ II ^ § Y g ^ Oh ^ -^ ^ II u X p fO u □ — ■ ^uadrui le \ R=Re jenerat ve / 1 / / / / / \ V /. f ?R / / / 1 Tl / / i ^! -£i / / / ,J <^ / 4 ' V— \ A B / / / §,100 9 i N> J / t^ / / 1 t> ^ J / / / l/L ^ X ^ V-^ — ^ / / / 50 ^ ^ — y J / ^ Claus -Atm. us Exh. y 28 lusius Vac. 10 12 \L 16 18 20 Thermal Eff. on the I.H.P 22 24 26 28 32 Fig. 231. does not follow that it is accompanied by low water rate and high cylinder efficiency. (b) Figs. 230 and 231 show respectively the variations of B.t.u. per i.h.p.-min. and the thermal efficiency on the i.h.p., with initial and exhaust pressure, with superheat, with type of engine, etc. Reference to these figures shows that, as compared with the Clausius cycle with 28-inch vacuum, the losses of various types of real engines are about as follows in the best condensing practice: 358 HEAT-POWER ENGINEERING Quadruple 20% Triple 25% Compound 33% Simple 50% (c) Table VIII gives a brief summary of steam-engine efficien- cies, including some of the best. Table IX gives the pounds of steam consumed per i.h.p.-hour by ordinary engines which op- erate under the usual commercial conditions and in which no special provision is made for improving economy — such as super- heating, jacketing, etc. Larger engines, of course, give better results than smaller ones. TABLE VIII. — SUMMARY OF EFFICIENCIES OF STEAM ENGINES. Carnot cycle efficiency * 10 to 32% Clausius cycle efficiency * 8 to 28% Indicated efficiency " 40 to 88 . 2% Thermal efficiency on i.h.p 5 to 25 . 05% Mechanical efficiency 85 to 97% Thermal efficiency on d.h.p 4 to 23 . 9% Over-all efficiency 35 to 84% Heat used per i.h.p.-min 169.3 to 700 B.t.u. TABLE IX. — STEAM CONSUMPTION. Type of Engine. Lbs. i.h.p.-hour Simple " high-speed " engines (noncondensing) 28 to 36 Simple Corhss engines (noncondensing) 25 to 28 Compound slide-valve engine (noncondensing) 24 to 26 Compound slide-valve engine (condensing) 15 to 21 Compound Corliss engine (condensing) 14 to 16 Triple-expansion (condensing) 12^ to 13 * Obtained from Figs. 73 and 75 respectively with the following assumptions: The lower limit of pi is assumed at 50 pounds pressure and ^2 = 212° F. The upper limit of pi is assumed at 150 pounds pressure and h = 100° F. CHAPTER XXII. STEAM TURBINES. 179. Introductory, (a) The earliest steam-driven prime mover recorded in history is Hero's steam turbine (about 200 B.C.) , which is shown in Fig. 232. It was a "reaction turbine," driven by the repulsive force produced by a jet of steam issuing rearwards as regards the direction of rotation. Branca's "impulse turbine" Fig. 232. Fig. 233. (1629), shown in principle in Fig. 233, is the next historical refer- ence to the use of steam in a turbine. The first patents in foreign countries appeared about 1820 and the primary patent in the United States was issued in 1831. Although many steam turbines v/ere invented in the succeeding years, it was not until the latter 80's of the last century that the modern commercially successful types began to be developed. (b) A steam turbine may be defined as a device in which one or more jets of the working substance moving at high velocity (and therefore possessing kinetic energy) act or react on vanes or buckets on one or more wheels, or drums, in such manner as to cause them to rotate and transmit power by means of the shaft on which they are mounted. The shaft, the wheels or drums, and their attachments con- stitute the "rotor." The working substance is steam, which may have moisture entrained in it. The velocity of the jet is acquired by the expansion of the steam through a nozzle, or its equivalent, during which process some of the heat energy of the steam is converted into the kinetic energy of the issuing jet. 359 360 HEAT-POWER ENGINEERING In " impulse turbines " the nozzles are stationary and the jets act on the turbine vanes; in the "reaction" type, the nozzles, or their equivalents, are mounted on the rotor, which is driven by the reaction of the jet. In sortie turbines the rotors are driven by both impulse and reaction. (c) The velocity diagrams used in designing the buckets of the steam turbine are similar in many respects to those used for water turbines. But, despite this resemblance, the problems of design and construction in the former differ greatly from those in the latter. This is principally because, in the steam turbine, (i) the jet velocities are enormously greater (in some cases this velocity exceeds 3600 feet per second, or 41 miles per minute), (2) the .bucket velocities are very much higher, (3) the working substance is elastic and tends to expand as fully as the surround- ing media will allow, and (4) because the kinetic energy of the jet is obtained from heat conveyed by the working substance and not from "hydraulic" head. (d) The steam turbine differs as much from the steam engine as to its mechanism and method of operation as does the water turbine. Although both of these steam-actuated prime movers use the available heat of. the steam, the turbine utilizes it in increasing the velocity (kinetic energy) of the jet of working sub- stance, whereas this heat in the steam engine produces certain pressure- volume changes within a cylinder. (e) The thermodynamic problems encountered in the steam tur- bine are centered in the nozzle, where (theoretically) all the heat- energy transformations occur. After the jet has issued from the nozzle end the problem becomes a dynamic one, namely, to con- vert the jet's kinetic energy into power which can be delivered by the shaft. The problem of nozzle design and the thermodynamic theory involved will be considered in detail in a later chapter. For present purposes it is only necessary to know that high veloc- ity can be attained at the expense of associated heat and that this transformation occurs entirely within* the nozzles or their equivalent. (f) In turbines, there is a certain definite ratio of bucket velocity to jet velocity that will theoretically give the best economy. In practice, however, if the full expansion from initial to final pres- sure takes place in a single set of nozzles, the bucket velocity for STEAM TURBINES 361 best economy is usually greater than the structure of the rotor will stand, because of the enormous centrifugal force produced. Also, the high rotative speed involved with high bucket speeds usually prohibits the direct connection of the driven machinery to the turbine shaft. Hence, if the expansion occurs in a single set of nozzles, it is usually necessary to use lower bucket veloci- ties than those which would give the highest economy, and also to use gearing of some kind between the turbine and the machine it drives. In order to obtain lower jet and bucket velocities, most turbines are of the "multi-stage*' type. Fig. 234 shows dia- grammatlcally an impulse turbine of this type. In such tur- bines each stage by itself constitutes a simple turbine, in the nozzle of which the steam expands through a small range and therefore acquires relatively low velocity. The stages are usu- ally arranged in series with diaphragms between and with all rotors mounted on the same shaft. In Fig. 234, the sections of the turbine casing and the dia- phragms are shown by crosshatching, and the nozzle and tur- bine wheel sections are black. Steam enters at the left, ex- pands through the first nozzle (or ring of nozzles) Ni, in which it acquires a relatively low velocity, and discharges \X] against the buckets on the wheel in the first-stage casing, in which the pressure is but little lower than the initial. The steam then expands through the nozzle (or ring of nozzles) N2, in the diaphragm between the first and second stages, and acts on the buckets of the wheel in the second chamber, where the steam pressure is somewhat low^r than it is in the first stage. In similar manner the process is continued in a third stage, and in many instances in from twenty to forty stages, until the exhaust pressure is reached in the last stage. The nozzles in all the stages must all deliver the same weight of working substance per second. They may be designed to do this with equal velocities, in which case the bucket velocities in all stages would be the same and the mean diameters of the steam Fig. 234. 362 HEAT-POWER ENGINEERING wheels would be equal ; or the jet velocities may be varied and the bucket velocities and wheel diameters be made to correspond. As the steam traverses the turbine it expands by increments in the successive nozzles, and increases in volume, hence the nozzle areas must increase in like manner through the series, as is illustrated in Fig. 234. By properly proportioning the cross-sectional areas of the inlet and outlet nozzles of any stage, the designer can fix at any desired value the pressure that will be maintained in that stage. / I 180. Thermodynamics of the Ideal Steam Turbine, (a) In all types of steam turbine the steam is expanded through noz- zles, or their equivalent, and the velocity of the working sub- stance itself is increased by the conversion of some of its own associated heat into available mechanical energy, which appears as the kinetic (velocity) energy of the issuing jet. As the nozzles, or their equivalent, are relatively small, and as the velocity of the steam through them is enormous, there is little I opportunity for loss of heat, as A such, to the surrounding media, j or for the reception of heat, as ! such; hence, the conversion of heat energy into kinetic energy i must in practice be almost strictly adiabatic, and it will be shown in a later chapter that the expansion may be considered equivalent to an isentropic pro- i cess in the ideal case. (b) Assuming that the steam is initially wet, and that its state is represented by point 1 on the T0-diagram in Fig. 235, the heat (A(2i) supplied per pound of steam delivered to the turbine is represented by the area bounded by the bold line. Let point 2 represent the state of the working substance after isentropic expansion to the exhaust pressure and temperature. Then the hatched area represents the heat (A(22) STEAM TURBINES 363 remaining in the steam at the end of the process. Thus the heat theoretically available for the turbine to deliver as useful work is ^E = AQi - AQ2, and this is shown by the stippled area, abl2, which is seen to have the same boundary lines as those of a Clausius cycle, with the same conditions of expansion. The isentropic process from 1 to 2 may occur in one nozzle, converting AE into kinetic energy, or it may occur in any number (n) of nozzles in series, each con- verting part of AjE, but with cumulative effect equal to that produced by AE in the single nozzle. Thus, regardless of the number of stages, it may be said that the heat energy available for doing work in the steam turbine is equivalent to the AE avail- able with the Clausius cycle having the same expansion line and same weight of steam. The value of AE per pound may be computed by the method given on page 173; or it can be ob- tained from the area on the T(/>-diagram ; or it can be more conveniently found from the Mollier chart (Appendix). (c) Having determined the number of B.t.u. represented by AE, the steam consumption per h.p.-hour, or water rate, in the ideal turbine is ^'=1f (3H) and if the turbine drives an electric generator the theoretical water rate per kilowatt-hour is ^^ 0.746 AE AE ' \ ' ' ' ^'^^^ (d) The actual turbine of course has a poorer (larger) water rate than the ideal. If Wa is the actual water rate per h.p.- hour delivered by the turbine shaft, and WdK is that per kilo- watt-hour delivered by the generator, then the over-all efficiency of the turbine (alone) is om = ^y (316) and the over-all efficiency of turbine and generator is The OEfd corresponds to the OEf of the steam engine (p. 190). 3^4 HEAT-POWER ENGINEERING If it is dCvsired to estimate the probable performance of a turbine, and the OEf is known for similar turbines under similar conditions of operation, the probable water rate per d.h.p.-hour is, from Eqs. (314) to (317), W, = 2545 ^{AEX OEf,), . ._ , (318) and per kilowatt hour it is WaK = 3411 - (A£ X OE/k). .... (319) In very large turbo-generator outfits the value of OEJk should be 0.65 or more. In general the smaller the turbine the poorer the efficiency, as is shown in a very general way in Fig. 236. 80 50 40 5000 10 000 15 000 20 000 Kw. FuULoad 25 000 30 000 Fig. 236. (e) The ultimate comparison of the performances of turbines with each other and with steam engines is either on the basis of B.t.u.'s supplied per minute per unit of output, or on the basis of thermal efficiencies. In the ideal turbine the B.t.u. supplied per h.p. per minute are Bi = Wi (qi + xiri + CpDi — 52) -^ 60, in which ^2 is the heat remaining in the condensate, which heat is considered as being returnable to the boiler with the feed water (as in Seci. 115 (d)). In the actual case the B.t.u. sup- plied per d.h.p. per minute are Bd = Bi/OEfd = Wdiqi + xiri + C^Di - q^) -^ 60. (320) The B.t.u. supplied per kilowatt per minute in the ideal case are BiK = WiK (qi + xiri + CpDi - ^2) -^ 60, . . (321) and in the actual case BdK = Bik/OE/k = WM^i + xiri + C^^Di - q^) -^ 60. (322) The values of BdK vary from 250 to 800 B.t.u. per minute. STEAM TURBINES 365 (f) The ratio of the heat dehvered as useful energy to that supphed in the steam is the thermal efficiency. The thermal efficiency on the d.h.p., as in the case of the steam engine (page 210), is 2545 _ 2545 ^^^•^ 60 X Ba Wa (qi + x,r^ + CpZ^i and based on the kilowatt output it is 341 1 _ 341 1 22) TDEfK = (323) (324) 60 X BdK WdK (21 + X^Yx + CpZ>i - 2., (g) Fig. 237 shows typical curves for a large turbine-gener- ator outfit. It is seen that the curve of total steam consump- 1000 2000 3000 4000 Kilowatts at Switchboard Fig. 237. tion (T.C. curve) is practically a straight line; and this is a char- acteristic of such curves for nearly all types of turbines. If, in the figure, the T.C. curve is extended to intersect the Y-axis, the intersept (Fo) represents the steam required to operate the turbine when delivering no power. It is the amount needed to overcome the friction of the turbine and the " windage " (or friction between the turbine disks and the vapor in which they rotate), that required for driving the governor, oil pumps, etc., and that for meeting the losses due to leakage and radiation. The water-rate curve (W.R.), or curve of steam used per kilo- watt hour, is also shown in Fig. 237. The water rates at the different loads are obtained by dividing each total consumption by the corresponding kilowatts as found by test, i.e., by dividing 366 HEAT-POWER ENGINEERING the ordinates of the T.C. curve by the corresponding abscissas. If the T.C. curve passed through the origin, as it would in the ideal case, the W.R. curve would be a horizontal straight line, and the economy of the turbine would be the same at all loads. The greater the Y intercept of the T.C. curve the more curva- ture does the W.R. curve have, and the greater are the consump- tions of steam under light loads ^as compared with those under heavy loads. It will therefore be noticed that the best economy is obtained when the turbine is operated at its maximum power. As a turbine when operating under its usual load should have some reserve power (or ** overload capacity "), it must normally operate at a load and an efficiency less than the maximum. On this account, and because wide fluctuations of load may occur, a flat water-rate curve is desirable. Many turbines have an auxiliary " overload valve" which admits live steam to the low-pressure stages of the turbine when it is considerably overloaded. At such load the T.C. curve and W.R. curve change character, as in Fig. 237 at and 0^ In Fig. 237 is also shown the curve of over-all efficiency of turbine and generator {OEJe)' In this case A£ has been taken as the available heat in the steam just before it reaches the throttle valve. Thus OEJk includes the losses entailed by the governor valve throttling the steam, which is the principal reason for the decrease of this efficiency when the turbine output is diminished. Why this loss occurs is explained in (k) of this section. (h) Fig. 238 shows on a Mollier chart an expansion line starting with dry saturated steam at p pounds pressure and Fig. 238. extending to various lines of terminal pressure. It is seen that ex- pansion to 15 pounds pressure theoretically makes available heat represented by a, and that further expansion to one-half pound absolute back pressure would add to this an amount of heat represented by g. Thus, if steam from an ideal noncondensing engine or turbine is expanded in a second ideal turbine to one- STEAM TURBINES 367 half pound absolute pressure, the total power obtainable would evidently be nearly twice (in this instance) that derived from the noncondensing unit. Many "low-pressure " or "exhaust-steam " turbmes are operated with steam received from an engine at about atmospheric pressure, and these in many instances give as much power as do the engines which furnish the steam. Again referring to the expansion line in Fig. 238, and starting with terminal pressure 2| lbs., it is seen that the succeeding half- pound drops are accompanied by the heat increments lettered c, d, e, and /, the amounts of which, in this particular case, in- crease the available energy respectively in the percentages 4.7, 5.6, 6.3, and 10. It is apparent that these heat increments rapidly become larger as the back pressure is lowered, hence a one-inch change in vacuum from 28 to 29 ins. is much more effective than one from 26 to 27 ins. The actual case would, of course, differ somewhat from the ideal, but the real gains from improving the vacuum are about proportional to the theoretical; hence, with steam turbines, it is desirable to use as low back pressures as the other considerations will permit. (i)' In the T(/>-diagram in Fig. 239 the Clausius cycle is super- imposed on the Rankine, ge being the constant volume line at release in the latter. Now, by de- creasing the back pressure, with tem- perature reduction from T2 to T3, the increased amount of heat made avail- able in the ideal turbine is shown by area abed, whereas in the engine it is only aefd. Actually there is still greater difference between the gains, for in the engine the increased range of temperature augments the loss due to cylinder condensation, whereas in the turbine there is no equivalent to such condensation since the steam flows continuously in the same direction, and there- fore constantly comes in contact with parts which have pre- viously become heated to its own temperature. Evidently, then, the turbine can use very low back pressures to better advantage than the engine, other things being equal. (j) The gain due to using superheated steam is illustrated on the Mollier chart in Fig. 240. In expanding from dry satu- Fig. 239. 368 HEAT-POWER ENGINEERING ^, A? Fig. 240. rated steam at p pounds pressure to 1 pound pressure, B.t.u. represented by AE are seen to become theoretically available, whereas in expanding through the (^ same pressure range but starting with steam superheated 150 de- J^ grees, B.t.u. represented by AE^ are made available. ,, If ^ is 165 pounds absolute, a gain of nearly 1 1 per cent is effected per pound of steam, and only about 0.9 as much steam would be used as with saturated mate- rial. The gain in fuel economy is not in this proportion, how- ever, as additional heat was supplied per pound of steam in superheating it. The heat (above 32 degrees) of 1 pound of the superheated steam is seen to be 1277 B.t.u., and in the case of the saturated steam it is 11 95. If the feed water is at 72° F., it contains about 40 B.t.u. above 32 degrees. The fuel used per pound in the two cases will then be in the ratio (1277 — 40) -^ (1195 — 40) = 1.07. Thus the heat supplied by the fuel per unit of work when superheated steam is used is 0.9 X 1.07 = 0.96 times that needed with saturated steam, and the theoretical saving in fuel is 4 per cent in this instance. The actual saving may be greater than this, for superheating results in the steam having less moisture after the adiabatic expansion, and the presence of moisture somewhat increases the friction that the steam en- counters in passing over nozzle and blade surfaces. In the steam engine, superheating may effect greater improve- ment in economy than occurs in the turbine, because of its influ- ence in preventing cylinder condensation. (k) It is quite common practice to decrease the power output of a turbine by throttling the steam supply. This process not only reduces the amount of steam, but lowers its pressure and changes its entropy in such manner that the heat available per pound with any fixed terminal pressure is reduced despite the fact that the total heat of the steam remains the same. This is illustrated in Fig. 241, in which AE is the heat available per pound of steam before throttling, and AjE' is that after throttling, the total heat AQi of the steam being Fig. 241. STEAM TURBINES 369 initially the same in both cases. It is therefore evident that the throttling process must theoretically decrease the economy of the turbine. 181. Thermodynamics of Actual Turbines. In the energy stream of Fig. 242, A£ is the heat that wouy be made available for doing work when there is complete expansion of i pound of Av ailable Energy TTTTTTT Energy aeliyered by Shaft Fig. 242. steam through the nozzle, or nozzles, of a single stage of an ideal turbine, and AQ2 is the unavailable, or waste, heat. (a) In the actual case, some of the steam may not pass through the nozzle, for there may be leakage to the exhaust. For ex- ample, in Fig. 234 some of the steam may leak from chamber 2 to chamber j through the clearance space a between the third diaphragm and the shaft. This leakage loss (which may repre- sent from zero to 5 per cent, or more, of the total energy) is shown by stream line a in Fig. 242, and the energy still available for doing work is represented by ^ . (b) Because of the frictional resistance offered by the nozzle walls, and because of eddy currents, etc., all of the heat theo- retically made available by the steam expanded through the nozzles is not converted into kinetic energy of the jet. The portion of A£ not* utilized remains in the steam as heat ; hence in the figure the nozzle loss h is shown as subtracted from the available energy and added to that wasted. This loss may be 370 HEAT-POWER ENGINEERING from 3 to 15 per cent of the total available energy. The energy- still available is shown in the figure by B. (c) Similarly, not all of the kinetic energy of the jet is ab- stracted by the turbine buckets. The remainder, or bucket loss, which may be from 10 to 30 per cent, is reconverted into heat by eddy currents and by the reduction of velocity in the turbine chamber, and this heat is added to that already in the steam before it reaches that point. This loss is represented by c in the figure, and the energy still available, by C. (d) Further, because of the " windage," or friction between the rotor and the enveloping vapor, not all of the energy absorbed by the buckets is transmitted to the turbine shaft. This loss may be from 2 to 8 per cent with the high velocities of rotation prevailing. This frictional energy is converted into heat by the eddy currents set up in the vapor, and this heat is added to that already stored in the vapor, as shown at d in the figure. The energy still available for doing work is shown by D. (e) The heat not utilized remains in the steam and is shown by H in the figure. If the steam from this casing is used in another turbine, or as another stage of the same turbine, the diagram of energy flow for this second element would also resem- ble Fig. 242, but the initial width of the steam line would be H, (f) In addition to the foregoing, there are the radiation loss and the mechanical losses from bearing friction and (possibly) from the driving of oil pumps, governor, etc. These are shown at e, f, and g. G represents the energy finally delivered by the shaft. The ratio of G to AE is the over-all efficiency of the turbine * (not including the generator) . (g) Losses a, b, c, d, and e constitute the equivalent of the cylinder losses in the steam engine; hence, the ratio of the heat shown at E to AE may be called the cylinder efficiency (lEf). (h) Fig. 242 will also apply qualitatively to multistage tur- bines considered as a whole, in which case a, b, c, d, and e show the combined losses of all stages. (i) On the Mollier chart in Fig. 243, let the initial state of the steam be shown by point 1, with pressure pu entropy 0i, quality Xi, and associated heat Aft per pound. In the ideal case, after expansion through the nozzle to a pressure of p2 pounds per square inch, the state point would be at 2, with * This is sometimes called the "shaft efficiency." STEAM TURBINES 371 entropy 0i, quality X2, and associated heat Aft- The heat theo- retically made available is shown by AE. In the real case, as has been seen, only a part of AE is actually delivered to Fig. 243. the shaft by the wheels or drums. This amount is shown by AE' = {lEf X AE) in the figure. Evidently the heat remaining in the exhaust steam is shown by AQ/ = (AQi — AE'). With this amount of heat in the exhaust steam and with the terminal pressure P2 as before, the state point showing the con- dition of steam in the actual case must be at 2\ the point on the pressure line having heat value equal to AQ2\ Thus the actual condition of the exhaust steam is such that the quality is X2, the entropy is 02, and the heat above 32 degrees is AQ2. This is the condition of the steam exhausted to the condenser or to the atmosphere, or to the of next stage, as the case may be. (j) Fig. 244 is a T0-diagram correspond- ing to the MoUier chart in Fig. 243 and is similarly lettered. AQi is shown by the area bounded by heavy lines, AQ2 by area 0ab2(f)i, and AQ2' by the hatched area. AE' is the difference between the areas AQi and AQ2' and is not shown directly by any area on the diagram. 182. The Dynamics of Impulse Steam Turbines, (a) In dis- cussing the dynamics of turbines, it is necessary to distinguish between the " absolute " velocity and the " relative " velocity of the jet of steam. Absolute velocity is the linear speed (v) of the jet with respect to things that are stationary; the relative velocity (R) is the speed of jet relative to the buckets, which themselves are moving with a velocity u. 372 HEAT-POWER ENGINEERING (b) The available energy of w pounds of steam flowing through the nozzle per second is ^^ X 778 X A£, and the kinetic energy which it imparts to the jet is wv KE = j^, (325) in which v is the absolute velocity of the jet in feet per second. Hence, if the nozzle efficiency is £/„, wv EfnXwX 778 X AE = from which the velocity of the jet is found to be (feet per second) V = 223.8 VAE XEfn (326) (c) To completely utilize the kinetic energy of the jet in an impulse turbine, the absolute velocity of the jet must of course be reduced to zero (regardless of the final direction of motion), and it is the function of the blades on the rotor to perform this reduction and receive the energy. If, after passing over the blades, the jet still has velocity {V2), it is evident that there is loss of energy due to the residual velocity equal in amount to KE2= —...... . (327) (d) If in Fig. 245 the jet has an absolute velocity Vi and the bucket has an absolute velocity u = z^i/2 in the same direction, the relative velocity of jet to bucket is R = V1/2 as it enters. Then if the bucket directs this jet rearwards (op- posite and parallel to Vi) , the absolute velocity V2 of the working substance is zero, and the entire energy has been absorbed. Could the friction between the jet and the surface of the bucket, the eddying, and spilling of the working substance, be eliminated, the efficiency of conversion in such a case would be 100 per cent. (e) If in Figure 246 the line J represents the absolute velocity Vi of the jet and its direction of motion compared with that of the bucket, the direction and velocity of which are shown by u, the relative velocity of jet to bucket is shown in amount and direction by Ri, which is found by constructing the triangle STEAM TURBINES 373 abc with side be = u. If R2 is the relative velocity and direction in which the jet is discharged with re- ">^^^ ,^ spect to the moving bucket, then V2 is ^^>\n!^^*"*^\,^ jet, and its vector is found by con- -l -J^ -^^^^v .^ structing the triangle def with side ^ — ^j^ — ^^ ef = tc. Evidently the presence of this ~~\ "^/^ *'^^' residual velocity Vi represents a loss V^^/ja of energy which is equal to wU'^l^g. ^ ^y^ / Hence the bucket efficiency, neglecting 1* ^ other losses, is Fig. 246. ^ [2g 2g) ' 2g Vi^ It will be apparent from Fig. 246 that V2 can never be made zero if Vi and V2 are not both parallel to u, and that unless this is the case the bucket efficiency must be less than unity. It will also be evident that V2 is a minimum, and the efficiency is maxi- mum, when u is of such value as to cause V2 to be at right angles to u. This value of v can be determined either graphically or mathematically by methods which need not be considered here. If angle abc = 20°, which is about as small an angle as can be used when the nozzle is placed at the side of the buckets, and if Ri and R2 form equal and opposite angles with the direction of the bucket's motion, u will be about 47 per cent of Vi. Further discussion of the dynamics of turbines will be given in connection with the descriptions of the various types. 183. De Laval Type of Single-Stage Turbines. — This type of turbine (developed about 1888) is shown diagrammatically at A in the chart given on page 374; and the details of its mechanism are shown in Fig. 247. The velocity diagram resembles Fig. 246, but as the velocity (vi) of jet issuing from the nozzle may be from 3000 to 4000 feet per second, it is not usually possible to use bucket velocities (u) which correspond to maximum efficiency, for no available materials or possible constructions will withstand such speeds. The bucket velocities are therefore made as high as is safe. The wheels of the 300-horse-power De Laval turbine are about 30 inches in diameter and rotate at about 10,600 r.p.m., with peripheral speed of about 1380 feet per second. The 374 HEAT-POWER ENGINEERING CHART — Principal Commercial Types of Steam Turbines. Nozzle Blades A. De Laval Type. Velocity Exhausts Pressure \> , Lost , Velocity- Stages =1 2 S" 4 5 B. Rateau-Zoelly Type. NOTES. General. In each of the above diagrams the upper portion shows a longi- tudinal section of the turbine, the middle of the figure represents a transverse section through the buckets and nozzles, and below this are curves which show how the pressure and velocity of the steam vary during the passage of the vapor through the turbine. The pressures and velocities are shown respectively by the ordinates of the heavy and of the light curves. A. De Laval Type (see Sect. 183). In this type of turbine it is to be par- ticularly noted that the full drop in pressure and the entire increase in velocity of the vapor are completed before the jet issues from the end of the nozzle, as shown by the curves; thus there is no expansion of the steam after it reaches the wheel casing. The velocity curve also shows the jet's velocity- decrease resulting from the absorption of the kinetic energy by the buckets, and further shows the residual (lost) velocity associated with the kinetic energy not utilized. B. Rateau-Zoelly Type (see Sect. 185). Each pressure stage is seen to resemble a single-stage turbine of the De Laval type. STEAM TURBINES 375 CHART ^(Continued). — Principal Commercial Types of Steam Turbines. Telocity 1st Stage 2nd Stage C. Curtis Type. D. Parsons Type. NOTES (Continued). C. Curtis Type (see Sect. i86). The diagram shows a turbine having two pressure stages, each of which has two velocity stages. It is seen by the curves that the pressure-drops and velocity-increases occur entirely within the noz- zles iVi and N2 (i.e., there is no expansion of the vapor in the wheel casings). In each pressure stage the jet first passes over the moving blades Mi to which it surrenders part of its kinetic energy (thereby losing some of its velocity), and is then guided by the stationary blades 5" to act on the second set of mov- ing blades M2, which absorb still more of the energy by further decreasing the velocity of the jet. Thus the (kinetic) velocity energy is absorbed in two steps, or stages, in each pressure stage. D. Parsons Type (see Sect. 188). Expansion takes place in both the station- ary and the moving blades, as is shown by the steam-pressure line in the dia- gram. The steam is accelerated in passing through the first row of stationary buckets; the issuing jets are then retarded by coming in contact with the first moving buckets, to which they surrender part of their kinetic energy; and while passing between these latter buckets the stream is further expanded and issues from them with a reaction. Thus the moving blades receive energy by both impulse and reaction. This process is continued in each of the suc- ceeding pairs of stationary and moving sets of blades. 376 HEAT-POWER ENGINEERING 5-horse-power turbine has a wheel about 4 inches in diameter, the r.p.m. are 30,000, and the rim speed is 515 feet per second. To provide the maximum theoretical strength, the smaller wheels have sections resembling that in Fig. 247 at (a); while the larger wheels are without central hole, the shaft being made in two parts, each fastened to the side of the wheel by flanges. The buckets and the method of attaching them to the wheel are shown at (b) in the figure. The flanges on the bucket tips form a continuous " shroud ring," and this prevents the jets from flattening and " spilling " over the ends of the blades. Although the wheels are balanced with the greatest care, the gravity axis never exactly coincides with the geometrical axis of the shaft. To prevent difficulty which might arise with such high speeds from this lack of balance, the shaft is made slender and flexible so that the wheel can " gyrate " about its gravity axis. Owing to the high speed the " torque " on the shaft is small and a small diameter is therefore permissible. In most instances the rotative speeds are too great to permit of " direct connection " to the generator, pump, or other machine which is to be driven, hence reducing gears of ratio about 10 : i are used. To obtain continuity of action and noiselessness, the gears are of the opposed "herring-bone" type, with very narrow teeth, which are cut and adjusted with extreme accuracy. The pinion may drive either one or two pairs of large gears, each of the pairs delivering power independently. The power is delivered from the gear shaft through a flexible coupling, the bushings shown black in the figure being made of rubber. The governor shown at e is of the centrifugal fly-ball type. As the weights W, W, (pivoting on knife-edges at P) fly out due to centrifugal force, the rod R is moved longitudinally, thus moving the bell crank L (in view (c)) and regulating the amount of opening of the governor valve 5 (which is vertical on actual tur- bines). Thus the turbine is throttle-governed. There generally are several nozzles like d around the periphery of the wheel, and these are provided with hand-shut-off valves. If the load on the turbine is very small, it is better to close some of these valves, so that the nozzles remaining in action may operate at or near their maximum capacity (the most efficient condition) rather than have all the valves in operation with steam greatly throt- STEAM TURBINES 377 378 HEAT-POWER ENGINEERING Coupling Fig. 248A. Pelton Type. Fig. 248B. Multistage Impulse Turbine (Kerr). STEAM TURBINES 379 tied (with the 'accompanying loss). Sometimes there are two sets of nozzles, one to be used when operating condensing, and the other when noncondensing. 184. Pelton Type of Steam Turbine. Single-stage impulse steam turbines, with buckets like those used on Pelton water wheels, may be built; but the same difficulties are encountered in them that appear in the De Laval type of single-stage turbine. By making the turbine multistage, and using a sufficient number of stages, these difficulties may be avoided, the jet velocities may be reduced to twice the bucket speeds that can be used safely, — thereby obtaining the highest bucket efficiency (see Section 182 (d)), — and the rotative speeds may be made such as to permit the direct driving of electric generators, centrifugal pumps, blowers, etc., without the use of gearing. Fig. 248A shows the principal elements of a turbine which is of this type. In this figure (a) shows one wheel, the nozzles (one in section), the section of the casing of the adjacent stage of higher pressure, and the bucket. The longitudinal section of the turbine is shown in (b). The steam passes from A to the chamber S, thence through nozzles N to the first stage, i, where the jet impinges on the buckets on the wheel, the section of which is shown black. From the first stage the steam passes in like manner through the nozzles N in the diaphragm, to act on the buckets of the second wheel ; and so on through the turbine until the steam is exhausted at E. To prevent the possibility of any leakage of air through the stuffing boxes at B (which would affect the vacuum), a chamber is provided which can be filled with water (forming a " water seal/') or with steam at pressure slightly above atmospheric. The governor and gov- ernor valve are somewhat similar to those of the De Laval turbine. These turbines, formerly known as the " Kerr," have been replaced by the type shown in Fig. 248B. 185. Rateau Type of Steam Turbine. Turbines having from 20 to 40 stages arranged somewhat as in Fig. 234 were developed by Professor Rateau of Paris in 1897. The nozzles, instead of being of circular cross-section, are rectangular, and are grouped closely together so that the intervening walls are thin plates of uniform thickness. The buckets on all wheels, except the last 38o HEAT-POWER ENGINEERING '^' 'Y few, are of the same length. The group of nozzles in the first diaphragm extends over a short arc, that in the next diaphragm is a Httle longer, and so on; thus as the steam passes through the turbine the circular arc covered by the nozzles and the passage areas increase in size. (See B in chart on page 374.) The Zoelly turbine is similar to the Rateau, except that (i) about half as many stages, and higher nozzle and bucket speeds, are used; (2) in all the diaphragms the nozzle bands extend farther around the peripheries; and (3) the radial widths of the nozzle groups, and the lengths of blades on the wheels, increase from one end of the turbine to the other. Fig. 248B shows a modern turbine of the Rateau-Zoelly type. 186. Curtis Type of Steam Turbine. — Referring to Fig. 246, it is seen that the energy loss from the residual velocity, V2, is quite large. Curtis (in 1896) patented the arrangement whereby the jet, with this residual energy, is directed to act on other sets of rotating blades, from which it departs with residual velocity much less than in the previous case. This process is termed "velocity compounding." Theoretically, this process may be continued indefinitely, and the final residual velocity may be reduced to any desired value. In practice, however, the bucket fric- tion and other losses make it inexpedi- ent to use more than two or three rows of rotating blades per stage. Fig. 249 shows the arrangement of a single stage having two rows of moving blades (M) , with one set of stationary ones (5) between, all receiving steam from a set of nozzles (N) , each nozzle being controlled by a sepa- rate valve. Fig. 250 is the corresponding ideal velocity diagram. The velocities Ri, R2, and V2 are found in the same manner as in STEAM TURBINES 381 Fig. 246. The stationary blade 5" turns the discharge jet K to the direction J^ so as to cause it to act on the bucket M2 with ve- locity z^3 = V2 (neglecting losses). The velocity diagram VsR^R^Vi is constructed in the same manner as in Fig. 246; and Z''4 is the final velocity, the corresponding residual energy (loss) being wVi^/2 g. As the steam expands fully in passing through the nozzle, the pressure throughout the casing of the stage is uniform. This and the velocity variation are shown in diagram C on p. 375. The smaller turbines of this type usually have but one stage, while the larger ones have from two to five " pressure stages " separated by diaphragms, each diaphragm containing the nozzles for the following stage. These turbines have either horizontal or vertical shafts. In the latter arrange- ment, which is shown in Figs. 251 and 252, the shaft is stuffing Bosr with Carbon Packing Rings Fig. 251. supported by a " step bearing," to the center of which oil is sup- plied at sufficient pressure to support or float the shaft and all parts fastened to it. Fig. 251 shows diagrammatically a four-stage turbine in which the steam enters at the top and exhausts at the bottom. Such turbines rest on a subbase, which is either connected to the con- denser or itself forms the walls of a surface condenser, as in Fig. 382 HEAT-POWER ENGINEERING 252; the generator is placed above the turbine and the governor is mounted on the upper end of the shaft. Fig. 253 shows one arrangement of step bearing, and a portion of the rotating ■^ ^^j -^ ^ Shroud Ring Spacing Block Oil Drain STEP BEARING ~DF — OilSupply ( UnderJIigh Pressure) Fig. 253. " bucket segment," with buckets held in place by " dovetails.'' The buckets are separated by " spacing blocks " and their tips are riveted to shroud rings. On large turbines the governor usually moves a small " pilot valve " which controls the position of a hydraulically operated piston, the rod of which moves a shaft having cams which open or close the nozzles of the first stage. Thus the power output of the turbine depends on the number of first-stage nozzles in action. The governing is by the method of " cutting out noz- zles " or cutting them in. 187. Velocity Compounding with a Single Row of Rotating Buckets. Instead of using a second set of rotating blades in an impulse turbine to abstract some of the energy remaining in the jet when it leaves the first set, as is done in the Curtis type of turbine, this energy can be used (in part) by causing the same jet to impinge repeatedly on a single set of blades. Fig. 254 shows diagrammatically the elements of the " Elec- tra " turbine (European), which is of this type, and has blades perpendicular to the plane of the wheel disk. The full expansion of the steam occurs entirely within the nozzle N, and the guide passages G merely redirect the steam so as to cause it to im- pinge properly on the buckets. As the volume of the steam remains constant while passing through the guide passages, the STEAM TURBINES 383 cross-sectional area of these passages must increase as the veloc- ity (residual) of the steam decreases. The path of the jet, instead of being serpentine as in Fig. 254, may be helicoidal as shown at a in Fig. 255. It may be con- Fig. 254. sidered that the lower part of this path is in the semicircular buckets of the turbine wheel shown at h and c in the figure, and that the upper part is in the stationary guides of similar form. With this construction it is possible to obtain good steam econ- Fig. 255. omy with low rotative speeds, even though a single wheel be used. The same scheme is applicable to turbines having two or more pressure stages. The power ^at is obtainable with any wheel is limited by the number of nozzles and guide "blocks" that can be placed around the periphery. The forerunner of this type of turbine was the " Riedler- Stumpf " turbine (European), with double semicircular buckets like the Pel ton. In Fig. 256 is shown a Terry turbine with casing opened. The method of operation is as shown in Fig. 255. Flange B couples to the facing B' when the turbine is closed, and valve 384 HEAT-POWER ENGINEERING Governor Valve Fig. 256. X can be used to shut off some of the nozzles when the load is small. The casing is subjected to the exhaust steam only. The Sturtevant turbine, Fig. 257, operates in a similar man- ner, but is of somewhat different construction. The helical and serpentine paths are used in several other turbines. 188. Reaction Turbines, (a) A simple reaction wheel (sim- ilar to Hero's) is shown in Fig. 258. The pioneer developers (De Laval and Parsons) of the modern steam turbine and many other inventors have tried to produce a commercial form^ of turbine based on this principle, but without success. Experi- enced designers now recognize the fact that other forms are better for most purposes. The sectioned part a in the figure STEAM TURBINES 385 Fig. 257. constitutes a rotating nozzle of the converging type, correspond- ing to a small pressure drop from Pi to P2. (b) Another simple reaction turbine is shown in Fig. 259, with blades mounted on the periphery of a disk, or drum, which is arranged to rotate about axis XX. It is seen that the space be- xi^ ^x Fig. 258. Fig. 259. tween the blades, as shown at b, has the same form as the nozzle a in Fig. 258 ; hence there are as many rotating nozzles as there are spaces between blades. In this arrangement there is a " full peripheral discharge " of the steam around the entire circumference, and it is important to note that there is a difference between the pressures Pi and 386 HEAT-POWER ENGINEERING P2 on the two sides of the disk, a condition contrary to that present in the impulse type of turbine. (c) Fig. 260 may be used to show certain features of the modern type of reaction turbine. Between the tips of the blades, on the drum, and the casing there is necessarily a radial clearance space, and because of the inequality between the pres- sures Pi and P2 leakage occurs through this space. This clear- ance is of course always made the minimum practicable. The relative amount of leakage is evidently dependent on the ratio of this annular space to the passage area between blades; thus, the longer the blades are, the less the leakage, with the same ,~Water Seal Thrust Coupling Bearing > Fig. 260. clearance. If the peripheral diameter is decreased, not only is the annular space reduced, but the blades must be lengthened to maintain the same passage area between them; hence there is a twofold reduction in the leakage accompanying such change. (d) It is apparent that the difference between pressures Pi and P2 in Fig. 259 causes an end thrust on the shaft. The same is true of the arrangement in Fig. 260. This thrust may be resisted (i) by the thrust bearing T in this figure; or (2) by the balance piston B, which presents to the pressures Pi and P2 areas equal to those exposed by the blades and drum end; or (3) by using a " double-flow " arrangement of drum wherein there are two similar rows of blades having discharges which are equal but opposite in direction and hence give opposite end thrusts. In any case there must be a thrust bearing to main- tain the rotor in its proper position. (e) The leakage between the piston B and the shell is usually reduced by employing mating collars, as in Fig. 260, which STEAM TURBINES 387 Fig. 261. the reaction form a ''labyrinth passage" which becomes more or less sealed by the moisture present in the vapor. (f) In Fig. 261, R2 represents the velocity of the jet relative to the rotating blades, u is the blade velocity, and V2 is the abso- lute residual velocity of the jet. In practice the velocity u is rather low (usually from 150 to 300 foot-seconds) , hence the heat drop per stage is relatively very small, (g) The so-called Parsons' " reaction tur- bine," besides having the rotating reaction blades similar to those in Fig. 260, has station- ary guide blades which act as nozzles, the jets from which impinge on the rotating blades. HenCe such turbines combine the impulse and principles. Fig. 262 shows such an arrangement, S and M being respec- tively stationary and moving blades. It is seen that not only is there leakage at the tips Li of the moving blades, but also at the ends L2 of the stationary ones. These turbines are made multistage, with stationary and rotating blades alternating. The action of the steam on the mov- ing blades is twofold: (i) The direction of the jet is changed, and if no other action took place it would leave with low velocity — thus there is an impulse action; and (2) the steam expands while passing through the moving blades and acquires velocity by virtue of that expansion, so that when discharged rearwards there is a reaction effect. The residual velocity of the jet leaving the rotating blade is redirected and increased by the next stationary blades and discharged against the next row of moving blades, and so on from one end of the turbine to the other. (See D in the chart on page 375.) 3^8 HEAT-POWER ENGINEERING STEAM TURBINES 389 As the bucket velocities are small, it is necessary to use small heat drops per stage, hence a great many stages are used. As the volume of steam under high pressure is small, the passages between blades must be small, and the blades themselves are consequently short. To reduce the leakage the high-pressure stages are hence made small in diameter compared with low-pres- sure stages, where the volume of the steam is large and the blades are long. The heat drops in each of the first stages are about 2 or 3 B.tu., whereas in the last stages drops of about ID B.t.u. may be used. (h) One arrangement of the Westinghouse-Parsons turbine is shown in section in Fig. 263. After passing the governor valve the steam enters at A and flows between the blades on three cyl- inders, Ri, R2, and R3, which progress in diameter, until it reaches the exhaust opening X. The three balance pistons, Pi, P2, and P3, with equalizing pipes Ei, E-i, and £3, balance the thrust, and the thrust bearing T constrains the rotor to its proper position. The governor moves the pilot valve, which in turn controls the governor valve. The operation is such as to cause the latter valve to constantly move up and down, admitting the steam " by puffs," which vary in duration with the load. If the demand on the turbine becomes more than can be met by all the steam that can flow between the first blades, the turbine's speed will decrease slightly and the governor will then open the overload valve, thus admitting steam to a point (C) where the passage area between blades is greater, so more steam can be used to meet the emergency, although less efficiently than before. Fig. 264. (i) Fig. 264 shows the general arrangement of the Allis- Chalmers-Parsons turbine, which is of the same general type as 390 HEAT-POWER ENGINEERING the Westinghouse, but differs somewhat in its arrangement, construction, and method of governing. The largest balance piston P3 is placed at the exhaust end of the rotor and the gov- erning is by the throtthng method. . (j) In multistage turbines the elements in the different stages need not all be of the same type. It is sometimes desirable to use in the first stages that type which operates best with steam at high pressures, and in the remaining stages the type best suited for low-pressure conditions. See Chart on page 394a. 189. Applications of the Steam Turbine. Owing to the high rotative speeds and to the inability to vary these speeds sud- denly or to reverse the direction of rotation, there are many fields of " direct driving " which the steam turbine cannot enter. (a) Driving electric generators, which furnish current for almost an unlimited number of purposes, is the largest field of application. (b) Turbines are used with direct-driven centrifugal pumps which discharge against low or high heads (circulating pumps, boiler-feed pumps, etc.). (c) They are used for driving centrifugal air compressors (which are usually multistage), fans, blowers, etc. (d) In some instances small low-speed turbines have been used for belt driving. Ordinarily it is not feasible to reduce the rotative speeds by use of gearing unless specially designed and constructed for the purpose. (e) The torque on a turbine shaft is relatively very small, hence turbines are not applicable where a large starting effort is involved. (f) In many instances steam is available at pressures which are too low to use in an engine, but can be used advanta- geously in " low-pressure " or " exhaust-steam " turbines, pro- vided a high vacuum can be maintained in the condenser. In plants in which engines are operated noncondensing, there can be added turbines of this type to receive exhaust steam at about atmospheric pressure and to exhaust into a condenser having good vacuum. In such cases it is desirable to maintain a pressure slightly above atmospheric in the pipes between the engine and the turbine to avoid leakage of air into the steam STEAM TURBINES 39 1 with resultant decrease of vacuum. When the steam Is received at about atmospheric pressure, the exhaust turbine will develop a horse power with about 30 pounds of steam per hour, provided the vacuum is good. The probable water rate in any case can be computed by using Eq. (318). With this and the available amount of steam known, the power that can be developed by the exhaust turbine can be readily computed. Condensing engines can be operated noncondensing with late cut-off, thus giving about their normal power, and the exhaust steam can be used in a low-pressure turbine, the combined outfit thus giving power greatly in excess of (sometimes double) the normal power of the engine alone. Such arrangements usually are more economical than either the engine under the original conditions or a turbine which receives steam direct from the boiler. The less economical the engine, the more heat remains in its exhaust steam for use in the turbine. (g) If the supply of steam furnished a low-pressure turbine is intermittent, as in a rolling mill, a regenerator or accumulator can be used to make up any temporary deficiency which may occur. This device consists of a closed vessel which contains water over or through which the steam passes on its way to the turbine. Thus this water becomes heated to the temperature of the steam. Should the supply of steam cease, the steam pressure would decrease and as a result some of the water would vaporize and supply the turbine with working substance at continually decreasing pressure for a short interval of time. Usually there is also provision for supplying steam direct from the boilers, through a reducing valve, in case the normal supply fails for a considerable length of time; and sometimes the tur- bine has a high-pressure stage which is normally inoperative, but which is brought into action in such an emergency. (h) Marine propulsion is another large field for the appli- cation of the steam turbine. A saving in the weight of the turbine and of space occupied can be effected by using high ro- tative speeds, and the economy can be improved by using high bucket velocities. On the other hand, the propeller on a slow- moving vessel is inefficient if operated at rotative speeds which are high. Hence in applying the turbine to the direct driving of a propeller, a compromise must be effected ; evidently the best results should be obtained on high-speed vessels, and such is the case. 392 HEAT-POWER ENGINEERING There have been invented numerous speed-reducing devices (mechanical, hydrauUc, and electric) to be placed between the turbine and propeller shaft, but there is still doubt as to their feasibility, and until such devices are used the application of the turbine will probably be limited principally to vessels of high speed. Special provision must be made for backing; usually a small " backing element " is placed at the end of the turbine. As turbines are very uneconomical when operating below their normal speeds, they should not be used for low-speed cruising. Sometimes smaller " cruising turbines " are added for such ser- vice. Turbines are not satisfactory when much maneuvering must be done, and in some instances a combination of engines and turbines has been used for such service. 190. Advantages and Disadvantages of the Steam Turbine. (a) When operating under normal load (i.e., with the usual allow- ance for overloading), a comparison of the best performances does not show that the turbine has any advantage over the engine even when unusually good vacuums are used with the former. It is probable, however, that the average large con- densing turbine with high vacuum gives better performance than the average large condensing engine. In general, non- condensing and small turbines do not compare so favorably. In many cases it is found that from the standpoint of fuel economy there is little choice between the turbine and the engine, in which cases the selection must be based on other considerations. Comparison should be made at normal load and should be either on the basis of B.t.u. actually supplied per d.h. p. -minute, or of the thermal efficiencies, rather than on the basis of the steam used, unless the conditions of operation are identical. (b) The water-rate curve for the turbine is usually flatter than that of the engine, and hence with widely fluctuating load the average economy is nearer the best for that machine; espe- cially is this the case if the unit is overloaded. (c) The space occupied by the turbine is much less than by the ordinary engine, especially if the latter is horizontal. In some cases, however, this is partly offset by the greater space that may be occupied by the larger size of auxiliary apparatus frequently used with turbines. STEAM TURBINES 393 w^ (d) The turbines use no oil internally, hence the condensate is suitable for direct return to the boilers, and the heat-trans- mitting surfaces of the boilers, condensers, feed -water heaters, etc., being free from oily coating, operate under best conditions. (e) Turbines have the advantage of greater uniformity of rotation, and can give close speed regulation. If properly " bal- anced," they are practically free from vibration, hence do not require massive foundations or flywheels. (f) Other considerations are the first cost of turbine and gen- erator (which is generally less than that of the engine-generator outfit) , and the cost of auxiliary apparatus (which is often greater with high vacuums). The cost of ground occupied, the build- ing and foundations, the reliability, the cost of condensing water, supplies, attendance and repairs, the allowance for de- preciation, etc., must also be considered. Such matters, how- ever, relate to the Economics of Power-Plant Engineering, which will not be discussed here. (g) There are many fields in which it is necessary to operate at low angular velocity, at variable speed, with reversal of motion, or with large starting torque, which the steam turbine cannot enter. There are other fields in which high angular velocity is desirable, or not disad- vantageous, and in many of these the turbine is as satisfactory as, or more so 1 Jhan, the engine. 191. Steam-Turbine Performance, (a) Fig. 237 shows the general character of the steam-consumption curves for steam turbines, the curve for total con- sumption being substan- tially straight . The water- rate curve is usually flatter than that of the steam engine, which indicates less variation in economy with fluctua- tions of load. Inspection of this curve shows that the best econ- omy is obtained at the maximum load (not at the normal), — Cl4 (2 13 \ STEAM CONSUMPTION WHEN INITIAL PRESSURE =165 LBS.ABS. \ V SUPERHEAT =0° F. VACUUM =^28 INCHES V ^ ^Pe. Uk. hr. ■ V ^ „s eam^ •erD h.p.-t 1: I 2 J i I ) i " 3 i 10 Thousand K.W. Rated Power Fig. 265. 394 HEAT-POWER ENGINEERING 400 B.T. U. SUPPLIED INITIAL PRESS.= 165 LBS.ABS. SUPERHEAT=0° F. VACUUM = 28 INCHES \ ^ ^ ^ ii^perK.W.-Mii fl ^ ^ ^ SAD- ti.?.) .. u N ^^ --?- 1^} ■■c^ P. 200 pi y'' B.t. 1. pei D.h.i rMin / / 2 3 4 5 6 7 8 Thousand K.W ..Rated Power Fig. 266. unless there is an '' overload valve " which reduces the efficiency when open. (b) The curves in Fig. 265 show the economies of the larger sizes of standard American turbines when operating under rated loads which are used as abscissas. These curves are based on Prof. J. A. Moyer's tables,* in which the steam consumptions as obtained by test are reduced to the equivalent values which the same turbines would prob- ably give if operated under pressure of 165 pounds ab- solute, zero superheat, and 28-inch vacuum. The cor- rections were made by using the following reduction factors : For all types of turbine : Per pound of initial pressure, jV per cent. Generator efficiency, 91 per cent (300 to 400 kilowatts), 95 per cent (500 kilowatts), 96.5 per cent (1000 to 3000 kilo- watts), and 98 per cent (5000 to 10,000 kilowatts). For Parsons type: Per degree of superheat, jV per cent (300 to 1000 kilowatts) and J per cent (1200 to 7500 kilowatts). Per inch of vacuum, 4 per cent (300 to 1000 kilowatts) and 3 per cent (1200 to 7500 kilowatts). For Curtis type (may also be used for Rateau and Zoelly turbines) : Per degree of superheat, J per cent. Per inch of vacuum, 7 per cent (26 to 28 inches) and 9 per cent (28 to 29.5 inches). These correction factors should be used only when the changes involved are slight, otherwise the results may not be reliable. (c) In Fig. 265, the curve for " steam per d.h.p.-hr." is based on the brake horse power, or power delivered by the turbine * Page 287, Moyer's "The Steam Turbine." Wiley & Sons. STEAM TURBINES CHART 394a Turbines having Combinations of Stages of Different Types Fig. A. " Return Flow " (Terry) . Fig. B. Comparison of Lengths of Rotor (Reaction vs. Combination of Veloc- ity Stage and Reaction). Impulse Wheel Reaction Elements Fig. C. Double flow — 10,000 to 20,000 kw. (Westinghouse) . Fig. D. Seven-stage Impulse Turbine (General Electric). 394b HEAT-POWER ENGINEERING m W "^ I— ( fq a H en W O o o p^ Pi w o pii en rc^ (^ Remarks: (Data from r. A.S.M.E.. 912, p. 474, ex- ept as noted.) 1 s S i 1 i is' a If w 3 •| 13 ■| '.S "^ w' '^ G 6 to ^ ^ H H H ^ 03 -e si t-H M O M '^ •^ c2^ ^ ^ 1 o W ^ 00 00 t.- in m N „■ 00 00 r.. !S <0 > 0^ ?5^ •0 M 00 0^ in°°. ^ ^ ^ m 8 {:: 4) T! 0^ H t^ N ro rn 00 §> -£ 1 ° 5 00 ^ Oi Oi 00 8 "* M Tf (N 11 in vo J-- o> ^^ § " " i^ SIS i i iS^ <^ " 1 " " ^ P, M M *-* M pq ^' .^ in M l-l -s a£ 00 ^ in in ^ (N M t^ in vo M "S 5 '* ■ t^ «3 t~- m in t>. <^ S J: M in 00 M 01 Y •^ fo M M t- 00 vi «m" CO l^ H 5 d ^ d ^ tU ^ M r^ ^^ I_J ^ 15 m M M 0> H M M '"' ^ '^ mum 29.92" om.) , ches. ?-- s>s !« a> 00 po in ^ t^ ^ 00 t^ t^ o^ S" d^ ? ? d> t^ 00 s^ |g|^ ^ c .. M in N m M 10 M M 00 in 00 t^ 0^ VO M 1 2 o p. (N 2 "" P IN M t^ O^ ^ i ^ - - 2J ^ 8 .* t^ .2 S «5^ M M t- S M ^o in pj in N ■'t N 'i- rn MM.. m lO Init Press Lb AbsQ 1 . ^-- i^ is> i,S8 kss^ M M M M M "" . 8 8 8 g ^ 00 M M J^ 8 000 S § 8 8 1 Oh* §" 1 PI i m gp- m " '^ •^ iS3 f. in m M VD ro ^ 58« "^ Sl3 1 m ?s» -108 -124 2236 2460 § § M S"° §"" N § M . "^ m '^ •^ M M +H- ++ 1 _ 0) cd Cd r 1) tu a; W S a; >l 1 d. - i P^ s Curtis- Rate or Curtis- Zoel Zoelly or Rateau 1 si B f1 fl) c ii> & Xi a) ^ 3 (Tl d ^ .rt Tl •(J (U .Q ?1 n"> U rt V S II 03 P 3 d STEAM TURBINES 395 ;;70 shaft, and does not include the generator losses. The other curve includes the losses of both the turbine and the generator. (d) Fig. 266 shows the B.t.u. consumptions and the thermal efficiencies corresponding to the water-rate curves of Fig, 265. Values better than here shown can be obtained by using higher superheats, higher pressures, and lower vacuums — especially by using the latter. Some of the best results so far obtained with large turbines are given in Table X.* (e) Small turbines are generally much less economical in the consumption of steam than large ones. In most instances this is largely due to the use of bucket velocities which are much less than those cor- responding to the best per- formance, and which result from using small wheel di- ameters and low rotative speeds which permit of di- rect connection to genera- tors, pumps, etc. The economy of such turbines is greatly influenced by a change in bucket speed. Fig. 267 shows curves of steam consumption per brake horse-power for several types of small turbines, f It shows that in general the smaller sizes have poorer economy. (f) The results of some tests of the 59th Street Power Plant of the Interborough Rapid Transit Co., New York City,t can be used to compare the performances of the same power plant operating first without and then with exhaust steam turbines. This plant was originally equipped with condensing engine- generator units each developing 5000 kw. at normal (economical) load, and having a maximum rating of 7500 kw. Subsequently, exhaust steam turbines of 7500 kw. maximum capacity were * Also see Christie, "Present State of Development of Large Steam Turbines," Trans. A. S. M. E., 1912. t See Orrok, "Small Steam Turbines," Trans. A. S. M. E., 1909. t Trans. A. S. M. E., 1910, page 78. S 50 hi i) |40 u I30 20 A ^^ STEAM PRESS, 150 LBS. GAUGE DRY STEAM ATMOS. EXHAUST B --~-£!^ c C D ^^ E 0^ "JaT"^^^^^^:::!: 50 — E ^ 200 ill ad 'A ^ Load Fig. 267. m 396 HE AT- POWER ENGINEERING added, and these were arranged to operate with high vacuums on steam received at about atmospheric pressure from the engines, which latter were changed to have later cut-offs than before. The addition of the turbine to one of the engine units gave the following results: — (i) The maximum capacity was doubled. (2) The load giving the best steam performance (or load under which the unit should normally operate) was increased to about 2J times its former value. (3) The average steam economy (between 7000 and 15,000 kw.) was 25 per cent better than that of the old engine unit. (4) It was estimated that the average steam economy was 13 per cent better than would have resulted by using a high- pressure turbine of the best design in place of the combined unit. (5) The average thermal efficiency of the combined unit was 20.6 per cent (between 6500 and 15,500 kw.). CHAPTER XXIII. EXTERNAL-COMBUSTION GAS ENGINES. 192. Definition, (a) The name gas engine is applied to prime movers in which the working substance is material in gaseous form comparatively far removed from the conditions of liquefaction. Hence the working substances may be assumed to obey the laws of ideal gases, and each gas engine follows approxi- mately one of the gas cycles discussed in Chapter VI 1 1. (b) At present gaseous working substances consist of air mixed with other materials such as carbon monoxide, hydrocarbon vapors and gases, water vapor, and carbon dioxide. (c) The " hot body " is approximated in real engines by the burning of fuel in some chamber at a rate which maintains the required high temperature. In some types of gas engines the fuel, and resulting hot "products of combustion," are separated from the working substance by metallic walls through which the heat received by the working substance must pass. Such engines are known as external-combustion gas engines. In other gas engines the fuel and the air for its combustion .are burned inside the cylinder of the engine, and the hot products of combustion form the expanding working substance. Such engines are called internal-combustion gas engines, or simply internal-combustion engines. 193. The Hot- Air Engine, (a) Many attempts have been made to utilize air as a working medium in external-combustion engines, but only two such engines survive to-day in this country, and they are built only in small sizes and for special service. Inventors have long tried to produce an actual gas engine to work with close approximation to the Carnot cycle. Even if this were possible, it would be unwise commercially because of the excessive cylinder volume necessary for a given output of power. This may be made clear by drawing, as in Fig. 268, a Carnot cycle, an Ericsson cycle, and a Stirling cycle for comparable 397 398 HEAT-POWER ENGINEERING 100 conditions so as to show the greatest volume occupied by the gas in each case. This is best done by imagining one pound of gas (air in the figure) to receive the same amount of heat and to work between the same temperature limits in each case. The efficiency and work done will then be the same in each case, and will be Ef= (Ti- T,)/T,, and AE = A(2i XEf= AQ, (Ti - T2)/Ti. The figure shows that the maximum volume occupied by the working substance, and hence the necessary cylinder volume, is much greater in the case of the Carnot engine than for either of the others. (b) The cylinder volume, how- ever, determines to a consider- able extent the size and cost of the engine. As will be brought out later, the real external-combus- tion gas engines operating on the Stirling and Ericsson cycles are almost prohibitively large, and it is therefore obvious that the Carnot gas engine with external combustion must be commer- cially impossible. (c) The two external-combus- tion gas engines now in use in this country are the Rider hot- air engine and the Ericsson hot-air engine. The former approximates the Stirling cycle and the latter the Ericsson cycle. Both of these engines are direct-connected to small water pumps which utilize the net work of the engine. They are simple and sat- isfactory pumping engines, particularly for farm and suburban use. (d) The capacity, that is, the power made available, is limited by the slow rate of heat transfer between the metallic walls and the more or less quiescent gas ; by the slow rate of heat conduction in the gas itself; by the low specific heat and density of the gas; /Oa Ed 'l^;- i «■ ^d 1 lu-- Ph E ° m 'A v\ Cd ^"^ ^^^ Cc 10 20 Volume, Cu.Ft. Fig. 268. 30 EXTERNAL-COMBUSTION GAS ENGINES 399 and by the comparatively low maximum temperature at which it is advisable to maintain metal. In order that gas may absorb or give up heat rapidly, it must pass over the metallic surfaces in a thin stream and at high velocity. This necessitates a large engine. The time neces- sary for heat exchanges is so great that the engine must run at very slow speeds with few cycles per minute. Obviously, the smaller the number of cycles the greater must be the energy made available per cycle, and hence the greater the size of the engine to deliver a given amount of power. The effect of low specific heat is to increase the weight of gas necessary for a given heat change, and the low density results in a large volume for a given weight. Both effects increase the size and cost of engine for a given power. Ideal Engine 194. Rider Hot- Air Engine, (a) This engine, which approxi- mates the Stirling cycle (Section 54), is shown in Fig. 269, and by comparing it with Fig. 23, re- produced at {b) in the upper right-hand corner of Fig. 269, it is seen to have all the parts of the ideal engine following this cycle. In the two figures similar parts are designated by the same letter. The ideal hot body is replaced by a fur- nace, the gases of which at temperature 7"i jacket the hot cylinder F. The regenerator R is approximated by a pass- age filled with closely spaced plates HH. The cold cylin- der Fi is jacketed by water X from pump P and is main- tained at a practically con- stant temperature T2. The water replaces the cold body. By means of connecting rods / and J' the pistons D and C are connected to cranks / and /' which are fastened to the shaft, with the crank for the hot cylinder REAL ENGINE Fig. 269. 400 HEAT-POWER ENGINEERING leading the other * by about 90 degrees. The crank shaft carries a flywheel W which maintains uniformity of rotation, even though the power, developed and delivered, varies widely. (b) In the ideal cycle. Fig. 22, and (a) in Fig. 269, it is assumed that during the isothermal reception of heat by the gas, the left piston remains stationary at the bottom of its stroke, while the right piston rises; that during the isothermal rejection of heat the reverse action occurs ; and that during the isovolumic changes the two pistons move at such rates as to keep the total inclosed volume constant while the gas passes through the regenerator. In the actual case these actions are roughly approximated by connecting the pistons to cranks which are nearly at right angles. When either piston is at or near its lowest position, most of the working substance is in the other cylinder, where the piston is at about half-stroke (since the cranks are at about right angles). The material meanwhile is undergoing an isothermal change, which is expansion if the gas is in cylinder F, or compression if in Fi. In two intermediate positions of the cranks the pistons are moving with equal and opposite velocities, while the gas is undergoing isovolumic transfer from one cylinder to the other. Thus in the Rider engine the Stirling cycle is roughly approxi- mated, with considerable blending between the various processes. (c) The actual diagram obtained from this engine cannot readily be directly compared with the theoretical, and a reproduction is therefore omitted. The maximum and minimum temperatures are respectively lower and higher than the theoretical, and the corners of the diagram are very much rounded. (d) If the furnace temperature be assumed at 1500° F., a low value, and the jacket temperature at 60°, a rather high value, the Stirling cycle efficiency is The diCtudX thermal efficiency on the i.h.p. (TIEf) is seldom as much as 2 per cent, so that the best indicated efficiency is about lEf = 2/73.5 = 0.027 = 2.J per cent. * That is, preceding it in the direction of rotation. EXTERNAL-COMBUSTION GAS ENGINES 401 The corresponding efficiency for internal combustion gas-en- gines and steam engines is generally 50 per cent or more. The poor economy of this engine is thus very striking. 195. Ericsson Hot-Air Engine, (a) This engine, which ap- proximates roughly the Ericsson cycle (Section 55), is shown in Fig. 270, in which the parts are lettered to correspond with the REAL ENGINE Fig. 270. theoretical engine shown in Fig. 23. The furnace U replaces the hot body; below the " displacer " piston j is the hot cylinder Y, jacketed by the furnace gases, and above it is the cold cylin- der Fi with jacket X supplied with water from pump P. The upper or working piston 2 transmits the power. When the displacer piston j is up, most of the gas is below it in the hot cylinder. Upon descending, this piston transfers the gas to the cold cylinder Fi above, and when ascending, returns it to the hot cylinder F. The function of the regenerator R is performed by the walls of the cylinder and of the loose-fitting displacer piston, between which the gas passes in transferring from one cylinder to the other. The engine has an ingeniously arranged mechanism which gives such kinematic motion to the displacer and working pistons 402 HEAT- POWER ENGINEERING as to produce approximately the PV-changes of the theoretical Ericsson cycle. (b) The conditions of heat transfer are even poorer in this engine than they are in the Rider, and as a result the power developed for the same heat supply, and for same size of cylinder, is only about one-third of that obtained with the other engine. (c) It is worthy of note that a very large hot-air engine of a different type, which was constructed by Ericsson, gave a thermal efficiency of about lo per cent. It was, however, enormously bulky and mechanically unsatisfactory. C CHAPTER XXIV. INTERNAL-COMBUSTION ENGINES. Methods of Operation. 196. Advantages and Types, (a) Although external-combus- tion engines with gaseous working substance are not generally commercially successful, the internal-combustion engine, on the other hand, is widely used, and is capable of giving the highest economies now attained by any type of heat engine. The success of the internal-combustion engine is chiefly due to the fact that, since the products of combustion constitute the working substance, the maximum temperature is that due to combustion; whereas in the external-combustion engine the maximum temperature of the working substance is limited by the capacity of metallic walls to withstand high temperature, and to transmit heat. In internal-combustion engines with proper design the highest temperature attainable may be used without danger to metallic walls, and it is thus possible to approach theoretical efficiencies corresponding to temperatures of from 2500° to 3000° F. Be- cause of the high pressures that accompany high temperatures, the engines are also small for a given capacity. (b) During the past twenty years the use of internal-com- bustion engines has rapidly increased, until now many large power plants depend entirely upon them for power. These engines operate on either the Otto cycle or the Diesel cycle. Engines following the latter cycle were until recently a more or less special type adapted only to certain limited conditions, but this limitation is rapidly disappearing. (c) There are two distinct types of engine following the Otto cycle; one requires two piston strokes, and the other four, to complete a cycle. They are known as two-stroke cycle and four-stroke cycle engines, or improperly as " two-cycle " and " four-cycle " engines. The four-stroke cycle is in more 403 404 HEAT-POWER ENGINEERING To Atmosphere Fig. 271. common use, though it has several theoretical and practical disad- vantages as compared with the other type. 197. Cylinder Operations of Four-Stroke Otto Cycle, (a) The heat is evolved within the cylinder by the burning of a mixture of fuel gas, or vapor, with air, which supplies oxygen for combustion. The gaseous products of combustion form the working substance, which, after expansion, must be ex- pelled from the cylinder to give place to a fresh combusti- ble charge for the next cycle. The engine is shown diagram- matically in Fig. 271. (b) Imagine a cylinder as shown in the figure, with an inlet valve / and an exhaust valve E located in the head and arranged to open inwardly; and assume that the piston is in its extreme left position, that its motion can be controlled as desired, that a cycle has just been completed, and that the " clearance space'' or " combustion space " between the face of the piston and the cylinder head is filled with burnt gases at atmospheric pressure. Now with the valve E closed, and with / open to a supply of combustible mixture at atmos- pheric pressure, the first stroke of the piston (to the right) will cause some of this mixture to pass into the cylinder, where it will mix with the burnt gases, and thus diluted will fill the available space at approximately atmospheric pressure. The line ed in Fig. 272, 'at a height of 14.7 pounds per square inch above the horizontal axis, represents this process. Now imagine the inlet valve / closed and the piston moved to the left performing the second stroke. During this stroke the mixture will be compressed until, finally, its volume is reduced to that of the clearance space. This compression may be 600 6t \ \ s a ^ 31 .06 V Fig. 272. INTERNAL-COMBUSTION ENGINES 405 assumed to be adiabatic, although this would not be absolutely true in any real case on account of the thermal properties of the metallic walls. The ideal process is represented by the adiabatic compression line da, corresponding to the similar line in Fig. 26, page 94. At this point a the charge is ignited by an electric spark, or other means, and it may be assumed to burn^ completely with the piston stationary. This would cause an increase in tem- perature and pressure corresponding to the ideal isovolumic addition of heat, as shown by the line ah, Fig. 2^2. The piston will then make a third stroke, being driven out by the high- pressure gas expanding according to the curve he, which may be considered an adiabatic. In the ideal case heat would be given to the cold body accord- ing to process cd, while the volume remained constant, but in the actual case the exhaust valve E, in Fig. 271, is opened, allowing the high-pressure gas to expand into the atmosphere until the pressure in the cylinder falls to d. During the fourth stroke the returning piston expells the remain- ing gas according to the line de, and at e the starting conditions are restored, with the clearance space filled with burnt gases at atmospheric pressure. (c) Although four strokes are required to complete the prac- tical cycle, the work area under the line ed cancels that under de; thus the ultimate result is the development of a cycle inclosing the work area abcda, exactly as in the ideal Otto engine discussed in Section 56, page 94. The two strokes corresponding to ed and de axe really pumping strokes, used to draw in the new charge of combustible and to expel the burnt gases. They are, therefore, necessitated by prac- tical considerations, though not essential to the ideal cycle. (d) A real engine of this type is shown semi-diagrammatically in Fig. 273. The cylinder head has been broken away to show the valves, which correspond exactly to valves / and E of Fig. 271. Instead of using a mixture reservoir, assumed in the ideal case, the real engine forms its own mixture during the suction stroke, drawing the constituents through the pipes in the figure. The cylinder and cylinder head of the real engine are water- jacketed to prevent overheating of the metal. The valves in this case are positively operated by linkage 4o6 HEAT-POWER ENGINEERING (not shown) moved by cams on the " half-time shaft," or " cam shaft," shown along the side of the engine. This shaft is driven by gears from the crank shaft, the gears being so proportioned as to give the cam shaft one revolution for every two revolutions of the crank shaft. Fig. 273. 198. The Air Card, (a) The series of operations just described cannot be carried out perfectly in any real engine; thus the picture of what actually occurs in the working cylinder is quite different from Fig. 272. (b) The losses in the cylinder are commonly determined by comparing the actual diagram with the diagram of an ideal Otto cycle with air as the working substance. This ideal diagram is also called the " air card," or " air diagram,'' and it is constructed for an engine like that shown in Fig. 271, operating as described in the last section, but with air only in the cylinder. Referring to Fig. 272, it is assumed that at the point d the clearance and displacement volumes are filled with air at atmos- pheric pressure and temperature; that the compression da is adiabatic; that at a heat is added equal to that which would be liberated by complete burning of the combustible mixture used per cycle in the real engine; that from b the expansion is adia- batic to c; and that the heat is then removed, as in the ideal case, until the air returns to starting conditions at d. (c) The pressure at a can be found from Eq. (45 b) and the temperature can then be computed from Eqs. (51) and (52). INTERNAL-COMBUSTION ENGINES 407 The height of the point h is obtained thus: First find the theo- retical temperature to which this quantity of heat would raise the charge of air, with heating taking place at constant volume, and with specific heat of air constant; then determine the corre- sponding pressure Ph from the relation " = -~^ • Fig. 274. . 199. Real Indicator Card for Four-Stroke Cycle, (a) In Fig. 273 is shown a real engine with the cylinder surrounded by a water jacket to prevent overheating of the metallic walls. Fig. 274 shows another engine in which the cylinder is covered by ribs presenting large radiating surface so that air may be the cooling medium instead of water. The actual cards obtained from such engines differ in many respects from the ideal air card just discussed, because of (i) chemical and physical properties of the real working substances; (2) thermal properties of the metallic parts of the en- gine; and (3) mechanical faults, such as leaking piston and valves. The variations are shown in Fig. 275, in which the real card (full lines) has been superimposed on the ideal diagram (dotted). Parts of the real card have here been overdrawn to accentuate the variations. (b) Starting at the end c of the expansion line, in the ideal case with the mechanism of Fig. 271, the exhaust valve would be opened to allow the charge of the preceding cycle to escape into the exhaust pipe. In the real case, however, this valve must start to open before the end of the stroke, say at c' , which is usually at from 85 to 90 per cent of the out-stroke. This is neces- sary so that the valve, which cannot be opened instantly to its full extent, may have time to open fully before the end of the stroke is reached; and because the gas in the cylinder, due to its inertia, takes an appreciable time to pass through the exhaust valve despite the fact that the gas pressure of from 15 to 35 pounds or more above the atmosphere is available to accelerate it. From c' the expansion line drops rapidly to the end of the stroke, both because additional space is vacated by the piston 4o8 HEAT-POWER ENGINEERING as it continues outward, and because of the exit of gas from the cyUnder. (c) The line d'e^ is higher than the ideal exhaust line de. This is due to the pressure difference necessary to cause the flow of gas through the exhaust valve and pipe to the atmosphere. As the area opened by the valve is limited by practical consider- ations, a high average velocity of gas flow through this valve is 800 P400 necessary in order to empty the cylinder in the available time. This velocity varies from 80 to 125 feet or more per second, and to produce it the exhaust pressure line d'e^ must be from one to thr^e pounds above atmospheric. Instead of being straight, this line is generally more or less wavy because of the inertia of the gases. (d) At e\ with the piston at the end of the stroke, the clear- ance is filled with products of combustion at a pressure slightly above atmospheric and at a temperature probably 700° to 900° Fahr. As the piston starts on the " suction stroke," these gases expand to some pressure /, from one to six pounds below that of the mixture supply (which is usually at atmospheric pressure), before the new charge begins to flow through the open inlet valve into the cylinder. This flow continues as the piston moves out until the end of the stroke is reached at g, when the cylinder is filled with a mixture of the new charge and the INTERNAL-COMBUSTION ENGINES 409 burnt gas previously left in the clearance. This ''suction line,'" fg, is only approximately straight and horizontal. Evidently during both the exhaust and the suction strokes the piston must do work on the gas, and this decreases the power that the engine can deliver. (e) The compression line ga' is generally below da (i) because compression begins at g with pressure below atmospheric; (2) because the physical properties (7, etc.) of the real mixture are different from those assumed for air (3) because the process is not adiabatic, for there is heat interchange between the gas and the walls of the piston, cylinder, and head; and (4) because of leakage past piston and valves. This process is generally inter- mediate between an adiabatic and an isothermal. (f) At or near a' ignition occurs, and as it actually takes an appreciable time for the flame to spread throughout the mixture, and as the piston does not remain stationary at the end of the stroke during the complete process of combustion, the sloping ignition line a'h' results, instead of the vertical line ah of the ideal process. Combustion is seldom complete, even when the highest pressure is reached, hence heat is still being added when expansion starts. (g) The pressure does not rise as high as the ideal value b, presumably because (i) the initial pressure a' is less than the ideal at a; (2) the movement of the piston increases the volume during combustion; (3) the average specific heat of the mixture is different from that assumed for air and increases as the tem- perature rises; (4) the surrounding metallic walls absorb some of the heat generated; (5) the chemical reactions accompanying combustion may result in products occupying less volume than the original mixture; (6) there may be a certain amount of dis- sociation at the higher temperatures ; and (7) there may be leakage past the piston and through the valves. (h) The expansion line is at first generally above an ideal adiabatic curve h'l because of " after burning,'' or the continu- ation of combustion, which usually adds heat in excess of that absorbed by the metal walls and that converted into external work. Later, as the motion of the piston continues, the relatively cooler cylinder walls are uncovered and they rapidly absorb heat from the gas, causing the expansion line to drop below the adia- batic. 4IO HEAT-POWER ENGINEERING (i) During part of the compression, and all of the combustion and expansion, heat is absorbed by the inclosing metallic walls, from which part of it is carried away by the water or air jacket. This is a direct loss, but it is necessary in order to prevent over- heating the metal. (j) During the suction stroke the incoming gas receives heat from the confining walls and from the exhaust gas still remain- ing in the clearance space, until at the end of the stroke the gas and inner surface of the walls are probably at nearly the same temperature. Because of the expansion of the gas due to this temperature (which is often from 700° to 900° Fahr.), and because of the reduction of pressure below atmospheric during the suc- tion stroke, the weight of fresh mixture drawn in is reduced, and hence less than the theoretical work per cycle is done in a given cylinder. 200. Losses in the Four-Stroke-Cycle Engine, (a) A com- plete analysis of all the losses in the cylinder of an internal-com- bustion engine would be very complicated, and is as yet unsat- isfactory because of the lack of experimental data. For the purposes of this book, it will serve to indicate the principal sources of loss and to treat them qualitatively rather than quanti- tatively. (b) The Otto cycle efficiency is from Eq. (81) -/— tr It is seen to be dependent only on the compression ratio ( Va'/ Vg), which the designer can control, subject to practical considera- tions, by the selection of proper clearance volume, Va'. Thus theoretically, nothing is lost by the low pressure or high tem- perature at g. (c) Section 199 (j), however, showed that the actual weight of fresh charge drawn into the cylinder during the suction stroke is always less than the theoretical, and this of course reduces the power developed. Let Fa' be the volume corresponding to the actual weight of gas drawn in, and Vs be that equivalent to the piston displace- ment per stroke, both volumes being measured at atmospheric pressure and temperature. Then the ratio f-:!^) is called the INTERNAL-COMBUSTION ENGINES 41 1 volumetric efficiency. In practice its value may reach 90 per cent in well-designed slow-speed engines, or it may be reduced by high speed or incorrect design to 50 per cent or less. Evi- dently, in a given engine the amount of heat liberated per cycle depends on the volumetric efficiency, and hence for definite power output a lower volumetric efficiency makes necessary larger cylinder and greater cost of engine unless operated so as to give more cycles per minute. (d) The effect of the falling of the real compression line below the adiabatic, upon the performance and efficiency of the engine, is difficult to state in any general way. Since the line lies between the isothermal and adiabatic, the work done is slightly less than that which corresponds to an adiabatic process, and this compensates more or less fully for the loss of heat which makes this line fall below the adiabatic, and for the correspond- ing lowering of the efficiency. (e) The combustion line a'h' represents the most complicated process in the cycle and is the most difficult to investigate, as the phenomena take place with comparative rapidity and vary with the character of the mixture, the method of ignition, the surface form of the combustion space, etc. The real loss during this process cannot be accurately measured by comparison with the ideal air diagram, but could be determined by comparison with a card drawn for the working substance actually used in the real engine, considering specific heats variable and accounting for any other theoretical modifying conditions. As this would mean a different standard for every fuel, and for every different mixture of fuel and air, the " air standard " is retained for simplicity. In considering the sloping combustion line a'h\ it is again a case of balancing gains and losses. The piston movement reduces the maximum pressure and temperature, thus decreasing the heat lost to the cylinder walls, but this is offset more or less completely by the larger surfaces exposed while the temperature is high. The slope which will give the highest efficiency cannot be predicted, but usually an inclination which will bring the top of the combustion line at about 2 per cent of the stroke seems to give the best results. The loss of area between the real and theoretical combustion lines is partly compensated by the broad- ening of the top of the diagram. This change in form of the 412 HEAT-POWER ENGINEERING diagram improves the mechanical operation of the engine be- cause the pressure changes are less sudden and less intense. (f) The expansion line b'c' generally incloses slightly more area than the adiabatic b^l (Fig. 275), unless the engine is of such proportions as to expose excessive wall area. By opening the exhaust valve at c', as in Fig. 276 (a), less area of diagram is usually lost than if the opening is at the end of Fig. 276. the stroke, as in Fig. 276 (b) ; and as less hot gas remains in the cylinder the tendency to overheat the metal walls is reduced. The actual heat interchanges during exhaust are problem- atical. The enormous rush of gas through the exhaust valve consumes heat which is lost to the atmosphere, but there is a corresponding gain due to increased volumetric efficiency result- ing from contact of the new charge with cooler walls. Quite remarkable success has been achieved by engines in which cold air is blown through the cylinder during part of the exhaust period. This operation cools the walls and tends to remove the burnt gases from the clearance space, and hence the charge drawn in is cooler and purer than in the ordinary type of engine. Such engines are known as "scavenging'' or '^positive scavenging " engines. 201. Requirements for High Efficiency of Combustion. (a) There are two antagonistic requirements for high efficiency of combustion: (i) The final compression pressure and temper- ature (at a', Fig. 275) must be high, since this not only gives high efficiency theoretically (see Eq. (80)), but also because experience shows that the charge is often more readily ignited and burned from high pressure. The limit is reached when the pressure is so high as to cause " preignition,'' that is, spontaneous ignition of the mixture during compression. With other things equal, the greater the pressure and temperature at the end of compres- sion, the higher will be the final temperature at b\ (2) The maximum temperature attained (at the point b') should be as low as possible, because the specific heats and loss of heat to metallic walls increase rapidly at high temperatures. INTERNAL-COMBUSTION ENGINES 413 (b) These two requirements for high actual efficiency can be harmonized in practice by using a mixture with large excess of air. This may be highly compressed without danger of preigni- tion; it burns rapidly enough at high pressures for satisfactory combustion; and, because of the excess of air present, the final temperature attained is comparatively low. Unfortunately, however, the mixture which gives highest actual efficiency " on the brake " does not give maximum possible power from a cylinder of given size operating at given speed; thus there is a tendency to operate engines with mixtures " richer " in combustible than those giving the highest efficiency. 202. Indicated Work and Power of the Four-Stroke-Cycle Engine, (a) In the diagram shown in Fig. 277, with the " lower loop " Jghef considerably exaggerated, the arrows indicate the directions in which the various lines are traced. (b) If areas on a PV-diagram sur- rounded by lines generated in one di- rection (here clockwise) represent work done upon the piston, or positive work, ^ -p. then areas inclosed by lines of reverse direction (here counter-clockwise) indicate work done hy the piston upon the working substance, or negative work. Thus the work represented by the upper area or " loop," abcdea, is positive; the work corresponding to the " lower loop," fghef, is negative; and the net useful work on the piston would be represented by the difference between these areas. (c) The exact interpretation of "indicated power" in the case of a four-stroke-cycle gas engine is still unsettled. All things considered, it seems best to calculate i.h.p. from the upper loop alone. Then the difference between the i.h.p. and the d.h.p. is the work lost in overcoming both the fluid friction and the friction of the mechanism. The fluid-friction loss is measured by the area of the lower loop; it would equal zero with frictionless flow. The engine-friction loss is the difference between the total friction loss and that due to fluid friction ; it would equal zero with a frictionless mechanism. (d) The mechanical efficiency is the ratio . , - As applied to gas engines, it includes both kinds of friction loss when the 414 HEAT-POWER ENGINEERING i.h.p. is computed according to the method just given. It is advisable to adhere to this method because of the difficulty of obtaining the correct area of the lower loop. 203. The Two- Stroke- Cycle Otto Engine, (a) Comparison of single-cylinder single-acting Otto engines of the four-stroke- cycle and the two-stroke-cycle types shows that in the former there is one power stroke out of four, while in the latter there is one power stroke out of two. Hence with the same rotative speed and cylinder dimensions the two-stroke-cycle engine theo- retically should give twice the power of the four-stroke-cycle engine, and should require much less flywheel weight to main- tain the same degree of uniformity in rotative speed. Moreover, in the four-stroke-cycle engine the mechanism, which is designed for very high pressures, is used half the time for pump- ing gas at low pressure (while forming the lower loop of the diagram). And to make matters still worse, the density of the mixture, and therefore the weight of gas drawn in per cycle, is reduced by heat received from the hot cylinder walls, and this increases the cylinder size for a given power output. In the two-stroke-cycle engine, on the other hand, a separate, specially designed pump, with cool walls, may be used more effectively for this service. (b) The two-stroke-cycle engine is represented diagrammatic- ally in Fig. 278. The pump cyHnder has an inlet valve A, and To Atmosphere Fig. 278. a discharge valve /, which latter also serves as an inlet valve to the power cylinder. This cylinder has a ring of ports, E, cut through the walls at such a point that the piston, by uncovering them near the end of its stroke, acts as an exhaust valve. (6) , 14.7 Lbs. sq. in. J INTERNAL-COMBUSTION ENGINES 415 (c) Now imagine the ideal cycle performed without mechani- cal or thermal loss as follows: Consider the power cylinder filled with mixture at atmospheric pressure, the power piston just covering the exhaust ports E.. The first stroke is to the left, causing compression of the charge according to the line d'a in Fig. 279 (a). Combustion produces the line ab. Expansion during the second stroke occurs according to the line bc\ and when the piston passes the ports, E, exhaust occurs according to the line cd, thus nearly completing the cycle in the power cylinder. Meanwhile the pump piston has moved down and drawn in ,.. . . Fig. 279. from the reservoir a charge of mixture sufificient to fill the power cylinder, the theoretical process being represented by ^/ in Fig. 279 {b). The valve A is then closed, and after the pressure in the power cylinder has dropped to atmospheric at d in Fig. 279 (a), the valve / is opened and the pump piston is quickly raised, driving the mixture into the power cylinder, according to the theoretical line fe. While this is occur- ring the power piston moves from d to d' : In the ideal case the charge entering the power cylinder will drive the remaining exhaust gases out through the ports as it moves down the length of the cylinder in a solid column, and arrive at the exhaust ports just as the returning power piston covers them. The power cylinder is thus charged with a com- bustible mixture, with volume as shown at d\ at atmospheric pressure, and with the conditions assumed at starting. The theoretical pumping work, represented by the area under ef minus the area under fe, is zero, as in the case of the ideal four-stroke cycle. In the power cylinder the Otto cycle is followed except at the end cdd\ which is modified for practical reasons. (d) The differences between the actual-work diagram and the ideal Otto cycle are quite similar to those occurring in the four-stroke-cycle'engine, and arise largely from the same causes. The pump does not actually operate in the ideal manner. It is usually driven from a crank on the engine shaft, and in con- sequence the gas must be pumped to some intermediate reservoir, where it must be maintained at a pressure of from 0.5 to 7 pounds 4i6 HEAT-POWER ENGINEERING above atmospheric in order to fill the power cylinder in the short time available after the inlet valve opens. Energy is not only lost in overcoming the pump friction and resistance to flow, but is also expended in compressing the mixture in the pump cylinder. The work done on the gas is shown by the area of the actual pump card. Because of its great velocity, the entering charge generally mixes more or less with the burnt gases, and some portion usu- ally escapes through the exhaust ports before they are covered. Although theoretically the two-stroke-cycle engine would develop twice the power given by a four-stroke-cycle engine of the same size and r.p.m., the actual ratio is usually from 1.4 to 1.6, owing to the losses due to the method of operation. Fig. 280. (e) In some two-stroke-cycle engines the power cylinder is first scavenged by admitting air under pressure ahead of the mixture so that none of the fresh charge escapes with the ex- haust. The saving thus effected is, however, offset more or less completely by the necessity of using two pumps instead of one, with, increased complexity and greater expenditure of energy in pumping. One engine of this type is shown semi-diagram- matically in Fig. 280 and is known as the Koerting design. In some single-acting engines operating on the two-stroke cycle, the mixture is first admitted to the crank case, as in INTERNAL-COMBUSTION ENGINES 417 Fig. 281 (a), where it is compressed by the under side of the piston acting as a pump during the down stroke. The opening of separate inlet and exhaust valves is replaced by the uncovering of the inlet and exhaust ports by the piston when near the end of its stroke, as shown in Fig. 281 {h). The fresh charge entering through the inlet port is so baffled as to assist in driving the burnt gases toward the exhaust port. Fig. 281. 204. The Diesel Engine. (a) Engines commercially known by this name operate approximately on the cycle discussed in Section 58, and shown in Fig. 29. The real cycle may be com- pleted in either two or in four strokes. (b) The mechanical operations within the power cylinder of the real engines are very similar to those of the Otto engine. With four-stroke operation the suction stroke charges the cylinder with air, which on the return stroke is compressed into a clear- ance volume so small that the terminal pressure is very high, equal to 400 to 500, or more, pounds per square inch, with correspondingly high temperature. Just before, or when, the piston reaches the end of the compression stroke, a small quantity of finely atomized liquid fuel is blown into the clearance space by means of air at very high pressure. The fuel immediately ignites, due to the high temperature of the air that was compressed in the clearance space by the engine piston. The combustion which ensues continues a little longer than the period of injection. As the moving piston increases the volume a little faster than the gas tends to expand under the action of the heat developed, and as heat is lost in the cylinder walls, the upper line of the card slopes slightly, as in Fig. 282. In this figure the ideal and real diagrams are shown superimposed, with the lower loop exaggerated. Fig. 282. 41 8 HEAT-POWER ENGINEERING (c) Within the past few years several designs of two-stroke- cycle engines operating on this cycle have been made, and some of these give considerable promise of success. 205. Modifications to Suit Different Fuels. Theoretically, the internal combustion engines just discussed can use any fuel that can be introduced as gas or vapor (or even as finely divided solid) in a combustible mixture. In practice the fuels used are the combustible commercial gases, petroleum products,, the by- product tars from gas works and such, and alcohol. It is gen- erally necessary to make the design of some parts of the engines and auxiliaries special for each different fuel, and as a result commercial engines are often named after the fuel used; thus there are " producer-gas engines," "gasoline engines," ''kerosene engines," etc. The chief differences between types are given in the following sections. 206. Compression and Maximum Pressures, (a) In prac- tice one of the most important considerations is the final com- pression pressure. In theory the thermal efficiency will increase with the final compression pressure, and within limits this is true in the real engines (see Section 219). It is found, however, that compression above certain limiting pressures causes spontaneous ignition, or preignition, which tends to stop the engine. With some fuels the spontaneous-ignition temperature and pressure are so high that the compression limit is not set by preignition, but by commercial considerations. Thus, with very high compression the " up-keep " may exceed the gain due to increased thermal efficiency. For example, engines using blast- furnace gas usually compress only to about 175 pounds gauge, or even less, although the preignition pressure is much higher, and the thermal efficiency of engines compressing to 200 pounds has been shown to be better. (b) The usual compression pressures (terminal) in the differ- ent types of engines as now designed are given in Table XI. This shows that the lowest compression pressures are used with the fuels high in hydrocarbons, while high pressures are used with fuels low in these constituents. High compression increases the thermal efficiency, not only INTERNAL-COMBUSTION ENGINES 419 because it improves the theoretical cycle, but also because it aids ignition and makes combustion more rapid. This is particularly true with the weaker fuels, like blast-furnace gas. TABLE XI. — COMMON COMPRESSION PRESSURES. Fuel. Comp. Press. Lbs. above Atmos. Fuel. Comp. Press. Lbs. above Atmos. Kerosene Gasoline Illuminating g^as Natural gas 50 to 75 60 to 75 70 to 90 100 to 125 Producer gas Blast-furnace gas Alcohol 120 to 150 140 to 175 140 to 180 (c) In theory, with other things equal, the greater the calorific value of a charge and the higher the temperature before igni- tion, the higher will be the maximum temperature and pressure attained by the combustion. In practice this is modified by the considerations brought out in preceding sections of this chapter. In general, engines in which the maximum pressure is high because of rich mixtures and high compression must be stronger and heavier than those using "weak" mixtures and low com- pressions. CHAPTER XXV. INTERNAL-COMBUSTION ENGINES {cont). Mechanical Features. 207. Cylinder Arrangement, (a) In the theoretical discus- sion of preceding chapters, only single-cylinder, single-acting engines were considered. In practice there are three principal reason^ for making "multi-cylinder units'' and for making, " double-acting engines.'' These are: (i) The turning effort at the shaft of an internal-combustion engine with one single-acting cylinder is very uneven. This can be partly counteracted by the use of a very heavy flywheel, but this is objectionable for several reasons. As a result, both multi-cylinder and double-acting constructions are used to give overlapping cycles and therefore more even turning efforts. (2) The power which can be obtained from a given cylinder depends upon the quantity of heat which can be liberated in that cylinder by combustion. This, in turn, depends upon the volume of mixture which can be contained in the cylinder, and hence upon the cylinder dimensions. Experience has shown that a cylinder diameter of from 42 to 45 inches is about as large as is commercially advisable with present methods of construc- tion and with the materials now in use. As the length of the cylinder cannot be increased without limit, it results that the maximum power that can be obtained per cylinder is limited. A single-acting cylinder can be constructed to develop from 500 to 700 horse power, and when larger powers are required per unit, double-acting or multi-cylinder constructions must be used. (3) Because of the high pressure generated in gas-engine cylinders, the forces transmitted by the moving parts of the engine are very large, and these parts must be made correspond- ingly large. With the single-cylinder construction, the unbal- anced forces are of great magnitude. These can be decreased by a proper arrangement of several cylinders. 420 INTERNAL-COMBUSTION ENGINES 421 (b) The attainment of a more even turning effort than is possible with a single cylinder is of such great importance that very few single-cylinder engines are now built in sizes above 50 horse power, and they are seldom used in sizes above about 25 to 30 horse power excepting for work where close regulation is not very important. An idea of the handicap under which internal combustion labors in this respect can best be obtained by a comparison with a single-cylinder double-acting steam engine. To produce as many impulses in a given time as an engine of this type, a single- acting four-stroke-cycle engine, running at the same speed, would require four cylinders; if double-acting, two cylinders would be needed. The two-stroke cycle construction gives the same num- ber of impulses as does a steam engine of the same type, i.e., single- or double-acting. The double-acting, internal-combustion engine, however, offers more difficulties in construction and operation than does a similar steam engine. The piston and piston rod must be water- cooled in order to prevent overheating, and the maintenance of a tight piston-rod packing is more difficult with hot gases than with steam. 208. Classification, (a) Like steam engines, the internal- combustion engines are classified in a number of ways. The principal designations, and a brief discussion of each, are given in the following paragraphs. Such things as center-crank and side-crank construction, and right- and left-hand arrangement are common to all kinds of engines and need not be further considered. (b) Internal-combustion engines are made both vertical and horizontal. For sizes up to about 500 to 700 horse power either construction is used, each having certain advantages and certain disadvantages. Above 700 horse-power commercial economy generally dictates double-acting cylinders. Very few vertical engines have been built double-acting, as there is considerable difficulty in accommodating the valves for the lower cylinder end in this construction, hence the larger powers are nearly always supplied by horizontal engines. The vertical engine has the advantage of occupying much less floor space than the hori- zontal and can be mounted on a less massive foundation. It is generally operated at a higher speed, particularly in the larger 422 HEAT-POWER ENGINEERING sizes, and is usually built with an inclosed crank case so that lubrication can be somewhat simplified. (c) The cylinders of multi-cylin- der vertical engines are practically always arranged side by side and as close to one another as possible. These engines are designated as two-cylinder vertical, three-cylinder vertical, etc. A three-cylinder vertical engine is shown in Figs. 283 and 284. With horizontal engines, however, the cylinders are often widely separated, giving what is called a twin engine. It is also very common practice to place two horizontal cylin- ders with their axes coinciding. When so arranged, the engine is called a tandem. A com- bination known as a twin- tandem double-acting is shown in Fig. 285. Fig. 283. Mix Valve (d) Internal-combustion en- MixmgVaive' gines are sometimes classified according to the use to which they are put. Thus there are stationary engines, stationary electric lighting engines, marine engines, automobile engines, etc. From this classification has sprung another, an engine of one type being designated by its type name, even when used for a different purpose. There are thus " auto-type marine engines " and " marine- type stationary engines." (e) Since certain modifica- tions, or different fittings, are necessary with different fuels, internal-combustion engines are sometimes classified according to the fuel which they are intended Fig. 284. INTERNAL-COMBUSTION ENGINES 423 to use. Thus there are kerosene engines, gasoline engines, illumi- nating-gas engines, producer-gas engines, etc. (f) These engines are also occasionally classified on the basis of the type of governing used (see sec. 212). Thus there are hit- and-miss engines, throttling engines, etc. Fig. 285. 209. Methods of Producing Combustible Mixtures, (a) With fuels initially gaseous, a " mixing valve " is generally used to control the proportions of fuel and air, the two gases being made to mix intimately either before or during entrance to the cylinder. This mixing valve may be incorporated with the inlet valve or it may be separate and at some distance from it. Examples of both types are given later. (b) Fuels initially liquid must either be atomized or vaporized and mixed with air to support combustion. With the more volatile liquid fuels, such as gasoline and alcohol, the process generally takes place outside of the engine cylinder in a '* carbu- retor"; the mixture then passes to the cylinder as in the case of fuel initially gaseous. With the less volatile liquid fuels, like kerosene or crude oil, vaporization and mixing are more difficult, and generally take place within the engine cylinder, the fuel being sprayed in either by pump or air pressure and being vaporized by heat from hot walls or gas. Examples of such devices are given later. 210. Carburetors, (a) When an engine uses a volatile liquid fuel, like gasoline or alcohol, it is customary to mix the fuel vapor and air outside of the cylinder in a carburetor, in which air, which may or may not be previously heated, is brought into 424 HEAT-POWER ENGINEERING intimate contact with the Hquid and becomes charged with the vapor. (b) A great variety of types of carburetors has been per- fected and used. Thus there are bubbling carburetors, in which some or all of the air is made to pass or bubble through the volatile liquid, on its way to the engine. There are surface carburetors, in which the volatile liquid is spread over screens, marbles, or anything else which will give a large wetted surface over which the air may be drawn. Wick carburetors have also been used. In these the liquid is drawn up into wicks by capil- lary action, and the air passing over the surface of the wicks vaporizes part of the exposed liquid. (c) Practically the only type now used in this country is the jet carburetor. This apparatus is made in many forms, but the fundamental principle of all is the same. A fine jet of gasoline is injected into the air pipe and generally only during the suction stroke. The impelling force is usually either the pressure due to a slight head of gasoline or the difference between suction pres- sure and atmospheric pressure., or this difference augmented by the suction effect of rapidly moving air upon a nozzle immersed in it. (d) One of the most common types of jet carburetor, known as a carbureting valve, is shown in Fig. 286. The valve is some- times the inlet valve of the cylinder, but more often it is a separate valve through which air is admitted to the mixture pipe leading to the main inlet valve. A small hole is drilled in the seat of the carbureting valve in such a position that it is closed when the ^ latter is seated. When the valve rises (automatically) to admit air to the engine, the liquid under slight pressure issues from the hole in a very small stream, which mixes with the air and is partly or wholly vaporized before the mixture enters the cylinder. (e) Another form of jet carburetor is shown in Fig. 287. The liquid is maintained at such a height that its surface almost reaches the tip of the spray or injection nozzle when quiescent. From Pump INTERNAL-COMBUSTION ENGINES 425 The air passing around this nozzle on its way to the engine creates a partial vacuum at the nozzle, which vacuum augments the lowering of the pressure caused by suction in the engine. The air pressure on the surface of the liquid in the small tank then forces a fine jet out of the nozzle, and this is picked up by the surrounding air. The throat, or Venturi tube, increases the velocity of the air flowing through it, which materially assists in picking up and carrying the liquid during vaporization. This type is commonly used on stationary engines, the liquid level being maintained by a direct-connected pump and overflow as shown. Liquil Fig. 287, Fig. 288. (f) In Fig. 288 is shown a type of float-feed carburetor. This is similar in action to that last described, the principal difference being the float for maintaining the proper liquid lev^l. This operates by opening and closing the small valve shown as the liquid level sinks and rises, the liquid being supplied to this valve under pressure. This type of carburetor is most common on automobile and marine engines, the central float, which maintains approximately the correct level despite tipping of the carburetor, and the compact structure both recommending it for such purposes. (g) When an engine is run at widely varying speeds, it is a very difficult matter to adjust a carburetor of the type last shown to give a suitable mixture under all conditions. If the mixture is correct at low speeds, it is apt to be too rich at high speeds. This is overcome by introducing an auxiliary air valve between the spray nozzle and the engine This valve, operating auto- matically or under hand control, admits air, which, combining with the over-rich mixture, forms one of correct proportions. 426 HEAT-POWER ENGINEERING Similar devices are sometimes necessary with the carburetor used on engines which run at a constant speed, being used to make the adjustment of the carburetor easier or more certain. 211. Treatment of Heavy Oils, (a) The use of fuels like kerosene, distillate, crude oil, and such, presents greater difficulty than the utilization of. gasoline or alcohol. Kerosene can be handled more or less satisfactorily with carburetors similar to those described, but, being less volatile than gasoline, the action Fig. 289. is not so perfect. It is generally necessary to preheat the air and to jacket the mixture pipe with hot jacket water, or with exhaust gases. Even with these additions, it is often found difficult to operate satisfactorily, and most carbureting kerosene engines are arranged to spray water into the cylinder or to satu- rate the mixture with water vapor on its way to the cylinder," particularly when running under heavy loads. Just what the action of the water vapor may be is still undetermined, but it seems to give more certain, quieter, and cleaner combustion. (b) Many kerosene and other oil engines operate on what is known as the hot-bulb or hot-head principle. An engine of this type is shown in Fig. 289. The oil is injected into the hot bulb during the suction or com- pression strokes and is there vaporized by the hot walls. Air INTERNAL-COMBUSTION ENGINES 427 is compressed into the bulb during the compression stroke of the engine, and, when the mixture acquires the proper proportions, spontaneous ignition takes place. The bulb is heated to redness by a blow- torch before starting the engine, and thereafter is main- tained at the proper temperature by the heat generated during combustion. There is always a certain amount of carbon or lampblack deposited within the hot bulb by the " cracking " of the oil molecules during vaporization, and it is therefore necessary to clean the bulb periodically. (c) Practically the only other distinct method of using the heavier oil fuels in internal-combustion engines is that exemplified in the Diesel oil engine described in Section 204. This gives by far the most perfect combustion with the heavier fuels, but is open to criticism because of the high pressures involved. (d) To overcpme this difficulty, engines are now being built which may be considered a compromise between the hot-bulb and the Diesel types. The pressures are lower, but the hot bulb insures successful ignition and combustion. These engines are proving highly economical in the use of fuel, and can be kept in good mechanical condition with greater ease than can the high- pressure Diesel engine. 212. Methods of Governing Internal-Combustion Engines. (a) Stationary engines are generally mechanically regulated to maintain approximately constant speed of rotation. Automobile and marine engines are commonly hand-governed, although they are sometimes fitted with a limit governor to prevent over- speeding, or "racing.'' (b) In order to govern or regulate an engine, the i.h.p. must be varied to suit the demand, as shown in Section 134. There are three available methods of doing this: (i) The amount of energy made available per cycle may remain constant, but the number of cycles per unit of time may be changed ; (2) the num- ber of cycles may remain constant and the amount of energy made available per cycle may be varied; and (3) a combination of the two preceding may be used. (c) In general, there are four different ways of applying these methods. They are called : (1) hit-and-miss governing, (2) quan- tity governing, (3) quality governing, and (4) combination sys- 428 HEAT-POWER ENGINEERING terns. These are each considered in detail in the following paragraphs. (d) In hit-and-miss governing, the number of working cycles per unit of time is varied so as to adjust the average i.h.p. to the demand for power. With this system, some part of the mechanism for opening the inlet valve is under the control of the governor, so that when a " working cycle " is to occur it hits another part and opens the valve, but when the cycle is to be omitted it misses engagement and the valve remains closed. When a miss occurs, not only does the inlet valve remain closed, but the exhaust valve is usually held open, so that, during the strokes corresponding to the ordinary cycle, the piston pumps exhaust gas into and out of the exhaust pipe without waste of energy, except for the slight friction and heat loss. . In some engines, when the working cycle is to be omitted, a fuel valve, which is separate, is held closed while the inlet and exhaust valves act as usual; thus the piston draws in a charge of pure air, which it compresses, expands, and exhausts. This method is generally considered less satisfactory than the former, because of the cooling effect on the cylinder walls. With hit-and-miss governing all working cycles are theoreti- cally exactly alike, and are equal to the maximum for the particular engine. As all types of internal-combustion engines show greatest thermal efficiency when developing normal cycles of about maximum power, this method of governing has the theo- retical advantage of giving high thermal efficiencies at all loads. The cycles actually produced, however, are not all alike, because of irregular cooling and heating effects, the varying mixtures resulting from intermittent operation, etc. The variations become more marked with increase of the number of misses, and the method therefore gives lower efficiencies at light loads than would be expected. In general, however, it is the most economi- cal method of governing yet devised. As considerable intervals of time may intervene between "working" cycles, a very heavy flywheel is needed on engines governed by this method. Hit-and-miss governing is very satisfactory for engines where close speed regulation is not necessary, and is commonly used on the smaller sizes, say up to 25 or 50 horse power. Where close regulation is required, as for the operation of alternators in parallel, it is practically never used. INTERNAL-COMBUSTION ENGINES 429 (e) In quantity governing, the number of cycles and the pro- portions of the mixture are maintained constant, but the amount of mixture admitted per cycle is varied to suit the power demand. This is generally done in one of two ways, — by ''cut-off gov- erning," or by " throttling governing." In cut-off governing, after the amount of mixture necessary to produce the required power has been taken in, the inlet valve is closed, and the charge expanded as the out stroke, or suction stroke, continues. The cycle is then completed as usual, produc- ing under low load a diagram like that of Fig. 290, in which the lower loop is exaggerated for clearness. Fig. 290. Fig. 291. In throttling governing, except at the maximum load, the charge is throttled during the entire suction stroke to reduce the amount of mixture entering the cylinder. This gives a dia- gram like Fig. 291, in which the lower loop is again exaggerated. In both of these methods of governing, the reduction in quan- tity of mixture with decrease in load is accompanied by a lower- ing of the compression curve. If not carried too far, this is desirable from a mechanical standpoint, as it tends to produce more uniform turning effort, and reduces the necessary weight of flywheel. Of the two methods the cut-off is the better because it gives a smaller lower loop and less lost work. It also has the advan- tage that the governor action is delayed to the latest possible instant in the cycle, and hence each working cycle more nearly meets the power demand. (f) In quality governing the number of cycles and quantity of material per cycle are maintained constant, but the proportion of gas to air, or quality of the mixture, is varied, so that the power developed in the cylinder just meets the power demand. Since the same volume of mixture is drawn in each cycle and is compressed to the same pressure, the efficiency is theoretically 430 HEAT-POWER ENGINEERING constant at all loads. In practice, however, each fuel has an air-to-gas ratio that gives best results; thus it follows that this method of regulation gives maximum efficiency only at one particular load. With some fuels it is exceedingly difficult to obtain satisfactory ignition of the very " weak " mixtures intro- duced at low loads, and such mixtures also burn very slowly, the combustion continuing in extreme cases throughout the entire expansion stroke. A group of indicator diagrams Fig, 292. from a quality-governed engine is given in Fig. 292. The slow burning of the weak charges is shown by the gradual tilting of the combustion line as the load decreases. The constant compression pressure has an undesirable effect on the crank effort (see (e) of this section), as the m.e.p. of the compression line does not change with the m.e.p. of the expansion line. (g) Combined systems are sometimes used in an effort to obtain the advantages of the different methods previously described with as few as possible of their disadvantages. Thus hit-and-miss governing may be used at low loads and quality governing at the higher loads which call for sufficient gas to make a readily ignitable mixture. Or quality governing may be used at the higher loads, gradually merging into quantity govern- ing as the load decreases. All these combinations tend to complicate the valve gear and call for more or less sensitive and intricate adjustments. They are, therefore, commercially handicapped, though theoretically desirable. (h) As the form and area of the card may be changed by altering the time of ignition , this might be used for governing. It is actually used for that purpose to a certain extent in marine and auto engines. Since there is some best time of ignition for each mixture in each engine running at each speed, it is generally better to change the time of ignition to suit the conditions brought about by governing rather than govern by changing the time of ignition. In some combination systems an ignition timing device under INTERNAL-COMBUSTION ENGINES 431 control of the governor has been incorporated, but it has gener- ally been found more satisfactory to trust to hand timing. ^ ^'Mv. 2*13. Gas Valves, Mixing Valves, etc. (a) When gas is sup- plied an engine under pressure, as is generally the case in all except "suction gas-producer" plants (see Fig. 5), a gas valve of some sort is necessary to shut off the gas supply during all but the suction stroke of the engine. (b) This valve may be combined with the inlet valve of the engine, giving the arrangement shown diagrammatically in Fig. 293. The air and gas cocks shown are used for proportion- ing the mixture by hand, and the gas cock is also used as a permanent shut-off valve. Such an arrangement can be used with hit-and-miss or with quantity governing, but is obviously unsuited for quality governing because of the hand regulation of the proportions. (c) The gas valve is more commonly a separate valve, although it may be carried loosely on the same stem as the inlet valve, as a in Fig. 294. When thus made separate from the inlet valve, it can be put under governor control, so that any kind of govern- ing can be adopted, at the option of the designer. In all cases it is common practice to supply gas and air cocks or their equiva- lent so that the proportions of the mixture can be roughly regu- lated by hand and so that the gas can be permanently shut off from the engine. (d) The terms mixing valve and proportioning valve are used rather loosely to designate anything which has to do with the mixing of air with gas already measured out, or with the measur- ing and mixing of the constituents of the charge. In the strictest 432 HEAT-POWER ENGINEERING sense a proportioning valve, and to a certain extent a mixing valve, precedes the inlet valve, measures the combustible part of the charge, and mixes it with the air. A gas valve under governor control, combined with surfaces, or passages, which will mix the gas with the air before or during passage through the inlet port, is properly a mixing or proportioning valve. One example of this sort of arrangement is shown in Fig. 294. The small gas valve a is guided by the sleeve sliding on the stem of the inlet valve h. It is operated by separate linkage under governor control, so that the time, or extent, of its opening can be varied to suit the load. In operation, the inlet valve opens first, allowing fresh air to enter the cylinder and blow away hot burned gases. The gas valve a then opens, admitting gas, which, traveling downward, is thoroughly mixed with the air as it issues from the small holes shown. The valve a closes before the inlet valve b, so that the mixing chamber becomes filled with pure air before being shut off from the cylinder. Such a device is commonly known as a combined mixing and inlet valve, although the gas valve is occasionally designated as a mixing valve or a proportioning valve. (e) The elements of another type of mixing valve are shown in Fig. 295. The inner cylinder is supposed to be under governor control, so that it can be rotated more or less as the load varies, thus changing the effect- ive openings of the gas and air ports to suit the demand for power. By properly proportioning the gas and air ports, their areas may be made to change at the same rate under the action of the governor, thus giving throttling regulation; or the areas may be ^ made to change differentially, giving quality governing or mixed quality and quantity regulation. (f ) Experience has shown that proportioning valves of the type shown in Fig. 295, and others using sliding surfaces, are per- fectly satisfactory when used with such fuels as natural gas and illuminating gas. Producer gas and blast-furnace gases, how- ever, carry impurities which quickly foul such sliding surfaces and impair the action of the valve. For such gases, mixing and Fig. 295. INTERNAL-COMBUSTION ENGINES 433 proportioning valves made without sliding surfaces, such as that shown in Fig. 294, must be used. Even the valve shown in this figure might give trouble because of deposits on the stem of the main valve, and a design eliminating this possibility would prob- ably give better results. 214. Methods of Ignition, (a) In the early development of gas engines the charge was ignited by opening communication at the proper time between the compression space of the engine and a small chamber containing an open flame. This method was complicated mechanically, and had so many objectionable features that it did not survive. (b) Th'e methods at present used are: (a) Hot- tube ignition ; {h) Spontaneous ignition by heat of compression (as- sisted, or not assisted, by the action of a hot cham- ber, such as a vaporizer or hot bulb) ; {c) Electric ignition. 215. Hot-Tube Ignition, (a) A simple type of hot- tube igni- tion is shown schematically in Fig. 296. The tube a, generally made of metal, is closed at one end, while the other end opens into the cylinder. By moving the burner and chimney 6, the hot zone, which is at about red heat, can be located anywhere along the tube. At the end of the exhaust stroke the hot tube, like the rest of the clearance space, is filled with burned gases at a pressure slightly above atmospheric. During the suction stroke these gases are partly ex- panded, and during the compression stroke they are compressed into the tube by the combustible mixture until the lat- ter finally reaches the hot zone, where it is ignited. the compression stroke at which the mixture is ignited can be varied. (b) By this method ignition is generally certain, but the timing is untrustworthy because of variations in the condition of the Fig. 296. By moving the hot zone along the tube, the time in 434 HEAT-POWER ENGINEERING tube or of the mixture. Hence, despite its simplicity and lack of moving parts, hot-tube ignition is not now very widely used. " Timing valves " have been used to close the cylinder end of the tube and to thus control ignition, but few have survived. Hot-tube ignition involves a constant supply of gas to the burner, and this of course adds to the fuel consumption of the engine. 216. Spontaneous Ignition. In many engines using liquid fuels heavier than gasoline, ignition is produced by the tem- perature attained during compression. In the Diesel engine the compression pressure is so high that the resulting temperature alone causes ignition. In other engines, like the hot-bulb type (Fig. 289), ignition results from the combined action of compres- sion and a hot vaporizing chamber. This method of igniting has not proved applicable to the more volatile liquid fuels and to the gaseous fuels because of the diffi- culty of timing. 217. Electric Ignition, (a) The most satisfactory method of igniting is by an electric spark. All electrical ignition systems in use, with few exceptions, fall under either '' make-and-hreak " or '^jump-spark " ignition. The less descriptive terms, " low- tension " ignition and " high- tension " ignition, are often used in place of these. (b) In the make-and-break ignition system, two " electrodes " are brought together within the combustion space to " make,'' or close, the circuit, and are separated suddenly to ''break " the circuit and produce a spark. One arrangement of such a system is shown in Fig. 297, the " igniter block,''' or "plug," entering the combustion space through the center of the cylinder head. The " stationary electrode " is designated by i and the " movable electrode " by j. The wir- ing diagram is shown in Fig. 298. In this figure, B represents a battery or other low- voltage generator, Can "induction " or " intensifier coil," E the stationary electrode, which is insulated from the igniter block and engine frame, and 5 a stud or other convenient screw fastening on the engine. The movable elec- trode is in electrical contact with the igniter block and engine frame, as shown in Fig. 297. (c) The operation is as follows: The cam a, Fig. 297, pushes INTERNAL-COMBUSTION ENGINES 435 the rod b toward the igniter and the strike block d, engaging the flipper e on lever /, moves the latter toward the left. As / moves, it draws g after it by means of the one- turn spring shown. As g moves it rotates the movable electrode until the arm j inside of the cyHnder is brought into contact with the stationary Fig. 297. electrode i. The circuit is then made and current flows until the circuit is broken by the block d traveling past the edge of the flipper e. When this occurs, the spring h pulls the arm 7 out of contact with i, and the circuit is broken. The spark results from the action of the induction coil, at the instant of breaking the circuit. The rapid change in the number of lines of force Fig. 298. through the core causes sufficient self-induction to generate an electromotive force of such intensity as to bridge the gap between the separating electrodes. (d) The timing of the spark is effected by moving guide C across the path of the bar b in Fig. 297, thus changing the time at which block d releases flipper e. (e) The type of igniter just described is known as a " hammer m^ake-and-break igniter " to distinguish it from another known 436 HEAT-POWER ENGINEERING as a '' wipe-spark " or " wipe make-and-break igniter f'' in which a movable electrode periodically wipes or slides across a station- ary electrode. The wipe spark automatically cleans the contact surfaces within the cylinder, which is in a way advantageous, but it is not so extensively used as the hammer type. (f) The make-and-break system has the advantages of being electrically simple and operating with low e.m.f., so that short circuits are not so apt to occur as in the systems described in following sections. It is, however, complicated mechanically, and because of friction and inertia of parts is not generally used on engines operating at speeds above 500 to 600 r.p.m. The movable electrode is very apt to stick or to work loose, causing trouble because of no spark or because of loss of compression by leakage. (g) In the jump-spark system there are within the cylinder two fixed termi- nals, with short intervening gap, across which a spark jumps when sufficient difference of potential has been devel- oped. In its simplest form the apparatus has two circuits, as shown in Fig. 299, with heavy lines representing the ''low-tension circuit " and the light lines the ''high-tension circuit.''^ Fig. 299. Spark Gap, Fig. 300. In the figure, B is the source of electromotive force, 7" is a rotating "timer," C a "condenser," K a "coil," and S a " spark plug," several examples of which are shown in Fig. 300. INTERNAL-COMBUSTION ENGINES 437 (h) In operation the primary circuit is closed by the timer T and then suddenly opened, with the result that a spark jumps between the terminals of the plug. The action of the coil is as follows: When the primary circuit is closed by rotation of the timer, the magnetic field induces an electromotive force in the secondary circuit. This is not great enough, however, to cause a spark to pass between the plug terminals. But when the primary circuit is quickly broken, the sudden collapse of the magnetic field about the core of the coil induces for the instant in the secondary circuit a very high potential difference, which may be made sufficient to cause the passage of a spark, with resultant ignition. The Junction of the condenser, which bridges the timer in the primary circuit, is to prevent sparking at the contact points of that apparatus. Such sparking would cause rapid deterioration of the contact surfaces and is therefore undesirable. (i) A more common type of jump-spark apparatus uses a " trembler coil " instead of the plain induction coil shown in Fig. 299. This apparatus is so arranged that the trembler forms part of the primary circuit, and is in such position that it is at- tracted to the core of the coil when this is magnetized, and thus breaks the primary circuit. This in turn demagnetizes the core, hence the trembler flies back and makes the circuit once more; thus the core is again magnetized and attracts the trembler, breaks the circuit, and so on, as long as the timer is in position to close the primary circuit. This intermittent making and breaking of the primary circuit causes a succession of sparks at the spark plug in the secondary circuit, which action is generally supposed to insure more certain ignition. The great advantage achieved is really quick action and accurate timing, though these are often counterbalanced by considerable trouble with the trembler which may call for almost constant adjustment. (j) Both of these high-tension or jump-spark systems are easily timed by shifting the phase relation of timer, or commuta- tor, and engine crank, and they are particularly satisfactory for high speed. Recently there has been a tendency to adopt these systems for ordinary slow-speed stationary work; but as the spark does not seem to have the same igniting power as that of the make-and-break system, most applications have been limited to the more easily ignitable fuels like natural and illuminating 438 HEAT-POWER ENGINEERING gas and gasoline. Few simple high-tension systems have yet been used with producer gas and " blast-furnace gas." 218. Internal-Combustion Engine Valve Gear, (a) The slide valve, so common in steam-engine practice, is never used in its simple form on internal-combustion engines for admission or exhaust. It is sometimes used for mixing purposes, as was indicated in Sect. 213. The high temperatures to which inlet and exhaust valves are subjected make lubrication difficult and cause warping of the valve and seat, and the high pressures make it difficult to keep the valve on its seat to prevent leakage. When the fuel used contains sulphur, which is not an uncommon occurrence, the valve and seat are often quickly pitted and corroded. (b) Some highly specialized slide valves are, however, in use and give good satis- faction. The control of ports by the piston of the two-stroke-cycle engine is the most common example. Recently a number of " sleeve motors " have been designed for use on automobiles and seem to promise very satisfactory operation. One example of this type is shown semi-diagrammatically in Fig. 301. The two sleeves, reciprocating vertically un- der the action of eccentrics or cranks on a side shaft, act in conjunction with the \^ / cylinder head and external cylinder to ^"^- — -'"^ control admission and exhaust by means ig- 301- Qf ^hg ports shown. The advantages of this type are rapid opening and closing of valves, long period of approximately maximum opening, and silent operation. (c) The success of this type of valve has caused the appear- ance of a number of different varieties of slide-valve and piston- valve auto-engine designs. Few of these have been tested to any extent, and it is therefore too early to draw conclusions as to their ultimate success. (d) With the exception of the cases cited above, the poppet or mushroom valve is in practically universal use for internal- combustion engines. It maintains its correct shape under INTERNAL-COMBUSTION ENGINES 439 changing temperatures more perfectly than other types; it re- quires a minimum of contact surface between valve and seat; it opens inward and is therefore forced to its seat by the high pressures in such engines; it requires no lubrication; and it and its seat are easily kept comparatively true by grinding. (e) In modern designs, inlet valves are practically never water-cooled, as the ingoing charge cools them sufficiently during each suction stroke. Exhaust valves, on the other hand, are practically always water-cooled when larger than five inches in diameter, and often in smaller sizes. This is deemed necessary because of the high temperature of the exhaust gases in which the valve is immersed during the entire exhaust period, but it. should be noted in this connection that one European builder is obtaining satisfactory operation with simple uncooled cast iron exhaust valves in the largest sizes of horizontal engines. (f) In some four-stroke-cycle engines the operating condi- tions of the exhaust valve have been improved by the use of " auxiliary exhaust ports.'' These are ports in the cylinder wall which are uncovered by the piston when near the end of its stroke. The first discharge of exhaust gases takes place through these ports, so that a smaller quantity of cooler gases is handled by the exhaust valve. This construction necessitates the use of a larger cylinder for a given power than is required without the use of auxiliary ports, and it complicates the cylinder casting. It is practically never used on double-acting engines because of these reasons, and because of the additional fact that it would necessitate the use of an enormously long piston, similar to that shown in Fig. 280, thus materially increasing the weight of the reciprocating parts. (g) Two types of inlet valve are in use, — the automatic valve and the positively actuated valve. The automatic valve is held to its seat by a weak spring, and is raised by the difference between atmospheric and suction pressures during the suction stroke. The positively actuated valve is opened mechanically and gen- erally closed by spring pressure. Automatic valves are uncertain in their action, opening only after a considerable pressure difference has been created, and then more or less slowly. After opening they do not remain wide open during the remainder of the suction stroke, but *' chatter " more or less, thus materially decreasing the volu- 440 HEAT-POWER ENGINEERING metric efficiency of the engine. For these reasons they are seldom used on the better types or on the larger engines. Positively actuated valves, on the other hand, can be made to open at the time desired, can be given an amount of opening approximately equal to that theoretically required at each piston position, and can be made to close very nearly at the right time. (h) The valves of internal-combustion engines are generally operated by means of cams, or eccentrics, on a side shaft, or auxiliary shaft, driven by gearing from the crank shaft. On the smaller engines cams are most often used, but on the larger engines the eccentrics seem to be preferred, particularly in this country. Closure practically always occurs by spring pressure, the valve being released by the opening mechanism. The cam can be manufactured more cheaply than the eccentric, and when properly designed it is not very noisy in operation and wears slowly. In general, however, it is rather difficult to obtain as perfect valve operation with cams as it is with eccentrics unless linkage is introduced, which complicates the mechanism and increases the cost. Cam Shaft Fig. 302. Fig. 303- Fig. 304. Cams may be used to operate the valves by direct contact with the valve stem (Fig. 302) ; or by contact with one end of a pivoted lever, the other end of which contacts with the valve stem (Fig. 303) ; or through rolling, rocking, or floating levers, one arrangement of which is shown in Fig. 304. The eccentric always operates in conjunction with such levers as are shown in Fig. 304. INTERNAL-COMBUSTION ENGINES 441 (i) The time (with reference to crank and piston positions) at which valves open and close varies widely with the location of the valve and with the type of engine. The exhaust valve universally opens early, generally when the piston is at about 0.9 stroke. It may close before the end of the return stroke, or on dead center, or it may remain open until after the suction stroke has started. The object of leaving it open after dead center has been passed is to take advantage of the inertia of the moving exhaust gases and thus get more perfect discharge. Where the valves, manifolds, and cylinders are so arranged that this can be done, it represents good practice. The inlet valve very commonly opens after the beginning of the suction stroke, though it is sometimes opened just before, or on dead center, in order to obtain a wider opening by the time suction actually starts. It is very generally closed after tke end of the suction stroke in order to take advantage of the inertia of the moving column of gas, thus increasing the volumetric efficiency. In general, the higher the speed of an engine the later may the valves close, and the greater may be the overlap of exhaust closure and inlet opening if the valves are widely sepa- rated. (j) Because of the heavy springs necessary to close the valves of internal-combustion engines in the short time available, and because of the relatively great weight of the valves, the parts actuating the latter are generally very strong and heavy. This is particularly true of exhaust- valve gear. This valve must be opened against the combined action of high-pressure gas and a very powerful spring. Many designers have attempted to reduce the size and wear of the actuating parts by building balanced exhaust valves. As a general rule these have not survived, probably because they simplify the external gear by complication of the inclosed part of the valve system. Because of the great weight of the valves and actuating mechanisms in large engines and because of the great magnitude of the forces transmitted by these mechanisms, it is generally undesirable or even impossible to construct governors which can operate in any such direct manner as is common in the average steam engine. Governors could not be constructed powerful enough to operate directly unless made with such 442 HEAT-POWER ENGINEERING heavy parts, and to transmit such great forces, that their sensi- tiveness would be considerably impaired. In very large engines a differential governing device is now commonly used. In such cases the governor operates upon the equivalent of a small engine of some kind, which engine, in turn, supplies such power as is necessary for moving the valve gear. As an example, the governor might actuate a small pilot valve which by its motion admitted oil under pressure to one, or the other, end of a cylinder fitted with a piston suitably linked to the inlet- or mixing- valve gear. The motion of the piston in the proper direction and to the right extent, as controlled by the governor through the pilot valve, would then serve to give the re- quired adjustment of the main valves. In smaller engines it is customary to connect the governor to some light form of mixing valve, to a balanced or floating valve of some kind, or to a light link or equivalent which is easily moved and causes the necessary adjustment by the shifting of a fulcrum or the like in the main gear. CHAPTER XXVI. INTERNAL-COMBUSTION ENGINES (conL). Efficiency, Performance, and Power. 219. Efficiencies of Otto Four-Stroke Cycle Engines, (a) Not only does the thermal efficiency of the Otto cycle engine theo- retically vary with the ratio of compression, increasing as the final volume is decreased with respect to the initial volume, but real engines also show a similar gain. The rapid improvement in the efficiency of this type of engine during the past twenty years has been largely due to this increase in compression pres- sure. It is well shown by the following table : * TABLE XII — EFFICIENCIES OF OTTO FOUR-STROKE ENGINES. CYCLE No. Year. Type of Engine. Cylinder Size. Indicated Thermal Efficiencies. Brake Thermal Efficiencies. Mechanical Efficiencies. I 2 3 4 1882 1888 1898 1908 Deutz Crossley National Crossley Inches. 6.75 X 13.7 9-5 X 18 10 X 18 II. 5 X 21 Per cent. 16 22 28.7 36.8 Per cent. 14 18.9 25 32.2 Per cent. 87.6 86.1 87.0 87.5 (b) It should not be assumed, however, that by an indefinite increase of compression pressure the thermal efficiency of the real engine can be raised without limit. For even if the ten- dency of the fuel to preignition could be overcome, calculations based upon actual performances show that with the Otto type of engine the maximum practical thermal efficiency would probably be attained with a compression pressure of from 250 pounds to 300 pounds per square inch. Blast-furnace gas engines operating with compression pressure as high as 200 pounds have given thermal efficiencies on the brake of 32 to 34 per cent. But the tendency with this fuel is * The Gas, Petrol and Oil Engine, D. Clerk, page 243. 443 444 HEAT-POWER ENGINEERING now toward the use of compression pressures in the neighborhood of 1 60 to 180 pounds because of the mechanical difficulties encountered with the higher pressures; and in this case a little under 30 per cent is extremely good thermal efficiency on the brake for modern engines, while the average operating value for good standard American types of stationary engines is about 25 to 27 per cent at rated load, and of course decreases with reduc- tion in the load. (c) Besides the compression ratio, the thermal efficiency in general can also be increased by (i) Mixing the incoming charge more perfectly; (2) Producing fairly rapid and complete combustion at the compression end of the stroke, (note, however, that too rapid combustion is not desirable) ; (3) Preventing loss of heat from the charge to surrounding metal during combustion and expansion. Many modern engines have elaborate mixing valves which cause thorough intermixing of gas and air before, or just at the time of, entering the cylinder. In high-efficiency engines the combustion space is made as nearly as possible spherical, hemispherical, or in the form of a short cylinder; and all pockets leading out of this space are avoided as far as possible. This results in less surface for the vol- ume inclosed, and thus reduces heat loss to the metal and makes the combustion more rapid and complete for a similar reason. In pockets connecting with the combustion space the gases often burn long after combustion of the main part of the charge is complete. This can be prevented by placing the igniter in the pocket, and igniting the gas there first, in which case the rapid increase of temperature will cause a sudden pressure rise, blowing some of the burning gas into the main charge, thus causing very complete inflammation. Large engines generally have slightly higher thermal efficien- cies than small engines of the same type and proportions, because large cylinders have less wall surface per unit of volume inclosed than have small cylinders of the same proportions. This, how- ever, may be counteracted by difficulty of mixing the charge in the larger cylinder and difficulty in effecting rapid and complete combustion. When large cylinder diameters are used, two or more igniters INTERNAL-COMBUSTION ENGINES 445 at different points are often operated simultaneously in each combustion space in order to reduce the distance through which inflammation must progress from each igniter. Piston speeds of high-efficiency engines are carried as high as is mechanically ifeasible in order to reduce the time of contact between hot gases and walls. (d) The values of all the different efficiencies enumerated in Sect. 105 will vary considerably with the conditions, fuel, mix- ture, type of engine, etc. ; but for the purpose of giving a gen- eral idea of the order of these values a certain type and set of conditions will be assumed. The engine is supposed to operate with * ' producer gas ' ' as fuel and (in the ideal case for drawing the air card) to have a suction pressure equal to atmospheric, a pressure of 150 pounds per square inch absolute at the end of compression, a temperature at the end of suction stroke equal to 520° F. abs., a tempera- ture at the end of compression of 1000° F. abs., and a tempera- ture at the end of combustion of about 6500° F. abs. These figures are obtained by neglecting all losses in the real engine and by considering the specific heats constant. (e) The thermodynamic or Carnot efficiency is then ^, Ti — T2 6500 - 520 Efc = -j^ = 6500 = 92 P^^ ''^'''- (f) The cycle efficiency for this Otto cycle is from Eq. (80), CEf=l-^=l- -^^ = 48 per cent. Ta 1000 ^ Then in Fig. 305, drawn to scale for the assumed engine, the distance AB is 48 per cent ^ h^ ^^E f yj^, ^^^ ni q^ Oi AC. I S^nP * ' " ^ ^^'^ y^ ^^Mechauical p— M I — ^ ^tvJ^y^, Losses Thus the Otto cycle upon ^ =^F^ ^y^ ^cylinder Losses which this engine is to operate is less efficient than reversible cycles, and the real engine is ini- tially handicapped to that extent. ^^^' ^oS- (g) The relative efficiency is ^^, CEf 48 ,i?£/=£^ = ^=52.2 percent. 446 HEAT-POWER ENGINEERING This shows that the real Otto engine, if absolutely perfect, could only make available a little more than half the mechanical energy obtainable with the ideal Carnot engine. (h) The indicated efficiency measures the amount by which the cylinder of the real engine falls short of developing the 48 per cent of the supplied energy. The weight {Wi) of mixture that this engine would probably use is about 9 to 10 pounds per i.h.p.-hour, and the heat A(2 supplied by each pound of mixture is about 940 B.t.u. Then the theoretical Otto engine would make available 940 X 0.48 = 451.2 B.t.u. per pound as AE. One horse power is equivalent to 2545 B.t.u. per hour, and the heat theoretically available for doing work is (9 or 10) X 451.2 B.t.u.; hence lEf = 47% = ( , ^ w = 62.6 to 56.4 per cent. -^ WiAE (9 to 10) X 451.2 o 1 1- That is, the area of the upper loop of the real indicator card divided by the area of the ideal air card would give a value between 62.6 per cent and 56.4 per cent. This measures the proportion of the maximum energy of this cycle that is made available by the real engine. In Fig. 305, DE should be 62.6 per cent to 56.4 per cent of DF, (i) The thermal efficiency on the i.h.p. is easily determined to be TIEf = ^T^TS = 7 ^^v^. = 30 to 27 per cent, -^ WiAQ (9 to 10) X 940 which shows that the real engine actually converts into mechani- cal energy from 30 fo 27 per cent of all the heat supplied it. Some of this is, however, lost in fluid and mechanical friction, and the amount of such loss is measured by the mechanical efficiency. The TIEf is the ratio of GH to AC in Fig. 305. (j) The mechanical efficiency, MEf, of an engine of this kind would probably be about 85 per cent, thus the d.h.p. 'would be about 85 per cent of the i.h.p. In Fig. 305, JK is therefore 85 per cent of JL. (k) The thermal efficiency on the d.h.p. is from Eq. (220) TDEf = TIEf X MEf = (27 to 30) X 0.85 = 22.9 to 25.5 per cent, showing that the engine actually turns into useful, available power about one quarter of all the heat energy supplied it. In Fig. 305 the TDEf is given by the ratio of MN to AC. INTERNAL-COMBUSTION ENGINES 447 (1) The over- all efficiency would be by Eq. (221) OEf= lEf X MEf = (56.4 to 62.7) X 0.85 = 47.9 to 53.3 per cent, showing that the real engine losses (cylinder, fluid friction, and mechanical friction) consume about one-half the power which the - ideal engine with the same cycle would make available. In Fig. 305 the OEf is the ratio of MN to AB. 220. Efficiencies of other Commercial Engines, (a) Two- stroke-cycle Otto Engines, because of greater cyclinder and friction losses, generally have over-all efficiencies of from 0.7 to 0.8 of those of corresponding four-stroke engines. The indicated efficiency and mechanical efficiency may both be lower than in four-stroke engines, or the indicated efficiency may be lower while the mechanical efficiency is higher because of the absence of valves and such. ' (b) The thermal efficiency of the Diesel oil engine is generally higher than that of engines working on the Otto cycle. This is due to the higher compression pressure which can be carried in these engines (500 pounds per square inch or more), and to the fact that the combustion conditions are also probably somewhat better. Average thermal efficiencies on the brake with Diesel engines are about 30 per cent, and sometimes run as high as 35 per cent. 221. Heat Balance for Gas Engines, (a) In reporting an engine test, it is customary to account for all heat supplied. The statement of this account is called the " heat balance." There are only five possible destinations for heat supplied to a gas engine. They are: (i) Useful mechanical energy; (2) Loss to jacket; (3) Heat carried away in the exhaust gases; (4) Loss due to incomplete combustion; (5) Radiation, which includes energy converted into heat by friction. (b) The useful mechanical work has already been shown to equal from 15 to 30 per cent of the heat supplied. (c) The relative amount of heat lost to the water, or air, jacketing the cylinder varies in different engines, and in the 448 HEAT-POWER ENGINEERING same engine under different conditions. The loss to jacket is between 25 and 50 per cent, with an average from 30 to 35 per cent. In the case of air jacketing, it is not generally possible to distinguish between jacket and radiation losses. (d) The loss due to heat carried away by the exhaust gases, owing to their high temperature, generally falls between 25 and 40 per cent, increasing as the jacket loss decreases, and vice versa. (e) Combustion is almost always incomplete to a small extent and may at times be imperfect enough to account for a consid- erable proportion of the heat available. This loss should not be greater than i to 2 per cent of the total heat, and is often much less. (f) Radiation loss is supposed to include all heat radiated from the outer surfaces of the engine, and in the heat balance it would include all energy converted into heat by friction and subse- quently lost by radiation and conduction. It is generally found by subtracting the sum of the other four quantities of heat in per cent from 100; and when this method is used this difference includes ajl errors of the other results. When calculated in this way it may have a value of from 10 to 20 per cent, with an aver- age of about 15 per cent. (g) Another heat-balance method puts under (i) the energy represented by the upper loop of the diagram, instead of the mechanical energy delivered. Then the energy loss in gas and engine friction is already included under (i) and does not appear as radiation loss under (5). The latter value is then reduced to about 5 to 8 per cent of the total heat supplied. (h) The total heat supplied the engine may be taken as either the higher or lower heat value of the gas (see Chapter XXVIII). Obviously the use of the lower value results in a higher efficiency for the engine, and is therefore favored by gas-engine builders. In America the lower value is universally used, although in some countries of Europe the higher value is sometimes adopted. (i) It is important to note that the thermal efficiencies of steam and internal-combustion engines are not strictly compar- able unless the amounts of heat available are measured in a truly comparable way. This is usually not the case, for the fol- lowing reasons: The heat supplied a steam engine is generally figured as that in the steam above some datum, such as 32° F., or feed-water temperature, or exhaust temperature and is not in INTERNAL-COMBUSTION ENGINES 449 terms of the fuel used or its cost. On the other hand, the heat suppHed an internal-combustion engine is based upon a calori- metric determination of the fuel, with certain corrections in case the lower calorific value is sought. This amounts to figuring the heat supplied above a datum equal to the existing atmospheric temperature for all the constituents of the exhaust gas excepting; the water formed by the combustion of hydrogen. The heat value of this combustible is figured above a datum which often corre- sponds roughly to 212° F. (See Chapter XXVIII for further discussion.) The datum used is thus arbitrarily chosen for convenience in each case, and the results are not strictly comparable. It might seem that, since the steam engine is given credit for the heat of the liquid in the exhaust steam, or for that part of it above feed- water temperature, some sort of similar device might be adopted in the case of the internal-combustion engine. This is incorrect, however, because the exhaust of the latter engine is absolutely useless so far as the engine is concerned. Part of the heat carried may be abstracted by generating steam, heating water, or in a number of other ways; but this should not affect the figure for heat consumption of the engine, although it is properly taken account of in determining the efficiency of the plant as a whole. (j) The only true comparison of heat expenditure is between heat-power plants as a whole and not between engines only. If the fuel is the same in both cases, the ratio of the amounts of fuel per d.h.p. may be used; otherwise relative economy is shown by the ratio of the costs of the respective amounts of fuel con- sumed per d.h.p.-hour. The true comparison for economic purposes should include not only the fuel cost, but expenditure for labor, lubricants, supplies, repairs, interest, depreciation, insurance, and all other costs involved in power generation ; and only on such a basis are two systems truly comparable. 222. Performance of Internal-Combustion Engines, (a) There are so many different kinds of internal-combustion engines that it is difficult to make broad statements to fit all cases. The fol- lowing must, therefore, be regarded as very general, and appli- cable only to the average lines of engines. 450 HEAT-POWER ENGINEERING (b) American engines built to run on natural gas are gener- ally guaranteed to deliver a brake horse power on from lo to ii cubic feet of gas at rated load. This gas is commonly assumed to have a calorific value (lower) about looo B.t.u. per cubic foot; so this guarantee is from 10,000 to 11,000 B.t.u. per horse- power hour at rated load, corresponding to thermal efficiencies of from 23 to 25.5 per cent on the d.h.p. Many engines at present in operation give better results than these by several per cent at rated loads; and the efficiencies are still better at loads from 10 to 15% greater than the normal. At three-quarter load they are generally guaranteed at 11,000 to 13,000 B.t.u.; at half-load, 13,000 to 15,000; and at one-quarter load 20,000 to 23,000 B.t.u. 25,000 Fraction of Rated Load H Developed H.P, 25 Fig. 306. The curves of the total consumption and rate per d.h.p.-hour for average lOO horse- power natural-gas engines are given in Fig. 306. In each case the two curves correspond to the limits above given. The exact shape of these curves will, of course, depend upon the type of engine, method of governing, etc., but those given may be taken as representing average practice. It is convenient to remember that practically all internal- combustion engines (with the possible exception of some oil engines) will require about twice as many thermal units per horse- power hour at one-quarter load as at the rated load. INTERNAL-COMBUSTION ENGINES 451 (c) Engines intended to operate on illuminating gas are generally guaranteed with lower efficiencies than natural-gas engines. The B.t.u. per d.h.p.-hour is usually from 12,000 to 13,000 B.t.u. at full load. The poorer performance is principally due to the fact that these engines are, as a rule, not so carefully designed, as they are not built in large sizes or in great numbers because of the high cost of this gas. Some of the highest thermal efficiencies on record have, however, been obtained with engines using illuminating gas. (d) Producer-gas engines are generally guaranteed on a basis of coal used per horse-power hour rather than cubic feet of gas or B.t.u. The average figure is I to i.i pounds of coal per horse- power-hour at rated load, and most producer-gas installations of good design can be counted on to produce a d.h.p.-hour on less than 1.2 pounds if operated continuously at full load. Under accurate test many of them have developed a brake horse-power hour on 0.8 to 0.9 of a pound of coal. To give an idea of the meaning of these figures, it is sufficient to state that a consumption of only 0.8 pound of coal per d.h.p.-hour corresponds to a thermal efficiency on the brake for the engine alone of about 31 per cent; while i pound corresponds to about 25 per cent. (e) Gasoline engines (stationary) are generally guaranteed to deliver a d.h.p.-hour on one pint of gasoline, at rated load. This corresponds to a heat consumption of about 14,000 B.t.u. per d.h.p.-hour, or a thermal efficiency of about 18 per cent. As a matter of fact, all of the better types are capable of deliver- ing a d.h.p.-hour on about two-thirds of the guaranteed quantity, when everything is in perfect adjustment. Between rated oad and maximum load the efficiency will first increase and then due to the use of rich mixture will slowly decrease. At about one-quarter load the consumption per d.h.p. will be about twice that at full load. (f) Alcohol engines are not as yet a commercial product in this country, and very few figures are available from practice. Tests show that such engines can safely be guaranteed on the same or a smaller volume consumption than gasoline. It is safe to assume a thermal efficiency of 25 per cent on the brake with these engines, and figures as high as 32 per cent and more have 452 HEAT-POWER ENGINEERING 13 15 17 19 21 B.H.P. and I.H.P. Fig. 307. 75 , , ^ 100 fc Load Fig. 308. 5fi 60- •s ^20- 01 55 H. P, SINGLE CYLINDER eiNGLE-ACTING,riORIZONTALGAS ENGINE USING ILLUMINATING GAS ..>'' CS:ii ^ / H J^ / / 1^ ^j?:^ -^ <^ i:^' ^^ p. 20 iO B.H,P. Fig. 309. 5-30W ^ -3 INTERNAL-COMBUSTION ENGINES 453 50f« 15% 100^ % of Rated Load Fig. 310. 100^ fc of Rated Load Fig. 3". 3,000,000 2,000,000 1,000,000 250 H.P. MARINE TYPE DIESEL ENGINE. A \ \, ^ k y i >< 4 ^ /^ 13000 11000 10000 9000 8000 D.h.p.50| 100 I 150 [200 250 300 ^Normal Load 25 50 75 100 120 Fig. 312. 454 HEAT-POWER ENGINEERING been obtained. This high efficiency is largely due to the high compression pressure that can be used with this fuel. (g) Oil engines (kerosene, distillate, and crude) differ widely in fuel consumption, but the newer and better American types are capable of producing a d.h.p.-hour on from 0.7 to as low as 0.5 of a pound of oil. These figures correspond roughly to thermal efficiencies of from 18 to 28 per cent on the d.h.p. (h) The curves given in Figs. 307 to 312 inclusive show results of tests of several different types of engines with different fuels. They illustrate in a general way how the various efficiencies of commercial importance vary with such things as load, size of engine, kind of fuel, etc. CHAPTER XXVII. FUELS. 223. Fuels, (a) In the discussion of ideal engines in preceding chapters, a hot body was assumed to be available and it was imagined to be so constituted that it could deliver heat at any time and in any desired quantity, with no change in its own temperature. No such hot body is really available, and in practice supplies of heat are obtained by burning " fuel." (b) In the broadest sense fuel is any material which can he made to combine with other material in such a way as to liberate heat. In the commercial sense, however, fuel is any material the greater part of which can be made to combine with oxygen, usually from the air, so as to liberate heat, and which is purchasable at such a price that its use will yield a profit. (♦c) Fuels may be solid, liquid or gaseous. The principal Natural Fuels dire Coal, Wood, Petroleum Oil or Crude Oil, and Natural Gas. The principal Prepared Fuels are Coke, Briquets made from coal. Charcoal, Distillation Products of Petroleum, Artificial Gas made from solid or liquid fuel, Hydrogen Gas and Acetylene Gas made from noncombustibles, and Alcohol. There are also certain kinds of municipal refuse and manufacturing wastes which have fuel value. 224. Geology of Coal, (a) Formation. Beds of coal in the different stages of formation are scattered over the earth's sur- face. Geologists believe that coal results from collections of vegetable matter, deposited in swampy places or under water, which are subsequently covered by silt and other material and during geological ages are gradually changed in physical and chemical composition until they finally become coal. (b) Vegetable matter may here be assumed to consist of carbon, hydrogen and oxygen combined in definite proportions, together with certain incombustible inorganic salts in the cell structure. This vegetable matter when under water changes 4SS 456 HEAT-POWER ENGINEERING very gradually, losing some of its material in the form of gas (usually methane or marsh gas, CH4) and as water. These trans- formations continue after the deposit has been deeply covered with earth, and eventually only the carbon and the inert salts remain. The extent of these changes is principally dependent on time, measured in geological ages, on temperature, and on the pressure, depth and porosity of the overlying material. The combustible part of coal consists principally of volatile matter (which is released upon heating to a high temperature in 100 90 80 70 fo Volatile Matter 60 50 40 30 20 04 V ---- s, V V -- — Vegetable \ Matter \ |Peat \ ^ t \ X:.. \ B \ > ■ - \ \ \ tuminouB \ \ \ \ V^ s. \ B Semi- \ tummous \ \ [ ^ 1^°':. ithracite \ ^v„„.,v„ _± , A G laphitic 10 20 30 10 50 60 70 80 90 100 | fo Fixed Carbon Fig. 313. a closed crucible) and of fixed carbon which remains after such treatment. As the formation of coal progresses the .percentage of volatile matter and moisture decreases with corresponding increase of fixed carbon. (c) Classification. In the early stages of transformation the material is called (i) Peat or Turf. Later, with increased pres- sure of overlying material resulting in greatly reduced volume, it becomes (2) brown or black Lignite. Later still, after addi- tional physical and chemical changes, the material becomes (3) Soft Coal or Bituminous Coal. Subsequently, it becomes FUELS 457 successively (4) Semibituminous, then (5) Semianthracite, (6) Anthracite, and finally (7) Graphitic Coal. The last is practically pure carbon. These are the seven groups into which coals are generally classified.* (d) Fig. 313 shows in a very general way the relation of fixed carbon to volatile matter during the transformation of vegetable matter into coal. The horizontal width of the diagram represents the sum of fixed carbon and volatile matter. The inclined line divides the horizontals into parts which represent fixed carbon (at the left) and volatile matter (at the right). Percentages may be read from the scales. The progress of the transformation is shown by the classi- fication at the right of the diagram. This grouping would seem to indicate well-defined divisions between adjacent classes; but in reality the groups blend into each other. The diagram is simply for illustration and should not be used otherwise. (e) There is as yet no really satisfactory basis for the classi- fication of coal. Formerly the classification was according to the percentage of fixed carbon in the dry combustible, as given in Table XIII. This, however, is not very satisfactory for coals high in volatile matter. TABLE XIII. — OLD CLASSIFICATION OF COALS. Kind of Coal. Anthracite Semianthracite Semibituminous Bituminous, Eastern. Bituminous, Western Lignite Fixed Carbon. Per cent. 97.0 to 92.5 .5 to 87.5 ■5 to 75.0 .0 to 60.0 .0 to 50.0 Under 50.0 Volatile Matter. Per cent. 3.oto 7.5 7.5 to 12.5 12.5 to 25.0 25 .0 to 40.0 35.0 to 50.0 Over 50.0 (f) A recently proposed classification, based on the ratio of volatile carbon to total carbon and known as Parr's Classifica- tion,! appears to be more satisfactory. Omitting the subgroups under bituminous coals and lignites, this classification is given in Table XIV. * One other group falling between (2) and (3) above and known as " subbitumi- nous " is sometimes recognized. t Bull. No. 3 Illinois State Geol. Survey. 458 HEAT-POWER ENGINEERING TABLE XIV. — PARR'S CLASSIFICATION OF COALS. {Abbrev.) Kind of Coal. Volatile Carbon Total Carbon Inert Volatile. Anthracite . . Per cent. Below 4 Between 4 and 8 Between 10 and 15 22 to 44 27 and up Per cent. Semianthracite Semibituminous Bituminous Lignite 5 to 16 16 to 30 (g) Coal Fields in the United States.* The main deposits in this country are shown in a very general way in Fig. 314, in which the average character of each deposit is indicated by the Fig. 314. kind of hatching. In Rhode Island there is a little graphitic coal. Most of the anthracite is found in beds of less than 500 square miles area located in eastern Pennsylvania. The princi- pal deposit of semibituminous coal is about three hundred miles long by twenty wide and lies along the eastern edge of the Northern Appalachian Field. The bituminous coals extend from this deposit westward. Starting with the graphitic coal in * See Coal Fields in the U. S. by C. W. Hayes, U. S. Geological Survey, and Kent's " Steam Boiler Economy." FUELS 459 Rhode Island, broadly speaking, the farther west a coal is located the less advanced it is in the process of transformation. It is important to note, however, that there are many exceptions tO' these very general statements, for there are numerous other small fields, not shown, scattered over the country. For instance, a little anthracite coal is found in Colorado and in New Mexico, and some semibituminous in Arkansas.' 225. Composition of Coal, (a) Coals consist principally of the elements Carbon, Hydrogen, Sulphur, Oxygen, and Nitrogen, together with moisture and ash. The elements named, par- ticularly Carbon, Hydrogen and Oxygen, seem to be combined in various ways in the solid coal, though little is known of the formulas of the compounds in which they exist. The ash contains the inert salts of the original vegetable matter, together with silt and similar impurities acquired after deposition and submersion. (b) ''Moisture " is arbitrarily defined as the material lost when a finely powdered sample of the coal is maintained from half an hour, to an hour, at a temperature of about 220° Fahr.; or, more exactly, as the maximum loss which can be made to occur at this temperature. The material driven off in this way is not necessarily all moisture, for, with some coals, part of the more volatile combustible material may distil off. Moreover, all the water content may not be driven ofT by maintaining the material at this temperature. The definition is, therefore, only an arbi- trary one, but it seems to be the best that can be devised. (c) ' ' Dry Coal ' ' is coal from which the moisture has been driven by heating, as above described. (d) " Volatile Matter'' (or " volatile ") is the name given to all material driven off when " dry coal " is maintained at a very high temperature (between a ''red " and "white heat") in a covered crucible (out of contact with air) until there is no further loss of weight. This definition is again purely an arbitrary one, but it is useful in that it gives a measure of the material which will be similarly given off in a furnace or in a coke oven. (e) ''Fixed Carbon " is defined as the portion remaining after subtracting the ash from the material left in a crucible after driving oflt the volatile matter. (f) "Combustible " is the term used to designate the part of the coal other than moisture and ash. It is, therefore, the sum of 460 HEAT-POWER ENGINEERING fixed carbon and " volatile," as above defined. It is composed principally of carbon and hydrocarbons but it is important to note that it also contains noncombustible matter such as Nitro- gen and Oxygen and hence the term is a misnomer. When the coal contains sulphur a large part of this is also found in the so- called combustible. 226. Coal Analyses, (a) Two types of analysis are in common use — one gives what is known as an " Ultimate Analysis," the other a " Proximate Analysis." (b) In an ultimate analysis of so-called "dry combustible'' the percentages of Carbon, Hydrogen, Oxygen, Nitrogen, and Sulphur are determined. The ultimate analysis of "dry coaV also includes the percentage of ash, and in some cases a chemical analysis of the ash is also made. Ultimate analyses are seldom made by engineers, being more often obtained from chemical laboratories. Table XV gives in a general way the approximate ranges of the ultimate analyses of the combustible in different kinds of coals. More accurate tables of analyses of coals from dif- ferent localities can be found in text books on fuels and on boilers, in engineer's " pocket books " and in reports and publications of the geological surveys of the United States and of various states. In consulting such references it is necessary to bear in mind that ultimate analyses are sometimes incorrectly made on the basis of coal " as received," i.e., on wet coal. In such cases the percentages of H and O include the hydrogen and oxygen of the moisture. TABLE XV. — ULTIMATE ANALYSES OF COALS. Per Lb. of Dry Combustible. c H N S Anthracite 92-98 905 87-3 75-83 70-78 61 1-3-5 5 4- 5-5 -5 5-6.8 5 6 .-3 4-5 3-4.8 4-1 1 10-15 33 I o-i .5 Semianthracite Semibituminous . 9-1 . 8 1-2 2 . 6-1 . 3 Bituminous 0.4-3 Lignite 1-3 Peat . .... (c) The proximate analysis divides the fuel roughly into the several parts which have already been described in Section 225, b FUELS 461 as Moisture, Volatile Matter, Fixed Carbon, and Ash. While this analysis is less exhaustive than an ultimate analysis, it has two marked advantages over the latter: (i) It is easily made by the engineer and involves the use of very simple apparatus; and (2) it indicates, in a general way, the behavior which may be expected of the coal during utilization as fuel. (d) Proximate analyses are given both on the basis of "dry coal " and coal " as received." For purposes of comparison with other fuels, the dry-coal basis is the better because the conditions of storage and transportation may materially change the moisture content. It would be obviously unfair, for instance, to charge against a coal, in comparison with others, the fact that it had been rained on, or had been stored under water. On the other hand, when coal is being purchased by weight, it is as ob- viously unfair to pay for water at the price of coal, and there- fore for this and similar purposes analyses should be on a basis of coal "as received," or else, in addition to the proximate analysis of dry coal, there should be a statement of moisture content. (e) Table XIII gives the approximate range of percentages of fixed carbon and volatile in the combustible of the different kinds of coal. The proximate analyses of " dry coals " may be obtained by introducing average ash contents and altering the percentages accordingly. Proximate analyses of coal from different localities may be found in the books and reports to which reference has already been made. (f) It will be shown in later chapters that such data as are given by the ultimate analysis can be used for calculating the calorific value, and that they are also needed for computing losses occurring in furnaces and boilers. For these reasons ulti- mate analyses are often desired, even though their actual deter- mination is outside the engineer's field. It has been shown by Professor L. S. Marks* that, in the case of most coals occurring in the United States, the ultimate analysis can be approximated from the proximate analysis with sufficient accuracy for deter- mining the distribution of boiler and furnace losses and for general engineering work. The results which Professor Marks gave by curves have been put into the form of equations by Professor * Power, vol. 29, p. 928, Dec, 1908. 462 HEAT-POWER ENGINEERING H. Diederichs. Only the principal ones of these equations will be given here.* Letting V represent the weight-percentage of volatile matter in the combustible, then the approximate weight-percentages of hydrogen (H), of volatile carbon (C), and of nitrogen (N) are respectively ^ = ^(l^-o-oi3) • • (329) C = 0.02 V^ ) for anthracite and ) . . or = o.Q (V— 10) ) semianthracite. ) C = o.Q {V — 14) for bituminous and semibituminous (331) C = o.q{V — 18) for lignites (332) N = 0.07 V for anthracite and semianthracite. . . (333) N = 2.10 — 0.012 V for bituminous and lignite. . . (334) The occurrence of oxygen and sulphur is apparently more or less accidental in character, showing no uniformity, and is not expressible by equations. The greater part of all the sulphur and some of the oxygen will appear in the proximate analysis as volatile, and will therefore be accounted for as hydrogen and carbon in the use of these equations. 227. Fuel Values of Coals, (a) The methods of determining the fuel values of combustible materials will be discussed in detail in the next chapter; there are a few considerations, how- ever, which it is necessary to mention briefly at this point. It is customary to state the calorific value of a material in terms of the B.t.u. made available by burning one pound. When a material containing uncombined hydrogen is burned, this hy- drogen unites with the oxygen and forms superheated water vapor. If this vapor passes off without surrendering its heat, the calorific value of the fuel is less than if that hea.t is made available. Hence the terms lower heat value and higher heat value are used to distinguish between the two conditions of combustion. (b) As will be explained in Chapter XXVIII, the Calorific Value of a coal can be very roughly determined from the ulti- mate analysis by the use of Dulongs Formulas. These are given * For more complete explanations, percentages of accuracy, etc., see Carpenter and Diederichs' " Experimental Engineering," p. 507, and the original article in Power referred to in the preceding footnote. FUELS 463 in Section 243 as Eqs. (376) and (377) and are stated as follows: Higher B.t.u. = 14,600 C + 62,000 (H — 0/8) + 4000 S. i Lower B.t.u. = 14,600 C + 52,000 (H — 0/8) + 4000 S. If for C, H, 0, and S are substituted the weights of these elements per pound of combustible, the results will be B.t.u. per pound of combustible. If weights per pound of dry coal are used, the result will, of course, be B.t.u. per pound of dry coal. As will be explained more in detail in the next chapter, Du- long's formulas are only approximate because they assume all the oxygen originally present in the fuel to be combined with 60 70 SO 90 fc Eixed-Carbon ia. the Combustible Fig. 315- hydrogen, and because they take no account of the disappear- ance of heat accompanying the dissociation of hydrocarbons and similar obscure phenomena occurring during combustion. For accurate determination of the calorific value, some form of fuel calorimeter should be used. These calorimeters will be dis- cussed in Section 244.^ (c) Various empirical formulas have been proposed for giving the heat value per pound of fuel in terms of the proximate analysis. These usually contain "constants," which are given in tables, and which vary with the locality of the mine, or with the ratio of certain constituents, such as volatile matter to total com- bustible. These formulas will not be given in this brief treatment. (d) Fig. 315 gives Mahler's Curve,* which shows in a general * Redrawn from curve given in U. S. Geol. Survey Professional Paper No. 48. I 464 HEAT-POWER ENGINEERING way how the heat value per pound of combustible varies with the percentage of fixed carbon present, and which also shows the range of percentages of the fixed carbon in the different kinds of coal as they are usually classified. This curve shows clearly that of all coals the semibituminous has the combustible of the highest heat value; and in connection with the map in Fig. 314, it is seen that in general the coals are of decreasing heat value the farther they are located from the main semibituminous bed. It is afso true, generally, that the difficulty encountered in burning a coal efficiently increases with the distance of the mine from this same bed. (e) Coal when mined always contains moisture and often takes up more afterward. Moisture is generally undesirable because it is not combustible and because it is vaporized and superheated during combustion, thus absorbing heat that might otherwise be utilized. Eastern coals, as mined, contain from one to five per cent of moisture, western coals from three to fifteen per cent, and lignites from ten to thirty per cent. (f) Ash not only decreases the heat value of fuel, but it also increases the cost of transportation and handling of the coal per unit of heat produced, and in addition there is the cost of its disposal after combustion. The presence of ash also interferes with combustion, especially if it is of such composition as to form clinker. The percentage of ash in commercial coals ranges from three to fifteen ordinarily, and is usually greater in the smaller sizes than in the larger. (g) Sulphur, although combustible, usually makes the fuel un- suitable for use under boilers and for many other purposes, if present in large quantities. The products of its combustion may, under certain circumstances, form acids by combining with water and these may attack the metal of boilers, etc. The pres- ence of considerable quantities of sulphur is supposed to indicate a readily fusible ash which causes trouble in the boiler furnace, or in the " gas producer," by the formation of clinker. (h) Peat, in its natural state, is a poor fuel containing a large percentage of moisture. Its value is improved by drying, but it is not yet generally used when other cheap fuels can be obtained.* * As an indication of what may be expected when other fuels become scarcer, see Bulletin 16, U. S. Bureau of Mines, " The Use of Peat for Fuel and Other Purposes." FUELS 465 (i) Lignite is an unsatisfactory fuel when burned in furnaces, but recent investigations seem to indicate that it may be of great value for the making of " producer gas " for which there is a rapidly growing demand for power purposes. (j) Western bituminous coals are a little harder to burn effi- ciently than eastern on account of the larger proportion of volatile matter contained. The higher the percentage of volatile matter in the coal the more difficult it is to burn it smokelessly and efficiently (see Chapter XXIX). (k) Bituminous coals are sometimes classified as caking and noncaking. The fragments of the former kind coalesce into cakes while burning, which is desirable in the making of coke but may interfere with the supplying of air for combustion when the coal is burned upon grates. (1) Cannel coals are bituminous coals which are very rich in hydrocarbons and burn like a candle, hence the name. These are used as " enrichers " in gas making. Coals high in hydrocarbons burn with a long flame and are more difficult to burn efficiently than short- flame coals. (m) Semihituminous coals, as has been shown, have the highest heat value per pound, and, as they burn with a comparatively short flame, they are the most desirable coals for use in boiler and similar furnaces. TABLE XVI. — COMMERCIAL SIZES OF SOFT COAL. Name. Through Bars Spaced Apart. Over Bars Spaced Apart. Lump Inches. Inches, li 3 4 Nut Slack f (n) Anthracite coal has an advantage over the other classes in burning smokelessly, and consequently is in great demand where smoke is not permitted. The available supply in the eastern part of the United States is rapidly diminishing and the price is, in general, higher than for other coals. To obtain the best results with anthracite it must be of uniform size. As the price decreases with the size, only the smaller grades, usually those less than \" in diameter, are used for power purposes. Table XVII gives the usual classification, but unfortunately the names and sizes in some instances vary with the locality. 466 HEAT-POWER ENGINEERING TABLE XVII. — SIZES OF ANTHRACITE COAL. Name. Through Screen with Mesh. Over Screen with Mesh. Broken . 2| 2 h i 1 Unscreened Effe. . 2f 3 4 i Unscreened Pea Buckwheat No. i. Buckwheat No. 2. Run of mine (o) Coal dust, produced in mining the material, is almost always a waste product. Such dust is now successfully used in firing rotary kilns and similar apparatus, but is seldom used for ordinary power purposes although special devices for burning it under boilers and in producers have been used to a limited extent. Coal dust and similar waste, known collectively as " culm " may represent from 10 per cent to as high as 50 per cent of all the coal recovered from the mine. It is, therefore, apparent that sooner or later some method of utilizing this waste will have to be adopted because of the decrease in the available supply of coal. Such material has been very successfully recovered in Europe by forming it under high pressure into briquets in which such materials as pitch, resins, wax tailings, starch, and several inorganic salts are used for " binders." These briquets can often be used more efficiently than ordinary lump fuel, because of their uniformity of size, advantageous shape, and general good behavior in the furnace; hence it often proves to be economical to purchase briquets at a slightly higher price than that asked for similar lump coaLj 228. Coke is the solid material left after driving off the volatile part of coal by heating with total or partial exclusion of air. Only certain coals yield coke of commercial value. Nearly all of the coke made is used in metallurgical processes, and but little as yet for power purposes. * There are a number of other sizes, such as " stove," " chestnut," etc., which need not be considered here as they are not commonly used in heat-power engineering. t For investigations relating to the manufacture and utilization of briquets under American conditions see bulletins of the U. S. Geol. Survey and of the U. S. Bureau of Mines. FUELS 467 Coke contains from 80 to 93 per cent of fixed carbon, from 5 to 18 per cent of ash, from 0.5 to 1.5 per cent of sulphur, and traces of volatile. It is interesting to note that the volatile is not entirely eliminated, and that, as all the ash in the coal remains in the coke, the percentage of inert matter present in the product must be greater than that in the original material. The calorific value per pound of combustible is about the same as for carbon; that is, it is in the neighborhood of 14,600 B.t.u. 229. Wood, (a) As wood is about half moisture when felled, it must be dried before it is of much value as fuel. Air-dried wood generally has from 15 to 20 per cent of moisture, about 50 per cent of carbon, from J to 2 per cent of ash, and the rest is volatile matter, largely inert. The heat value per pound of dry material is from 6600 to 9800 B.t.u. When other cheap fuel is available wood is not generally used for power production. However, refuse from sawmills and other wood- working factories may be profitably utilized. (b) Charcoal is made from wood in much the same manner that coke is made from coal. It is ordinarily used in power plants only when it is the by-product of some local process, such as the manufacture of turpentine or wood alcohol. It may con- tain from 80 to 97 per cent of carbon, depending on the tempera- ture and treatment used in carbonizing it. 230. Municipal and Industrial Waste. In cities and indus- trial centers there is a constant accumulation of combustible waste and in some cases this material is burned directly as fuel, or it is gasified in suitable apparatus and the resultant combustible gas used as fuel. Installations of this character are still rare but are of growing commercial importance. 231. Natural Oil and Its Products, (a) Petroleum, or Crude Oil, has come into extensive use as fuel in the last twenty-five years. It is a more or less viscous, dark brown or greenish colored liquid occurring in natural reservoirs in the earth's crust. These reservoirs may be subterranean pockets, but are, in general, .oil-saturated strata buried beneath other strata which are prac- tically impervious to petroleum. (b) Petroleum in its crude form generally has a specific gravity between 0.82 and 0.92. It is a mixture of various hydrocarbons 468 HEAT-POWER ENGINEERING which are liquid at ordinary temperatures and pressures, and which hold in solution numbers of other hydrocarbons which otherwise would be gaseous or solid under existing conditions. In general, oils from one field are composed of the same hydro- carbons in about the same proportions, but each field has its own characteristic composition. American crude oils have from 82 to 87 per cent of carbon, from 12 to 15 per cent of hydrogen, and from o to 4 per cent of oxygen in their composition. The lower heat value per pound of crude petroleum varies from 18,000 to 22,000 B.t.u. (c) Many of the more highly inflammable volatile components tend to distill ofT when the oil is brought to the earth's surface and is exposed to atmospheric conditions. These volatiles, some of which boil at temperatures as low as 80° F., are usually dis- tilled off progressively in a refinery. The distillation products most commonly used as fuels are naphtha, gasoline, kerosene, and distillate, given in order of decreasing inflammability and increas- ing density and distillation temperature. The greater part of the remainder can be sold as " fuel oil." (d) Gasoline is the name given to the group of hydrocarbons which distill off at temperatures between 150 and 300° F. Gaso- lines of various specific gravities are obtained by fractionating the material obtained between these temperatures, the lower gravities corresponding to the lower temperatures. The com- monest grades range from 74 to 64 degrees gasoline as measured by a Baume hydrometer. The corresponding specific gravities are 0.686 and 0.722. The relative proportions of carbon and hydrogen in gasolines are roughly 85 per cent and 15 per cent, and the lower calorific value is about 19,200 B.t.u. per pound. The flash point of gasoline, that is, the temperature at which readily inflammable vapors are given off from an exposed surface, is generally well below 70° F. (e) Kerosene is the name of the next important group of hydrocarbons which distill over after the gasolines. Their specific gravity is from 0.78 to 0.82 and the flash point is from 70° to about 150° F. for the different grades. The B.t.u. per pound of kerosene is about 18,500 lower value. (f ) Fuel Oil, having little highly volatile matter, can be handled without danger and, being very cheap, is quite widely used under boilers and in furnaces. The lower calorific value per pound is FUELS 469 extremely variable, but may be taken roughly at 18,000 B.t.u. per pound. (g) The higher calorific value of U. S. petroleum and its dis- tillates, ranging from crude oil to gasoline, varies quite regularly with the specific gravity of the material, and is expressed ap- proximately by the following formula,* which may be assumed correct within 2 per cent, B.t.u. per pound = 18,650 -f 40 (5 - 10), . . (335) in which B = degrees on the Baume hydrometer. Since the Baume scale increases as the density of the material becomes less, this formula indicates that the lighter distillates have greater heat values than the heavier ones, when figured on a weight basis. The reverse is true for heat value per gallon, a unit commonly used with liquid fuels; hence a barrel of light petroleum distillates of any kind will, in general, have less heat value than a barrel of heavier distillates or of the original oil free from water. 232. Alcohol, (a) Both Methyl (" Wood ") and Ethyl (" Grain ") alcohol are used as fuel to a limited extent. Methyl alcohol (CH^O) is poisonous and is produced during the dry dis- tillation of wood. Ethyl alcohol {CiH^O) is made, by a fermen- tation and distillation process, from grain, fruit, or vegetable matter containing starch or stigar. (b) The material known as Denatured Alcohol consists of ethyl alcohol with the addition of from i to 10 per cent of Methyl alcohol and other substances which prevent its use in beverages and give it an unpleasant odor. Commercial alcohol generally also contains 10 per cent or more of water by volume. Denatured alcohol has many theoretical and practical advan- tages over gasoline as a fuel for certain purposes, but at present its relative cost, in this country at least, is so great as to prevent its extensive use. (c) The higher calorific value of Absolute Ethyl alcohol (i.e. containing no water) is about 13,000 B.t.u. /lb.; the lower value is about 12,000 B.t.u. /lb. The heat value of " Commercial " alcohol, containing about 10 per cent of water, by volume, varies with the materials used in denaturizing. The lower heat value is generally near 10,500 B.t.u. /lb. * H. C. Sherman and A. H. Kropff, Jour. Am. Chem. Soc, Oct., 1908. 470 HEAT-POWER ENGINEERING 233. Natural Gas. (a) This material is found in various places, but particularly in certain regions of the United States, either escaping through cracks and faults in the earth's crust, or held at high pressure in huge underground reservoirs which may be tapped by drilling wells similar to those used for ob- taining oil; in fact, most oil wells yield a certain amount of natural gas. (b) Natural gas is a mixture of combustible and incombustible gases, the latter generally occurring in very small quantities. The proportions and even the constituents of the gas are seldom the same in different districts and occasionally vary unaccount- ably even in the same well. The principal combustible constituents are Methane (CH^), and Hydrogen ( H2) . The former generally occurs in far greater pro- portion than the latter. The other combustible gases which usually occur in very small proportions are Carbon Monoxide, (CO) J sulphur compounds such as Hydrogen Sulphide (H2S), and certain hydrocarbon gases, such as Ethylene (CiH^), a,nd others. The principal incombustible constituents are generally small proportions of Carbon Dioxide (CO2), Nitrogen {N2), and Oxy- gen (O2), if this latter may be considered an incombustible. (c) Natural gas is an ideal form of fuel for many industrial purposes, and is readily piped distances of one hundred miles and more for use in industrial centers far from a natural supply. Unfortunately many of the wells are becoming exhausted and the price is rising in proportion. TABLE XVIIL* — TYPICAL ANALYSES OF NATURAL GAS. Analyses in Volumes, Per Cent. . . Location of Field. & . i is a! 0) 1 "^ Il^ Anderson Ind 1.86 1. 31 '"2;i8 13.50 93.07 87.7s f.Z 80.11 96.34 72.18 77.03 92.49 0.47 0.26 6.60 0.26 0.66 3.64 0.80 3.60 0.93 0.73 0.42 3.02 4.34 0.15 Louisville Ky Olean, N. Y 5. 72 1. 00 0.31 trace 6.30 4.80 4. II 0.50 0.50 2.00 0.34 Findlay Ohio 3.61 20 Harvey Well, Pa Creighton Pa Pittsburgh, Pa 20.02 1. 00 3.50 0.80 1.80 Pechelbrown, Germany 8.90 2.13 0.34 * Abstracted from Table in "Calorific Value of Fuels," Herman Poole, p. 241. FUELS 471 Table XVIII gives some typical analyses of natural gas from several different districts. The lower calorific value generally varies from about 950 to 1000 B.t.u. per cubic foot. 234. Artificial Gases, (a) The principal artificial gases are made from coal or crude oil, but there are also many processes for producing combustible gases from vegetable and animal by- products and wastes. Many of the latter are successful in iso- lated cases but they are not yet of great commercial importance. (b) Most of the artificial gases are made either by destructive distillation, by partial combustion, by chemical decomposition, or by various combinations of these processes. Destructive distillation occurs when the gas-making material is heated in a chamber from which air is more or less perfectly excluded. Illustrations of gases made by this process are " Illuminating," " Retort," or " Town Gas," used for illumi- nation, and gas made in " By-product " or " Retort Coke Ovens " used for illuminatipn and power. " Producer Gases " are the best examples of those which in theory are made by a process of incomplete combustion. Practi- cally this is always more or less combined with chemical de- composition. These gases have become so important of late in connection with the internal combustion engine that they will be discussed later in a separate chapter. (c) The use of artificial gases as fuel in internal combustion engines results generally in a greater output of available energy than would the use of the solid fuels, from which the gases are made, in other heat-power apparatus; hence these gases may be expected to become more and more important with the depletion of the natural stores of fuel and with the growth of the spirit of conservation of the earth's resources. CHAPTER XXVIII. COMBUSTION. 235. Definitions, (a) To the engineer Combustion means the chemical combination of certain elements with oxygen at such a rate as to cause an appreciable rise of temperature. Practically all chemical reactions are accompanied by libera- tion or absorption of heat. When heat is liberated the reaction is called exothermic; when heat is absorbed the reaction is called endo thermic. (b) During these reactions, with other conditions constant, (i) the amount of heat energy liberated or absorbed is independ- ent of the time occupied; and (2) for any material taking part in the reaction, the heat change is directly proportional to the mass of that material. (c) Materials which can be caused to unite with oxygen to produce heat are known as Combustibles. For engineering pur- poses they are limited to Carbon and Hydrogen; these, either pure or in various combinations, constitute practically the entire stock of available combustibles, although a trace of sulphur usually appears as an impurity. (d) In heat-power engineering the object of combustion is either the production of heat directly, or the formation of a more suitable kind of combustible, such as gas or coke, from the original material. Useful combustion data are given in Table XIX. In it the values of specific densities and volumes are given for an average atmospheric temperature of 62° F. as well as for 32° F. 236. Combustion of Carbon, (a) Carbon is the principal com- bustible in nearly all engineering fuels. This element combines with oxygen to form two oxides, — Carbon monoxide (CO), and Carbon dioxide (CO2). If CO is formed, the combustion is said to be " incomplete " ; if CO 2 is formed, it is said to be " complete " or " perfect." 472 COMBUSTION 473 ^\- o o o o , o s^ >1 s^^ O ° H vo lO J3 V t^ ; u M-. Tj- o H H ^ 3 03 V 4 o O vo , , ^ ~0C OS Xf ■) r< ■) vo CO ■^ f Ol +j » u ■) t- CO t^ -> CN 2 . O H tJ- H 1- M 04 d c d ir ^ oc lO oc ■^ 1> c/ :) o 00 CO 00 lO a ^4^ H 00 M - o M M ~ci IH p/^ d- lO CO vo (N 00 r- t-^ M r~^ !^ o t^ W o o O d O d H o d 00 ^o - ,; S p.^ o^!i (SI vo H '^ 00 w o \ 00 vo 00 CS '^ vo < > 1 n O n aj ^ aj o o o 1 1^ 474 HEAT-POWER ENGINEERING (b) The reactions occurring during combustion may be ex- pressed by chemical equations, the symbols used standing for definite proportions by mass or weight. For engineering pur- poses the atomic weight of Carbon may be taken as 12, that of Nitrogen as 14, and that of Oxygen as 16. (c) When carbon and oxygen combine to form Carbon Dioxide the reaction is expressed by C + 02 = C02; (336) the weights combined are 12 of C + (2 X 16) of = 44 of CO2, and dividing this by 12 gives lof C + 2f of = 3f of CO2. . . . (337) Thus if 1 pound of carbon unites with 2f pounds of the result is 3f pounds of CO2. It is also found that heat equal to about 14,600 B.t.u. is liberated per pound of carbon when this reaction occurs. (d) When carbon is burned to Carbon Monoxide, the reaction is expressed by 2 C + 02 = 2 CO; (338) the weights combined are (2 X 12) of C + (2 X 16) of = 56 of CO, and dividing this by 24 gives 1 of C + If of = 2i of CO. . . . (339) The heat liberated is, in this case, about 4500 B.t.u. per pound of carbon. (e) The gaseous CO formed as above can be burned to CO2. The reaction is 2 CO + O2 = 2 CO2; (340) the weights combined are \2 X (12 -f i6)J of CO + (2X 16) of = 88 of CO2, and dividing this by 24 gives 2i of CO + li of = 3! of COo. . . . (341) Thus the 2J pounds of CO, which would result from the com- bination of 1 pound of carbon as in Eq. (339), would combine with i| pounds of to form 3! pounds of CO2. This reaction is accompanied by the liberation of heat equal to about 10,100 B.t.u. per pound of carbon. Therefore the heat COMBUSTION 475 liberated per pound of carbon monoxide gas must be 1 0100/2 J = 4300 B.t.u. The specific volume of CO is 12.81 cu. ft. at 32° F. and 14.7 pounds pressure. Hence the heat liberated per cu. ft. of CO under these conditions is 4300 -^ 12.81 = 335 B.t.u. As CO is a con- stituent of many commercial fuel gases and as these are usually measured volumetrically instead of gravimetrically, this value is convenient for determining the heat available due to the CO present. (f) Equations expressing both the reaction and the libera- tion of heat per pound of material"^ may be written as follows: C + O2 = CO2 + (14,600 B.t.u. per pound C) . . (342) ] 2 C + O2 = 2 CO + (4500 B.t.u. per pound C) . . (343) V X^ 2 CO + 0=2 CO +1 (lO'ioo B-^-u- pe^ pou^d <^) (344) ^ ^ ^ (or (4300 B.t.u. per pound CO) (345) Noting that 4500 + 10,100 = 14,600, it is evident from these equations that when carbon is burned to CO2, the ultimate results are the same whether the process takes place in one or in two steps. Further, if part of the pound of carbon (say Cx pounds) is burned to CO2 and the rest (Cy pounds) to CO, the heat liberated is B.t.u. = 14,600 Cx +4500 Cy. ... (346) (g) If heat is the object of combustion, the carbon should of course be burned to carbon dioxide rather than to carbon mon- oxide. If CO is formed instead of CO2, the proportion of the heat lost is (10,100/14,600) = .69 +, or about 70 per cent. If, how- ever, the CO is burned later, the rest of the heat may be recovered. ' * As will be seen later, it is sometimes more convenient to modify Equation (342) so that the heat quantity as well as symbol C will correspond to 12 lbs. of carbon (the pounds being taken as numerically equal to the molecular weight of C involved). The equation then becomes C + O2 = CO2 + 175,200 . (342a) where 175,200 = 12 X 14,600. Similarly, for the 24 lbs. of carbon represented by 2 C and by 2 CO, Eqs. (343) and (344) become 2 C + O2 = 2 CO + 108,000 (343a) and 2 CO + O2 = 2 CO2 + 242,400 (344a) in which 108,000 = 24 X 4500, and 242,400 = 24 X 10,100. 476 HEAT-POWER ENGINEERING When there is less than enough oxygen to burn the carbon to carbon dioxide, both CO2 and CO will be formed and the relative amounts of each can be determined in the following manner: Assume first that there is 1 per cent deficiency in the oxygen supply needed to form CO2 and that in consequence 99 per cent of the carbon is burned to CO2 and 1 per cent remains C; then assume that this 1 per cent of C combines with some of the CO2 according to the equation C + CO2 = 2 CO; thus it is seen that there is finally 2 per cent of the carbon present in CO and 98 per N/ cent in CO2.* In general, then, if there is y per cent deficiency of oxygen there will be 2y per cent of the carbon burned to carbon monoxide instead of to CO2. Hence from the preceding paragraph it follows that with y per cent deficiency of oxygen there is (2 X .7) y per cent, or 143' per cent less heat developed than if all the carbon were burned to CO 2. The great importance of having a sufficient supply of oxygen is thus apparent. The discussion in the preceding paragraph presupposes that the oxygen supply is at least sufficient to burn all the carbon to CO, — that is, that the deficiency is not more than 50 per cent on a basis of combustion to CO2. Should y be greater than 50 per cent, some of the carbon will not be burned at all. The per- centage not affected will he 2 {y — 50) . (h) It is sometimes possible to reverse chemical reactions, — in the present case, for instance, to break up one of the oxides into the original elements. When this is done the same amount of heat will be absorbed during the decomposition as was origi- nally liberated during combination. Thus, if it is possible to break up the quantity of CO2 con- taining a pound of carbon into the elements C and O, it will require an expenditure of 14,600 B.t.u. Similarly, it will require 10,100 B.t.u. to reduce to the monoxide CO an amount of .CO2 containing one pound of carbon, and 4500 B.t.u. per. pound of carbon will be consumed in separating CO into its elements. 237. Weights of Oxygen and Air Necessary for Combustion of Carbon. It was shown that for each pound of carbon burned to CO2 there are required 2f pounds of oxygen, or if pound of * These statements should be limited to take account of certain " equilibrium " conditions which will be discussed in a later chapter. For the present purpose, however, they are sufficiently exact. COMBUSTION 477 if CO is formed. If , as before, Cx and Cy are the weights of carbon burned respectively to CO2 and to CO, then the number of pounds of oxygen used are Pounds of = 2| Cx + ij Q. . . . (347) TABLE XX.- -PRO PERT] [ES OF AIR. Relative Propor- tions. Ratio of Air toO. Ratio of AT' toO. Spec. Wt. at Atm. Pres. Spec. Vol. at Atm. Pres. Exact. Approx. Exact. Approx. Exact. Approx. 32° 62° 32° 62° By Weights. ( 0.766 iV i 0.234 ] 0.791 iV 1 0.209 0.23 0.79N 0.21 4.27 4.78 4-35 4.76 3.27 3.78 3. 35 3.76 0.08072 0.07609 12.39 13.14 By Specific Heats. Volumes. 0=0.238 Ct-=o.i69 Since, in ordinary engineering work, pure oxygen cannot, in general, be conveniently obtained, it is customary to utilize the oxygen of the atmosphere. Table XX shows that air is composed by weight of about 23 parts of oxygen and 77 of nitrogen; * thus the ratio of air to the oxygen it contains is about 100/23= 4.35, and of nitrogen to oxygen is about 77/23 = 3.35. Hence, for each pound of oxygen supplied there must be used 4.35 pounds of air containing 3.35 pounds of inert nitrogen. An equation for finding the weight of air required to burn Cx pounds of carbon to CO2 and Cy pounds to CO can therefore be found by multi- plying both sides of Eq. (347) by 4.35. This gives (approxi- mately) f . ' • i-" Pounds of Air = 11.6 C + 5.8 Cj,. . . . (348) 238. Volumes of Gases Involved in Combustion of Carbon. (a) The combustion formulas, like other chemical formulas involving gases, can be read in terms of molecules and of volumes as well as in terms of weights. Thus 2 C + O2 = 2 CO may be read, " two atoms of carbon unite with one molecule of oxygen to form two molecules of carbon monoxide." But accord- * This is the common engineering assumption. Atmospheric air always contains carbon dioxide and water vapor as well as a few rare gases such as argon. t The quantity 11. 6 (often taken as 12), representing the weight of air required for complete combustion of one pound of C, will be frequently used by the student hereafter; hence it should be remembered. 478 HEAT-POWER ENGINEERING ing to Avogadro's law the same number of molecules are con- tained in equal volumes of all the different gases when at the same temperature and pressure. Therefore, since every molecule of oxygen in a given volume of gas is capable of yielding two molecules of carbon monoxide, it follows that one volume of oxygen will yield two volumes of CO, both being measured at the same temperature and pressure. Similarly the equation C + O2 = CO2 shows that one volume of oxygen yields one volume of carbon dioxide; and the equation 2 CO + O2 = 2 CO2 shows that two volumes of carbon monoxide combine with one volume of oxygen to form only two volumes of carbon dioxide. (b) In the first case cited there was an increase of gas volume, in the second there was no change, and in the third there was a diminution. If the gases appear in terms of molecules (O2, N2, H2, CO, etc.) in the chemical equations, the coefficients of the molecule symbols represent relative volumes. (c) Since air is composed of about 21 parts of oxygen and 79 parts of nitrogen by volume, every volume of atmospheric 79 oxygen will carry with it-^ = 3.76 volumes of nitrogen. When air is used to support combustion the nitrogen takes no chemical part in the reactions considered but simply mixes with the products of the combustion and is known as a diluent."^ A simple relation can now be shown: Since the volume of CO2 formed by combustion of carbon equals the volume of the oxygen used in the process and since oxygen forms 21 parts of air by volume, it follows that with *' complete " combustion the products will consist of 2 1 parts CO2 and 79 parts N by volume when not diluted by the presence of excess air. (d) Then if the carbon is burned in air and if analysis of the " flue " gas shows that the volume of CO 2 is less than 21 per cent, it follows that either (1) there is more air present than is required for complete combustion, the excess acting as a diluent, or (2) that there is a deficiency of air, with the result that only a part * Under some conditions part of the nitrogen burns to an oxide, but the quantity thus consumed is small in all the ordinary engineering processes. COMBUSTION 479 of the carbon is burned to CO2, the rest appearing in CO. If the percentage of CO 2 is less than 21 and no CO is found in the flue gas it indicates that there is excess air; and if CO is present there is a deficiency.* (e) The percentage of CO2 by volume in the flue gas mixture can be computed for any condition of combustion, by using the following formula, T» r ^^ 1 1 vol. of CO2 rer cent 01 CC'2 by vol. = wY total vol. of gas wV X 100 X 100 = X 100, (349) (wV) + (^V)i + etc. '^ ^^^ . S (wV)„ in which w = weight of CO 2 present in the mixture, Wi, W2j etc. = weights of the other gases present, V = specific volume of CO2, Vi, V2, etc. = specific volumes of the other gases. The specific volumes of gases are given in Table XlX.^y**' (f) If an excess of air is supplied, say x per cent more than is required for perfect combustion, the maximum per cent of CO 2 by volume which could be present in the flue gas can be computed in the following manner, based on the combustion of one pound of carbon. In this case the combustion of the pound of carbon will result in 3I pounds of CO2', it will theoretically require 11.6 pounds of air; there will be 0,77 X 11. 6 = 8.9 pounds of nitrogen accompanying the oxygen used for combustion; and there will be ( 1 1 .6 X ) pounds of excess air. The following table gives the weights (w) of gas present per pound of C burned to CO 2, their specific volumes (V) at 62° F., and the products of these quan- tities (wV). TABLE XXI. — FLUE GAS CONSTANTS. Gas. w Ve2 wW CO, N (fheareticaV) Air 3l 8.9 II .6 X 100 8.62 13.60 13-14 31-6 121 .0 1.52 X * These statements should be limited to take account of certain " equilibrium " conditions discussed in a later chapter. For the present purpose, however, they are sufficiently exact. 48o HEAT-POWER ENGINEERING The sum of the last column is, 2 (wY)n = 31.6 + 121. + I.52X = 152.6 + 1.52 a: Then from Eq. (349) Per cent CO2 by vol. = 31-6 (1+^) \ 100/ X 100, approx., (350) 153 which gives the proportion of CO2 in the flue gas. (g) Again, since the per cent of CO 2 by volume decreases directly as the quantity of total air is increased, it is evident from (c) that Per cent CO 2 by volume == 21 -r- (l + x/ioo), . (351) in which x, as before, represents percentage of excess air. Sim- plifying Eq. (350) results in the same equation (approximately). The relation of the CO 2 to x is shown in Fig. 316 by the curve to the right of oO. ® 30 s O O 15 «10 o o -^ 5 \ \ \ \ \ X ^ \ K ^ J \ 0^ /■ \ \ 50 40 30 20 10 J/ ^Deficiency 50 100 150 200 250 300 « /o Excess Fig. 316. (h) The expression (l + xJYOO) is known as the excess coefficient X. In words, — the excess coefhcient is the number by which the theoretical amount of oxygen, or air, required must be multiplied to find that actually supplied. If the CO 2 percentage is known, and if the combustion is complete (and only in that case) the per cent of excess air x, can be found from Eq. (351). Thus X = ( T ^^—,^-\\ioo (352) \per cent CO2 I (i) For the case of complete combustion, the percentage of COMBUSTION 481 excess air can also be found when both the total volume (iV) of nitrogen and the volume {Ox) of that part of the oxygen which remains free after combustion are known. The volume of nitrogen accompanying the excess oxygen is 79/21 X Ox = 3.76 Ox, and that corresponding to the oxygen used in combustion is iV — 3.76 Ox. Hence, since the nitrogen undergoes no change, the percentage of excess air is :^ =100 (3.76 Ox) -^(iV- 376 Ox), . . (353) and the excess coefficient is 3.76 Ox X = l + 100 = 1 + (354) iV- 3.76 Ox* • • (j) In most cases it is possible to have incomplete combustion of part of the carbon although sufficient air is present, since the air may not be properly distributed. In such cases x and X can be determined if the volume per cent of CO is known in addition to the N and 0. Since each volume of CO present could have combined with half its volume of oxygen to form CO2, it follows that, on the basis of complete combustion, the excess oxygen is equal to — CO/ 2. The nitrogen accompanying this is 3.76 (O — CO/ 2), and that corresponding to the oxygen required for complete combustion is N— 3.76 (0 — J CO), The percentage of excess air for this case is, then 3.76 (0 - i CO) X 100 N - 3.76 (O - i CO) and the excess coefficient is 3.76 (0 - . X=l + 100 = 1 + CO) (355) (356) iV-3.76(0-iCO)' • (k) In case there is a deficiency of air amounting to y per cent, there is 2y per cent of the carbon burned to CO, as has already been shown (in Sect. 236 g) ; in burning one pound of carbon there will result 23// 100 X 2\ pounds of CO, (l — 23;/ 100) X 3f pounds of CO2, and the nitrogen present will be (l — 3;/ 100) X (0.77 X 1 1.6) pounds. Tabulating these values gives: TABLE XXII. — FLUE GAS CONSTANTS. Gas. w V62 wY CO2 CO N (l-23'/ioo)X3f (2^/100) X 2^ (l-y/ioo)X8.9 8.62 13.60 13.60 31.6 (l-2}'/ioo) 31.7 (23'/ioo) 121 .0 {l—y/100) > 482 HEAT-POWER ENGINEERING The summation of the last column gives 'Z {wY)n = 152.6 —1.21 y. Then, from Eq. (349), Per cent CO. by vol. = 31-6 (l- 23-/100) ^ 152.6 — I.2I y ^^^'^ and Per cent CO by vol. = 3i7 (^y/ioo) ^^^ ^ ^ •^ 152.6 — 1.213/ The relation of the percentage volumes of CO2 and CO in the flue gas to the percentage deficiency of air, is shown in Fig. 316 by the curves to the left of oO. 239. Temperature of Combustion, (a) When combustion occurs, the heat energy liberated tends to be dissipated. But if the combustion can be imagined to occur within a vessel perfectly impervious to heat, then all the liberated heat must remain within the vessel, and the products of combustion would be raised to a high temperature. This temperature is known as the theo- retical temperature of combustion and is readily calculated. (b) First, assuming only one gas as the product of combustion, and no heat absorbed by the surrounding vessel, the theoretical temperature rise will be obtained by dividing the available heat by the product of the weight and the specific heat of the gas formed. If the vessel is assumed not to change in size, the specific heat for constant volume must be used; but if the vessel is the equivalent of one fitted with a movable piston so arranged as to maintain constant pressure, the specific heat would be that for constant pressure. For example take the reaction 2 C + O2 = 2 C0]-\- (4500 B.t.u. per pound of C). Since 2 J pounds of CO are formed per pound of cg-rbon, the theoretical rise of temperature with the theoretical supply of pure oxygen will be Rise= 4500 C n X 23 in which Cn is either the specific heat at constant volume (C^), or at constant pressure (Cp), as the case may be. (c) If air is used to furnish the oxygen, the nitrogen must also be heated. Then, since the weight of iV, accompanying the COMBUSTION 483 used per pound of C, is \\ X 77/23 = 447, the resulting temper- ature rise is Rise= 4500 Cn X 2i + Cn' X 447 in which the primed specific heat is for the nitrogen, and the other for CO as before. Similar equations may be written for other combustibles and other products of combustion. (d) The temperature theoretically attained will be the sum of temperature ta existing before the start of the reaction and the temperature rise as found above. In general, for any number of products of combustion. t = to-{- CqWo + CiWi + C2W2 + CsWs + etc.. ^« + sTa^.' (359) in which to = initial temperature, AQ = heat liberated, Co, Ci, C2 = the specific heats of the products of combustion, at constant volume or pressure, as the case may be, and Wo, Wi, W2 = the weights of the products of combustion. The specific heats of the products of combustion * are given in Table I on pages 40 and 41. (e) It is evident that the larger the denominator of the frac- tion in Eq. (359) the lower will be the theoretical temperature of combustion. If, then, an inert gas such as nitrogen is carried through the heating process, as when air is used instead of pure oxygen, the theoretical temperature will be lowered; and should more air be supplied than is needed for complete combustion, the temperature will be still further reduced. Diluents, though taking no essential chemical part in the reaction, thus play a very important part from the physical side; they always reduce the theoretical maximum temperature attainable by the combustion. The way the temperatiire rise theoretically varies with excess or deficiency of air, when carbon is burned at constant pressure, is shown in Fig. 317. (f) If any heat is lost during the period of combustion, as, * See also (g) of this section. 484 HEAT-POWER ENGINEERING & 2000 I ^" 1000 for instance, by radiation, the numerator of Eq. (359) will be diminished by the amount lost and the theoretical temperature rise will, of course, be decreased. This indicates the advisability of caus- ing combustion to take place as rapidly as pos- sible, because, despite the fact that the same a- mount of heat is liberated during slow as during rapid combustion, the ac- tual time allowed for radiation in the latter case is less, and hence, other things being equal, the temperature attained will be greater. (g) In the chapters on the theory of the ideal gas it was stated that for ordinary work the specific heats of real gases might be considered constant. They are, however, really not constants, and some of them increase rapidly in value at high temperatures. From the previous consideration of the behavior of superheated steam this is just what would be expected. There is still considerable lack of agreement between the values of the high temperature specific heats of gases as deter- mined by different investigators. The later work in this field does, however, give sufficiently concordant results to definitely settle the fact that such increase with the temperature does occur, and to warrant the engineer in assuming some of the values obtained as sufficiently accurate for practically all engineering calculations. The values for mean specific heats given in Fig. 318, taken from curves prepared by Prof. G. B. Upton, and published in ''Experimental Engineering" by Carpenter and Diederichs, repre- sent the most probable values for the different gases named. It will be noted that no account is apparently taken of variation of the specific heat with pressure. Such variation is negligible for most gases with which the engineer ordinarily deals, — the principal exceptions being water vapor and ammonia. For water vapor the variation with pressure is rapid at low temperatures but becomes less so at higher temperatures, as was shown in Fig. 40. COMBUSTION 485 (h) Since the specific heat increases with temperature, the value of the denominator of Eq. (359) must increase when the numerator becomes greater, other things being equal; thus the higher the temperature the less effective is a given quantity of heat in causing a rise of one degree. It follows that in practical work, even if all radiation could be prevented, the temperature will never rise as high as Eq. (359) would indicate when the ordinary values of the specific heat are used. Mean_S.pecificJB[eatj (C ) at Constant ^ Pressure -4t2 -4.1- 4.0 h-3;9 -0;30 -0.29 -0r28 0:66 -0.64 -0:62 0: To Obtain Meaa Specific HeatCCy) At Constant Volume Substract From Cp The Following Constants : O N Air CO2 H2O CO 0.063 0.072 0.069 0.045 0.112 0.009 1 200 400 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 Temp. Deg. Fahr. Fig. 318. To determine the real temperature rise (neglecting radiation loss) for any given heat supply, the mean specific heats must be used in the denominator of the equation. The only satisfactory way of doing this would be to guess at the temperature expected, choose the corresponding mean specific heats, determine the re- sultant temperature and compare with the value assumed. If the difference is great a closer approximation can be made, and so on. This is similar to many of the calculations used in con- nection with superheated steam. 486 HEAT-POWER ENGINEERING 240. Combustion of Hydrogen, (a) Hydrogen burns accord- ing to the following equation: 2 H2 + 02 = 2 H2O (360) The weights combined are (2 X 2) of H+{2 X 16) ofO=36 of H2O, and dividing this by 4 gives lof H + 8ofO = gof H2O. . . . . (361) Then, for each pound of hydrogen burned, 8 pounds of oxygen must be supplied, and 9 pounds of water will result. It is also found that about 62,000 B.t.u. are liberated per pound of hydro- gen burned. i (b) Problems involving the combustion of hydrogen are often complicated by the fact that many of the real combustibles contain some oxygen, which may exist as a constituent of a CxHyOz compound, or in combination with some of the hydrogen as H2O, or in a number of other different ways. Obviously, to calculate the heat that would be liberated by a pound of such material would require a knowledge of the condition of all oxygen present; but unfortunately such knowledge is seldom available, hence it is customary to consider that all oxygen present is combined with hydrogen as H2O and that only the remainder of the hydrogen can burn to liberate heat. This combustible part of the total hydrogen is known as available or uncombined hydrogen. According to the assumption just given, the "available" hydrogen can be determined in any case by subtracting from the total hydrogen the amount which could be combined with all the oxygen present. Equation (361) above shows that a given weight of oxygen could be combined with one-eighth its weight of hydrogen and it follows from this that the weight of the unavailable hydrogen must be one-eighth of the weight of oxygen present in a compound. Then if H represents the total weight of hydrogen present and if there are pounds of oxygen which are assumed to be already combined with part of this hydrogen, the available hydrogen must weigh {H — 0/8) pounds. The oxygen required for the combustion of the available hydrogen is Pounds of = 8(^-0/8),. . . . (362) COMBUSTION 487 and the weight of air required to supply this oxygen is found by multiplying this equation by 4.35; thus Pounds of air = 34.8 {H — 0/8) (approx.)- • (363) (c) If hydrogen at 60° F. is burned to H2O and the latter is afterwards cooled to 60°, the quantity of heat obtained varies according to the conditions of cooling. If the material is con- tained in a vessel equivalent to a cylinder closed with a movable piston exerting a constant pressure and if at the end of the cool- ing process all the water exists as liquid, a certain amount of heat equal to about 62,000 B.t.u. (experimental value 61,950) per pound of available hydrogen will be obtained. In this book this will be called the " higher heat value " of hydrogen. On this basis the higher heat value may be defined as the quantity of heat obtained when the products of combustion are cooled in such manner that the water vapor resulting from the combustion of one pound of hydrogen (initially at 60° F.) is com- pletely condensed at constant pressure to a liquid at a tempera- ture of 60° F. Then, when a combustible containing H pounds of hydrogen and pounds of oxygen is burned, the heat obtained ■ from the available hydrogen, on the basis of this higher heat value, would be B.t.u. = 62,000 (H - 0/8). (d) Other definitions of higher heat value are sometimes given. Instead of cooling to 60°, some other (higher) temperature, such as 212°, may be used, in which case the amount of heat involved is slightly less. Should the cooling be conducted in a vessel inclosing a greater volume than that occupied by the liquid water, only a part of the vapor will condense, the rest remaining to fill the surplus space at the existing temperature. This vapor will of course have associated with it its latent heat of vaporization, and there- fore the heat value found will be less than that obtained when all the water is condensed. (e) Another calorific quantity, known as the "lower heat value," is used by engineers but is not very accurately defined. It is generally assumed to be the heat obtained if all the water formed remains saturated or superheated vapor at the tempera- ture of the products of combustion. This would be numerically )y nXj>^ \rt^- y i\ \^ h __. .__ -+— K the curve in Fig. 321. As the combustible part of the coal is mostly carbon these same percentages hold substantially in the actual case.* Thus, a knowledge of the CO2 content in the flue gas indicates in a general way the operating conditions within the furnace and enables the boiler attendant to intelligently adjust the air supply. Experience has shown that if the supply of excess air is such as to give CO2 by volume between 10 per cent and 15 per cent, the furnace will be operating at its highest efficiency, the exact best percentage varying with different conditions. A value below 10 per cent nearly always in- dicates too great an amount of air and a value above 15 per cent is generally indicative of too small an amount, as it is usually accompanied by the formation of prohibitive quan- tities of CO. In Fig. 321 the region for the best results is that shown by the portion of the curve lying between (a) and (b) ; in Fig. 320 it falls between the points bearing similar letters; and it ap- proximately corresponds with excess coefficient (X) between 1.3 and 2.0, given in (b) of this section. (d) In order that the' boiler attendant may obtain an indica- tion of the amount of air being supplied, various devices known as CO2 Recorders, Econometers, Combustion Recorders, Com- posimeters, etc.f are used to indicate the CO2 content of the flue gases. Some of these appliances operate, or indicate, intermit- tently, some continuously, and some give a continuous graph- ical record so that the owner or manager of the plant can check the operation over any desired period of time. In the use of all these instruments it is, of course, necessary to obtain samples of gas truly representative of the average and to guard against the infiltration of air through the boiler setting or the flues between the furnace and the sampling point. 8 6 9 12 15 18 % CO2 in Flue Gas by Volume Fig. 321. * Although the percentage of CO2 is somewhat less because of the other combus- tible and noncombustible constituents present in the flue gas in the actual case. t For description and method of using such apparatus see Carpenter and Diede- richs, " Experimental Engineering," published by John Wiley & Sons. 5o6 HEAT-POWER ENGINEERING 251. Conditions for Complete and Smokeless Combustion. (a) If air is passed upward through a deep bed of ignited carbon devoid of volatile matter, there is a tendency for any CO2 that is formed in lower layers to be reduced to CO when coming into contact with the carbon above. If this CO is not subsequently supplied with a proper amount of air while still at a high tempera- ture it will pass off unoxidized and this will result in a loss of heat which would otherwise be made available. It is, therefore, important that an adequate air supply and a suitable tempera- ture be maintained in the upper part of, and just above, the bed of fuel. This air may either pass through the bed or be supplied from above. The foregoing applies of course to the combustion of coke and charcoal as well as to carbon. Anthracite coal, which is mostly fixed carbon, behaves similarly, but in this case there is also a small amount of volatile matter which must be properly burned. These fuels, which have little or no volatile matter, give short flames above the fuel bed, the flames being due to the combustion of CO and the small quantity of volatile matter present. (b) When coal possessing a considerable amount of volatile matter is placed on a hot bed of fuel, the greater part of the vola- tile portion distills off as the temperature rises, and the residue, which is coke, burns in the manner just described. The more serious problem that confronts the engineer in this case is the complete oxidation of the combustible part of this volatile mat- ter. Evidently in the ordinary up-draft furnaces that are fired from above the combustion of this part of the fuel must occur above the fuel bed, just as is the case with C0\ and in order that the combustible gases may be completely burned, the following four conditions must exist: ( I ) There must be sufficient air j ust above the fuel bed ,. supplied either from above or through the fuel bed itself; (2) this air must be properly distributed and intimately mixed with the com- bustible gases; (3) the mixture must have a temperature suffi- ciently high to cause ignition (some of the combustible gases, when mixed with the burned gases present above, the fuel, have an ignition temperature of approximately 1450° F.) ; and (4) there must be sufficient time for the completion of combustion, that is, the combustion must be complete before the gases ACTUAL COMBUSTION OF FUELS 507 become cooled by contact with the relatively cold walls of the boiler (which are at a temperature of about 350 degrees) or with other cooling surface. (c) To prevent the stratification of the air and gases, special means are sometimes adopted, such as employing steam jets above the fire and using baffle walls, arches, and piers in the passage of the flame, to bring about an intimate mixture. (d) In order that the air used above the fuel bed shall not chill and extinguish the flame, it should be heated either by passing it through the fuel bed, or through passages in the hotter parts of the furnace setting, or in some other way before mingling with the gases; or else the mixture of gases and air should be made to pass over or through hot portions of the fuel bed, or should be brought into contact with furnace walls, or other brick- work, which is at a temperature sufficiently high to support the combustion. (e) In order that the flame shall not be chilled and extinguished by coming in contact with cold objects, it should be protected by the hot furnace walls until combustion is complete. The furnace should have proper volume to accommodate the burning gases, and, when the conditions are such that the flame is long, the distance from the fuel bed to the relatively cold boiler sur- faces with which the gases first come in contact, should be at least as great as the length that the flame attains when the fire is being forced. The length of flame depends on the amount and character of the volatile matter in the fuel, on the rapidity of combustion and on strength of draft. It varies from a few inches, with coke and anthracite coal, to 8 feet or even more with highly volatile coals — even 20 feet has been reached with some western coals. (f) In order to have complete combustion of all the fuel in a furnace it is necessary that uniform conditions prevail through- out the fuel bed; and to bring this about it is essential that the fuel itself be uniform in character. Therefore, the best results are obtained with coal that has been graded as to size. Espe- cially is this true with anthracite coal which ignites slowly and is more difficult to keep burning than volatile coals. This coal requires a rather strong draft and unless the bed is uniform the rush of air through the less dense portions tends to deaden the fire in those regions, hence good results can be obtained with this 508 HEAT-POWER ENGINEERING coal only when it is uniform in size and evenly distributed. The more common sizes of coal are given in Tables XVI and XVII, on pages 465 and 466. (g) Smoke may be composed of unconsumed, condensible tarry vapors, of unburned carbon freed by the splitting of hydro- carbons, of fine noncombustible matter (dust), or of a combina- tion of these. It is an indication of incomplete combustion, and hence of waste, and in certain communities is prohibited by ordinance as a public nuisance. Smoke can be avoided by using a smokeless fuel, such as coke or anthracite coal; or, when the more volatile coals are used, by bringing about complete com- bustion of the volatile matter. In general, the greater the pro- portion of the volatile content of the coal the more difficult it is to avoid smoke, though much depends on the character of the volatile matter. Coals which smoke badly may give from 3 to 5 per cent lower efficiencies than smokeless varieties. For each kind of coal and each furnace there is usually a range in the rate of combustion within which it is comparatively easy to avoid smoke. At higher rates, owing to the lack of furnace capacity, it becomes increasingly difficult to supply the air, mix it and bring about complete combustion. Hence when there is both a high volatile content in the coal and a rapid rate of com- bustion it is doubly difficult to obtain complete and smokeless combustion. However, although smoke is an indication of incomplete and hence inefficient combustion, it may sometimes be more profitable, because of lower price or for other reason, to use a coal with which it is difficult to avoid smoke, provided the latter is not a nuisance or is not prohibited by statute. 252. Value of Coal as Furnace Fuel, (a) The principal factors which determine the commercial value of coal, used in furnaces are: (i) price per ton, (2) calorific value, (3) moisture, (4) volatile matter, (5) ash, (6) clinkering tendency, (7) sulphur content, (8) skill and attention required in firing, (9) suitability for the furnace and grate in which it is to be used, (10) size of coal and (11) available draft. These will be briefly discussed in this section. (b) As exposure to weather (sun and rain, humidity, etc.), during transportation and storage, may affect the amount of ACTUAL COMBUSTION OF FUELS 509 moisture and may also alter the chemical composition and heat value of the fuel, especially if rich in volatile matter, the various analyses to which the coal may be subjected should be made after the coal is received, or as received, if it is desired to deter- mine its value to the consumer. The calorific value is preferably determined by using a fuel calorimeter (see Sect. 244) ; it may, however, be approximated by any of the methods given in Sect. 227(a) to (d). The moisture, fixed carbon, volatile matter, and ash per pound of material may be found by making a proximate analysis (Sect. 226(c)). (c) If payment is made on the basis of weight of coal " as received," and if the heat value is stated per pound of "dry coal," part of the expenditure is for an unknown weight of moisture and the true value of the coal is unknown. Evidently, from the consumer's standpoint, the purchase price should depend directly on the calorific value per pound of the moist coal as received. In any case the ultimate test of the commercial value is the cost per B.t.u. delivered, or the number of B.t.u. received for a unit of money expended, other things being equal. (d) The moisture in the coal is undesirable as it not only (i) reduces the heat value per pound of material fired, but (2) adds to the transportation expense per B.t.u. delivered, and this in direct proportion to its weight, and (3) decreases the furnace and boiler efficiency since it becomes superheated steam, thereby absorbing heat (latent and sensible), which is carried up the chimney with the flue gases. The heat thus carried away per pound of moisture is the same as that per pound of water vapor formed from the combustion of hydrogen and is given approxi- mately by Eqs. (364) or (365). Roughly, the loss of the total heat value of dry fuel is about xV per cent for each per cent of moisture present. In eastern coals the moisture normally ranges from i to 5 per cent, and in western coals from 3 to 15 per cent. (e) Coals in which the volatile matter is proportionately very high usually give very long flames, and cannot be burned com- pletely or smokelessly unless used with furnaces of proper type, size, and proportions and unless special means are provided for regulating the air supply above the grate. Even with the most careful management it is usually difficult, and in some cases impossible, to obtain complete combustion with such coals even 5IO HEAT-POWER ENGINEERING ;65 60 55 ^ N s. \ 10 20 30 10 50 60 ^ Volatile'Matter .in:Dr.y Cgmbustible Fig. 322. though an extreme amount of air is used; hence, the calori- metric test is not a true measure of the commercial value of such fuels in furnaces. Fig. 322 shows in a very general way how the efhciency of combustion varies with the percentage of volatile matter in the dry combustible.* Coals moderately rich in volatile matter, such as semibituminous and the less volatile bituminous coals, not only have the highest calorific values (as shown by the Mahler curve in Fig. 315), but, when properly fired, generally produce the highest efficiencies of any of the coals used, and with suitable conditions and reasonable atten- tion can be burned smokelessly, or practically so. (f) The ash detracts from the value of coal in a number of ways. The greater its percentage the more difficult it is to obtain complete combustion because of its tendency to pack and obstruct the passage of air; also the greater may be the proportion of coal lost through the grates with the ash, and the less is the capacity of a given furnace because of the reduction of combustible per square foot of grate The way in which the value of 100 90 ^80 f'70 I 60 ,•^40 I 30 «20 10 - ■^ ^^ --N \ s. \ \ fA.B ement-"! A.i)r;25;li Powt r" \ \ \ 1 1 5 2 2 5 80 35 iO Per Cent Ash in Dry Coal' Fig. 323- area. the fuel decreases as the percentage of ash increases is shown in Fig. 323, which in a general way applies to any kind or grade of coal. When the ash constitutes 40 per cent of coal, the fuel is practically valueless in ordinary furnaces. The expense of generating a given amount of heat is increased (i) by the cost of transporting the inert matter in the coal, (2) by the transportation and disposal of the ash, (3) by the extra labor involved in handling the larger weight of material, (4) by the unconsumed coal carried through the grates with the ash (which may be from 10 per cent to 60 per cent of the latter), and (5) by the heat absorbed by the ash (specific heat = 0.2 to 0.24) and carried with it to the ash pit. In commercial coals the ash * " Steaming Tests of Goals," Bull. 23, U. S. Bureau of Mines. Page 233. ACTUAL COMBUSTION OF FUELS 511 10.0.0 1.25 1 .75 .50 .25 Size of Coal(Inches) Fig. 324. generally ranges from 4 per cent to 25 per cent of the total weight. The smaller the size of coal the more difficult is it to remove the inert portion, hence the greater is the proportion of ash present, as is shown by curve i in Fig. 324 for one particular kind of coal. (g) If the ash is fusible at a comparatively low temperature, it will form clinkers when a hot fire is maintained, as when the capacity of the furnace is being forced. This clinker, of course, detracts from the value of the coal. Steam, or water vapor, passed through the fire with the air, is supposed to decrease the tendency to clinker be- cause of absorption of heat and the consequent lowering of the tempera- ture of the ash. For this reason steam- blasts are sometimes used under the grate with clinkering coals and often water is kept in the ash pit to furnish vapor. If clinker is formed, the fused mass must be frequently broken up to permit the free passage of air through the fuel bed to support the combustion. (h) Sulphur in coal is objectionable not only because of its relatively low heat value, but because of the deleterious effect on the boiler materials, and because it is thought that in some instances it indicates the presence of clinker-forming matter, although clinker also occurs when it is absent. The sulphur should not exceed 3 J per cent. ^ (i) In general, in using the same coal with a given furnace and draft, the efficiency and capacity of a grate will vary with the size of the coal, as is shown by curves 2 and 3 in Fig. 324, for one particular kind of coal tested under a certain boiler.* The best size for given conditions can be determined from experiment or from a study of data relating to similar coals burned under like circumstances. If for some reason it is necessary to burn a given size of a particular coal, there is usually some design of furnace and some set conditions which will give best results; these can be * Abbott, " Characteristics of Coals," Jour. Western Soc. of Eng'rs., Oct. 16, 1906, p. 528. 512 HEAT-POWER ENGINEERING determined experimentally if no information on the subject is already available. In general, the smaller the coal the harder is it to burn com- pletely and the greater is the percentage of unburned coal lost through the grates with the ash. In consequence there is less general demand for the smaller sizes, hence they cost less per ton than the larger grades and therefore are widely used in boiler furnaces even though their heat value per pound is low because of the large percentage of ash present. Very fine coal and dust are difficult to burn on ordinary grates as they tend to pack and check the flow of air through the fuel bed, or else, with strong draft, are carried along with the air to be deposited within the boiler setting or to be carried up the stack to become a nuisance to the surrounding neighborhood. They may, however, be burned successfully by the methods which will be given in Sect. 253- (j) Caking of the coal, if excessive, is in general undesirable because of its tendency to prevent the passage of air ; but where provision is made to break up the bed, continuously or inter- mittently, a certain amount of caking may be advantageous. (k) The different kinds of coal, and the various sizes, do not generally burn at the same rates under equal drafts. With a given grate and draft, it is of course necessary to use a coal which will develop the amount of heat that is needed for the particular purpose for which the furnace is used, for example, if used under a boiler, it must be possible to burn enough coal to evaporate the maximum amount of steam required of the apparatus. Hence under certain conditions the possible rate of combustion may have an influence in the selection of a coal. Sometimes when there is uncertainty as to the kind of coal which will eventually be used, — the grate is made of such size that the heat output will be sufficient even though the slowest burning coal is used, — then it will be ample for freer burning kinds — and, subsequently, if desirable, portions of the grate can be blocked off to reduce its area when the latter are used. Further, there is some rate of combustion (pounds of coal burned per square foot of grate surface per hour) which will give the best combined boiler and furnace efficiency for each kind and size of coal. Fig. 325 shows the variation in the case of one particular kind and size. In general, the rate and heat develop- ACTUAL COMBUSTION OF FUELS 513 Lbs.of Coal per Sq.Ft. of Grate Ai-ea Fig. 325- ing capacity of the furnace is least with coals low in volatile matter, rich in ash, and small in size, and is, of course, directly dependent on the rate of air supply, that is, on the draft. The best rate to adopt in each particular instance can be deter- mined experimentally, or from a study of similar cases, when data are available. (1) As the volatile matter is mostly burned beyond the fuel bed, the rate at which coal can be burned on a given grate area is largely dependent on the proportion of fixed carbon it contains. The best economies are usually ob- tained when from 12 to 16 pounds of fixed carbon are burned per square foot of grate surface per hour. The ordinary rates of combustion (under normal conditions) are about as fol- lows: Anthracite, from 15 to 20 pounds; Semi-bituminous, from 18 to 22 pounds; and Bituminous, from 24 to 32 pounds. Dividing the estimated total weight of coal which is normally to be burned per hour, by the proper normal rate, as here given, results in the necessary grate area and allows for an overload capacity of from 50 per cent to 100 per cent, depending on the intensity of draft that is available. Evidently with anthracite coal there must be a larger grate area for a given total capacity than with bituminous coal. Greater rates of combustion are possible; for example, in torpedo boats under forced draft (4I inches to 6 inches of water) the rate is from 55 to 65 pounds per square foot; and from 80 to 120 pounds, and even more, have been burned (with air pressure of from 4 inches to 8 inches of water). Rates as high as 90 pounds per square foot per hour are commonly used in loco- motive practice where exhaust steam nozzles are employed for inducing strong drafts. (m) The maximum capacity obtainable with a given furnace and with a certain intensity of draft available varies not only with the kind of coal but also with the size. Curve 3, in Fig. 324, shows how it varied with the size of one kind of coal tested under a certain boiler. It is to be noted that the maximum efficiency is not necessarily obtained with the size that gives the greatest capacity. 514 HEAT-POWER ENGINEERING The capacity per square foot of grate area with anthracite coal is limited largely by the fact that if this fuel is burned rapidly, it has a tendency to break up into small pieces which pack and clog the passage of air through the fuel bed. This action also increases the amount of unconsumed coal lost through the grates with the ash and this lowers the efficiency. 253. Burning Powdered Coal, (a) Powdered coal can be burned in much the same way as a liquid fuel (see Sect. (258)) if it is finely pulverized and properly injected into a furnace. When used in this way it has many of the advantages incident to the use of liquid fuel. However, the cost of crushing and the difficulty of uniform' feeding, combined with the complicated apparatus necessary, have thus far prevented any wide use of powdered coal as a boiler fuel although it has been very successfully and widely used for firing cement kilns in regions in which the price of oil is high. (b) Coal too fine to use on ordinary grates may be hriquetted by using a suitable binder, as has already been mentioned, and can then be used conveniently and efficiently on ordinary grates. (c) Where special dumping grates are used with air supplied from below, under pressure that can be readily regulated, very small anthracite coal has been successfully burned in the following manner: The fuel bed is not disturbed for cleaning for several hours, the ash being allowed to accumulate ; the intensity of air pressure in the ash pit is increased as the fuel bed becomes thicker, but is always such that it becomes atmospheric at the surface of the bed; the products of combustion are carried ofT by draft induced by a stack or other device above the fuel bed ; and the fuel is distributed as evenly as possible in firing. Owing to the fineness of the coal, there is a strong tendency for it to burn out in spots, to prevent which the surface of the fuel bed must be smoothed very frequently by using a distributing bar with a T-head. As the pressure just above the fuel bed is atmospheric there is no objection to the frequent opening of the doors which is necessary for thus working the fire. Culm and other low grade coal, which is ordinarily considered to be waste material, may in some instances be burned with satisfactory results by this method. ACTUAL COMBUSTION OF FUELS 515 254. Selection and Purchase of Coal, (a) The price per ton of the coal deUvered is the sum of the cost at the mines and the transportation charges; hence the distance from the mines may have an important bearing on the cost to the consumer. The cost at the mine depends on the difhculty in mining — hence for hard anthracite it is greater than for the softer bituminous coals. Also the price is, of course, dependent on the supply and demand. Thus the smaller sizes, being in the least general demand, are the cheapest per ton at the mine. Grades that are generally considered worthless cost least, hence much attention is being devoted to devising methods tor utilizing these grades. (b) In selecting coal for boilers the problem is to find that kind and size which will give the greatest number of useful heat units, or which will evaporate the largest weight of water, per dollar expended for the fuel and its firing. In default of avail- able information on the subject, a series of tests under varying conditions may be conducted to determine the coal best suited to a given furnace and to find the size of that coal, thickness of fire, strength of draft, method of firing, etc., which will give the best results under the prevailing conditions. But such tests may be as much a determination of the skill of the fireman as of the quality of the coal, and, therefore, may not give the true value that the coal would have when properly used. Although many such tests have been made, the published data of this kind at present available are rather meager. (c) The principal sources of data are reports of the U. S. Bureau of Mines, of State Geological Surveys, Engineering Ex- periment Stations, engineering "pocket books," special treatises on fuels, combustion, and boilers, catalogs of boiler manu- facturers, etc. Nearly all of these reference books give tables of the chemical and proximate analyses of the fuels from the more important coal fields and while the coals from a given field, and even from the same mine, vary considerably in character, such data may be used in default of tests of samples of the coal actually under consideration. (d) Some large consumers have adopted the following plan for the selection and purchase of coal: By actual test in their furnaces they determine what kind is cheapest and most desir- able to use under the prevailing conditions and thus a standard specification as to heat value, size, ash, volatile matter, mois- 5l6 HEAT-POWER ENGINEERING ture, sulphur, etc., is drawn up. Then a "standard price" for such coal is agreed upon with the dealer, with adjustments by premiums and penalties for variations from the specification. The adjustment is directly, or almost directly, according to the variation in the heat value per pound of the moist coal (or coal "as received"), and is dependent on, but not directly propor- tional to, the variation in the percentage of ash, volatile matter, and sulphur from the standard. For example, the Interborough Rapid Transit Company (New York City) accepts a run of mine bituminous coal without penalty or premium if it contains 20 per cent or less of volatile matter, 9 per cent or less of ash, and i J per cent or less of sulphur. The standard heat value per pound is 14,250 B.t.u. with penalty and premium averaging about one cent per ton per 50 B.t.u. variation from standard. Penalties per ton range up to 18 cents for 4 per cent excess in volatile matter, and to 23 cents for 4 J per cent additional ash, and to 12 cents for i per cent excess sulphur.* Some concerns specify as standard a run of mine, semibitumi- nous coal with i per cent moisture, 20 per cent volatile carbon, 7 per cent ash, and not over i per cent of sulphur. If x is the per cent of variation from standard, the adjustment in the price is inversely proportional to x for moisture, to 2 x for volatile carbon, and to 3 jc for ash. The government awards contracts on competitive bids which are accompanied by specifications of the kind and composition of the coal (ash, B.t.u., and size), which the bidders propose to furnish. The analyses are made on the coal "as received," which takes care of the effect of moisture. The coal is rejected if it clinkers or produces smoke excessively and if it exceeds certain limits in the amount of ash, volatile matter, sulphur, fine coal, and dust. A small variation from the specified stand- ard is tolerated without penalty or premium; but if there is much difference, the price is varied directly with the heat value of the coal "as received" (including moisture) and is adjusted according to a sliding scale for variations in ash and sulphur. f * Am. El. Ry. Eng'g. Assoc, Report, 191 1. t U. S. Bureau of Mines, Bulletin 11, "Purchase of Coal, etc.;" Bull. 41, " Results of Purchasing Coal under Government Specifications;" and Technical Paper, No. 15, " Sampling Coal, with Specifications.' M ACTUAL COMBUSTION OF FUELS 517 255. Furnace Operation, (a) The efficiency and capacity obtained with a given coal and furnace depend much on the knowledge, skill, and attention of the furnace attendant and especially is this the case if the furnace is hand fired. (b) In addition to the considerations already discussed it is important with many kinds of coal to have the right combination of thickness of fuel bed and draft. For, in general, with each quality and size of fuel, and with each method of firing and rate of combustion, there is some combination of thickness and draft which will give best results — although there is considerable latitude with some coals. Thin beds tend to let an excessive amount of air pass through and require frequent and careful firing and close regulation of draft. Very thick beds require less attention and give quicker response to sudden increase in de- mand, but necessitate stronger drafts and are conducive to the formation of CO. With a given draft and coal the maximum rate of combustion is largely dependent on the thickness of bed. In general, the coarser the coal and the stronger the draft, the thicker should be the bed. But here, again, it seems impossible to give any rule that would be at all general in application; for with anthracite coal, the thicknesses used vary from 4 inches to 12 inches and, with bituminous, from 6 inches to 16 inches, depending on the quality and size of coal, the draft, method of firing, etc. Hence the best combination must ordinarily be found by experience in each instance. (c) With anthracite coal not only must the bed be kept uni- form but it must be disturbed as little as possible in cleaning the fire. Hence shaking grates, which cut off the lower part of the bed with minimum disturbance of the upper part, can be used to special advantage with this coal. (d) The intensity of draft pressure needed is directly dependent on the resistance offered to the passage of air through the fuel bed. Its pressure is usually stated in terms of "inches of water." For the usual kinds and sizes of coal and for ordinary conditions the drops in air pressure through the fuel bed are shown by the ordinates of the curves in Fig. 326,* in which the abscissas are rates of combustion expressed as pounds burned per square foot of grate surface per hour. * Modified from curves given in "Stirling," published by the Stirling Co. (1905). 5i8 HEAT-POWER ENGINEERING (e) In an up-draft furnace, fired from above, the air ordinarily enters through the ash doors below the grates, the draft being induced by the stack, which in some instances is assisted by steam blowers, or by fans. The amount of air and the rapidity of combustion can be regulated by adjusting the dampers in the flues leading to the stack, by regulating blowers or fans, and by varying the openings in the ash doors. If coal is fired inter- mittently, as in hand firing, the layer of fresh coal temporarily §3 1.40 5 10 15 20 25 30 35 40 45 50 Pounds of Coal per Sq.Ft. of Grate Surface per Hour Fig. 326. chokes the air supply received through the bed and this occurs at the time when the most rapid distillation of volatile matter is in progress. Hence, immediately after firing a fresh quantity of coal, particularly if it is rich in volatile matter, an adequate supply of air should be introduced above the fuel bed and this amount should be diminished gradually as the rate of distillation decreases. This air may be furnished through the fire doors, which may be gradually closed by hand or by some automatic device so arranged that the rapidity of its action can be adjusted to suit the fuel, or it may enter through inlets in the boiler front or in furnace walls, or through passages in the bridge wall at the back of the grate. In hand firing there is also a loss due to the relatively long period of time during which the doors are open while firing, ACTUAL COMBUSTION OF FUELS 519 which permits large quantities of cold air to enter and pass over the boiler heating surfaces. As the conditions in the furnace vary widely and quite rapidly with the method of firing, the best results can only be obtained by close attention on the part of the attendants and especially is this the case when the fire is being forced — a time when it is the most difficult to give such at- tention. (f) The way the coal Is distributed on the fuel bed is of importance. In general, there are three methods of hand firing commonly used: (i) In one, called spread firing, the fresh coal is each time spread evenly over the entire surface of the bed. This is the method commonly adopted with anthracite coal. (2) In the second, known as alternate firing, fresh coal is placed on but one-half of the grate at a time, which permits excess air to pass through the other, thinner and brighter half for the combustion of freshly evolved volatile matter. Spot, or checker, firing is similar ; alternate spots on an imaginary checker- board are fired simultaneously, and, as before, the volatile matter from the fresh coal is supplied with heated air by the excess amount that passes through the remaining portions of the bed. In these methods of firing, the coal is placed each time on the brighter portions of the fuel bed. (3) In coking firing, which is used only with caking coals, the fuel is placed on the front edge of the fuel bed and allowed to coke, the volatile matter passing back over the bed and mixing with the hot air passing through this portion. After distillation is complete the coke is pushed back and distributed over the bed. This method, while effective, does not permit of high rates of combustion. (g) Evidently the best results can be obtained only when the conditions are maintained uniform, that is, when the coal is fired continuously and uniformly and there is no variation in the air supply. Thus, with hand or intermittent firing, the coal should be fired frequently, in small amounts, and it should be distributed with skill, while, in addition, the draft should be carefully adjusted. However, such close attention is opposite to the natural tendencies of furnace attendants, and even with it, it is impossible with some coals to obtain complete and smoke- less combustion with hand firing. 520 HEAT-POWER ENGINEERING (h) By the use of automatic mechanical stokers, however, the coal-feeding operation is made continuous and the conditions are kept uniform. They involve but little labor or attention and with them it is possible to obtain practically smokeless combus- tion with nearly all kinds of coal provided that (i) the grates and the furnace setting are properly proportioned to suit the fuel, (2) proper attention is given to the firing and air supply, and (3) a suitable rate of combustion is used per square foot of grate surface. Mechanical stokers will be described in Sect. 257^-^ 256. Grates and Furnaces, (a) The number of square feet of grate surface may be determined in the manner described in Sect. 252 (1). The width of grate is commonly made equal to the distance between the walls of the boiler setting, and the length of grate is ordinarily found by dividing the desired area by this width. With hand firing, grate lengths up to 10 feet have been used with dumping grates, while with ordinary grates the limit of length is usually 6 feet because of difficulty in cleaning the fire. Fig. 327. (b) To prevent the grate bars from burning away they should be of suitable material (white C. I. is generally used), and should be of such shape as to present relatively small surface to the fuel bed and expose large radiating surface to the current of air. They must be in short lengths (not over 3 feet ordinarily), set so as to allow for expansion and contraction and also for warping. They must provide sufficient passage for air, and must permit the ash, but not the coal to pass through. In addition they must be readily cleaned of clinker. (c) Of the great many kinds of grate bars in use four of the most common forms are shown in Fig. 327. In this figure, (c) ACTUAL COMBUSTION OF FUELS 521 is for sawdust and the rest are for coal. For fine coal flat plates like (d) with small perforations are sometimes used; and these may have the exposed surface recessed so as to become filled with a permanent layer of fine ashes in order to protect the bar from the heat and also to prevent the adherence of clinker to the metal. (d) Fig. 328 shows one form of shaking grate, of which there are a great many dif- ferent kinds in use. With such grates the fire is not only more easily cleaned, but the fire doors do not have to be opened during the operation; and the bed is disturbed but little, which is especially valuable when anthracite and noncaking coals are burned. Some are provided with means for breaking the clinker, or the caked coal bed, and others for dumping. Their cost is, of course, greater than for ordinary grates but they often give from i per cent to 5 per cent better efficiency than flat grates. Fig. 328. Wicke ^'='•3- Fig. 329. (e) Fig. 329 shows a typical furnace with fittings. The arrangement shown in Fig. 330 is the roofless furnace suitable for coals low in volatile matter, say with less than 20 per cent. Fig. 331 shows the tile roof arrangement in which the flame is protected by a roof of refractory material supported by the 522 HEAT-POWER ENGINEERING lowest row of boiler tubes. This arrangement is suitable for long flame coals, for ordinarily there is little difficulty in making the roof at least as long as the flame. (f) Fig. 332 shows a Dutch oven which can be built in front of any type of boiler. It offers an incandescent roof and walls to Fig. 330- Fig. 331- reflect the heat and makes possible the complete combustion of volatile matter, but it adds to the radiation losses because of the increased surface exposed. When possible it should be confined within the regular boiler setting, so as to reduce this external surface. In the Dutch oven the roof and walls are sometimes made double with passages between for the circulation of air which is supplied to the furnace. ( I j ■ This arrangement serves the nJ_^ I psS^ double purpose of furnishing hot- ter air and of reducing the radia- tion loss by lowering the temper- ature of the outer walls. (g) In all these figures of fur- naces the distance A should at least equal the flame length, and the external radiating surface of the setting should be made as small as is expedient. The fur- naces and passages for the hot gases must be lined with fire brick, using only the best grades in furnaces in which the firing is forced. Baffle arches, piers, wing walls, etc., are sometimes introduced in the passageway of the gases to mix them and perfect the combustion. (h) Fig. 333 shows a down-draft furnace. In this form of furnace the upper grate bars are cooled and are rather widely spaced. The coal is fired on the upper grate and the volatile matter is carried downward by the draft so as to pass over the hot, partly burned coals which have fallen to the lower grate. Fig. 332. ACTUAL COMBUSTION OF FUELS 523 Fig. 333- (i) The efficiency of a grate is, of course, lowered by the loss of unburned coal with the ashes, while that of the furnace is de- pendent on the completeness of combustion and on the radiation from the external walls. As these efficiencies have an intimate bearing on the performance of the boiler, they will be con- J\\l sidered in connection with the general discussion of boiler ef- ficiencies in Sect. 259. 257. Automatic Mechanical Stokers, (a) The principal ad- vantages derived from the use of mechanical stokers are: (i) Continuous firing and uniform conditions; (2) progressive distillation of volatile matter and proper provision for burning it; (3) a saving of from 30 to 40 per cent labor cost in large plants (in small plants there may be no saving because a certain number of firemen are always neces- sary and the introduction of stokers may not reduce the number) ; (4) relief of men from strenuous duties and from exposure to heat ; (5) greater ease in obtaining good economy ; (6) the elimi- nation to a large extent of the personal element in firing ; (7) the greater possibility of smoke prevention with the poorer grades of coal; and (8) greater rates of combustion than are possible without smoke. (b) The main disadvantages (which may, or may not, be pres- ent in any given make of stoker) are: (i) Greater first cost (and interest on same); (2) possible lack of durability and greater cost of repairs ; (3) cost of power to operate ; (4) greater compli- cation; (5) inability to meet sudden changes in load; (6) failure to distribute coal evenly; (7) loss of unburned coal with ashes; and (8) loss due to use of steam in the air-blast. What was said about the design and arrangement of grate bars and furnaces in general in the preceding sections also applies to automatic stokers. (c) At the lower rates of combustion it is possible to obtain about as good results with hand firing as with automatic stokers, but this involves the employment of painstaking men of great skill who command higher wages than the ordinary. With automatic stokers and furnaces designed to suit the coal and 524 HEAT-POWER ENGINEERING draft, the best results are obtainable with very little effort or skill on the part of the attendants. Most plants using auto- matic stokers are also equipped with automatic coal conveying machinery and means for delivering the coal by gravity to the hoppers of the stokers, and in such cases the labor is, of course, reduced to a minimum. (d) No one type of mechanical stoker is equally valuable for all kinds of coal, but practically any kind of coal can be burned efficiently and smokelessly with a suitable stoker, provided the rate of combustion does not exceed a certain value which is dependent on the kind of coal.* • (e) In hand firing one man can effectively attend to from 200 to 500 boiler horsepower, and at the same time wheel the coal and ashes, and regulate the feed water pumps, draft, etc. In such case from 1000 to 2500 pounds of coal are handled per hour. When merely firing, with coal delivered by others, one man can hand fire about 1000 boiler horsepower, i.e., handle from 4000 to 5000 pounds of coal per hour. With automatic stokers provided with coal fed by gravity from overhead bunkers, one attendant can ordinarily care for from 2000 to 4000 boiler horsepower, using from 8000 to 20,000 pounds of coal per hour, (f) Mechanical stokers may in gen- eral be classified as: (a) Over feed (including (i) front feed, (2) side feed, and (3) chain grate) and (b) underfeed. These will now be discussed in a very general way. (g) In most over-feed stokers (see Fig. 334) the coal is deposited in a hopper from which it is automatically and continuously fed to the grate and made to pass under a more or less extensive coking arch, which is maintained at a high temperature and serves the same purpose as the roof of the Dutch oven. Air, heated or otherwise, is usually admitted with the coal under the coking arch. The grate bars are moved in such manner as to carry the bed of coal constantly in one direction and as it progresses it * Bull. 40, U. S. Bureau of Mines, " Smokeless Combustion," an investigation of several hundred plants. Fig. 334. ACTUAL COMBUSTION OF FUELS 525 gradually burns out. As the coal approaches the hotter portion of the fuel bed a progressive distillation of the volatile matter occurs. The resulting gas mixes with the air above and the mixture then passes under the coking arch which, being heated to incandescence, reflects the heat from the bright portions of the bed and deflects the gas so as to make it pass over the rest of the bed. Thus the conditions are excellent for the complete combustion of the volatile content. The rate at which coal is fed from the hopper to the grates and at which it is carried along the latter can be varied and should be so adjusted that combustion of the coal is just completed when the end of the grate is reached. If completed before this point cold air will force its way through the thin bed of ashes at the end and reduce the efficiency; and if not completed unburned coal will be lost with the ashes. The stokers may be driven in various ways, such as by small steam engines, by electric motors, or by belting from conveniently located line shafting. (h) Fig. 335 shows diagrammatically a typical arrangement of a front-feed stoker with inclined grate. It has a hopper, coal- pusher feeding-device, dead plate, coking arch, and air inlet under the latter. The grate bars are stepped and inclined, and they are mechanically oscillated, or reciprocated, in such way as to cause the bed of coal to gradually descend. The rapidity and amplitude of motion of the pushers and grates can be so regulated that the coal is just burned out by the time it reaches the bottom of the grate. The ashes and clinker become de- posited on the ash table, which is dumped by hand from time to time. When the ash table is tilted a guard is brought into position (as is shown at (a) in the figure) to keep the fuel bed from sliding down and being dumped at the same time. In the figure, the upper reciprocating grate bars are hollow and the air, which is injected into their interiors by steam jets S, issues through openings in the risers of the steps. The lower grates rock or oscillate about the trunnions shown in (b) and have replaceable bars. There are, of course, many other designs and arrangements of front-feed stokers. (i) The typical arrangement of side-feed stokers is shown diagrammatically in Fig. 336. Coal is fed into the magazine from above or through doors (a) in the front and is pushed, by 526 BEAT-POWER ENGINEERING Adjustment ^^N^ DUMPING vj/j/y/////m////////// -:^/m7W?77777777777777777m Fig. 336. ACTUAL COMBUSTION OF FUELS 527 some suitable mechanism, to the coking plate at the top of the inclined grates. The whole bed of fuel is covered by a fire-brick arch, and air, which is heated by passing over the arch, is dis- charged into the furnace just above the entering coal. The coal gradually descends on the inclined grate bars, the alternate ones of which are constantly moving. The ash and clinkers are crushed by rotating (or reciprocating) grinders located at the bottom of the grates. Some grinders are made hollow and are connected to the draft in such way as to cause cold air to pass through them to prevent overheating. When clinkering coal is used, steam (from the stoker engine, if there is one) is dis- charged through the bed of ashes to reduce the amount of clinker and to make crushing easier. I Fig. 337. I The advantageous features of this type of stoker are the large coking spaces, the ample coking arch, and the voluminous com- bustion chamber. These stokers operate successfully with both uniform and variable loads and under a great variety of condi- tions. With some, when certain types of coal are used, there is difficulty in getting rid of the ash and clinker. The types differ principally in the manner of feeding the coal and getting rid of the residue. (j) The typical arrangement of chain-grate stokers is shown in Fig- 337' This has the hopper, the coking arch with air ducts 528 HEAT-POWER ENGINEERING and the "feeding device common with the other forms of over-feed stokers already described. The grates consist of a series of endless chains carried on sprocket wheels which slowly rotate and thus carry the coal toward the back of the grate. The whole mechanism is usually mounted on wheels on a track and can be pulled forward for inspection or repairs. These stokers are particularly adapted to the smaller and poorer grades of non- caking coals. To operate satisfactorily the thickness of fire, the draft, and the speed of the grate must be adjusted to suit the load. Combustion should be complete when the coal has just reached the back of the grate. (k) In the under -feed stokers, a typical arrangement of which is shown in Fig. 338, the coal is fed forward from the hopper, by a Fig- 338. reciprocating pusher, as shown (or by a screw conveyer or other suitable feeding device), into a retort, around the upper edges of which are replaceable tuyere blocks, through which air is supplied under pressure. The combustion takes place at the top of the bed towards which the fresh coal is fed from below. The ashes and clinkers fall to the sides of the retort on dead plates from which they can be readily removed through doors in the furnace front. The volatile matter is liberated as the coal becomes heated and this must pass through the intensely hot coals above, where it is mixed with the entering air and is completely burned. Even with volatile coals, the combustion is completed within a very short distance from the surface of the fuel bed, hence only a very short combustion space is necessary. Such stokers give satis- ACTUAL COMBUSTION OF FUELS 529 factory results even when placed in corrugated flues as small as three feet in diameter, such as are used in internally fired boilers. With such stokers it is necessary to use very strong draft (about three inches of water) which must be furnished by some forced draft system, hence the operation is independent of weather conditions. In some instances the rate at which air and coal are supplied is controlled automatically by the steam pressure. In one such arrangement the speed of the blower- engine is regulated by the steam pressure (a drop in pressure, due to a sudden demand on the boiler, causing an increased speed and hence a greater delivery of air) and the valves for the steam- actuated coal feeder are operated by this same engine ; hence the rates at which the air and coal are supplied are changed simultaneously, are kept properly balanced, and the boiler pres- sure is automatically maintained substantially constant. With these stokers it is possible to obtain very high rates of combustion in a very limited space, from 500 to 600 pounds of coal per hour being consumed in each retort. They operate best with bituminous coals which are low in ash and they are not ordinarily satisfactory with fine anthracite coals.* There are, of course, numerous possible arrangements of such stokers. In some the retorts are inclined and have two hori- zontal pushers, one above the other. 258. Burning Liquid Fuel, (a) Both crude petroleum and the product of its partial refinement, fuel oil, are very extensively used as fuel in boiler plants. The fuel oil is generally preferable to crude petroleum on the score of safety as, due to the removal of the more volatile constituents during the refining process, its flash point is higher. Most fuel oil also has a lower water content than the crude material and for this reason there is less danger of the flame being extinguished by water collecting in the fuel pipes and then passing as a "slug" through the burner. (b) To successfully burn fuel oil it is necessary to spray, or "atomize," it very effectively and to mix this in the furnace with the necessary air. The furnace should be well lined with brick which, becoming incandescent during operation, will insure satisfactory combustion so long as there is sufiicient air well mixed with the fuel. It is also essential that the furnace be so large and so shaped that the burning fuel does not come in con- * Bull. 40, U. S. Bureau of Mines. 530 HEAT-POWER ENGINEERING Sleam Valve — »( Fig. 339- Fig. 340. Oil under pressure 1 Fig. 341. By-pass of heater Oil l^y-pasB Valve \^I»ump n cj Steam Cyl. Exhaust- Steam jj^ from Pump LH Oil from Heater i& Fig. 342. Fig. 343- ACTUAL COMBUSTION OF FUELS 531 tact with boiler heating surface ; failure iu this respect will result in incomplete combustion of the fuel, as in the case of long flaming bituminous coal, and is also liable to result in the over- heating and ultimate failure of the exposed heating surface. (c) The oil is generally atomized or sprayed by compressed air or by steam, 'the latter being now the more common method. It is also occasionally atomized mechanically. In most cases the oil is pumped from storage tanks to burners by small steam- driven pumps. On the way to the burners it is heated by means of the exhaust steam from the pumps, after which it enters the nozzles or "burners," from which it is so sprayed as to give a long jet of finely divided fuel which can thoroughly mix with air admitted to the furnace. The amount of steam required in handling the oil varies from about 2.5 per cent to 5 per cent of the total amount generated — usually it is about 3 per cent and is about evenly divided between the pumps and the burners. Fig. 344- Fig. 345. (d) The principal advantages of burning oil under boilers are: I. Ease of handling from tank car to furnace, as no man- ual labor is required even in the smallest plants. Small weight and volume, since the oil has 30 per cent higher calorific value for equal weight, as compared with coal. Lack of clinkers and ash. Higher average operating efficiency because of (a) ease of operation, (b) ability to properly gauge and main- tain necessary air supply, (c) smaller excess of air required because of ease of forming good mixture, and 2. 3. 4. 532 HEAT-POWER ENGINEERING (d) more uniform furnace conditions because there is no necessity to open doors at frequent intervals. 5. Practical elimination of soot and smoke. 6. Decreased labor bill in large plants because of ease with which one man can handle several thousand boiler horse power. 7. Ease with which boiler can be made to follow rapid fluctuations of load. (e) To offset these advantages are high cost of oil fuel in comparison with coal in many parts of the country and the increased danger of fire due to the more inflammable character. (f) Figs. 339, 340, and 341 show several burners, of which there are a great many other forms in use. One of the numerous possible arrangements of the oil-feeding system is shown in Fig. 342; and in Figs. 343, 344, and 345 are illustrated three of the many arrangements of furnace in use. 258A. Burning Gaseous Fuels, (a) Low-priced, blast-furnace, natural and coke oven gases are frequently used in boilers. Air for combustion is generally admitted through or around the burner, and with gases of high heat value a number of small burners is preferable to a single large one, to prevent a blow- pipe action. The gas and air should have a rotary motion or else a checker-work wall should be used to insure proper mixing. The sizes of gas and air openings depend on the heating value and pressure of the gas. The furnace arrangements are similar to those for oil fuels, with volume from | to if cu. ft. per rated horse power. A stack 130 ft. high is ordinarily sufficient. , (b) If a combustible mixture of gas and air is passed through a mass of finely broken refractory material in a tube at such rate that the flame will not ''strike back," the combustion will take place at a fixed point in the refractory mass which will become incandescent and transmit heat at rapid rate, by radiation and conduction, to the water surrounding the tube. This method of burning gas, which has been called Surface Combustion, has been used in experimental boilers by Bone and others with highly efficient results, due principally to the small amount of excess air, the perfect combustion, and the low temperature of flue gas. The rapid rate of heat transfer permits the use of less heating surface for given output.* * London Engr., Apr. 14 and Nov. 14, 191 1, Jr. A.S.M.E., 1914, Eng. Survey. CHAPTER XXX. BOILERS. 259. Losses Connected with Steam Generation, (a) Be- cause of the very intimate connection between the boiler proper * and the other parts which make up the steam generating appara- tus, it is most convenient to discuss the losses and efficiencies of boiler, furnace, and grate at the same time. Reference to the energy stream in Fig. 346 will assist in following the discussion. (b) It should first be observed that it is the function of the furnace to receive fuel, with its supply of heat in latent form, and to make the maximum possible amount of this heat avail- able for use. The furnace may therefore be called the " heat generator." It is then the function of the boiler proper to serve as a " heat absorber " and to transmit to the contained water and steam as large a part of this heat as possible. But losses always occur in making the heat available in the furnace and similarly there are some that are unavoidable in utilizing that heat. There are in general three losses in the furnace: (i) Some of the combustible is not burned, but is lost with the ash; (2) some, which is not so lost, is incompletely burned and passes off with the products of combustion in fine particles; and (3) some of the heat actually made available in the furnace is lost by radiation and cannot therefore be utilized by the boiler. Thus, only a fraction of the heat originally supplied with the fuel is really brought to the boiler heating surfaces for utilization and part of this must always be unavailable even in an ideal boiler, for after the products of combustion are cooled to the boiler (steam) temperature there can be no further transfer of * The term " boiler " is ambiguous. It is used to refer to the boiler proper (or vessel containing the water and steam) and also to this element in combination with the furnace, setting and other parts, which collectively comprise the whole steam generating apparatus. However, this should not lead to confusion as the context always makes clear the sense in which the term is used. 533 534 HEAT-POWER ENGINEERING heat to the boiler.* This unpreventable loss is equal to the heat required to raise the temperature of the flue gases from atmos- pheric to boiler temperature. Including this one there are three losses of heat associated with the boiler proper or " heat absorber." These boiler losses are: (i) The unpreventable loss (in the ideal case) equal to the heat utilized in raising the flue gases to boiler temperature; (2) a loss resulting from the fact that in commercial boilers the temperature of the flue gases is never reduced to that of the steam; and (3) a loss resulting from the radiation from external surfaces of boiler and setting. ' r. .-' : ^ rj ^at er; an d -.steani;:..- if ' "^' '-.---■"f f^ >^^ f l'^;V''.'!^'^^^^^^ (1) Combustible in Ash (3)Radiatioa (Furnace) (2) Imperfect Combustion (6) Radiation (Boiler) (5) Stack loss above "i *. § Steam Temp. / o<5 ,-»■ (4) Heat used in }" -g J -* raising flue gases V >2« to temp.of steam 1 W a Fig. 346. The exact values of the total radiation loss of the complete apparatus and the proportions chargeable separately to furnace and to boiler are generally indeterminate, but they may be approximated more or less closely in some instances. (c) During a boiler test, it is possible to obtain data which can be used in determining the distribution or destination of the known heat value of the fuel actually fired. The tabulation of such information is called a heat balance and accounts for all the heat utilized and lost. It is usually stated both in terms of B.t.u.'s and on the percentage basis. A complete heat balance would include the following eleven items: (i) The heat utilized (absorbed by the water heated and the steam generated) ; the * There is an exception to this statement in the special case of boilers that operate on the "counter flow principle." This will l?e discussed later. BOILERS 535 losses due (2) to unconsumed combustible in the ash and (3) to the removal of ash from the ash pit while at high tempera- ture; the stack losses (Sect. 248) occasioned by (4) moisture in the fuel, (5) humidity in the air supplying the oxygen, and (6) water formed by the combustion of hydrogen, and that due to (7) the sensible heat in the flue gas; the losses due to (8) uncon- sumed CO, (9) unburnt hydrogen and hydrocarbons and (10) to the solid fuel (such as fine coal dust and soot) carried off by the draft; and (11) the losses not otherwise accounted for — principally radiation. The sum of the items on the B.t.u. basis must, of course, equal the heat in the coal actually fired, and on the percentage basis it must total 100 per cent. (d) In real tests it is seldom practicable to make any such complete balance as that just given. It is common practice * to limit it to the following six items: — (i) Heat absorbed by the boiler proper and the losses due to (2) moisture in the coal, (3) moisture formed by the burning of hydrogen, (4) sensible heat in flue gases, (5) unconsumed CO, and (6) those not other- wise accounted for (including that due to unconsumed H and hydrocarbons, moisture in air, radiation and others not listed above) . A complete discussion of the method of determining the vari- ous losses is outside the province of this book. For further details the student is referred to books devoted to Boilers and Furnaces and to Experimental Engineering. 260. Efficiencies Connected with Steam Generation, (a) After the preceding discussion of the losses occurring in boilers and after a study of the energy stream in Fig. 346, it is evi- dent that numerous ratios between the widths of the stream at various points will give efficiencies of the different elements of the steam generating apparatus and of their combinations. The more important of these efficiences will now be given, but as they are clearly shown in Fig. 346 the discussion will be very brief. (b) Of the combustible placed in the furnace, a part may be lost through the grates with the ash. That which is not thus lost must ascend from the grate as volatile combustible, as gaseous products of combustion, as unburnt solid matter, or as a mixture of these; it will be called "combustible ascending * Rules for Conducting Boiler Trials. Code of 1899, Trans. A.S.M.E., 1899. 536 HEAT-POWER ENGINEERING from the grate " or " ascending combustible." Obviously, the Grate Efficiency is n7f — ^^'^^^^ (^^ ^^^^ value) of ascending combustible Weight (or heat value) of combustible fired ' which is shown in Fig. 346 by the ratio CD/CE. (c) The Efficiency of the Combustion Space (including the coking arch, gas mixing structures, and other parts of the furnace above the grate) is n7f — ^^^^ made available for absorption by boiler , . Heat in ascending combustible ^ This is shown in Fig. 346 by the ratio FG/FH. (d) The furnace, or ** heat generator " includes both the grates and the combustion space. Hence the Furnace Efficiency is prpr _ Heat made available for absorption by boiler , ' Heat value of combustible fired = GEf X CEf (401a) In Fig. 346, FEf is the ratio IJ/IK. The numerator in Eq. 401 is evidently equal to the sum of (i) the heat absorbed by water and steam, (2) the heat in flue gases leaving boiler and (3) the radiation from the boiler and its walls. Items (i) and (2) can be determined without difficulty, but the radiation losses can in general only be approximated. For this reason the Furnace Efficiency is often omitted from reports of tests. (e) It has been seen that the heat used in raising the flue gas from the temperature of the atmosphere to that of the steam is not ordinarily available for use in the boiler proper; * hence, if the products of combustion are at a temperature equalto, or below, that of ebullition there will be no heat used by the boiler, even though the furnace itself has high efficiency, — and as far as the boiler proper is concerned, all of the heat is then wasted. To have the boiler use the maximum amount of heat evolved, the unavailable portion must of course be made as small as possible. This useless amount is not only dependent on the temperature difference between the air and steam, but also on the weight of the gas heated. It can, therefore, be minimized * See footnote on page 534 for exception. BOILERS 537 by decreasing the weight of excess air supplied for combustion. Furthermore, the benefit of such reduction is twofold, for not only does it decrease the amount of heat unavailable, but it results in higher temperature of the products of combustion, which makes the unavailable portion a smaller percentage of the total heat evolved, which in turn increases the efficiency of the steam generating apparatus as a whole.* (f) The Apparent Efficiency of Boiler (alone) may be defined as . „ „ . Heat absorbed by water and steam , . ABEf = ^iT—n — 7 . J ■ X • • (402) Heat developed tn furnace and in Fig. 346 ABEf = LM/LN. The determination of this efficiency involves a knowledge of the furnace losses, — hence, like the Furnace Efficiency, it is difficult to determine accurately. (g) But some of the heat developed in the furnace has been shown to be unavailable for the ordinary boiler,* and it is hardly just to charge against such a boiler the non-utilization of this portion; hence, the apparent efficiency is not a true measure of the performance in such case. Calling the heat with tempera- ture above that of the steam "potential heat," then, what may be termed the True Boiler Efficiency is, evidently, _, „ -r. . Heat absorbed by water and steam , . ^^^^ = Potential heat ' " ^403) In Fig. 346, TBEf = OP/OQ, the unavailable heat being shown by<2^. (h) What is called '' Boiler Efficiency " in the A.S.M.E. codef applies to the combined efficiency of boiler proper and combus- tion space and is expressed as follows: T>rj7f — Heat absorbed by water and steam , . Heat available in ascending combustible' = ABEfXCEf (404a) * It has been suggested (Bull. 23, U.S. Bureau of Mines) that the numerators in Eqs. (400) and (401) should include only the heat above the steam temperature. However, while this limitation would be satisfactory for comparison between boilers of the ordinary type, it would be inapplicable to those using the "counter flow" principle. Hence, in this text, the numerator will be taken as the total heat evolved in the furnace, regardless of its temperature. t Trans. A.S.M.E., 1899. 538 HEAT-POWER ENGINEERING In Fig. 346 BCEf = ST/SU. This efficiency measures the perfection of operation of the boiler and combustion space com- bined (not including the grate) and as it can be readily deter- mined it is generally given in reports of boiler tests. In practice '* Boiler Efficiencies " as high as 85 per cent have been obtained with oil fuel in short tests under exceptional con- ditions. In continuous running, 75 per cent efficiency with coal, and 80 per cent with oil, are attainable under uniform conditions. With variable loads and ordinary conditions, average efficiencies of 60 to 65 per cent throughout the year represent good perform- ance. (i) The Overall Efficiency (OEf = VW/ VX in Fig. 346) includes the Grate Efficiency as well as the " Boiler Efficiency," and in the A.S.M.E. code is termed the " Efficiency of boiler including grate." It is a measure of the perfection of the combined per- formance of the boiler, furnace, and grate, and is affected by the skill of tlie firemen, the suitability of the coal and draft, the dropping of coal through grate bars, etc. Hence nwf — ^^^^ absorbed by water and steam . . Heat in the combustible fired ' - - - \^ o) = BCEf X GEf = GEf X CEf X ABEf. . . (405a) The OEf can be readily determined and hence is usually incor- porated in reports of boiler tests. With solid fuels its numerical value is slightly less than the BCEf. (j) Except in the case of ''Boiler Efficiency " {BCEf) and of " Boiler Efficiency including grate " (OEf), there is lack of agree- ment among engineers as to the definitions and names of the efficiencies of the various elements of the steam generating apparatus. Hence, before proceeding with the discussions including the use of such terms it is always important to first arrive at an understanding of their meanings. The terms and definitions used in the foregoing treatment appear to the authors to be the most satisfactory ones. 261. Boiler Heating Surface and Heat Transmission, (a) The water heating surface (H.S.) of a boiler is the surface of those parts of the shell which are in contact with water on one side and with the furnace gases on the other. As the transmis- sion of heat from the flue gases to the boiler shell is less rapid BOILERS 539 than that from the shell to the water, the heating surface should theoretically be measured on the gas side of the plates or tubes. In the case of tubes, however, it is common practice to consider the outer (larger) surface as heating surface, regardless of whether it is exposed to water or gases. (b) With a given amount of potential heat in hot gases, the more extensive the heating surface the nearer will the flue gases be cooled to boiler temperature and, neglecting radiation, the higher will be the true efficiency of the boiler. This is shown by curve E in Fig. 347 where ordinates are efficiencies, or relative performance, and abscissas are extent of H.S. With infinite sur- face all the potential heat would be absorbed and thus this efficiency would be 100 per cent on this assump- Fig "S?!?" tion. However, it is, of course, neces- sary to include the effect of the radiation losses which evidently depend directly on the extent of the radiating surface which is proportional to the heating surface. In Fig. 347 the percentage of this loss is represented by the ordinates of the line R. The net result, or percentage of heat usefully utilized, is given by the difference between the ordinates of the two curves and is shown by line E-R. Evidently the maximum efficiency, considering radiation, occurs when the boiler heating surface has an extent represented by the abscissa OM. (c) Since the cost of boiler, together with that of its floor space and housing, increases with the extent of heating surface, and since the interest on first cost plus the amount set aside yearly for depreciation, insurance and taxes also increases at the same rate, there is also a commercial reduction in value with the extent of surface, which may be shown by some line such as C in the figure. Hence, the true or commercial value of the heat- ing surfaces would be shown by some such curve as E-R-C, and the maximum value corresponds to a heating surface shown by OM' . Either greater or smaller amounts of heating surface would give less return per dollar expended, hence the extent of heating surface should correspond to this abscissa. (d) The mean rate of evaporation per square foot of heating surface per hour for the whole boiler is obtained by dividing the 540 HEAT-POWER ENGINEERING i Jrl^ AM- ^^ N / s ^ \ ^ ^. ^ V P \\" U-E. per Sq. Ft. H.S. per Hi Fig. 348. total weight of equivalent evaporation per hour by the total heating surface. From data obtained from tests of many boilers operated at different rates, points may be plotted with abscissas representing these mean rates of evaporation and with ordinates representing either efficiencies or Units of Evaporation per pound of combustible per hour. Average curves drawn with respect to such points resemble those shown in Fig. 348 * and are seen to be similar to E-R in Fig- 347- They indicate that the maximum efficiency occurs when the ''equivalent" mean rate of evaporation for the whole boiler is between 2 and 4 pounds per square foot per hour, corresponding ap- proximately to a transmission of from 1900 to 4000 B.t.u. per square foot per hour. (e) But all parts of the heating surface are not equally effec- tive. Evidently those parts in the direct path of the gases are of greater value than those exposed merely to stagnant gases, and those nearest the source of heat are the most effective of any. Heating surface exposed to the "radiant" heat of the fuel bed and burning gases is very much more effective than that not so exposed. Thus, in some cases, the small heating surface immediately over the fire may transmit as much as two-thirds of the total heat absorbed by the boiler, and at this point from 20 to 35 or more pounds of water may be evaporated per square foot of heating surface per hour, whereas the average for the whole boiler may not be more than one-tenth as much. It follows that surfaces farthest away from the furnace must neces- sarily transmit very much less than the average. Hence impor- tance should be placed not only on the amount of heating surface but also on its distribution and location^ (f) Without going into a detailed discussion of Heat Trans- mission at this point (for this will be given in Chapter XXXV) it will be advantageous to mention here the manner in which the heat generated in the furnace is transmitted to the steam. Briefly, the heat from the fuel bed is first brought to the heat- * Such curves are given in Kent's "Steam Boiler Economy" and in Donkin's "Steam Boiler Performance." BOILERS 541 ing surface by direct radiation from the glowing coal and burn- ing gases (i.e., as " radiant " heat), and by convection by the gases which come from the furnace; it is then passed through the metal walls by conduction, to be absorbed by the water which may also transport it by convection due to the circulation of this liquid; and finally, when the water has reached the tem- perature of ebullition, the further addition of this' heat results in the formation of the vapor. (g) The rate of transmission * per unit of area of heating surface depends, among other things, on (a) the difference in temperature between the transmitting and the receiving media; {h) the rapidity (velocity) with which the gases are brought in contact with the heating surface, and {c) the rapidity with which the heat can be carried away by the water (rapidity of water circulation) ; {d) the amount of scale and grease on the water side of the plate, and {e) the amount of soot on the surfaces exposed to the flue gases. (h) The effectiveness of each part of the heating surface is dependent, among other things, on the difference between the temperature {tg) of the gases on the one side and that {tw) of the water on the other, i.e., on {tg — tw). In the case of the ordinary boiler, as has been shown, tw is constant and equal to the tem- perature of the steam, since all the water is (approximately) at that temperature. As the gases progress over /> the heating surface this temperature differ- /^^"flfwi ence diminishes and the heat transmission per ! |j fe^Xy square foot becomes less until the limit of r~^^l&iiHj3 effectiveness is reached, which generally occurs \^ d^^^ when the temperature difference has been re- J^^m" duced to around 100° to 200° F. 1^^^ (i) There is, however, one way of obtaining f^^^ a value of tw that is below the steam tempera- "IT^T ture and therefore of making it possible to ^^-3^^^ absorb more of the heat from the flue gas „. Fig. 349. than can be accomplished in the ordinary boiler ; this involves the use of counter current flow. The prin- ciple under which this operates can be explained in connection with Fig:^349, in which the arrangement is such that the pump * Reference, U. S. Bureau of Mines, Bull. 18, "The Transmission of Heat into Steam Boilers." 542 HEA T-POWER ENGINEERING forces the water downward through the heating coils, whereas the hot gases pass upward — that is, the heat-conveying and heat-absorbing media flow in opposite directions. With such arrangement it is obvious that the addition of more heat absorb- ing coils at the top (as shown dotted) will result in lowering the temperature at which the gases leave, and that by adding a suffi- cient number this temperature could be reduced to that of the entering water. Hence, with the counter current principle, /«, is not limited to the steam temperature and more heat can be absorbed by the heating surface than is possible in the ordinary arrangement of boiler. Parenthetically it may be remarked that without considerable modification the simple arrangement shown diagrammatically in Fig. 349 would probably not be satisfactory as a boiler element. The counter current arrangement is approximated in some instances by placing an "economizer" (to be described later) beyond the boiler so that the hot gases after leaving the boiler surrender some of their heat to the water which passes through the economizer on its way to the boiler. So far, the counter current principle has been ignored in the design of most boilers, but it is approximated in a few types. (j) The rapidity with which the gases flow over the heating surfaces has a twofold influence on the rate of heat transmission : for (i) more heat is conveyed to the surface in a unit of time, and (2) the gases are brought more intimately in contact with those surfaces, since there is less opportunity for a stagnant nonconducting film to adhere to the surfaces. (k) The rapid circulation of water within the boiler is of especial importance when it ife necessary to have high rates of heat transmission, for it brings larger amounts of water in contact with the heating surfaces in a given time and also prevents the metal from becoming overheated. This circulation is brought about by providing a free and unrestricted path for the current of water and by applying the more intense heat at the proper point in this path. In Fig. 350, (a) and {h) show elements of common forms of boilers and the arrows indicate the direction of circu- lation. The water just above the furnace is less dense than that in the other portions of the boiler, since it has absorbed more heat and is charged with bubbles of steam, and it therefore rises, being replaced by an equal amount of water which descends at BOILERS 543 points in the boiler where it is colder and denser. This is the manner in which the current is established and maintained in nearly all the .standard types of boilers, as will be seen in study- ing the figures in the subsequent sections. (1) In some cases this circulation can be made so powerful that the water in the ascending column can be discharged at an elevation even considerably above that of the surface of the body of water from which the descending column receives its supply. This can be accomplished with the arrangement shown in Fig. 351, in which the arrows indicate the direction of flow. The circulation is due to the fact that material in riser A is sufficiently charged with vapor to make it weigh less than that in the down-comer B, although the altitude H is greater than h. As the liberation of the steam from the water is supposedly more effective when the ascending column discharges in this manner, some boilers have arrangements somewhat like that shown in the diagram. Sometimes a nonreturn valve like V is inserted to insure the proper direction of flow. After the circulation is once estab- lished, however, this valve is no longer neces- sary, as the current is then very positive. (m) The effectiveness of the heat transmission depends on the cleanliness of the heating surface. It is diminished by any deposit of soot and dust on the exterior surfaces as well as by any interior coating of soft scale (mud) , of hard scale, or of grease. Water in its natural state contains more or less foreign matter in suspension or in solution. Some of the latter precipitates when the temperature reaches about 200° F., still more when 300° is approached, and the remainder, which is left when the water becomes steam, gradually becomes concentrated until it Fig. 351- 544 HEAT-POWER ENGINEERING reaches the stage where deposition occurs. Deposits on the water side of the walls of the boiler reduce the heat transmitting ability of the plates from o to 20 per cent, depending on the thickness of the scale and on the chemical and physical proper- ties of the material. The formation of scale should be prevented as far as possible by purifying the water before feeding it to the boiler; but even then there will be some deposit formed which must be removed from time to time. Boilers are therefore always so arranged that they can be readily cleaned internally, and so that the deposit shall, as far as possible, occur at points where the heat is the least intense and where the blow-off pipe can be connected (as in Fig. 350) so that the softer material can be removed by blowing off some of the water from time to time. The exterior of the heating surfaces should also be accessible for remdving the soot and dust, 'y 262. Boiler Explosions. It has been seen that, by expanding steam, heat-energy can be made available which can h^ utilized in forcing water and steam through the orifice of a nozzle at very ^ "' high velocity. As a result of such discharge there is, of course, / a force of reaction which will move the nozzle and attached * parts unless prevented in some manner. The size of this force depends, among other things, directly on the area of the orifice. A similar process occurs when a boiler shell is ruptured, for, in passing through the rent in the boiler shell, the steam and boiling water are subject to a decrease from the original pressure to atmospheric, and surrender heat which is converted into the kinetic energy of the issuing mass. The reactive force acting on the boiler shell is dependent in amount on the area of the rent, and may be sufficiently great, compared to the weight of the boiler, to propel the vessel to a considerable distance In addi- tion to the probable destruction of property and possible en- dangerment of lives which may result, the escaping steam and ' water may itself cause considerable damage, — in fact persons near by may be seriously, and perhaps fatally, scalded, even though the reaction is not sufficient to displace the boiler. With boilers containing little water and having elements which are of small size and so designed as to have small rents when ruptured, the effect of an explosion is less disastrous than BOILERS 545 in the case where a large opening can occur and thus instan- taneously release a large mass of water and steam. 263. Selection of Boilers, (a) There are a great many items to be considered in the selection of a boiler for a given service; only some of the more important ones can be discussed here. Between the various kinds of boilers which have become well established there is little choice as regards the efficiency, as their performances are substantially equal, hence the selection among such standardized types depends largely on general suitability for the conditions of operation and space available, on personal prejudice and familiarity, on convenience in transportation and ease of erection, and on the first cost together with the various other items of expense. In considering an unfamiliar or untried design the following are some of the items to be checked : (b) Suitability. It should be decided whether or not the boiler is suitable for the coal that is available, and for the kind of grates (or stoker) and furnace best adapted to that fuel. In special cases where the water is bad and the draft poor these items must also be considered. It is not only important that the boiler should have sufficient size to meet the normal demands, but it should have overload capacity sufficient for all emergencies. (c) Safety and Durability. These depend on the design for structural strength, on the character of the materials used (castings under pressure being avoided) and on the character of the workmanship. The arrangement should be such as to avoid stresses due to the unequal expansion and contraction of the different parts of the boiler; and the method of support should be such that the structure, as a whole, is free to adjust itself with change of temperature. There should be no thick plates or other parts (such as boiler joints) and no projecting portions, or plate edges, exposed to the current of the hotter gases; nor should the blow-off pipe be exposed to these gases. (d) Accessibility. The ability to easily reach all parts of the boiler for inspection, cleaning and making repairs, must be in- vestigated. Doors in the boiler setting must be provided for access to all exterior parts; manholes, or handholes, must be so located as to render accessible all internal parts. In connection with internal cleaning cognizance must not 546 HEAT-POWER ENGINEERING only be taken of the number of manhole and handhole joints to be broken and subsequently made tight, but also of the time required for doing this, for cooling the boiler and its setting sufficiently to permit of starting such work, and for bringing the boiler into commission again. In some water tube boilers the dust and soot can be blown from the tubes by means of a blast of steam or air issuing from a small pipe which is passed through openings in the front and rear of the boiler or its setting. Other boilers are provided with openings in the side walls for this purpose. The design of the boiler should be such as to permit of making repairs without difficulty. In most types of boilers the principal difficulty is with the tubes. The arrangement should be such as to permit readily of the removal and replacement of any one of the tubes without disturbing the other tubes or other parts. If the tubes are straight but few need be carried in stock, whereas if they differ widely in curvature it may be necessary to have on hand a large collection to meet any emergency that may arise. (e) Circulation of Water. It is necessary to see that, the arrangement is such as to allow a free and unrestricted circulation of the water and that the heat is applied at such a point as to establish and maintain the current. The rapidity of circulation is of course limited by the smallest cross-section of the circuit. The arrangement of the structure should be such that there are no pockets where steam can form rapidly and keep the water away from the heating surfaces subject to high temperature, for under such conditions the boiler shell will burn away at such points. (f) Circulation of the Furnace Gases. It is desirable to main- tain a uniform velocity of the furnace gases and to avoid sudden contraction and expansion as they proceed through the boiler. Within limits, the greater the velocity the more rapidly will the heat be conveyed to the heating surface and the greater will be the amount of evaporation from a given surface. There should be no pockets where the gas can remain stagnant and it is de- sirable to have the gas baffled in such a way as to constantly bring the fresher portions into contact with the heating surface as the gas proceeds. (g) Dryness of Steam. To prevent priming, or the entrainment of a considerable portion of moisture in the steam, the liberating surface of the water from which steam arises should be ample. BOILERS 547 When the water contains certain impurities foaming may occur, and this always increases the amount of entrained moisture. By providing a large steam space the Ufe of the particles of steam within the boiler may be made sufficiently long to allow a more or less complete precipitation of the moisture to occur. Provision is often made within the boiler for the separation of moisture by means of " dry pipes," baffles, or other steam separating devices. (h) Quantity of Water. If the boiler contains a large volume of water there is less attention required in maintaining the water level, and the boiler has a greater reserve to meet sudden demands than is the case in boilers having a small volume; but greater damage would ordinarily result in case of explosion. In marine and similar service the greater weight involved is of course objectionable. (i) Feed Water. The boiler feed should be introduced in such manner as not to retard the circulation of the water, and, if cold, should not come in contact with the boiler shell. Certain of the impurities in solution in the entering water precipitate when the higher temperatures are reached and are deposited as mud. The water should be introduced at such a point that this precipi- tate will be deposited where it will do no damage and from which it can be readily removed, see Fig. 350 (a) and {h). Sometimes a " mud drum " is provided as in the latter figure, or a '' settling chamber," as in Figs. 362 and 363, from which the mud may be blown off from time to time. (j) Space Occupied. In addition to the floor space and height occupied by the boiler and furnace, there must be charged against the apparatus the amount of space that must be provided for the replacement of tubes and for cleaning. In some horizontal boilers there must be space in front (or rear) at least equal to the length of the tubes (see Fig. 361). This fixes the minimum distance between parallel rows of boilers or between the boiler end and the wall of the building. In some types of vertical boilers sufficient room must be provided overhead for the replacement of tubes. When the exterior of the heating surface is accessible for cleaning from the front or rear of the setting, the boilers may be arranged in a continuous " battery " (with adjacent walls in common), in which case the walls between boilers are thickened slightly. When the cleaning is done from the side, the boilers 548 HEAT-POWER ENGINEERING are arranged in a series of batteries of two each, with sufficient space between the pairs to permit of access to the openings in one side of each boiler setting. (k) Cost. This, of course, is one of the items of fundamental importance. Besides the first cost of the boiler, with its setting and trimmings, and the expense of transportation and erection, it is necessary to consider charges for up-keep and depreciation. The size of the boiler and furnace and the space necessary for the removal of tubes and for cleaning must also be considered in con- nection with their influence on the cost of the ground and building. 264. Classification of Boilers. Boilers may be classified in many different ways, only a few of which need be given here. (a) In Internally fired boilers the furnace is located within the structure of the boiler and is usually made integral with it, while in externally fired boilers the furnace is placed below the boiler proper and is surrounded by a " setting ' ' which is generally of brickwork. (b) In fire tube boilers (commonly called " Tubular Boilers ") the furnace gases pass through the tubes which are surrounded by the water from which the steam is generated; whereas in water tube boilers (sometimes called " Tubulous Boilers ") the water circulates through the tubes while the hot gases pass over their exteriors. Fire tube boilers are shown in Figs. 352 to 359; and water tube boilers are illustrated in Figs. 360 to 366. These will be discussed later. (c) Sectional boilers are composed of small elements so ar- ranged that any rupture which may occur will produce only a relatively small opening and will result in but little damage to the boiler itself and to its surroundings. Such boilers may be shipped in small parts which are assembled when being installed. Examples of this type of boilers are shown in Figs. 360 and 365. (d) In vertical boilers the tubes are arranged perpendicularly, or approximately so. In general, such boilers demand less floor space than horizontal ones but their height is greater. (e) In straight tube boilers it is comparatively easy to clean and inspect the tubes. The use of curved tubes is inherent in the design of some boilers and they give a certain degree of flexibility to the structure. (See Fig. 363.) (f) Boilers are also sometimes classed according to their use; for example, there are locomotive boilers, marine boilers, portable BOILERS 549 boilers, stationary boilers, etc. The descriptions which will follow, will be limited in most cases to the stationary types. (g) There are innumerable arrangements of boilers and their settings; only a few of the more typical ones will be considered in the following sections, y^ 265. Internally Fired, Tubular Boilers, (a) Such boilers are generally compact and self contained; they are shipped com- Fig. 352. — Tubular Boiler. Submerged Tube Type. Fig- 353- — Tubular Boiler. Exposed Tube Type. plete, and immediately upon arrival are ready to connect to the flues and steam system. While they cost more than ordinary boilers, they avoid the expense of special brickwork " setting " and eliminate the possibility of leakage of air through cracks which may develop in such brickwork. Sometimes there is difficulty in transporting the larger sizes. (b) Fig. 352 shows a small vertical boiler of this kind with 550 HEAT-POWER ENGINEERING water level above the tubes. Such boilers are of the submerged tube type. In Fig. 353 is a somewhat similar boiler in which the tubes extend above the water level — the exposed portions pre- senting surface to the steam. Boilers of this kind are called ex- posed tube boilers. The one shown in this figure is of such large Hana Eoles Fig. 354. — Locomotive Type of Boiler. size that the space at a can be occupied by a man while cleaning the tubes, the crown sheet and the plates around the furnace. (c) Fig. 354 shows a Locomotive type of boiler with a steam dome which provides additional steam space. Such boilers are Valve Connection Fig. 355- — Continental T5^e of Boiler. not only used for locomotives and for traction engines, but also for stationary service. (d) In Fig. 355 is a longitudinal section of a boiler of the Continental type, the exterior of which resembles Fig. 356. The furnace wall is a cylindrical flue with strengthening cor- BOILERS 551 rugations. The combustion chamber is lined with fire brick or other refractory material and is located in a casing of thin metal extending from the main shell of the boiler. These boilers have large liberating surface, voluminous steam space and large volume of water. They usually have either one or two furnace flues, and because they are compact and have short tubes, they can be used in places where the space is limited. (e) The Scotch Marine type of boiler is shown in Fig. 356 and is similar to the Continental except that its combustion chamber Urtake i Fig. 356. — Scotch Marine Type of Boiler. (see Fig. 357) has metal walls and is entirely surrounded by water. As these walls tend to collapse under the external pressure to which they are subjected, they are carefully stayed. Such boilers have from one to four corrugated furnace flues, and their outer shells range from 5 J feet to 16 feet in diameter. Be- cause of the very short tubes, large steaming capacity for space occupied, absence of brick setting, and accessibility, they are particularly adapted to marine service. 266. Externally Fired Tubular Boilers, (a) Boilers of this type generally require a separately constructed " setting " (usually of brickwork with lining of firebrick) to surround the r 552 HEAT-POWER ENGINEERING furnace and boiler. This is so arranged as to properly confine the flue gases and guide them to and from the boiler. It takes considerable time to construct and dry out the brickwork setting Fig- 357- — Submerged Combustion Chamber. and the expense involved must be added to the cost of the boiler itself. Such boilers usually occupy more space than internally fired boilers and the setting should be kept in repair so as to Fig. 358. —Horizontal Return Tubular Boiler with "Half Front." avoid air leakages, which have a detrimental effect on the draft and boiler performance. (b) An externally fired boiler classified as of Horizontal Return Tubular type (" H.R.T. boiler ") is shown in Fig. 358. In this BOILERS 553 boiler the smoke box is formed in an extension of the boiler shell which projects beyond the brick front wall. The cast iron " boiler front " covers only the portion of this wall located below the smoke box, and is therefore commonly called a '' half- jronty The boiler shown in this figure is suspended from cross beams or " Gallows frames." (c) In Fig. 359 is shown a H.R.T. boiler with '' jull flush front, ^^ the smoke chamber being formed in the brickwork of the front wall. The boiler is shown to be supported by brackets, 3uck Stave Fig. 359. — Horizontal Return Tubular Boiler with " Full Flush Front." the rear pair of which is mounted on rollers to allow free ex- pansion. The brick setting is braced by " buck staves." As most of the scale is deposited at the rear of the boiler, as in Fig. 350 {a), the blow off is located at this point. The back end of the boiler is lowered slightly to aid in draining the shelL As the boiler shell is exposed to the direct heat of the furnace, the thickness of metal must not be so great as to make it liable to burn thinner, and as the shell thickness must increase with the diameter of the boiler, these boilers cannot be constructed beyond a certain size. They are not ordinarily built larger than 200 boiler horse power and are seldom used with pressures above 150 pounds. The H.R.T. boilers are about the cheapest made, hence are quite widely used for low pressures. 554 HEAT-POWER ENGINEERING 267. Water Tube Boilers, (a) Figs. 360 and 361 illustrate sectional water tube boilers known as the Babcock and Wilcox type (or " B. and W." type). The tubes are expanded into pressed steel front and rear " headers " to form tube " sections." The sections, the drums, connecting nipples- and other parts are shipped " knocked down," and are assembled at the power house. The parts to be transported and handled are therefore relatively small. Being of the sectional type with small elements, the danger of disastrous explosions is slight, as ruptures seldom occur £low QfE Valve- Header Fig. 360. —B. and W. Type of Boiler. elsewhere than in the tubes. Opposite each tube is a hand-hole cover which can be removed for cleaning and replacing tubes. Doors for external cleaning are provided in the side walls, hence these boilers cannot be arranged in continuous batteries, but they may be grouped in batteries of two each. The boiler has elements similar to (b) in Fig. 350, with mud drum located at the bottom of the rear headers. It is hung from above, hence is free to expand or contract. As shown in the figure the furnace has an exposed roof and the gases are bafiled so as to make three '' passes " across the tubes. BOILERS 555 Other arrangements of baffles and furnace can of course be used. The tubes are not arranged in vertical rows, but are '* staggered," Safety Valve rf%§5--- -£"fee, ^.^,/ Fig. 361. —B. and W. Type of Boiler. as shown by the header at (a) in Fig. 360, so as to further baffle the gases. (b) In Fig. 362 is shown the Heine type of water tube boiler having the front and rear '' water legs " made of steel plates and Stop Valve OajandJBLolfr- Fig. 362. — Heine Type of Boiler. riveted to the drum. The front and back plates of each water leg are held together by hollow stay bolts having holes large enough to permit the insertion of a steam or air pipe for blow- ing the soot and dust from the exterior of the tubes ; and opposite ■'556 HEAT-POWER ENGINEERING steam each tube in each water leg is a hand hole giving access to the interior of tubes. The feed water enters a '' mud drum," where it remains quiescent for a considerable time before it mixes with the water which is circulating through the tubes. As this feed water be- comes heated certain of the impurities are precipitated in the mud drum, from which they can be blown off at intervals. The water legs of the boiler shown in the figure rest on the brickwork and have rollers under the rear one. The boiler may, of course, be supported in other ways. This boiler is shipped com- pletely assembled, ready to have the set- ting constructed im- mediately upon its arrival. As no clean- ing doors are located in the side walls, such boilers can be arranged in continuous batter- ies. As shown, the fur- nace has a tile roof supported by the lower row of tubes and the furnace gases are baf- fled so as to pass along the tubes. The same type of boiler is often used with baffles arranged similar to those in Fig. 361. (c) Fig. 363 shows the Stirling type of water tube boiler which may be classed as a vertical one. It is composed of- drums and tubes which are not assembled until they reach their destination. Since the elements are simple and easy to make, the cost of such boilers is less than that of those having more complicated parts. The feed water enters a precipitation pocket in drum D and is heated as it descends to drum C. The circulation of water is through tubes joining drums A, B and C. All the upper drums are connected by steam pipes. The rows of tubes running circumferentially around the drums Fig. 363. — Stirling Tj^e of Boiler. BOILERS 557 are arranged in pairs, between which is sufficient space for the removal or insertion of tubes located in the interior of the nests. The tubes are curved and the mud drum is suspended by the tubes — an arrangement which gives flexibility and permits of expansion and contraction accompanying temperature changes. All drums have man holes which give access to their interiors and to the tubes. The side walls of the setting are provided with cleaning doors exposing the exteriors of the tubes, hence -■SM :^^f :i:v--S-sP . . Blow'Off l^ M iPkP' Fig. 364. — Wickes Tj^e of Boiler. these boilers cannot be arranged in continuous batteries — - they may, however, be arranged in pairs. The arrangement provides for large combustion space and for an ample coking arch, or Dutch oven roof. (d) There are many other arrangements of boilers composed of simple horizontal drums and vertical tubes. In some the vertical tubes enter a single upper drum and a single lower one, and the gases are baffled so as to make two or three passes. In other boilers there are two drums above, with steam and water connections between, and two lower drums, with water 558 HEAT-POWER ENGINEERING connections, and between these pairs are vertical tubes. The furnace gases pass up along the tubes joining the front drums and down along the rear tubes, to a flue connection near the bot- tom of the setting. There are still other arrangements, but those given will suffice to show the possibilities of this construction. (e) Fig. 364 shows the Wickes type of vertical water tube boiler having single upper and lower drums with vertical axes. The tubes are removed and inserted through hand holes located in the dome of the steam space; hence, it is necessary to provide overhead room, or sky-lights, immediately over the boilers. . Sream Nozzle Fig. 365. — Parker Type of Boiler. (f) In Fig. 365 is shown the Parker type of boiler, which differs radically in several respects from the ordinary types, since it makes use of the counter-flow principle (Sect. 261 {i)) and de- livers the steam and water at points above the water level (Sect. 2§i (/)). Under the best conditions of operation, the feed water enters the system at A (check valve E being closed), passes downward through the zig-zag tubes in a general" direction opposite to that of the ascending flue gases (just as in Fig. 349) and is finally delivered at B into the drum, with a temperature high enough to cause the precipitation of most of the impurities. The water from the drum enters another set of zig-zag pipes at C, constituting the vaporizing element, is further heated as it descends and is finally discharged as steam into the drum at D. BOILERS 559 Owing to the countercurrent flow it is possible, by providing sufficient heating surface, to cool the flue gases below the temper- ature of the steam. Hence, sometimes a third nest of tubes is added, in which case the upper is called an " economizer element." Should the feed valve be shut off the circulation will still con- tinue, for water will then pass through check valve E into the upper element of tubes, but the operation will be somewhat less efficient than before. The " junction boxes " joining the ends of the tubes have hand holes and some have non-return valves which ensure the circulation of the water in the proper direction. Besides the scale pocket F there is a blow off (not shown) located under the diaphragm in the bottom of the drum. (g) In boilers of the porcupine type, the tubes, with closed outer ends, project from a water drum, or header, into the path of the flue gases. Fig. 366 shows an arrangement having a double header and concentric tubes. With such arrangement the cold water descends through the left water leg, passes through the inner tube to the end, then returns through the annular passage between the two tubes and ascends in the riser to the steam drum above. But little use is made of this arrangement, however, because of the expense of construction. t t t t t JFlue Gas 1 \ \ 31 Fig. 366. — Niclausse Tubes. (h) Fig. 367 shows a double-furnace boiler arranged to be fired from both front and " rear "; thus it has about double the grate area and generates steam nearly twice as rapidly as in the ordi- nary case. However, as the rate of evaporation is high the efficiency is slightly less than is obtained under less intensive conditions. Such arrangements are frequently adopted when floor space is limited or when the cost of real estate is great, as is the case in power plants located in congested districts of large cities. The same scheme can, of course, be used with boilers of other types than that shown. ^^ 56o HEAT-POWER ENGINEERING 268. Boiler Accessories. In addition to the fittings already described, boilers are always fitted with steam gauges, glass water gauges, try cocks, safety valves, feed valves, blow-off valves and steam stop valves. In addition they frequently have " water columns " with floats to operate sentinel whistles when Fig. 367. — Double-furnace Boiler. the water level becomes too high or too low ; and they may have " fusible plugs " which, when the water level becomes danger- ously low, become uncovered and melt, and thus allow steam to escape and attract attention before the plates become over- heated. Automatic feed -water regulators are sometimes used, and in plants where the load fluctuates rapidly damper regula- BOILERS 561 tors, controlled by the steam pressure, are also provided to automatically adjust the draft. When water tube boilers are used, the boiler room equipment generally includes mechanical tube cleaners, of which there are many varieties. 269. Boiler Performance, (a) In stating the evaporative performance of boilers and similar apparatus, it is customary to use the latent heat of vaporization of one pound of steam at atmospheric pressure as the ** Unit of Evaporation " (U.E.). The value of this unit is, therefore, 970.4 B.t.u. (old value 965.7) ; and, as this is the heat absorbed by one pounid^of steam in being converted from water with temperature of 212° F., to steam at the same temperature, 'the performance may also be stated in terms of the " Equivalent Evaporation " or " number of pounds of wa.ter from and at 212° F.'' that would be evaporated by the same amount of heat:/ Evidently there would always be the same number of pounds of Equivalent Evaporation as there are Units of Evaporation. When boilers are tested, the temperature of the feed water, the actual weight of steam generated per hour, and the quality (or superheat) are all determined. With these quantities known, the equivalent evaporation from and at 212° F. can be determined by dividing the heat given to water and steam by 970.4 (965.7). (b) This same unit can also be used for expressing the value of fuels when used for generating steam; thus, the Theoretical Equivalent Evaporation (T.U.E.) per pound of fuel is found by dividing the calorific value per pound by 970.4. Based on the usual calorific values, the T.U.E. 's per pound of combustible, are about as follows for the different kinds of fuel : — • Carbon, 15 pounds; good anthracite, 15.4 pounds; semi-bitumi- nous, 16.3 pounds; bituminous, 14 to 15.8 pounds; and oils, 18.5 to 22 pounds. Obviously the Theoretical Equivalent Evaporation per pound of fuel can be obtained by multiplying the foregoing figures by the percentage of combustible present. (c) The steam generating apparatus as a whole delivers with the steam only a portion of the calorific value of the fuel, the percentage depending on the overall efficiency of the apparatus. These efficiencies were given in Sect. 260 {h) and (i). With good coal the Actual Equivalent Evaporation should be at least 562 HEAT-POWER ENGINEERING 9 pounds per pound of combustible, and in the best instances 12J pounds have been reached. With oil this evaporation is from 144 to 16.9 per pound of fuel. When the rate of evaporation is under consideration, the unit of time generally adopted is the hour — hence the terms "Equiv- alent Evaporation per hour " and " Units of Evaporation per hour " are in common use. If no unit of time is specified the hour is implied. (d) In boiler computations it is sometimes convenient to make use of a quantity called the " Factor of Evaporation " (F.E.). This quantity is the ratio of the heat absorbed per pound of steam generated to 970.4 (or 965.7 as the case may be). Hence T7 . fT7 .• (q -^ xr + CpD)* - (t - 32) . ^, Factor of Evaporation = — 7 7 ^^—^. . (406) 970 (or 965.7) in which q, x, r, D and Cp are respectively the sensible heat, quality, latent heat, degrees of superheat and specific heat of the steam leaving the boiler, and t is the temperature of the feed water. Evidently the Factor of Evaporation is the ratio of the equivalent evaporation to the actual weight, and as this ratio is ifrequently used its values are generally tabulated in reference books for different pressures of dry saturated steam with various temperatures of feed water. (e) The rated size and the maximum capacity of boilers are usually stated in terms of a unit miscalled a " Boiler Horse Power" (B.P.). It has been suggested that this be changed to " Boiler Power,'' as the term " horse power " is inapplicable to boilers. The Boiler Horse Power is defined as the equivalent of 34-5 pounds of steam evaporated "from and at" 212° F. per hour; (i.e., 34J U.E. per hr.). It is, therefore, merely a measure of the heat given to the water and steam and is equiva- lent to the transfer of 33,479 B.t.u. per hour (with U.E. = 970.4 B.t.u.). The " horse power " of a boiler which is evaporating a given weight of steam per hour at a certain pressure, with a certain quality, and from feed water at a certain temperature, can there- fore be found in two ways: — First, by dividing the equivalent evaporation by 34!; second, by dividing the total heat supplied * The expression in this parenthesis is written so as to apply to both super- heated and saturated steam, as was first done on page 173. BOILERS 563 to the water and steam per hour by the number 33,479 given above. (f) In this connection, however, it is important to note that there is no definite relation between engine horse power and the so-called boiler horse power; the ratio of the engine h.p. to the " boiler h.p." in any plant depends entirely upon the economic performance of the engine, hence it is not necessarily the same in different plants. 270. Proportioning the Boiler for Power Output, (a) The American Society of Mechanical Engineers has made the follow- ing recommendation regarding boiler ratings. " A boiler rated at any stated capacity should develop that capacity when using the best coal ordinarily sold in the market where the boiler is located, when fired by an ordinary fireman, without forcing the fires, while exhibiting good economy. And further, the boiler should develop at least one-third more than the stated capacity when using the same fuel and operated by the same fireman, the full draft being employed and the fires being crowded, the available draft at damper, unless otherwise understood, being not less than one-half inch water column."* Boilers of the commercial types generally have overload capacity considerably in excess of the 33 J per cent here specified. Some boilers are being operated continuously under loads double those for which they were originally intended, and triple outputs have been obtained in a few instances. (b) The total amount of heating surface needed by boilers can be determined either by multiplying the boiler " horse power ". by the number of square feet needed for developing one horse power, or by dividing the total equivalent evaporation pier hour by the allowable rate of evaporation per square foot. (c) Most stationary boilers of the '' water tube " type have 10 square feet of heating surface per boiler horse power under normal load, the corresponding rate of equivalent evaporation per square foot per hour being about 3J (= 34.5 -^ 10); while the more common types of stationary " fire tube " boilers usually have 12 or more square feet per boiler horse power, the equivalent evaporation being 3 pounds per square foot or less. However values both larger and smaller than these are sometimes used. * Trans. A. S. M. E. 1899. 564 HEAT-POWER ENGINEERING When there are limitations as to space or weight, less heating surface and higher rates of evaporation are used. For example, in marine boilers from 4 to 8 square feet of heating surface are provided, the corresponding evaporation being from 8 to 4 pounds per square foot per hour, and in some instances marine boilers of the water tube type have been operated continuously with average rates as high as 16 pounds.* (d) The fuel needed per boiler horse power hour can be readily determined by dividing 34J by the equivalent evapora- tion per pound — or by dividing 33,476 by the actual calorific value per pound corrected for boiler and grate efficiencies. Thus the combustible required per boiler horse power ordinarily ranges from 3 to 4 pounds per hour, depending on the kind of coal, and the weight of coal is roughly from 3.5 to 5 pounds. , / * Melville, Engineering Magazine, January, 191 2. CHAPTER XXXI. SUPERHEATERS. 271. Advantages of Superheating, (a) It has already been shown (Sect. 128 and i8oj) that the water rates of steam engines and turbines may be materially improved by the use of super- heat, but that the improvement in steam consumption is not a correct measure of the gain effected, since one pound of super- heated steam contains more heat than an equal weight of satu- rated steam at the same pressure. Leaving out of consideration, for the time being, certain incidental advantages of superheating, the true measure of gain is on the basis of the heat economy resulting from its use and this is given by the ratio of the number of heat units supplied to the superheated steam, per horse power delivered by the engine or other prime mover, to that used when saturated steam is the v/orking substance. (b) In addition to such gains as may be effected in the prime movers themselves by the use of superheat, there may be a two- fold reduction in the heat lost in the connecting pipe lines, be- cause (i) superheated steam loses heat much less rapidly than does wet steam and because (2) the radiating surfaces of the pipes may be made less — for smaller pipes can be used, as super- heated steam may be allowed to flow at higher velocities than are permissible with saturated vapor. (c) But the ultimate test of the advisability of installing additional apparatus, such as superheaters, is always on the basis of the financial economy effected. In the case in question the addition of the superheaters may not increase the total expense for the. power plant equipment, for the improvement in heat economy may permit a reduction in the size and cost of the boilers, and the diminution of the water rates may make possible a decrease in the size and cost of the condensers and other auxiliary apparatus. Then, the operating expenses may be reduced not only by the saving in the expenditure for fuel but also by the reduction in the outlay for purchasing and pumping 56s 566 HEAT-POWER ENGINEERING the water used for feed and for condensation. To offset the gains is the additional expense involved in the operation and mainte- nance of the superheaters. The use of the smaller pipe lines, which are permissible with superheated steam, may not effect a saving in their cost, as the materials, construction and fittings must be of better quality than is required when saturated steam is used. 272. Types of Superheaters, (a) There are two general types of superheaters — (i) separately fired superheaters, and (2) built in, or boiler draft superheaters. The first class is installed in a separate setting of its own and receives hot gases from its own furnace. The second class is located inside of the boiler setting and in line with one of the " passes " of the products of combustion. (b) In each type the saturated- steam, generally containing from 2 to 4 per cent of moisture, is led from the steam nozzle on the drum of the boiler, through the superheating apparatus on its way to the steam consumer. (c) Superheaters of both types generally consist of a multi- plicity of elements containing a small volume but exposing a relatively great surface. There are, however, several super- heaters in which a few very large elements are so constructed that, by means of baffles or equivalents, the steam flowing through them is divided up into thin streams in contact with extended wall areas. (d) Generally the metal used is mild steel, and the elements are composed of seamless tubes which are of small diameter (i inch to I J inch bore) with thick walls (0.15 to 0.2 inch thick) and which are connected with built-up, forged, or cast steel headers or their equivalents. In a few instances cast-iron ele- ments with comparatively thick walls are still used, but there is a growing tendency to look with suspicion on the use of this ma- terial in cases where temperatures and pressures are high and where Fig. 368. temperature changes are great. Figs. 368 and 369 show the two elements most commonly used in this country. Instead of hav- ing the tube ends enter separate headers, they are sometimes SUPERHEATERS 567 connected with a single one arranged with suitable partition plates or baffles. The element shown in Fig. 369 has a thin annular steam passage between a sealed inner tube and an outer one which is surrounded by flanges. The flanges, which are of cast iron, present large heat-absorbing surfaces to the hot gas, protect the steel tubes and store heat, but add to the expense of construction. The steam is brought intimately into contact with the walls of the larger tube, since it can flow through the thin annular passage only. (e) Experience has shown that the ideals to be attained in superheater construction and arrangement are: (i) perfect free- dom of expansion; (2) ability to withstand high temperature, high pressure, and violent changes in temperature; (3) avoid- Fig. 369. ance of screwed joints; (4) the protection of all joints from ex- posure to the hot gases; (5) provision for cleaning externally and internally; (6) means for adjusting the superheat to any desired temperature; (7) natural, or automatic, regulation to maintain that temperature; (8) means of bypassing the steam around the superheater when the latter is out of commission; (9) provision for flooding the elements (in some cases) with water and for draining them; (10) small space requirements; (11) low first cost; and (12) small expense of operation and maintenance. 273. Separately Fired Superheaters, (a) Two examples of separately fired superheaters are illustrated in Figs. 370 and 371. In all such apparatus it is nearly always necessary to prevent the flame and very hot gases from impinging directly on the super- heating surface, it being generally considered that temperatures of from 1300 to 1500° are the highest allowable for the gases which are in contact with such surfaces; hence, the use of inter- cepting brick arches and walls through which the hot gases must 568 HEAT-POWER ENGINEERING pass, as shown in Fig. 370, though a greater degree of security is attained by combining a water element with these walls, as shown in Fig. 37 1- (b) The temperature of superheat may be controlled directly by varying the rate of combustion, by means of a damper, as in Fig. 371 ; by bypassing the gases, or by both of these methods, as in Fig. 370. But even if the dampers be made to normally follow the delivery temperature exactly, as can be done by means of thermostatic control, the heat stored in the walls of the setting will cause an abnormal rise of temperature when the y///////////////////////^^^ Fig. 370. demand for steam suddenly decreases to any considerable extent. Then there may also be sudden drops in the temperature due to the inflow of cold air when the furnace doors are opened for firing. (c) Compared with the built-in type, the separately fired superheater has many disadvantages, of which the principal ones are: (i) Greater first cost because of the separate setting and grate; (2) larger maintenance cost because of separate setting; (3) greater cost of operation because of separate furnace to be fired; (4) greater floor space occupied; (5) grate losses, which in this case are added to those of the boiler; (6) lower efficiency because the flue gas enters the stack at a temperature which must be higher than with built-in type, where superheater is followed by water heating surface; (7) greater radiation loss SUPERHEATERS 569 because of individual setting; and (8) difficulty of controlling temperature of steam, as explained in (b) above. The separately fired superheater has the advantage that the boilers can still be used to supply saturated steam even when the superheater is out of commission; that it permits the variation in the degree of superheat to be made independently of the operation of the boiler, and one superheater can be used for several boilers. (d) Although it has many disadvantages, the separately fired apparatus may be of value in many instances. In some plants, steel mills for instance, there are often large quantities of hot gases which, by such apparatus, can be used to superheat the steam coming from the boilers, but which would otherwise Fig. 371. be wasted. Then, there are also many industries in which steam exhausted from engines is used in some manufacturing process, and in many such cases it is desirable to superheat this steam in separatel}^ fired superheaters. Again, either as a means of im- proving the economy or of increasing the capacity of a boiler plant already installed, it may be desirable to superheat the steam generated, and in such cases it wiU generally appear upon investigation that the separately fired unit is the better invest- ment, as it will involve least changes in piping and settings. 274. Boiler Draft Superheaters, (a) Examples of this type are illustrated in Figs. 372 to 374. In nearly all cases built-in superheaters are installed at such a point in the flues, or gas passes, that the temperature of the gas reaching them can never greatly exceed about 1500° F. There are a few instances, 57 o HEAT-POWER ENGINEERING however, as in Fig. 372, in which the superheaters are installed in a separate brick chamber within the boiler setting and are supplied with hot gases directly from the furnace, by means of a passage in the brick walls st^m outtet^^^ ^^ ^^ ^^^ boiler setting, the flow of gas being controlled by a damper in the passage, (b) Two distinctly dif- ferent methods of main- taining an approximately constant temperature of superheat are in use. In one, the superheating ele- ments are located at such a point (as in Fig. 373) that the gases reaching them vary in temperature and quantity as nearly as possible in propor- tion to the amount of steam flowing. The attainment of such conditions is generally more ideal than real, but is fairly well approximated in a few instances, since the amount of steam gen- Safety Valvfe Fig. 372. Front Drain Valve Gases from Furnaces Fig. 373- erated depends directly on the quantity and temperature of the gases coming from the furnace. In the other method the superheating elements are installed within a separate chamber, as in Figs. 372 and 374, and a damper, which regulates the supply of hot gases, is put under some sort of control, which may be thermostatic. These superheaters have a certain temperature lag, as do the separately fired variety, SUPERHEATERS 571 but it is not as great as in that case because of the smaller amount of brickwork surrounding them. 275. Protection of Superheater, (a) No superheater, no matter what its construction, will last for any considerable length of time if exposed to the hot furnace gases when steam is not flowing through it. To prevent damage in this way, during the period of firing up and when cooling down or standing idle, some protective device is essential. (b) With separately fired superheaters the hot gases may be deflected, as in Figs. 370, 372, and 374, so that they bypass the superheater and flow directly from the furnace to the stack, or protecting rings like those in Fig. 369 may be used, or provision may be made for " flooding " the superheater — that is, filling it with water whenever the flow of steam ceases. The latter method is open to the objection that scale-forming material may be deposited in the superheater, thus decreasing its ability to transfer heat from gases to steam, which would ultimately result in main- taining the metal of the superheater at too high a temperature when in opera- tion and thereby shortening its life. (c) When boiler draft superheaters are located in a separate chamber within the boiler setting, either of the above methods may be used, but the objection to the last holds equally well for this case. (d) When boiler draft superheaters are located directly in one of the passes the most customary method of protecting is by flooding. They are generally so arranged (as in Fig. 373) that when flooded they form part of the boiler evaporating or heating surface, practically being connected in parallel with it, but so that they can be drained and connected in series with the boiler when superheat is desired. (e) In connection with this latter arrangement, an auxiliary safety valve is sometimes placed between the superheater and the main stop valve, so that if this latter valve is suddenly closed, 572 HEAT-POWER ENGINEERING or if the demand for steam suddenly ceases, before the fires can be deadened, the rising pressure of steam will pop this safety valve (before the main safety valve opens), and allow steam to pass through the superheater, thus protecting it temporarily and warning the attendant of the necessity for checking the fire and, possibly, for flooding the apparatus. 276. Superheater Surface, (a) The determination of the amount of surface required by a superheater to give a definite degree of superheat, when fired in a certain way, or located in a given position, is largely a matter of experience with each manu- facturer of each different type of boiler. There are several distinct methods of approximating the amount of super-heating surface required; the three most common are given below. (b) The superheating surface may be taken as a multiple of the grate surface. Thus for water tube boilers, the heating sur- face of built-in superheaters is generally taken at from 8 to 12 times the grate area, depending upon location within the setting, average rate of firing, superheat desired, character of coal, etc. With long flaming coals the gases often arrive at the superheater at a higher temperature than with short flaming fuels and a smaller surface may therefore be used. For internally fired boilers, values between 25 and 35 times the grate area are used. (c) The superheating surface may be taken as a fraction of the boiler heating surface. For water tube boilers it varies between 10 and 40 per cent of the boiler heating surface, though it rarely exceeds 20 to 30 per cent. For internally fired boilers a greater ratio is required, reaching in some cases to values almost equal to the boiler heating surface, and seldom dropping below 50 per cent of that surface. (d) The number of square feet of superheating surface (5) required may be determined by calculations, taking account of rate of heat transmission per square foot per hour, which depends both on the coefficient {K) of heat transmission and mean temperature difference {9m) between steam and gases. In this case, the heating surface required to transmit per hour an amount of heat equal to AQ is '-& <«> SUPERHEATERS 573 The coefficient (K) is the heat (B.t.u.) transmitted per square foot of surface, per degree difference of temperature, per hour. Its value varies widely with conditions and is found by experi- ment or experience. High velocity, thin streams of steam or gas, violent agitation, and high temperature and pressure, in- crease its value. The condition of the superheater also has considerable effect; when scaled internally and covered with ash and soot externally, the rate of transmission is very low. In general, values of K vary from i to as high as 10, and con- siderable experience is required in choosing a proper value. CHAPTER XXXII. DRAFT AND DRAFT APPARATUS. 277. General Principles, (a) The flow of air and products of combustion through the steam-generating apparatus is re- tarded by the resistances encountered in the various portions of the passage. The total resistance (R) , from the point where the air enters the boiler setting to the base of the stack, is the sum- mation of the resistances of the fuel bed (Rf), of the boiler passages (Rp), of the flues or breeching (Rb) and of any other passages (Rx) (such as that through an "economizer") which are traversed. Thusi? = Rf -^ Rp -{- Rb -\- Rx. It is of course desirable to have the total resistance as small as possible, hence each component resistance should be reduced to the fullest extent allowable. (b) As the gases flow only from places of higher pressure to those of lower (through a process of expansion) the gas pressures must decrease progressively from the point of entrance to the point of exit, the pressure drops through the different portions depending on the respective resistances of the parts. The way in which the pressure varies, as the particles of gas advance through the steam-generating apparatus, is shown in a general way in Fig. 375 by the curve abed, in which the abscissas represent the decrease of pressure below that at the point of admission and the ordinates are distances along the passage, measured from the same point. Evidently, the same curve would apply (in this particular case) regardless of whether the inlet pressure is atmospheric, or greater or less than that, for the same pressure drops' and the same gradients to the curve would still be required. The differ- ence between the abscissas of any two points on this curve gives the pressure drop required to overcome the resistance between the corresponding points in the apparatus. The final abscissa represents the pressure drop developed through the whole ap- paratus, and is evidently equal to the summation of all the pressure drops, i.e., AP= AP/ + APp + AP^ + AP«, in which 574 DRAFT AND DRAFT APPARATUS 57S oA^APp the subscripts refer to the same parts as before. It is the func- tion of the stack, or other draft-producing device, to develop this difference in pressure. (c) As the pressure variations of the flue gas, measured from atmospheric pressure, are very low, they are ordinarily deter- mined by means of water manom- eters, as shown in Fig. 375, and are therefore commonly expressed in terms of inches of water column (" hydraulic inches ") as compared with atmospheric pressure.* The total pressure drop from air inlet to base of stack is generally between 0.4 and 1.2 inches of water when determined in this way. The velocity of flow is generally so small that the velocity head can be neglected in the ordinary prob- lems that arise in connection with the subject under discussion. (d) According to Bernoulli s theorem (which can be applied to the steady and continuous flow of gases in long pipes when there are small pressure drops) , the total head is the same at all points in the passage. At the point (o) of entrance it is the sum of the velocity head ( — ) , the pressure head (-r) , and the potential head Zq] and at any subsequent point {x) it is the sum of the similar heads for that point together with friction head F of the intervening passage. Thus {T.-h-HT^^hh'' ■ ■ '««> in which v = velocity of flow in feet per second, P = pressure in pounds per square foot, 5 = specific density = weight per cubic foot of gas, and z = elevation in feet. The friction head (ft.) is Fig. 375- 62.5 (409) ^ * One inch of water column corresponds to ^^^^ =5.2 pounds per square foot; or one pound per square foot corresponds to .192 inches of water column. 576 HEAT-POWER ENGINEERING in which L = length of flue in feet, / = coefficient of friction, 5 = length of perimeter of the cross-section in feet, A = area of passage in square feet, and the ratio A/S is called the " mean hydraulic radius, ^^ In the passages through the boiler the variation in velocity and in elevation can ordinarily be neglected, hence the quantities v and z disappear from Eq. (408) in this case. Then from Eqs. (408) and (409), using a mean density bm and letting AP = (Pq — Px), the change in pressure head is which shows that the pressure drop is dependent solely on the frictional resistance, which varies directly with v^, L and the character of the surfaces and inversely with the mean hydraulic radius {A/S).. The velocity of flow is, from Eq. (410), v = V2g^PX{A-^fLSbm). . . . (411) and for any given passage V = const VAP ' . . . (412) Evidently the rate of combustion, which is dependent on the velocity (amount) of the air passing through the fuel bed, can be reduced by decreasing A in Eq. (411), other things remaining the same, as by partly closing the damper. (e) But in the actual case of flow of gases through steam-gen- erating apparatus, the conditions are quite different from the hypothetical ones assumed in connection with Bernoulli's The- orem, — for, through part of the passage there is air of a certain density, through the rest is a complicated mixture of gases varying as to composition, density and temperature ; the passages are circuitous, have sudden changes in areas and in direction and have eddy pockets; the resistance through the fuel bed is constantly varying and the flow of gas is neither steady nor necessarily continuous, — hence, the analysis of the laws gov- erning the actual case is difficult and as yet these laws are not well established. There are, however, a few general statements which can be made and which are more or less applicable to most cases; they DRAFT AND DRAFT APPARATUS 577 may serve as rough guides in approximating the solution of problems connected with boiler draft.* These are given in the following paragraphs. (f) Other conditions remaining the same (temperatures, re- sistances, etc.), the weight (w) of air entering the furnace in a unit of time is dependent on the velocity of flow, and appears to vary about as the square root of the pressure drop (AP) through the passages. f As the rate of combustion (R) is directly dependent on the air supply it varies approximately in like man- ner, i.e., R = const. VAP, where the constant varies with the size and kind of coal, method of firing and other conditions. Thus, doubling the pressure drop increases the rate to about 1 .4 ( = V 2) its former value ; and to burn fuel twice as rapidly as before involves nearly quadrupling the draft pressure. (g) It is also approximately true that if the resistances remain unchanged, the pressure drop through any portion of the passage will remain the same fraction of the total, regardless of the vari- ation in the over-all drop, that is, the pressure gradients would vary proportionally. For example, for the case shown in Fig. 375, with change in draft, the curve would merely be re- plotted with all abscissas changed proportionally to the varia- tion in the over-all drop, or the same curve could be used with suitable change in scale. (h) The resistances encountered vary about as the square of the velocity (as in Eq. 409), although probably the exponent should be slightly less than 2, say 1.8. Hence, doubling the velocity, to obtain a twofold rate of combustion, necessitates about four times as intense a draft, and nearly four times as much work will be done in moving the gases. (i) As the power is the product of resisting force by the velocity of motion, the amount required for removing the gases varies about as the cube of the velocity of flow, i.e., as the cube of the amount of air supplied, or as the cube of the rate of combus- tion. Thus, in order to double the rate of combustion, or boiler output, the draft-producing apparatus would have to do nearly eight times as much work. Therefore, while from the stand- point of space occupied by the boiler it may be desirable to * Bull. 21, U. S. Bureau of Mines, "Significance of Drafts," contains discussions of experiments on draft. t Thus it follows approximately Eq. (412). 573 HEAT-POWER ENGINEERING force the rate of combustion as much as possible, the additional expense for power and apparatus for handling the gases with greater velocity places a limit beyond which it is financially unprofitable to go. 278. Amount of Pressure Drop Required, (a) The pressure drops {hf inches of water) generally needed for overcoming the resistance through the fuel bed have already been given in Fig. 326 for the different rates of combustion of several sizes of various kinds of coal when burned under the usual conditions. But much variation from these curves exists, since the intensity of draft depends also on the thickness of the fuel bed, character of the ash and clinker, method of firing and other items. (b) The drop in pressure (hp inches of water) through the boiler passages depends on the length and cross sections of pas- sages, arrangement of baffles, arrangement of tubes, etc. Under ordinary rates of combustion it ranges as in Table XXIV and varies about as the square of the rate of combustion (as explained in Sect. 2^7 (f)) when operating at greater or lower rates. TABLE XXIV. — PRESSURE DROPS THROUGH BOILERS.* B. and W. — double deck 0.4 in. I Stirling or Heine 0.2 in. B. and W. — standard o-3 " I Return Tubular. o.i " (c) To overcome the resistance of the breeching, or flues, be- tween the boiler and the stack, a pressure -drop (h) of about yV inch of water is generally assumed per 100 feet of length of smooth round passage when the boilers are being forced, and half as much for each elbow, though much depends on the mean hy draulic radius (-ft) of the passage, on the curvature of the bends, character of wall surface, etc. It would of course reduce the cost of the breeching if small cross sections and high velocity of flow were used. But since the re- sistance varies as the square of the velocity, greater draft would then be needed to overcome it, and this would, in general, add to the expense for the stack (or other draft-producing apparatus) an amount greater than the saving effected in outlay for the breeching. Hence, the breeching is usually given a liberal cross sectional area, one at least equal to that of the stack and gener- * Kingsley, Eng. Record, Dec. 21, 1907. DRAFT AND DRAFT APPARATUS 579 ally 20 per cent greater, the velocity of flow being not more than that in the stack, and generally about 20 per cent less. (d) The total pressure drop (hi) inches of water between air inlet and base of stack evidently equals the sum of the drops through these various elements of the passage and of any others, such as those through economizers, which may be located between the boiler and stack. Thus hi = hf -\- hp -{- h -{- hx. The draft-producing apparatus should of course be proportioned to give a pressure drop at least sufficient to cause the greatest rate of combustion that will ever be demanded with the poorest fuel which is likely to be used ; then, smaller rates can be obtained by reducing the amount of air supplied, which can be done by regulating the dampers and air inlets either by hand or by some automatic device, the latter being generally operated by the slight variations in steam pressure which accompany the changes in the demand for steam. (e) The current of gases through the boiler can be caused either by " natural' ' draft of a chimney (or stack), or by "arti- ficial " draft maintained either by steam jets or by power-driven fans. The duty of the draft-producing apparatus is twofold — first, it must produce the needed intensity of draft and, second, it must provide means for carrying off the products of combustion. 279. Chimney Draft, (a) When one pound of carbon is com- pletely burned in air to CO 2, the latter gas will have the same volume at the same temperature and pressure as did the oxygen with which the carbon united (in accordance with Sect. 238 (a)) ; but the resulting flue gas will have one pound more material than was in the air which supplied the oxygen. Thus, for ex- ample, if the excess coefficient is two, 24 pounds of air with specific density = .0807 * are supplied for the complete combus- tion of one pound of carbon and there will result 25 pounds of gas, which will have a specific density * of (||) X .0807 = .084. Hence the weight of a column of air one foot high, at sea level and at temperature ta° F., is D = (.0807 X 492) - (la + 460), . . . (413) * Pounds per cubic foot at 32° F. (or 492° Absolute) and under 14.7 pounds square-inch pressure (measured at sea level) . 58o HEAT-POWER ENGINEERING and that of a similar column of flue gas, with excess coefficient equal to two and with temperature tg° F., is d = (.084 X 492) ^ (tg + 460). . . . (414) (b) In Fig. 376 (a) the intensity of pressure exerted on the side of the partition X by the column (A) of cold air at tempera- ture ta, and that exerted by the equal column (G) of hot gas at tg° F., are respectively, in inches of water,* ha = .192 HD = 7.64 H/(ta + 460), . . . (415) and hg = .ig2 Hd = 7. gsH/(tg + 460), . . . (416) where H is the height of the columns in feet, and D and d have the values given in Eqs, (413) and (414). This is of course on ^ \ \ i 1 '' ta B (d) '■•■;•.■•: --- X ■:■■:■•■ m ... M ) 1// /I (S) ! 1 my/A /zmMwy///M/M W77 Fig. 376. the assumption that equal pressures of air are exerted on the tops of these columns. The difference between these pressure intensities on the opposite sides of the partition is (at sea level) .64 7.95 hi = i}la — hg) :^ (417) + 460 tg + 46oy and, if the partition is removed, this will be the draft pressure tending to cause the flow of gases upward through column G. (c) If means are provided for maintaining the high temper- ature {tg) in column G, there will be a constant flow of gases, and as the air in column A is under atmospheric conditions the enveloping shell around that column can be omitted. Under these circumstances the conditions are those existing when a * See footnote, page 575. DRAFT AND DRAFT APPARATUS 581 furnace and chimney (stack) are in operation, as in Fig. 376 (b) ; hence Eq. (417) can be used for obtaining the theoretical draft pressure ht developed by a stack of height H feet when the re- sistances through the stack are neglected, and it gives the draft pressure that would occur when the ash-pit doors are closed and no gases are flowing. Then, the theoretical height (Ht) of stack needed for producing / a draft pressure of h inches of water at its base is (from Eq. 417) at sea level (14.7 lbs. per sq. in.). Obviously Ht will vary with changes in the atmospheric pressure (barometer). (d) Under normal conditions the temperature of the flue gas at the base of the stack generally lies between 500 and 600° F. in difi^erent types of boilers; but if "economizers " are used, it will be less and in some instances may be reduced to 300° F. When the boilers are being forced the temperature rises above the normal, which helps to augment the draft. In using Eqs. (417) and (418) for the draft and the height of a new stack, tg should be taken as the lowest flue temperature and ta as the highest atmospheric temperature that are liable to exist simul- taneously. As the gases become cooled in passing up the stack, tg should be the mean temperature; it is customary, however, to use the temperature at the base of the stack and then to correct for the error, and for the resistances within the stack, by making the actual height about 25^j)er ceat greater than the theoretical one. The effects of the column of hot gases above the stack and of the wind are generally neglected. Whether the wind assists or retards the draft depends on the arrange- ment of the chimney top. In practice the height of stack is from 80 feet, with free burn- ing coals and little resistance, to 175 feet, or more, with fine anthracite coal and with considerable resistance in the passages. But in settled districts the height should always be sufficient to satisfactorily dispose of the obnoxious gases. (e) The cross sectional area of the stack should, of course, be made ample for accommodating the gases when the boilers are forced to their maximum capacity, and in fixing the size allow- ance should always be made for any possible growth. 582 HEAT-POWER ENGINEERING Having found the actual height of stack, it is quite common practice to compute the cross sectional area by using Wm. Kent's empirical formula, which was derived as follows: — Assuming that the volume of gas formed per hour is dependent on the amount of coal burned, which in turn is proportional to the boiler horse power (BP) developed, and that the velocity of flow varies as the square root of the height 77 (feet) of stack, it follows that the area is a function of BP -^ Vh. Then, from an analysis of numerous chimneys, Kent found that the effective area (£), in square feet, should be about E = .3{BP)^Vh. ..... (419) It is also assumed that if it is considered that the chimney has a two-inch lining of stagnant gas, the flow through the remainder of the cross section can be taken as being without resistance. Hence the actual diameter of a circular chimney and the length of side of a square one are made four inches greater than the corresponding dimensions determined for the effective area. Kent's proportions are liberal as they provide for the com- bustion of about 5 pounds of coal per B. P. -hour, whereas not over 4 pounds are ordinarily used. They allow for velocities of gas through the stack ranging from about 20 ft. /sec. with 100 feet of height to about 30 ft. /sec. in a 200-foot stack. (f) A more rational method of determining the proportions of a stack for a given set of conditions may be carried through in the following order: 1st. Assuming from 250 to 300 cubic feet of air at 60° F. as the amount needed to support the combustion of one pound of coal, and knowing the maximum weight of fuel to be consumed per unit of time, compute the corresponding total volume of gas at stack temperature. 2d. Assuming a velocity of flow of from 20 ft. /sec, for short stacks, to 30 ft. /sec, or more, for very tall ones, compute the effective cross sectional area needed to discharge this volume; and then, allowing for a two-inch lining of stagnant gas, deter- mine the final dimensions of the cross section. 3d. Find the loss of draft {h2 inches of water) arising from the stack resistances, which are due to (a) change of direction of the gases upon entering the base of the stack, (b) the skin friction and (c) the displacement of the atmosphere by the issuing DRAFT AND DRAFT APPARATUS 583 stream. From Kingsley's experiments * this loss for a velocity V ft. /sec. was found to be given approximately by the equation /?2 = .000361^^ (420) 4th. Determine the pressure drop hi up to the base of the stack and compute the theoretical height (Ht) from Eq. (418). 5th. Then find the actual height (H) of stack from H = Ht{hi + h2) ^hi (421) (g) By using the higher velocities, the stack diameter is de- creased, which would result in a reduction in the cost of the stack if other things remained the same; but these greater velocities necessitate an increase in the height of stack, thus en- tailing an additional expense which either partly or wholly offsets that saving. Evidently for a given set of conditions there is some velocity which will give a proportion of height to diameter requiring a minimum amount of material for con- structing the stack, and hence involving the least outlay of money. (h) For rough estimating it can be assumed that a 100-foot stack with gases at 500° and air temperature at 70° will exert a theoretical draft pressure of .6 inches of water at its base; that the draft varies directly with the height; and that the effective cross sectional area in square feet is equal to the number of pounds of coal burned per minute. For ordinary conditions with bituminous coal the stack area is about ^th the grate area and with anthracite coal about ^th. (i) The different parts of a chimney and its foundation must not only carry the weights above but must also withstand the wind pressure. Chimneys are made of (i) common brick, (2) radial brick, (3) reinforced concrete and (4) steel plates. A comparison of Figs. 377 to 380, which illustrate stacks of the different types but of the same height and internal diameter, will show roughly the relative thickness, weight, extent of foun- dation and space occupied with the various constructions. (j) If made of ordinary brick (Fig. 377) the chimney must be lined at least for part of its height with fire brick so set as to have perfect freedom to expand or contract with temperature * Engineering Record, Dec. 21, 1907. 5^4 HEAT-POWER ENGINEERING -12" IBRICK CHIMNEY 8±txl80ft» 7-^ RADIAL BRICK CHIMNEY 8 ft. X 180 ft. Fig- 377- Fig. 378. DRAFT AND DRAFT APPARATUS 585 changes. By using special radial brick (Fig. 378), composed of suitable material, and commonly made perforated, (i) the lining may be omitted, (2) the shell may be thinner and of lighter weight, and (3) the foundation may be smaller; besides which (4) the construction is better and (5) can be more rapidly done than with ordinary brick. The tallest chimney in the world is of this type. It is located at Great Falls, Mont., and is 506 feet high with 50 feet diameter at the top. (k) Many chimneys are now made of reinforced concrete (Fig. 379), the steel reinforcing bars being arranged both circum- ferentially and vertically, the latter extending into the founda- tion, which is similarly strengthened. Such chimneys are (i) thinner than the brick, (2) weigh less, (3) occupy less space, (4) require but small foundations, (5) are free from joints and (6) can be rapidly constructed. The inner shell may be either of brick or reinforced concrete and in some cases is entirely omitted. (1) In order to withstand the wind, steel stacks are either guyed with wire or wire rope, or else have flared bases bolted to the foundation, in which case they are said to be self-supporting. They are preferably lined with brick to protect the metal from the heat and corroding action of the gases. The lining may either be self-supporting or else be constructed in independent sections each resting on a bracket extending from the steel shell. Such chimneys are (i) of light weight, (2) easily and rapidly constructed, (3) cost little, (4) occupy small space (except when flared) and (5) are free from air leakage if properly calked. They must be painted frequently to protect the metal from the weather and from the gases. 280. Artificial Draft, (a) In a new power plant artificial draft apparatus is frequently employed as a substitute for a tall chimney, or to assist a short one, under the following conditions: (i) when the temperature of the stack gases is low, as when an economizer is used; (2) when the rates of combustion are high; (3) when fuels requiring intense draft are to be burned; (4) when certain stokers, like the underfed, are used; and (5) in certain other cases where in the long run it may be more de- sirable or more economical to purchase, operate and maintain such apparatus rather than have a chimney of large size. 586 HEAT-POWER ENGINEERING s'o" U r V Inner Shell Outer Shell REINFORCED-CONCRETE CHIMNEY 8 ft. xi 180 ft. Fig. 379. y /r. r , r. '^ ^ '^ STEELiSTACK 8ft.3b.8Oft. Fig. 380. DRAFT AND DRAFT APPARATUS 587 Fig. 381. — Forced Draft. In an old plant it may be desirable to install artificial draft apparatus (i) to assist the original chimney when the plant has been increased beyond the capacity of the natural draft; (2) when it is desired to adopt unusual rates of combustion, or (3) to burn fuels requiring intense draft; (4) when there may be large emergency overloads or peak loads of short duration; and (5) when there are large and sudden changes in demand on the fur- naces. (b) In addition to its advantages in the instances already dis- cussed, the artificial draft apparatus is (i) easily installed; (2) is transportable and (3) occupies but little space; and (4) it also permits of careful adjust- ment of the air supply, which makes possible more perfect condi- tions of combustion. The regulation of air can be automatic, the controlling device being operated by the slight changes in steam pressure accompanying the varying demand on the boiler. (c) Artificial draft is produced either by steam jets or by power-driven fans, and when developed by the latter it is generally called mechanical draft. With forced draft (Fig. 38 1 ) the ash pit is ' ' closed ' ' (hermetically sealed) and the apparatus supplies it with air at a pressure above atmospheric (at a "plenum ") ; with induced draft (Fig. 382) the appa- ratus draws the gases from the boiler outlet, thus decreasing the pressure at that point below atmospheric; and with balanced draft these two systems are used in combination in a manner which will be discussed later. Fig. 382. — Induced Draft. S88 heAt-power engineering Fig. 383. (d) Fig. 383 shows one of the many forms of steam, jets used for forcing the draft. Somewhat similar devices can be placed in the base of the stack (as is universally done in locomotives) to produce induced draft. Such apparatus is relatively low in first cost, but is very wasteful of steam, using generally not less than 5 to 8 per cent of the total steam generated, and it increases the stack loss because of the added moisture in the flue gas. Steam jets are conven- ient auxiliaries for meeting sudden or abnormal demands on the boilers, and the presence of the steam in the air supporting combustion tends to avoid the formation of clinkers. Fig. 384 shows a disc fan which is used in a similar manner. (e) With mechanical draft, the fans and their driving appa- ratus must be so designed as not to be affected by the dust, and with induced draft they must also be suitable for handling the hot gases without injury. If entire dependence is placed on fans for providing the draft, there should be duplicate (or auxiliary) apparatus installed to avoid plant shutdowns from failure of the draft apparatus. With a very short stack the fan equipment for forced draft costs roughly from 20 to 30 per cent as much as the equivalent brick chim- ney; while with induced draft the cost is about double that for forced draft as a larger fan ("exhauster") must be used because the gases are at high temperature. But though low in first cost, such apparatus depreciates rapidly, involves considerable expense for attention and maintenance, and uses for power from i| to 5 per cent of the steam generated. (f ) With forced draft the gas pressure within the boiler setting is above atmospheric, hence the tendency for hot gases and flames to issue through cracks in the walls and also to belch forth upon the opening of the fire doors. To avoid the latter occurrence the blast is shut off, usually automatically, when the doors are opened.* The air should always be introduced into the ash pit in such manner as to subject the fuel bed to * Some steamships using forced drafts have " closed firerooms " (stoke-holds) under pressure, and in such cases all leakage is into the interiors of the settings. Fig. 384. DRAFT AND DRAFT APPARATUS 589 static pressure, or plenum, rather than to any localized blast action. With induced draft (either natural or artificial) the pressure within the boiler setting is below atmospheric, hence there may be detrimental infiltration of cold air through cracks in the set- ting and through the fire doors when opened. With this system, however, the fuel bed burns more evenly, and demands less attention than in the other, and it is not necessary to shut off the draft before opening fire and ash doors. Usually a by-pass flue is provided (as in Fig. 382) so that natural draft alone can be used for light loads, or in case of accident to the apparatus. With balanced draft the air is forced into the ash pit at suffi- cient pressure to become just atmospheric upon issuing from the surface of the fuel bed, and the gases are carried away from the combustion chamber by induced draft (either natural or arti- ficial) of such intensity as not to cause a decrease of furnace pressure below atmospheric. The proper balance between the forced and induced draft is usually maintained by some auto- matic device which regulates the two systems simultaneously. With balanced draft (i) there is no tendency for leakage either into or from the furnace; (2) the fire is not affected by opening the furnace doors for adding coal or ''working" the fire; (3) it is possible to burn the smaller sizes of fuel, which are otherwise worthless, and which must be burned at high rates of combus- tion but cannot be used with forced draft because of their fine- ness; and (4) very high rates of combustion can be used with- out detriment to economy. ^ -^ |^ ■-'■1 "^ ^^ii^A' CHAPTER XXXIII. GAS PRODUCERS AND PRODUCER GAS. 281. Essentials of Producer-gas Apparatus. (a) Broadly speaking any apparatus in which gas is made is a ^' gas producer,'" but in engineering the term is almost exclusively applied to a class of apparatus producing gas largely by a process of partial or incomplete combustion. The gas made in such apparatus is known as ^^ producer gas." (b) This gas has long been used for the heating of furnaces, the melting of metals, and a large number of similar purposes, but during the last twenty years it has come into particular prominence as a power gas, that is, a gas for use in internal com- bustion engines. It happens to be so constituted as to permit of high compression in the engine, thus giving high thermal efficiencies and, what is of greater importance industrially, it can be made at the point of consumption more or less easily and very cheaply as compared with most of the other combustible gases. (c) Although the necessary apparatus differs considerably with the kind of fuel from which producer gas is to be made and with the purpose for which the gas is to be used, there are certain essential parts which generally exist in one form or another in all such apparatus. They are: (i) The fuel gasifier or "pro- ducer"; (2) some sort of "preheater" or "economizer"; (3) cleaning apparatus; and occasionally (4) a gas storage reservoir of some kind, large or small. The first three parts are all shown in Figs. 5 and 391 to 394. In the particular types of plant shown in Figs. 5 and 391, the gas storage reservoir is practically nonexistent unless the pipe connecting the top of the scrubber with the engine cylinder be considered as partly serving that purpose. 282. Simple Theory of Producer Action, (a) As indicated above, the ideal producer makes gas by what is known as par- tial or incomplete combustion. In its simplest conception this 590 0+000=2 00 COo&N GAS PRODUCERS AND PRODUCER GAS 591 depends upon the combustion of carbon to carbon dioxide and then the reduction of this carbon dioxide to carbon monoxide by passing it over incandescent carbon. These reactions can be illustrated by means of Fig. 385. (b) Assume the vessel there shown to be filled with a column of carbon, the lower part of which is heated to incandescence. If air enter at the bottom of this fuel bed, as indicated by the arrows, its oxygen will unite there with carbon to form carbon dioxide, according to the equation (see Eq. (342a)) C + O2 = CO2 + 175,200 B.t.u., (423) which means that twelve pounds of carbon combine with thirty- two pounds of oxygen ^^' ^ ^' to form 44 pounds of carbon dioxide and that (12 X 14,600 =) 175,200 B.t.u. are liberated per twelve pounds of carbon. (c) This carbon dioxide would then be reduced to carbon monoxide while passing up through the incandescent carbon above, and the reaction would occur according to the equation CO2 + C = 2CO - 67,200 B.t.u. . . . (424) This means that the 44 pounds of carbon dioxide formed in the lower part of the fuel bed unite with twelve more pounds of carbon which will result in the formation of fifty-six pounds of carbon monoxide and the absorption of an amount of heat equal to 67,200 B.t.u., which quantity is easily obtained analytically in the manner described in the next paragraph. (d) Imagine the process occurring in two steps : First assume that the forty-four pounds of carbon dioxide break up into twelve pounds of carbon and thirty- two of oxygen. This could only occur with the absorption of 175,200 B.t.u., equal to the quantity liberated when the combination took place. Then imagine the carbon and oxygen to combine witH an additional twelve pounds of carbon to form the fifty-six pounds of carbon monoxide. This would be represented by (see Eq. (343a)) 2 C + O2 = 2 CO + 108,000 B.t.u., . . (425) which merely states that twenty-four pounds of carbon burning to carbon monoxide liberate (24 X 4500 =) 108,000 B.t.u. 592 HEAT-POWER ENGINEERING The first process involved the absorption of 175,200 B.t.Uo in breaking up CO 2, the second liberated 108,000 B.t.u. in the formation of CO, and the net result is the absorption of (175,200 — 108,000 =) 67,200 B.t.u., as given in Eq. (424).* (e) The composition of the gas formed and the thermal effi- ciency of the process can now be determined : — To produce the gas according to Eqs. (423) to (425), thirty- two pounds of oxygen are required per twenty-four pounds of carbon used and this oxygen will bring into the producer (32 X 77/23 =) 107. 1 pounds of nitrogen; hence the 163. i pounds of gas leaving the producer will contain this weight of nitrogen in mixture with the fifty-six pounds of carbon monoxide result- ing from the partial combustion, and will therefore have a com- position of about 34.4 per cent CO and 65.6 per cent N by weight. By volume the composition would be practically the same because the densities of CO and N are practically identical. 283. Efficiency, Simple Producer Action. (a) Had the twenty-four pounds of carbon used in Sect. 282 (c) been burned directly to carbon dioxide, they could have liberated 24 X 14,600 = 350,000 B.t.u. Burned 'to carbon monoxide they liberated only 24 X 4500 = 108,000 B.t.u. The difference, 350,000 — 108,000 = 242,000 B.t.u., must be the quantity of heat which can be produced by subse- quently burning the carbon monoxide of the producer gas to carbon dioxide. This corresponds to 10,100 B.t.u. per pound of carbon. (b) If the thermal efficiency of the producer be taken as the ratio of the heat which can be obtained by burning the cold gas to the heat which could have been obtained by burning the original carbon, it is in this case . _ Calorific Value of Gas ^ 242,000 ^ ^ . ,. '^ ~ Calorific Value of Fuel 350,000 ^/^' ^^ ^ Looked at in this way the process does not promise very well from a power-engineering standpoint. If the theoretical pro- * It will be shown in a subsequent paragraph that this treatment does not tell the whole story, but for a first analysis it is accurate enough. GAS PRODUCERS AND PRODUCER GAS 593 ducer-efficiency is only 69 per cent, the real efficiency could hardly be expected to be more than 50 to 60 per cent, and, with thermal efficiencies of internal combustion engines ranging from 20 to 30 per cent as an extreme value, the overall thermal effi- ciency of such a producer in combination with an engine would be low indeed. It will be shown later, however, that higher efficiencies are obtainable by modifying the process. (c) The efficiency given above is what is called the cold gas efficiency and is really not the correct efficiency to use under all conditions. For power purposes the gas must be cooled approxi- mately to room temperature before it can be advantageously used in an engine. This means removing all of the sensible heat given the material in the producer, and the cold gas efficiency is the proper value to usje under such circumstances. (d) The process as outlined results not only in the production of 163 pounds of gas, which can liberate 242,000 B.t.u. when burned, but also in the liberation of 108,000 B.t.u, in the pro- ducer. In any real case part of this latter heat will of course be used to supply unavoidable radiation and similar losses, but the rest will raise the temperature of the carbon and of the air fed to the producer and of the gas formed. Hence the gas would actually leave the producer with a very high temperature, about 2000° F. or more, and, by cooling it to room temperature, all of the heat liberated in the producer, and which was not lost by radiation or in other ways, could be obtained. The temperature rise resulting from the liberation of a cer- tain number of B.t.u. is equal to this number divided by the sum. of the products of weight by specific heat of all the gases resulting from the combustion. The higher the temperature of the combustible gas and of the air before combustion, the higher will be the ultimate temperature attained.* Therefore, for fur- nace and similar work, where the object in burning the gas is to obtain high temperature, it is decidedly advantageous to have the apparatus located near the producer so that the sensible heat is not lost by radiation during transmission. For such purposes the thermal efficiency of the producer is * As the specific heats of gases increase comparatively rapidly at high tempera- tures, the temperature ultimately attained by any combustion will be lower than that given by the form of calculations suggested, as has already been shown. The error will be greater the higher the temperature attained. 594 HEAT-POWER ENGINEERING correctly taken as the so-called hot gas efficiency, which Is the quotient resulting when the sum of the total calorific value and the sensible heat of the gas leaving the producer is divided by the total calorific value of the fuel entering. Remembering that all heat which is liberated within the apparatus, and not lost by radiation and such, must be present in the gas leaving, the "hot gas efficiency " must be J-, . _ Total Calorific Value of Gas + (Heat Liberated in Producer — Losses) . . . ^^ ~ . Total Calorific Value of Fuel ' ^^^Z; and if all the losses in the case previously considered be assumed at 20 per cent of the heat liberated in the producer, the hot gas efficiency for this case would be ^. 242,000 + (108,000 — 0.2 X 108,000) 350,000 328,400 350,000 = 93-5 per cent (approximately), a figure which is evidently much more promising than that pre- viously obtained. 284. More Advanced Theory of Producer Action, (a) If the combustion processes indicated in the equations of the preceding section really occurred as there given it would be possible to pass a stream of carbon dioxide into one end of a tube containing hot carbon and have nothing but carbon monoxide issue from the other end. Experiment, however, shows that this is impos- sible, for, no matter what the conditions are, there will always be a certain amount of carbon dioxide mixed with the issuing carbon monoxide. (b) Experiment further shows that, other things being equal, the higher the temperature in the tube the greater will be the proportion of carbon monoxide in the gas issuing, and the lower the temperature the greater will be the proportion of carbon dioxide. (c) This is explained chemically by what is called "chemical equilibrium." Briefly, if no other variables need be considered, at each given temperature, there are certain definite proportions of carbon monoxide and carbon dioxide which will be in equilibrium with carbon. If a mixture of these gases in other proportions is GAS PRODUCERS AND PRODUCER GAS 595 1892 1472 900 1000 Tempf C. 1652 1832 2012 Temp.°F 1200 2192 2312 Fig. 386. brought into contact with carbon, reactions will occur and con- tinue until the equiUbrium proportions corresponding to the given temperature are attained.* (d) This equilibrium is well shown by the diagram of Fig. 386 which is plotted from experimental results obtained with carbon in a tube, as described in (a) of this section. In this figure the abscissas represent temperatures in Centigrade and Fah- renheit degrees and ordi- 20 nates represent per cent of CO by volume. Sub- d^ tractmg these ordinates "^o from 100 gives the per- centages of CO 2, which are evidently shown to. 100 scale by distances from the curve to the 100 per cent line. The curve shows that for low temperatures probably a very small amount of carbon monoxide would be found to be issuing from the tube in the experiment described above, while at high temperatures it shows the issuing gas to be composed almost entirely of carbon monoxide. (e) In giving the effect of temperature on the composition as deduced from experiment, it was limited by the phrase "other things being equal." Experiment shows that the pressure at which the gases exist also has a certain effect upon the compo- sition. The higher the pressure the greater the percentage of carbon dioxide in the equilibrium mixture at any temperature- Pressure variations are, however, so slight in producer work that their effect may be safely neglected. (f) The time of contact is also of great importance. Chemical reactions do not occur instantaneously (that is, in time measured in infinitesimals) and the reactions in question, which lead to the equilibrium conditions plotted in Fig. 386, take a very appreciable time for completion. The higher the temperature the shorter the time necessary for the attainment of equilibrium conditions. * Whether reaction then ceases, or whether counterbalancing reactions which do not further change the proportions of carbon monoxide and carbon dioxide continue, is a matter of indifference for the present discussion. 596 HEAT-POWER ENGINEERING o •^60 80 -i-lGO^ e_(.o-w;xii2Fj_ 1 f- ^^ZPSVOO^ tr-cis 32^Fr- ^- — ' ^^ A .8Rn2/a =rl 60 -^ // ^ -800^ ' (117 *°F) 6 20 // / Exp eriraei its wit hCha ■coal / 40 60 80 100 120 liO Time of Contact, Seconds Fig. 387. This is well shown in Fig. 387 which gives results obtained in experiments with carbon in the form of charcoal. In the figure each curve is an isothermal; that is, it shows the proportions of carbon monoxide and of carbon dioxide that will exist after gas, which was originally all carbon dioxide, has been in contact with carbon at a certain temperature for different lengths of time. As before, the ordinates represent percentages of CO and the distances from the curve upward repre- sent percentages of CO2. It will be observed that, while it takes a time period of from 120 to 160 seconds to attain ap- proximate equilibrium at 8oo°C. (as shown by the tendency of the curve to become hori- zontal at this point), it requires only 5 seconds to attain equi- librium with a very much higher percentage of CO at 1100° C. (g) The effects of both time and temperature are well shown in Fig. 389, in which the three coordinates are time, temperature and volume per cent, of CO. The curves shown are those of Fig. 387, but here each curve is located in its own tem- perature plane. A sur- face can be imagined as passed through these curves and the coordi- nates of any point in it will show the relative 100-" 40 60 80 100 120 140 Time of Contact, Seconds Fig. 388. percentages \ of CO and CO2, which result at any temperature after any period of contact. (h) Unfortunately the surface condition of the carbon has an effect upon the time required for the attainment of equilibrium. In general the more porous the carbon, and the smaller the lumps, the shorter will be the time required to attain the equi- librium corresponding to the given temperature. This is just what would be expected, as carbon of porous character and in GAS PRODUCERS AND PRODUCER GAS 597 small lumps will expose most surface on which the reaction may occur. The effect of surface (and possibly other) conditions is shown by a comparison of Figs. 387 and 388. The full lines in the latter represents the results of experiments made with carbon in the form of coke in lumps about the same size as those of the char- 5C= Temperature," C. Fig. 389. coal used in obtaining the results shown in Fig. 387. The dotted lines show similar curves for anthracite under approximately like conditions. The curved surface shown in Fig. 389 is then only one of a number which differ in curvature with the character of the carbon. The more porous and the smaller the lumps the sharper will be the rise of the curves as they leave the temperature axis at the front, and the sooner will they become flatter as they recede. 598 HEAT-POWER ENGINEERING (i) The preceding discussion is purely theoretical and leads to the following conclusions: For best producer operation (that is, the manufacture of gas containing the maximum amount of carbon monoxide and the minimum amount of carbon dioxide and nitrogen) the requirements are : — (i) High temperature within the producer; (2) Long time of contact between entering air, gas in process of formation, and hot carbon; (3) Maximum porosity and minimum size of fuel ; / (4) Theoretical air supply. 285. Practical Limitations, (a) In the real producer there are a number of practical considerations which materially modify the conclusions just given for the theoretical case. For instance, all real fuels contain ash and this will fuse arid form clinker if the temperature becomes high enough.* Such clinker is very undesirable because it obstructs the gas passages between the lumps of fuel, making it difficult or impossible for gas to flow through certain areas. This results generally in more violent combustion in the parts of the bed which are still unobstructed, and this localized combustion materially augments the trouble by raising the temperature locally and causing the rapid forma- tion of more clinker. The more or less complete obstruction of the ga,s passages will ultimately make continued operation im- possible. Clinker also gives considerable trouble by fusing to the walls of the producer itself. Thus, in actual operation, the fusing temperature of the ash sets the limit to the temperature allowable in the producer and this temperature varies considerably with different fuels; but, with those adapted to use in present-day producers, the tem- perature can generally be carried at such a value as to give a theoretical proportion of from 96 to 98 per cent of CO (with 4 to 2 per cent of CO 2) by volume in the issuing gas. (b) Caking fuels also cause trouble in producer operation. The coalescence of the individual lumps decreases the percentage * A number of experimenters are now operating producers at what are ordi- narily considered exorbitantly high temperatures, by mixing with the coal some cheap material, such as limestone, which acts on the ash as a flux. The ash is thus made very fluid and is drained off just as it is in the case of blast furnaces. Several plants of this character are said to be in successful operation in Europe but they have not yet been commercially adopted in this country. GAS PRODUCERS AND PRODUCER GAS 599 of voids in the fuel bed and thus obstructs the flow of gas. It also assists in causing "arching " so that the lower part of the fuel column may burn to ash and drop down while the upper part remains suspended above. Constant or intermittent stir- ring of the fuel bed (often combined with the maintenance of a fairly low temperature) are necessary with such fuels, although both stirring and low temperature have a detrimental effect upon the gas made. Stirring is often improperly done, and opens up fairly large free passages through the bed, thus allowing CO2 and even air to pass through without coming into intimate contact with hot carbon. (c) The theoretical requirement of long time of contact is more or less a relative consideration, as previously indicated ; and the length of time needed was seen to depend both upon the tempera- ture and upon the physical character of the fuel. Remembering that a producer operates with a continuous flow of gas through the fuel bed, the time of contact between gas and carbon must be measured in the actual case by the length of time it takes a given particle of gas to pass through the fuel bed, and hence depends on the velocity of the gas passing through the producer and the length of the passage through the bed of fuel. There is a practical limit to the allowable depth of fuel bed with any given fuel, in any given size, with any given type of pro- ducer. This limit is set by the difference of pressure necessary to cause flow through the bed. The length of the gas path through the producer being thus limited, the time of contact varies with the velocity which, in turn, depends on the diameter of the fuel bed. Large diameters will correspond to low veloci- ties and long times of contact; small diameters will correspond to high velocities and short times of contact. (d) This consideration would indicate a large diameter of producer to be desirable in every case, but there are two practical limitations which must be recognized: (i) The cost of the in- stallation will increase as the size of the apparatus required per horse power increases; and (2) there will be difficulty in operat- ing the producer under light loads, for when a producer which is of such diameter as to have a low gas velocity at full load is operated at a small fraction of that load, the small amount of air passing through may not be sufficient to keep the temperature 6oo HEAT-POWER ENGINEERING of the large bed of fuel up to that necessary for the formation of a high percentage of carbon monoxide. The diameter of any given producer must therefore be a com- promise between the large value desirable at full load and the smaller value which is desirable at light load and which involves less expenditure for equipment. (e) Practice has shown that certain proportions are advisable with certain types of producers and certain kinds of fuel. In general it may be said that producers are built of such diameters that the amount of fuel gasified when carrying rated load is from 10 or 12 pounds per square foot of cross section of fuel bed per hour in the simpler types, up to 30 to 40 pounds per square foot per hour in the more complicated types of producers oper- ating on particularly suitable fuels. The overload capacity is determined by the blast pressure available, by the clinkering temperature of the ash and the fusing or fluxing temperature of the producer lining. (f) In the purchase of fuel, porosity can hardly be considered except in a general way, it being merely incidental to other con- siderations. The size of lumps can, however, be taken into account both as to effect on the operation of the producer and on the price, the smaller sizes generally costing less than the larger. The smaller the size of the fuel, with a given depth of column, the greater the difference of pressure required to pass the necessary volume of gas through the producer; and with a given maximum blast pressure, the lower is the capacity of a producer, if the same depth of column is maintained. Given a certain difference of pressure it is of course possible, by de- creasing the length of path through that bed, to make any given quantity of air enter the bed per square foot of section in a given time; but this detrimentally shortens the time of contact or else necessitates an increase of diameter in order to reduce the velocity of flow to a satisfactory value. Furthermore, with very small sizes the necessary velocity in a producer of a given diameter may be so great that parts of the fuel will be picked up by the gas and be carried out of the producer. This occurs to a greater or less extent with every producer in actual operation. Finely divided ash or a certain amount of finely divided or powdered fuel is practically always carried out by the issuing gas. GAS PRODUCERS AND PRODUCER GAS 6oi The larger the size of fuel the greater are the voids, hence the passages through the fuel bed are of greater cross section and the allowable velocity and blast pressure are less, but smaller surfaces are exposed for reaction. (g) There are thus practical limits to the largest and smallest sizes of fuel which can be satisfactorily used in any given case. Sizes commonly used vary from about eight inches in diameter to pea anthracite. The larger sizes are generally mixed with smaller ones to decrease the passage areas in the fuel bed, while the smaller sizes very often have the finer particles screened out to increase the free areas. (h) Lastly, practically no producer can be operated with the theoretical air supply. In order to supply the amount of oxygen necessary to produce the required quantity of CO (and the CO2 which must necessarily accompany it), air in excess of the the- oretical requirement must be passed through the producer. In general the smaller the size of fuel and the lower the velocity, the smaller need this excess be, but it can never be entirely eliminated. As a result, producer gas practically always con- tains more or less free oxygen and consequently an excessive amount of nitrogen. The typical analyses of producer gases in Table XXV show this. . 286. Artificial Cooling of Producers (General), (a) In con- sidering the difference between cold gas and hot gas efhciencies, it was shown that a large amount of heat in excess of that re- quired to supply radiation and similar losses must be liberated within a producer by the very process to which the formation of producer gas is due. In actual producers using any of the ordinary fuels, the excess heat would quickly raise the temper- ature to a prohibitively high value. Clinker troubles would assume such magnitudes as to entirely prevent successful oper- ation and in many cases there would even be danger of fusing the refractory lining of the producer shell. (b) To prevent such difficulties producer operation is modi- fied in several different ways by introducing some heat absorb- ing process to lower the operating temperature. Part of the excess heat is absorbed naturally to a certain extent with all real fuels, for they contain hydrocarbons and water which are vaporized (and to a certain extent modified chemically) at the 6o2 HEAT-POWER ENGINEERING w tn yj w 1 OJ > >. >i >-> a 03 o3 a c C c 0) c aJ 03 03 03 ^ o O O w o rO ^ >1 M -(J -M +j 03 d 03 4-> ^3 ^ d j3 o o o o X! ^ XJ ^ 03 03 03 03 ., 1 "^ o o O O O u l-t u u u 0) 0) <0 > > > > * < < < < < rn X X ffi o ^ o t^ a. O • vO eg On NO - 3 u M (N CO O H c^ CM CO CM rt M CM "i^ CO CM CM CO Cq NO 00 to O O O O 00 O CO O O O c^ o a?8 00 O to ro CN ro C^ rO O O to o^ O r^ NO to CO M to w c3 X Ol 00 IJ^ t^ CO t^ 04 O CM On M OnOO to to 00 00 ^ H CO to to pq H t3 >- ci; rO a Ti o a; U o - (1) o o M oi r! t^ P^ 'd G 6 o .2 *4J p^ s * B o U GAS PRODUCERS AND PRODUCER GAS 603 temperatures attained; but it is only with exceptionally wet fuels, such as poorly dried peat, that enough heat is absorbed in this manner to make operation practical. The reduction of tem- perature due to the presence of CO2, nitrogen and moisture in the air (from the atmosphere) is also slight. Hence in actual operation it is necessary to have some artificial means of cooling. (c) Two methods of artificially controlling the temperature are in use. They may be called 1. The ''Carbon Monoxide'' Method, in which burned pro- ducer gas is returned to the producer in mixture with the air supply, and absorbs heat largely by the reduction of contained CO2 to CO] and 2. The Water Vapor Method, in which water vapor is mixed with the air supply and absorbs heat by reduction in contact with hot carbon. The details of these two methods are considered in the follow- ing sections. 287. The ** Carbon Monoxide " Method of Temperature Con- trol, (a) Burned producer gas may be roughly said to consist of carbon dioxide and water vapor, mixed with nitrogen. Re- turning such material to the producer will effect cooling in two distinct ways: (i) The carbon dioxide passing over heated car- bon will be more or less completely reduced to carbon monoxide; and (2) the water vapor in contact with hot carbon will be more or less completely broken up to form hydrogen, carbon monoxide and carbon dioxide. "^ (b) Under ordinary circumstances the first way will be the only one of appreciable magnitude because of the small amount of water vapor generally present when this method of cooling is used. The quantity of carbon^ dioxide which must be returned in order to maintain a given temperature in a theoretical case can be approximately determined if the amount of carbon dioxide and carbon monoxide which will be in equilibrium at that tem- perature and the amo^unt of heat which must be absorbed to maintain the desired temperature are known. Knowing the amount of heat (see Eq. 424) which is absorbed for each unit weight of carbon present in carbon dioxide when the latter is reduced to monoxide, it is possible to determine how much carbon dioxide will have to be reduced and how much carbon 6o4 HEAT-POWER ENGINEERING monoxide will result. It is then only necessary to find the amount of carbon dioxide which will be in equilibrium with this CO, to add this amount to that used in forming the monoxide, and the result is the total quantity of carbon dioxide which must be thus returned. (c) It is interesting to note that nearly all carbon returned in the form of carbon dioxide is used repeatedly, being reduced to carbon monoxide in the producer, burned to dioxide in the ap- paratus utilizing the gas, and returned to the producer again for reduction, and so on. Hence the carbon furnished by the fuel will be less than the total carbon in the issuing gas by just the amount which is thus used over and over again. It should, however, be noted, that there is a natural limit to the amount that can thus be used. The carbon dioxide can be reduced to, car- bon monoxide only with the absorption of heat and this heat can come only from fuel carbon burned in the producer. The method is then simply one which results in the entrapping in available form of some of the heat which would otherwise be wasted. The actual amount of carbon which can thus be used repeatedly in any given case is com- paratively small and the principal advantage of the process lies in the temperature control and uniform composition of gas (see (d) below) rather than in the saving of fuel. The operation of arti- ficially cooled producers is shown diagrammati- cally in Fig. 390 (b) in comparison with the uncooled method of operation- shown in Fig. 390 (a). The way in which more heat is made available at the expense of what would otherwise be lost is well shown by the width of the various streams. (d) The fact that the time of ignition in internal combustion engines should ordinarily be varied with the composition of the fuel was mentioned in Sect. 212 (h) . When gas is made in a pro- ducer controlled by the carbon monoxide method its composi- tion is remarkably uniform from light loads to full loads, hence Sensible Heat Heat Value of Issuing Gas power of-material -- «.turned Fig. 390. GAS PRODUCERS AND PRODUCER GAS 605 the time of ignition can remain fixed without danger of large variations in thermal efficiency. This must be considered an advantage possessed by this process in comparison with that considered below. 288. The Water Vapor Method of Temperature Control, (a) Experiment shows that when steam is passed over incandescent carbon a certain amount of hydrogen is released, that the oxygen previously combined with it unites with some of the carbon to form carbon monoxide and carbon dioxide,* and that some of the steam will still remain unchanged regardless of the tempera- ture attained and of the amount of carbon present. It is again a case of chemical equilibrium similar to that considered in Sect. 284 and the resultant composition will depend largely on the temperature. No matter what the temperature is, a certain amount of heat will be absorbed in the process of decomposing the water and this is always greater than that liberated by the combination of liberated oxygen with carbon to form either CO or CO2. Hence, the process, when used in a producer, must result in lowering the producer temperature, and by properly proportioning the amount of steam per pound of air the temperature can be directly con- trolled. (b) The gas made by this process will contain hydrogen, and a small amount of methane as well as carbon monoxide, as a com- bustible constituent ; and since all of the hydrogen and some of the carbon monoxide were formed in such a way as not to necessitate the introduction of nitrogen, there will be a smaller percentage of nitrogen in the resulting gas than when made by either of the processes previously described. The gas may, in fact, be considered as made by the theoretical process outlined in Sect. 282, with an admixture of hydrogen, carbon monoxide and a small amount of carbon dioxide, all resulting from the action of the steam. (c) As a result of the presence of the hydrogen and of carbon monoxide not accompanied by its proportion of nitrogen, the calorific value of gas made by this process is higher than that made by those previously described. (d) One of the disadvantages of this process is that the com- * A small amount of methane, CH4, is also found in all cases. 6o6 HEAT-POWER ENGINEERING position of the gas is very changeable, the hydrogen content increasing from a very small amount at light loads to very large ones at heavy loads. This necessitates a constant shifting of the time of ignition if a uniformly high thermal efficiency is to be obtained, — the ignition occurring earliest with minimum hydrogen content. Such constant shifting with rapidly varying load is, however, not practicably attainable, hence the engine is apt to operate at widely varying efficiencies, and, in extreme cases, may not even operate satisfactorily. (e) There are also many methods of applying this process which give poor results because of the method rather than the intrinsic nature of the process. Any method of controlling the steam supply which depends only on the instantaneous load on the engine must cause unsatisfactory operation in the following way: During a period of very light load the fuel bed has a ten- dency to cool down and if continued for any great length of time the temperature drop will be serious. Imagine full load to be demanded suddenly after such a period. The fuel bed tempera- ture is hardly high enough to make the necessary quantity of monoxide, and if the producer is fitted with a device which will immediately throw on full steam supply with demand for full load, the fuel bed will be still further cooled by the deluge of water vapor. Many failures of otherwise successful producers have been due to just such actions. , Forms of steam control which depend upon the temperature of the gas issuing from the producer, or the equivalent of this, seem to give better results. (f) The fact that water must be vaporized before it can be mixed with the entering air is often taken advantage of to con- serve some of the sensible heat in the gas leaving the producer. An apparatus variously known as a vaporizer, an economizer, or by several other names, is so arranged that these gases, while passing through or around it, heat and vaporize water contained within it. Somewhat similar devices also called economizers, or, more correctly, prehealers, are often arranged to preheat the air on its way to the producer so that it may pick up more water vapor and also return to the producer some of the heat that would otherwise be wasted. The upper part or cover of the producer shown in Fig. 5 forms a vaporizer, the vapor being picked up by the air supply as it GAS PRODUCERS AND PRODUCER GAS 607 passes over the surface of the water. A somewhat similar de- vice is shown in Fig. 393. Other forms, better known as econo- mizers, are shown in Figs. 391 and 392. 289. Effects of Hydrocarbons in Fuels, (a) The behavior of real fuels in producers and the composition of the resulting gases are much modified by the presence of volatile hydrocarbons. These are distilled off within a producer and are very much modified by the high temperature of the heated fuel and refrac- tory material before finally issuing with the gas. (b) The tendency of all such mixtures of hydrocarbons when heated is to undergo changes, yielding carbon, hydrogen and new hydrocarbons, some of which are more volatile than the originals and others less volatile. If heating is continued long enough and at a sufficiently high temperature the ultimate prod- ucts are practically hydrogen, methane and carbon (lampblack). The hydrogen and more volatile hydrocarbons, such as methane, form desirable constituents of the producer gas * and the carbon can be gasified if it remains in the producer, or it is compara- tively easily separated if it passes out with the issuing gas. The less volatile hydrocarbons, however, if allowed to issue with the gas, will subsequently condense, giving a thick, viscous, or semi- solid material known either as tar or pitch, depending upon its composition and consistency. Such material is apt to cause pipe stoppages, to clog the gas cleaning apparatus, the engine valves and such. (c) With anthracite fuels the amount of tar formed is com- paratively small and gives little trouble as it is easily separated from the gas. Bituminous fuels, on the other hand, yield large quantities of tar if used in producers of the simpler kinds. Such tar must be separated from the gas if the latter is to be transported any distance from the producer, or is to be used in internal combustion engines or in any apparatus requiring it to flow through small orifices. This elimination not only entails the use of more or less costly apparatus, which generally con- sumes power, but also results in lowered thermal efficiency, as * This statement is true as far as definite knowledge goes at present, but it seems probable that under certain conditions some of the products may prove undesirable because of chemical instability leading to spontaneous ignition at low compressions. 6o8 HEAT-POWER ENGINEERING the calorific value of the separated tar represents, in many cases, a considerable portion of that of the original fuel. (d) The most successful method of elimination so far produced depends upon the destruction of the tar within the producer. This is accomplished by passing the tar forming vapors (dis- tilled off the freshly charged fuel) through an incandescent fuel bed before leaving the producer. The process taking place is called cracking and results in the formation of hydrogen, methane, small quantities of other very volatile hydrocarbons and solid carbon. The solid carbon largely remains within the Gas to Dry ScrubbeTr — ^& Engine or direct to Engine Fig. 391. — Up Draft Suction Producer. producer bed and is subsequently gasified, while the hydrogen and other products of the cracked hydrocarbons pass off with the gas. (e) This process .can be carried on in an ordinary up draft producer operating much like that of Fig. 391, but modified so that, while the gas to be used is drawn off from the top of the main fuel column, the volatiles distilled off from the top of the freshly charged fuel in the extended hopper are piped around and introduced with the air entering at the bottom. This method has not met with great commercial success, although it is used to some extent in Europe for large installations. (f) Another and a very successful method is to reverse the direction of flow of gas through the producer, introducing air GAS PRODUCERS AND PRODUCER GAS 609 6io HEAT-POWER ENGINEERING and fuel at the top and removing gas at the bottom. This gives what is known as a down draft producer, one example of which is shown in Fig. 392. In this particular type, a bed of coke is ignited upon the brick arch which forms the grate, and the bitu- minous coal is fired upon this from above. (g) Few of the down draft producers so far constructed have permitted of continuous operation because of the difficulty of removing the ash and clinkers without shutting down the pro- ducer. They are, therefore, generally operated intermittently, say for a week, after which they are cleaned out and restarted. The type shown in Fig. 393, which is known as a water bottom Air Supply^ Fig. 393. — Down Draft Producer, Continuously Operated. (Akerlund Type.) ptoducer (see next section), overcomes this difficulty and per- mits of continuous operation. (h) To circumvent the difficulties met in attempting to gas- ify bituminous and similar fuels in up draft producers, the so-called double zone type of producer is also used. One exam- ple of this type is shown in Fig. 394. This producer may be regarded as a down draft producer superimposed upon one of the up draft kind. Air enters both top and bottom and gas is drawn off near the middle of height. The only draw- back is the necessity of carefully watching operations so that the upper incandescent zone may remain extensive enough to successfully crack the hydrocarbons and so that the combus- tion below the "gas offtake " may occur at just the proper rate to completely gasify all the coked material coming down from above. •^MO^'^ GAS PRODUCERS AND PRODUCER GAS 6ir 6l2 HEAT-POWER ENGINEERING "Vfater Sealed Charging Hopper is brought over different parts of bed by rotating top •Water Sealed Sight and J>oli:e Hole Water Seal for Tbj) Cooling ^ and Cleaning Apparatus Cooling apparatus may contain W-.T* Boiler to Generate for blower Mechanically or ' Manually revolved. Basket Grate Fig- 395- 290. Water Bottom and Grate Bottom Producers, (a) No matter what the type of producer, the column of fuel must be supported in some way. Producers are divided roughly into two types depending upon the way in which the fuel bed is supported. Producers arranged like those in Figs. 393 and 394, in which the bed of fuel is supported on a pile of its own ash, resting in a saucer shaped depression filled with water, are called water bottom pro- ducers. The shell of the pro- ducer must dip into the water by a sufficient amount to prevent the passage of air into the producer, or the escape of gas out of the pro- ducer, under the action of the greatest difference of pressure which will ever occur during - operation. Producers of this kind possess the great advantage of permit- ting the convenient withdrawal of ash at any time during opera- tion. They also dispense with almost all of the metal work found in other types at the bottom of the fuel column where the temperature is apt to become dangerously high if attendants are careless and where the rough work and sharp ash and clinker cause rapid depreciation. (b) Producers in which the column of fuel is not supported by ashes in a water sealed saucer may be roughly ^^shPocketf^ grouped under the head of grate bottom pjg ^96. producers. Examples are shown in Figs. 391, 392, 395 and 396. The grates may be of any degree of complexity from the simple grid of cast iron bars or of plain iron pipes, or the arch of fire brick shown in Fig. 392, to the most complicated of mechanical grates, such as the rotating and scrap- ing devices shown in Figs. 395 and 396, or a rocking grate much like that used under steam boilers, as shown in Fig. 391. (c) Mechanical grates, operated continuously by power in GAS PRODUCERS AND PRODUCER GAS 613 large sizes and intermittently by hand in small ones, are decidedly advantageous. They make possible the easy working down of ash and clinker, which in other cases would have to be barred down by poking from above, from the sides and through the bottom. When continuously in motion they tend to maintain uniform conditions within the producer, shaking the fuel column sufficiently to keep it open, to work down ash and to break up clinker. Combined with a depth of ash sufficient to seal against leak- age in or out, or with a water bottom, they afford ideal operating conditions. 291. Induced Draft and Forced Draft, (a) In developing the theory of the producer it was assumed that air could be made to enter and the resultant gas to leave. This flow can only be produced by maintaining a difference of pressure between inlet and outlet orifices. Two distinct methods are used for creating flow in this way. In one the pressure on the entering side is raised above that of the atmosphere; that is, air is pumped into the producer. Such producers, which are operated under what corresponds to forced draft in boiler practice, are called pressure producers. The pressure of air and gas within the producer is greater than the atmospheric pressure outside of the producer shell by the amount necessary to cause flow through the pro- ducer and all subsequent apparatus. One great disadvantage of such types is the fact that a leak anywhere in the apparatus results in the outflow of poisonous producer gas. Opening of poke holes for inspection of the fire or for stirring up the bed will result similarly. For such reasons pressure producers must always be operated in well ventilated structures, preferably with- out side walls where climatic conditions permit. Air, is generally pumped into such producers by a steam jet blower similar to that shown in Fig. 395. With proper propor- tions the amount of steam can be regulated so as to just equal that required for cooling the producer by decomposing in con- tact with the hot carbon. In general this steam must be under so high a pressure that a separate boiler is necessary for its gen- eration, but in large plants this is not a great disadvantage. In some types the steam is generated in a vertical water tube boiler which receives the hot gas coming from the producer. In this 6l4 HEAT-POWER ENGINEERING way part of the sensible heat in the gas is returned to the fuel column. Any other form of air pump can be used; a very common one is that shown at the right in Fig. 394. As shown it is used as an exhauster, but an exactly similar device can be used as a blower, the only difference being in its location and method of connection. (b) The other method of operation referred to above causes flow through the producer and subsequent apparatus by lower- ing the pressure at the outlet to a value below that of the sur- rounding atmosphere. Atmospheric pressure at the inlet is then sufficient to cause flow. Such producers, operated under condi- tions corresponding to induced draft in boiler practice, are known either as induced draft producers or as suction producers, depend- ing upon the apparatus used for reducing the pressure. When an exhauster like that in Fig. 394, or any similar appa- ratus, is used the producer is called an induced draft apparatus; when a gas engine operated by the producer draws its own charge through the system by lowering the pressure during each suction stroke as shown in Fig. 391, the apparatus is called a suction producer. (c) One great advantage of all induced or suction draft sys- tems is that any leak always results in the flow of air into the apparatus rather than escape of gas out of the apparatus. Such air may, in extreme cases, furnish oxygen sufficient to burn an appreciable quantity of the gas within the apparatus, as for in- stance in case the leak is immediately above the fuel bed in the producer where the gases still have a high enough temperature to ignite, and this would result in a diminished output of power gas, but could not ordinarily endanger human life. A leak at a point beyond the producer would result in the mixture of air and cold gas which could be entirely counterbalanced by the admission of less air to the apparatus in which the gas is subsequently burned. However, such mixtures of air and gas within the apparatus represent a possible source of trouble as they may sometimes acquire explosive proportions and there is always the possibility of ignition. The high pressures resulting from explosions would endanger the apparatus and possibly human life, but can easily be guarded against by providing some form of pressure relief such as a water seal or large flat door, or plate, with minimum GAS PRODUCERS AND PRODUCER GAS 615 inertia so as to permit of rapid opening with minimum pressure rise. (d) There are a few types of producer plants so constructed that they operate on what is known as a balanced draft. This is generally achieved by using the equivalents of one blower and one exhauster. The combined action of the two is such that the pressure within the producer itself is not greatly different from atmospheric, that on the outlet side being generally main- tained at a value equal to atmospheric. The dangers associated with leakage in or out are thus minimized. Jhz- 292. Mechanical Charging, (a) Most of the producers used in power plants are charged by hand, particularly in the smaller sizes. With small producers the shell is generally made of such depth that it will hold sufficient fuel for from three to six hours' operation without recharging. Such producers are commonly charged when starting in the morning, again at about midday and finally at night before shutting down. (b) With large producers it is gener- ally found best to charge at shorter intervals because more uniform results are thus obtained and because the fuel column is more easily handled when this is done. Where frequent charging is necessary a mechanical device such as is shown in Fig. 397 has many advantages, the most prominent of which are: — (i) Uniform rate of charging so that there are no sudden fluctuations in quality of gas as happens when large quantities of green fuel are charged at long intervals; (2) Uniform distribution of fuel over the entire diameter of producer, — a very difficult matter in hand charging of large producers unless much hand leveling is done, which generally permits the admission of considerable quantities of air or the discharge of large volumes of gas during the operation; and (3) Saving of labor and hence of operating expense. Lower End of Feeder forme a Spiral Fig. 397- 293. Cleaning Apparatus, (a) The gas leaving a producer has a comparatively high temperature and carries in suspension 6i6 HEAT-POWER ENGINEERING more or less solid matter and also vapors which, upon cooling, will condense to form water and tar. The function of the clean- ing apparatus is to cool the gases and to remove solids, water and tar. (b) ' In the broad sense every part of the apparatus beyond the producer outlet flange is cooling and cleaning apparatus, but commercially the term is applied to the several distinct units such as wet and dry scrubbers, tar extractors and such. (c) The methods employed for cooling are almost obvious from the figures of actual producers shown. A certain amount of sensible heat is removed from the gas by air or water, or both, in the economizer or its equivalent. Part of the sensible heat of the gas is lost by radiation from the pipes connecting the various parts. By far the largest amount is generally removed in wet scrubbers, by bubbling the gas through water, or by passing it through a space filled with a very fine spray of water, or over water films on coke or on similar solid material, or by a combina- tion of these methods. (d) The methods of removing solids (and in some cases liquids) depend upon three principles: (i) Separation by gravitation, (2) separation by change of direction, and (3) separation by wetting solid particles and retention of such wetted material. Settling of solid (and liquid) matter will result to a certain extent when the velocity of flow is sufficiently reduced. This reduction in flow may be brought about either by an enlarge- ment in the size of the passage or by decrease in volume due to lowering the temperature of the gas, or by both these processes. In fact more or less separation of the kind always occurs in the pipes because of natural cooling. Separation by change in direc- tion occurs whenever the gas passes through an elbow or similar fitting, the solids (and liquids) having a tendency to travel to the outside of the curve. Special apparatus for utilizing these first two principles is seldom fitted to producers, and particularly not to those used for power work, though the fact that such separation must always occur to a certain extent as the gas flows through the passages may be utilized in design to lighten the work required of the following apparatus. It should also be taken into account in designing the piping by arranging openings through which cleaning can be easily effected. GAS PRODUCERS AND PRODUCER GAS 617 By far the largest amount of solid material is removed by wet scrubbing which is also used for the cooling effect. The appa- ratus is so constructed that the solid particles are well wetted and are then allowed to separate out by gravity, or they are "scrubbed" out by bringing them in contact with wetted surfaces to which they adhere. Separation by gravity is well shown in the cases where gas is bubbled through water, the particles of dust on the surface of the "bubble " being wetted and caught by the liquid, after which they slowly settle to form a sort of mud. Separation by wet scrubbing is well illustrated by the opera- tion of coke or grid filled towers or "scrubbers " such as those shown in Figs. 391 and 392. Even the best wet scrubbers will allow a small amount of dust to pass through them. This material, together with me- chanically entrained water and some tar, is often finally sepa- rated in a "dry scrubber " filled with excelsior or sawdust, such as that shown in Fig. 392. After the tar- forming vapors have been condensed, the small particles or " droplets " of tar behave in much the same way as do the dust particles. The apparatus used for dust removal, and in particular the wet scrubber, removes large proportions of tar as well. (e) When the tar content of the gas is great, as when bitu- minous coals are used in a producer which does not provide for breaking up the hydrocarbons within the fuel bed, it is often necessary to use a separate ** tar remover." These are generally mechanically operated scrubbing devices in which the gas is well wetted by a spray of water and then brought into forcible contact with moving and stationary surfaces. The tar collects upon these surfaces and the liquid is driven off or drained off continuously. Such, separators often take forms resembling fan blowers, or series of propellers or impeller wheels, with adjacent units rotating in opposite directions. 294. Producer Gas from Oil. (a) Many attempts have been made to construct producer-gas plants which would successfully gasify crude oil and fuel oil, but most have resulted in failure. There are, however, a few plants, of several different types, in successful operation, which indicates that the problem of gasi- fying oil in a producer is not impossible of solution. 6l8 HEAT-POWER ENGINEERING (b) The difficulties met in attempts to gasify oil are similar to those experienced with the gasification of the volatiles in bitu- minous coals and similar fuels. Either tar, or lampblack, is generally produced in large quantity, and gives trouble in clean- ing, besides reducing the efficiency. (c) One of the solutions of this problem is notable for its sim- plicity. The producer is arranged for down draft and is built with a brick arch grate similar to that shown in Fig. 392. A bed of incandescent coke is maintained on this arch and the oil is sprayed into the upper part of the producer, the resulting gas passing downward through the coke bed. All tar- forming vapors are destroyed by cracking and the resultant lampblack is nearly all caught in the coke bed which is thus automatically replenished. CHAPTER XXXIV. UTILIZATION OF WASTE HEAT — FINANCIAL CONSIDERATIONS. 295. General, (a) It has been seen that in connection with steam power plants very large amounts of heat are wasted in the flue gas (loss c in Fig. 3) and in the exhaust steam (width E in Fig. 3). The profitable reduction of these losses is obviously of the greatest importance, and it is the object of this chapter to outline briefly the different methods of its accomplishment and some of the more important problems connected therewith. In most cases it will be seen that some of the waste heat is used in increasing the temperature (sensible heat) of the feed water, thus reducing the amount of fuel required to convert the feed water into steam. 296. Utilization of the Heat in the Flue Gases, (a) One very common method of saving some of the heat that would ordina- rily be wasted up the stack is to heat feed water by passing it through tubes which are surrounded by the flue gases after they have left the boiler. The heating apparatus in this case is commonly called an '^Economizer.'' Its use effects a saving of heat which in exceptional cases may amount to as much as 15 per cent of the total calorific value of the fuel. The apparatus, its method of operation, advantages and disadvantages, etc., will be discussed in detail later. (b) In certain instances, some of the heat of the flue gas can be used profitably for heating the air used in the furnace; and if the local conditions are favorable, the hot gases may be used in drying-kilns and such. But in all cases where the temperature of the flue gas is de- creased there is a detrimental effect on the draft (if natural), to offset which entails an additional expense for an increased height of stack, or for artificial draft apparatus and its opera- tion. 6ig 620 HEAT-POWER ENGINEERING 297. Utilization of the Heat in the Exhaust Steam, (a) It has been seen that lowering the pressure of the exhaust steam issuing from a prime mover results in an increase of the available percentage of the total heat furnished by the boiler and hence reduces the proportion wasted in the exhaust. This decrease of pressure is commonly effected by using a condenser, of which there are many types. But there is in each power plant a limit of vacuum beyond which it does not pay to go ; and even where the best vacuums are used, the exhaust steam still contains the larger part of the heat that is brought from the boiler, and this heat is nearly all surrendered to the condensing water. How- ever, some of this heat may be returned to the boiler with the feed water (this being saved) but the proportion is generally quite small if the vacuum is good. In Fig. 3 this return is shown by the lower stream line, for one particular arrangement of plant. Condensers and methods of supplying the feed water with heat from the exhaust steam will be discussed more in detail later. (b) When the steam is exhausted at atmospheric pressure, the feed water can be heated nearly to 212° by it and thus quite a considerable saving may be accomplished; but only a small percentage of the total exhaust steam of the entire plant can be profitably utilized in this manner. Frequently the main prime mover is operated condensing and the auxiliary apparatus non- condensing, the exhaust steam of the latter being used for feed- water heating. This results, in most instances, in more profit than arises from operating the auxiliaries condensing. The pieces of apparatus in which the feed water is heated by the exhaust steam are called feed-water heaters; they will be discussed in de- tail later. (c) When the local conditions are suitable, some of the heat of the exhaust steam can be used in industrial processes which require temperatures lower than that corresponding to the ex- haust pressure. Thus, for example, a steam prime mover might furnish power for an industry in which the heat of the exhaust steam could be utilized in dryers, or in kettles used for digesting various materials, and the condensate, with its sensible heat, might be returned as feed water to the boiler. In other indus- tries in which solutions, having temperatures of vaporization below 212°, are evaporated in ''evaporating pans " at atmospheric UTILIZATION OF WASTE HEAT 621 pressure, or in ''vacuum pans " under partial vacuums, the latent heat of the exhaust steam can be used to supply the heat neces- sary to evaporate the water from the solution; and in such cases not only may the vacuum pan act as a condenser for the power plant and thus reduce the back pressure on the prime mover, but the hot condensate may be returned as boiler feed. (d) Many plants are situated in localities where the artificial heating of buildings is necessary for a large portion of the year. For such heating, low-pressure steam, i.e., steam at or near atmospheric pressure, is satisfactory; hence, the exhaust steam from engines suitably located can often be used for heating pur- poses for many months in each year. As in the case of vacuum pans, the heating system can some- times act as a condenser for the power plant, but in such cases the vacuum carried (if any) is very imperfect, the pressure not being much below atmospheric. Such ''vacuum systems " are generally operated at a pressure of but i or 2 pounds below atmospheric, despite the fact that the lower the pressure of condensation, the greater is the latent heat surrendered by the steam. The reasons for not using greater vacuums are: (i) Lowering the temperature of the steam in the radiator neces- sitates a greater amount of radiating surface (which involves greater first cost), and (2) lowering the pressure makes it more difficult to keep the joints tight (that is, to prevent the inflow of air), for even if the heating system is of only moderate extent, there are hundreds of joints and it is difficult to insure perma- nent tightness in all of them. In other heating systems, called Pressure Systems, the steam is at a pressure somewhat above atmospheric, the back pressure on the engine being generally from 5 to 20 pounds gauge pres- sure. (e) Supposing that the condensate from the heating system is used for feed water (without loss of temperature) and that all the heat in the exhaust steam above feed-water temperature can be used for heating purposes, then, in the ideal case, the efficiency of the combined system is 100 per cent, for all of the heat which is given to the steam by the boiler and not converted into useful work is utilized in heating. In the actual case some of the heat is lost by cylinder radiation, by mechanical friction of engine and driving machinery, and by useless radiation in 622 HEAT-POWER ENGINEERING pipes between engine and heating system; but even then the efficiency of the combination is relatively high while it is in operation. In fact, the cylinder radiation and dissipation of heat due to friction and work may not be waste if the same amount of heat would otherwise have to be used for warming the engine room. Whether or not it would pay financially to utilize the exhaust steam for heating buildings depends on the location of the power plant, the length of the annual period of time during which the heating is necessary, the percentage of the total steam that can be used during such periods, the excess cost of equipment over that otherwise required and many other items which need not be considered in this brief discussion. 298. Heat Transmission. — In order to transfer the heat from the hot gases, or steam, to the feed water or other absorbing media, some kind of heat transmission must occur. Hence to properly understand the operation of condensers, economizers, feed-water heaters and similar apparatus, one must have a knowledge of the general theory of the transmission of heat. The subject will, therefore, be discussed (in the next chapter) before such apparatus is considered in detail. 299. Financial Considerations, (a) Suppose the installation of certain apparatus would effect a substantial saving in the weight of coal used; then from the standpoint of heat utilization there would be a gain. But suppose, further, that the expense chargeable against the installation and the operation of the apparatus itself would be more than the saving in the cost of coal; then, of course, the installation would not be profitable financially. Obviously the advisability of the adoption of additional equip- ment depends on whether it will effect, in the long run, a saving greater than all expenses in any way chargeable against it. (b) The capital invested in apparatus must be guarded against fall in value in order to protect the investor; but the apparatus is subject to decrease in value because of wear and possible acci- dents, and also because it may become obsolete by the introduc- tion of improvements. This decrease in value is called ''depre- ciation.'' Therefore, each year there must be set aside a certain FINANCIAL CONSIDERATIONS 623 sum (a) so that the amount thus accumulated plus the remaining market value of the apparatus will at least equal the investment. The more rapidly the apparatus deteriorates or becomes obso- lete the greater is the annual depreciation to be set aside. Furthermore, the capital must receive yearly interest (h) to be profitable ; and as the investment increases so also do the expenditures for taxes (c) , and insurance (d) ; and should addi- tional space be demanded by the apparatus, there may be in- creased annual rent (e) to pay. These items, and perhaps some others, constitute what are called the Fixed Charges against the apparatus. (c) Besides these items, the yearly cost of operating the appa- ratus must be considered, the principal items of such additional expense being some or all of the following: — (i) Labor or attendance; (2) fuel consumption; (3) water used; (4) oil, waste and other supplies; (5) repairs and maintenance, and possibly other items. If the saving in expenditure for fuel per year should be greater than the sum of items (a) to (e) and of (i) to (5) and of any others not included, the installation of the apparatus will be a source of profit, otherwise not. (d) It is not within the scope of this book to enter into the de- tailed discussion of the financial problems connected with power- plant engineering; but it is deemed necessary to show that the heat saving is not the final criterion. The foregoing very brief discussion is given for that purpose and to make clear to the reader what is meant when such phrases as ** aside from the financial considerations involved " are used in the chapters which follow, CHAPTER XXXV. HEAT TRANSFER. 300. General, (a) In previous chapters it has been assumed possible to transfer heat from body to body at will, limited only by the law that a body cannot gain heat from one at a lower temperature unless energy is expended to cause the transfer. It is now necessary to investigate more closely the phenomena connected with the ''flow " of heat under the ''driving force " of a temperature difference. (b) At the outset it must be clearly understood that from the engineer's viewpoint the whole subject of heat transfer is in a most undeveloped state. Many experiments have been made, numerous laws have been suggested, and much that is true has been recorded ; but there are still many points about the subject which are matters of dispute and the settlement of which is anxiously awaited. It will be shown later that this is not so much due to the lack of scientific knowledge as to the lack of means of applying known facts, and of inability to analyze the exact conditions under which the heat transfers occur. 301. Heat Conduction, (a) Assume the metallic bar shown in Fig. 399 to be so insulated along its entire length that no heat can be dissipated by it to the surrounding ' .- ^ atmosphere. Assume further that the ends are so arranged that heat can be continu- ously supplied to the bar at end A and the p. same amount continuously removed from end 5. Under these circumstances the heat supplied will all flow along the length of the bar, i.e., flow through the bar. Experience shows that under such conditions the tem- perature at B will always be lower than the temperature at A , that is, that there must be a temperature difference if heat is flowing. This is very similar to the phenomena met in the flow of electric currents in similar conductors. It is necessary that a difference 624 HEAT TRANSFER 625 of potential exist between two points, A and 5, if an electric current is to flow between them. In the one case then electricity- flows "because " of a difference of electrical potential or electro- motive force, in the other heat flows "because " of a difference of temperature, or, paralleling the above, a difference of "heat potential." (b) Since it is supposed that the molecules of a substance move faster when at a high temperature than when at a low one, the sensible heat associated with the substance may therefore be conceived as being measured by the intensity of molecular motion, and heat conduction may be considered as merely the imparting of such motion to successive groups of molecules along the path of heat flow. According to this view when one end of a solid body is heated the molecules begin to vibrate^ more and more rapidly but they impart some of their energy to those molecules immediately adjacent to them, and these in turn pass on some to their neighbors, and so on through the entire sub- stance. ' (c) The laws governing this sort of heat flow are compara- tively simple. To develop them assume the two parallel planes A and B, in the cond'ucting body shown in Fig. 400, to each have unit area, to be unit distance apart and to be maintained at temperatures Ta and Tb, the former being B^ one degree Fahrenheit greater than the Fig. 400. latter. Then there will be a flow of heat from A to B; and, assuming no loss from the walls of the inter- vening body, heat will have to be supplied at A and removed at B at exactly the same rate as it flows between these points, if these temperatures and the flow are to be maintained constant. (d) Experiment shows that under such conditions a very defi- nite amount of heat will flow from A to B per unit of time in any given material and this quantity is called the Specific Heat Conductivity. It will hereafter be designated by the Greek let- ter a* and, as used in most engineering calculations, it is the number of B.t.u. flowing per hour in the material between two parallel planes with area of each equal to one square foot, with * The letter X is very commonly used for this, but because it has already been employed in this book to represent another equally important quantity it is thought best to prevent confusion by adopting the above unusual symbol. 626 HEAT-POWER ENGINEERING one inch space between and with a difference of temperature of one Fahrenheit degree.^ (e) It is easy to see that if planes having areas of twice this amount, i.e., two square feet, are assumed, twice as much heat would flow between them in a given time. The heat flow, or conductivity, therefore varies directly as the cross section, in the same way that electrical conductivity does. Similarly, to cause heat in quantity a to flow between two planes of unit area, but at two units distance apart, will require twice the temperature difference that is needed when they are but one unit apart. This can easily be seen by imagining an intermediate plane at unit distance from each of the others. One degree of temperature difference will cause a heat units to flow from plane A to the intermediate one and plane B must be one degree lower than the intermediate to maintain the same rate of flow. In other words heat conductivity, like, electrical con- ductivity, varies inversely as the length of the conductor. ^^) ^^ A(2 = the heat flow between two parallel planes of equal area in a given material in one hour, d = the temperature difference in Fahrenheit de- grees, S = area of each of the two planes in square feet, and 8 = distance apart of the planes in the conductor, in inches, then, from the two statements in (e) above, A(2 = ^.^B.t.u.t (428) And, if Sa/8 be called the conductivity of the heat path, its reciprocal 8/Sa may be called the heat resistance, R, just as the reciprocal of electrical conductivity is called the electrical re- sistance. If this is done equation (428) may be written AQ = d ^ (8/Sa) = e/R, the last term of the expression resembling Ohm's Law, but giving the heat flowing in unit time in terms of temperature difference divided by heat resistance, instead of electrical flow in unit time in terms of voltage difference divided by electrical resistance. * This curious mixture of units is of convenience in engineering calculations, t For flow between inner and outer surfaces of a cyclindrical wall see Appendix. HEAT TRANSFER 627 This form of expression can be used to find heat flow with any complicated combination of resistances just as is done in elec- trical problems, and, in general, paths with resistances in parallel or in series might be considered. However, in practical cases resistances in series are generally the only ones of importance, and for such instances AQ = d-^(i:R) (429) (g) The specific heat-conductivity, a, varies, in general, with the kind of conductor in about the same way as does electrical conductivity; thus, good conductors of electricity are generally good conductors of heat, and vice versa. It also varies with purity of material, being different for instance for pure copper and copper containing small quantities of other metals, and with temperature much as does electrical conductivity. The con- ductivity at at any temperature above, or below, a chosen datum can be expressed in terms of the conductivity ao at datum tem- perature by the equation at = ao(l + I3t); and with 32° F. as datum this becomes at = asojl -\- ^(t- 2,2)1 .... (430) in which /? is a constant which has values varying with the mate- rial, being positive with some and negative with others. The values of as 2 and (3 are given in Table XXVI for some of the common heat conductors used by the engineer. Comparison of the specific conductivities tabulated will show that for metals they are several hundred times as great as for water, and that for this latter substance the conductivity is several times the value for gases. Stagnant gases are about the poorest conductors, and stagnant water is nearly as bad. 302. Heat Transfer by Convection, (a) When ^/^^*, representing the extreme angle with which the rays from surface 6* strike plane AB, approaches 180° as a limit, and that all energy radiated from S must be intercepted hy AB or pass through it. In such case the hot surface 5 is said to "see " nothing but the cold surfage and the radiant energy received from S hy the cold surface is given in Eq. (431). If, however, the surfaces are arranged as in Fig. 403, in which the cold surface is again represented by AB, it is evident that r^/^/////x//x///-ys^^^^^^^^^^ the solid angle ^ is considerably less than ' ^ 180 . All rays from o passing outside of this angle miss the cold surface entirely and are lost in the space beyond. The part of „. the total radiant energy intercepted by the cold surface would then be equal to that given by Eq. (431) multiplied by the. ratio of the solid angle dm^>Bm^>. . . dmn and each portion of the surface is less effective than those pre- ceding and more so than those following. The nearer the tem- perature of the gas approaches that of the water the less effective is the adjacent heating surface, although it costs as much per square foot as the more effective portions. Hence, as was seen in Sect. 261(c), there is in each case some particular extent of surface which will give the greatest financial return. Obviously as the curve of temperature change of the gases is not straight, the mean temperature difference for the surface as a whole is not one-half the sum of the initial and final differ- ences. Before the case can be analyzed mathematically it will be necessary to find the true value of the mean temperature difference. (c) Besides the foregoing case, the cold fluid may flow and the hot one may be at constant temperature, or both the cold and hot fluids may be flowing and the currents may be either in the same direction or in opposite directions. In each of these addi- tional cases the temperature difference varies over the surfaces, but the methods of variation are quite different from the case described in the preceding paragraph. All these cases will be considered in detail in later sections. (d) In all cases of heat transmission through plates from hot 638 HEAT-POWER ENGINEERING .fluids to cold ones it may be noted that, neglecting radiation losses, the heat surrendered by the hot fluid must equal that received by the cold one and must also equal that flowing through the intervening material ; hence aWn (Ta - n) = AQ = CcWc ih -to), . . (436) in which AQ = heat transmitted in a unit of time. Ch and Cc = the specific heats of the hot and cold fluids. Wh and Wc = weights of the fluids flowing per unit of time. ta and tb = temperatures of cold fluid at ends a and b (Fig. 406). Ta and T^ = temperatures of hot fluid at ends a and b (meas- ured on the same temperature scale as that used for ta and /&).* If the object is to have the cold fluid abstract a certain quantity of heat A (2 in a given time with initial temperature 4, it may be accomplished with large weight Wc of material leaving at low temperature 4, or by a small weight .leaving at high tempera- ture, and similarly in regard to the quantity of heat supplied by the hot fluid. Obviously the final temperature attained by either fluid may be controlled by regulating the weight of material flowing per unit of time. (e) Again, in all cases of heat transmission (neglecting radia- tion losses), the heat given up by one medium and received by the other must equal the conductivity of the path multiplied by the area of surface transmitting heat and by the temperature difference, as in Eq. (435). However, in case one or both fluids flow, the temperature difference is not constant but, as has just been seen, varies from point to point, hence a mean temperature difference dm must be used. For all conditions, then, AQ = KSdm, (437) in which AQ = heat transmitted (B.t.u. per hour) = heat lost by hotter medium = heat gained by cooler medium. * r is not here used to represent absolute temperature but merely that of the hotter medium measured on the same temperature scale as t. Its use avoids the employment of primes, additional subscripts, or other complications that would be necessary to distinguish between the temperatures of the hot and cold bodies if the same letter, such as t, were used for both. HEAT TRANSFER 639 K = conductivity of heat path (B.t.u. per sq. ft., per hr., per°F.). S = total surface (sq. ft.). 0m = mean temperature difference (° F.) = 6 when no flow occurs. (f) But before Eq. 437 can be used dm must first be deter- mined. As will be shown later it is given for all cases by the equation n a ^ ^ Ua — ^b / o\ " = ^^^^W)' ^««^ 6a = temperature difference at end a of the surface. Oh = temperature difference at end b of the surface. Therefore, no matter what the conditions of flow, ^ = ^^^-^^1^1^ (4*°^ 306. Cases of Heat Transmission through Plates, (a) There are five cases of heat transmission through plates, and Eqs. (436) to (440) apply to all of them. They will be described briefly in this section and in more detail later. (b) Case I. (T = const.) A hot substance at constant tem- perature T surrenders heat to a flowing cold substance, whose tem- perature t is increased. Surface condensers and feed water heaters are examples of this case, for in both of these heat of the exhaust steam (at constant temperature) ^^ is surrendered to water which is raised in temperature as it flows through the appa- ratus. This case is shown by the curves in Fig. 407, in which ordinates are temperatures and abscissas are extent of surface. The "^ ¥\g. aoi. upper curve is for the hot fluid and the lower for the cold one, the flow being toward the right. It will be seen that the final temperature of the cold body depends on the total length of surface, and that, as the flow progresses, the tempera- ture t of the cold medium gradually approaches that {T = const.) of the hot fluid, and the temperature difference and value of the surface (per square foot) becomes less. 640 HEAT-POWER ENGINEERING The efficiency of the heating surface is evidently Ef. = Heat transmitted -^ maximum amount absorbable CcWc {da - db) da - db CcWcOc (441) Fig. 408. (c) Case II. {t = const.) A substance at constant tempera- ture (t) receives heat from a hotter flowing substance whose tempera- ture (T) decreases. An example of this is the steam boiler, in which the boiling water (at constant temperature t) receives heat from the hot gases which decrease in temperature T as they progress. This case is the reverse of Case I, and Eq. (441) applies except that ChWh would be substituted for CcWc. Fig. 408 is the diagram for this case. (d) Case III. Parallel Flow. The term is understood by engineers to mean parallel flow in the same direction on opposite sides of the plate. The hot and cold substances both flow in the same direction, their temperatures converging nearer to equality as they progress, as shown in Fig. 409 in which the arrows show the direction of flow. With finite surface the heat transmitted is ChWh (Ta — Tb) = CcWc (tb — ta). If the object is to absorb heat, the maximum amount which the cold fluid could receive is CcWcda, and the Com- parative Efficiency (to be used in comparisons with other cases) is therefore CcWc (tb — ta) tb — ta CEfc CcWcdo (442) Fig. 409. But if the object is to cool the hot fluid the maximum amount of heat that could be surrendered is ChWhda and in that case the Comparative Efficiency is C^W, (Ta - Tb) _Ta-Tb CEfH = CnWnda d. (443) No matter how extensive the surface, Tx, in the figure, is the limit of temperature to which the hot fluid can be cooled and the cold one heated. The heat available for transmission is ChWhda (or CcWcOa) and with infinite surface only the part HEAT TRANSFER 641 ChWh (Ta — Tx)j or CcWc (Tx — to), could be transmitted. Hence the maximum possible efficiency is Eh = (Ta -Tx) -^da, (444) or Efc = (Tx -ta) -^da, (445) which is less than that attainable in any of the other cases. It would therefore appear that this arrangement should always be avoided ; however, if only a relatively small portion of the avail- able temperature head da is to be utilized, parallel flow may be advantageously used, as under these conditions it requires less heating surface (and hence the initial cost is less) to produce the same result than is required in some other arrangements. (e) Case IV. Counter flow. The hot and cold substances flow in opposite directions, the temperature of the former approaching the lowest temperature of the latter, and vice versa, as they proceed. This is shown in Fig. 410, in which the directions of flow are shown by the arrows, Ta being the initial tem- perature of the hot fluid and 4 being that of the cold one. The relation between the heat absorbing, or surrendering, capacities of the two fluids is given by the ratio of CcWc to ChWh and this determines whether the two curves diverge or converge or are parallel. With infl- Fig. 410.* nite surface it can be shown that the hot medium would be cooled to the initial temperature 4 of the cold one if ChWh < CcWc', or the cold medium will be raised to the initial temperature Ta of the hot fluid if CcWc < ChWh', and in this ideal case the efficiency is unity, since all the heat possible is trans- mitted with the materials in question. Hence the only limit to the efficiency is the extent of the heating surface. But a com- parison of Fig. 410 with Fig. 409 will show that the mean tem- perature head is less with counter current flow than with parallel flow, hence to accomplish the same degree of heating (or cooling) , and to obtain the same efficiency, more extensive surface (at greater cost) is required. Counter current apparatus is there- fore characterized by high possible efficiency and by economy of amount of heating or cooling material, as an ofl"set for the greater surface necessary. (f) Case V. (T and t both constant.) Transmission of heat from a hot fluid of constant temperature (T) to a cold one which * Fig. 410 is for CcWc > ChWh. If CcWc < ChWh then dt > da. 642 HEAT-POWER ENGINEERING remains at constant temperature (t). The vacuum pan is an ex- ample of this case, since the latent heat of the steam (at constant temperature) furnishes the heat for evaporating (at constant temperature) the other medium. (g) The mathematical treatment of these five cases will now Jbe discussed in the succeeding sections.* 307. Case I. (T = Const.) A Hot Substance at Constant Temperature Surrenders Heat to a Cold Fluid which Flows. (a) Assume the conditions shown in Fig. 411 and imagine that Wc pounds of the cooler material flow over the small surface 8S in a given time and that as a result their temperature is raised an amount 8t ( = 86). Then, if the specific heat of the cooler material be Cc, the heat 8Q absorbed from the area 8S per unit of time is dQ = CcWcdt = CcWc'dd; but this must equal the heat trans- mitted through 8S in the same time, hence 8Q= (T-t)K'8S = dK'8S, in which T and / are average tem- peratures (to same scale) over 8S and the other symbols have the same significance as in Sect. 305. Equating the two values of 8Q in the two preceding equations gives Fig. 411. CcWc' from which I Integration of this gives dK . 8S, K n ~ CcWcJa 8S. loge-r = KS which, rearranged and multiplied by {da — %) becomes * These sections may be omitted in a briefer study. (446) HEAT TRANSFER 643 Now from Fig. 411 it is seen that {da — 6b) = {k — to) hence but the last member of this equation is AQ, hence the equation above becomes cn a \ ^^ = ^^ii|TO) ^^^> which, in connection with Eq. (437), shows that ^»-log.(e./e,) ^448) as given in Eq. (438). (b) For certain purposes, however, it is more convenient to write the value of dm in another form. From Fig. 411 it is evi- dent that da = {T — ta) and 6b = (T — tb), substituting which in Eq. (448) and simplifying gives the more useful expression tb — ta " . T-ta ^""^'T^tb Transforming Eq. (446) gives (449) where n is the number whose Naperian logarithm is KS/CcWc, as given by the Log. Tables in the Appendix. Hence for any extent of area 5, the temperature difference at the end b, in terms of the known value at end a, is 6b = 6a-^n; . . . . . . . (451) and by taking different extents of area 5 and solving for the cor- responding values of 6b data may be obtained for plotting curves which show how the temperature difference varies as the flow progresses, for given values of K, Cc and Wc. (c) The efficiency of heat transmission (neglecting losses) for this case was given in Eq. (441). Substituting the value of 6b from Eq. (451) gives £/ = ^ = ^^S^ = i-^, . . . (452) "a "a '*' from which the values of the efficiencies corresponding to dif- ferent extents of area 5 can be readily computed in any given case, and the data thus obtained can be used for constructing a curve to show the variation graphically. rw 644 HEAT-POWER ENGINEERING 308. Case II. (t = Const.) A Substance at Constant Tem- perature (t) Receives Heat from Another Flowing Substance whose Temperature Decreases. This is the case shown in Figi 412 and is the reverse of Case I. The treatment is similar to the last case except that T, 8T and ChWh are substituted for t, U and CcWc. A(3 is given by Eq. (447) without change and dm by Eq. (448). Since in this case 6a— {Ta — t) and db = {Tb — t), substitution of these quantities in Eq. (448) gives Om — loge Ta-t (453) Fig. 412. Paralleling Eq. (450) da/db = e^KS/C'W'^^ =n, (454) where n is the number whose loge is (KS/ChWh). Using this value of n, Eqs. (451) and (452) can be applied to this case. 309. Case III. Parallel Flow in the Same Direction, (a) This case is shown by the curves in Fig. 413. As in the previous cases the heat lost by the one mate- i^^=^ rial in passing any area equals that ai transmitted through the wall and also equals that received by the j, second material (neglecting losses). Therefore, for an infinitesimal area, dS in the figure, 8Q = bTChWh = dtCcWc . (a) and for the entire area A(2 = ^TbaWH = MbCcWc, (b) where ATb and A 4 are the total charges in the temperatures of the hot and cold fluids. It is also evident from Fig. 413 that for surface 65 sT + St =^ (e - 6') = Se (c) and that AT, + 0, + Ak = 6. (d) HEAT TRANSFER 645 Equations (a) and {c) may now be used to derive two more which will be of value later. From {a) bTChWn - btCcWc = o, and multiplying Eq. (c) by CcWc gives STCcWc + StCcWc = deCcWc. Adding these last two equations and solving gives, for the small area 8S, q ^ which will be used later. By analogy it is also evident that for the total area S ^^^"-^"'^{awn + 'cM} ••••(/) Substituting now in Eq. {h) the value of A T^s just found gives AQ ^ {e. - e,) ^^^^ ^ ^^^^ (,) which will also be used later. (b) Returning now to fundamentals, it is evident, as in pre- vious cases, that 8Q = 8TChWh = Kd . bS. From which ^T/e = {K'bS)/{ChWK). Substituting for 57^ its value from Eq. {e) and rearranging gives 6 and integrating between the limits a and h yields ^""^'Wr^^ CWnCM. ^^^ Multiplying both sides by (9« — Bh) and rearranging gives But from Eq. {g) it is seen that the left-hand member is AQ, hence, as in the other cases. 646 HEAT-POWER ENGINEERING Comparison with Eq. (437) shows that "» - log. («.M) (456) as in the other cases. From Eq. Qi) iCcWc±ChWK\ = 6a^n, (458) where n is the number whose loge is KS I % -1^ ^ xtr ^ r V CcWcChWh J This last equation makes it possible to determine db when da and 5 are known. (c) From Fig. 413 it is apparent that ATb = (Ta — Tb). Substituting this in equation (/), putting db = 6a -^ w, and solv- ing gives / i\/ aWe \ . . ^'-^^'-'"V-nA aW. + Cw} ■ ■ ^459) And by analogy , i\ / aw, \ '^ = '^+H'-n)[ aw:+aw} ■ ■ (460) Then if db = o, which occurs when S = 00 , Tb becomes equal to tb and equal to the limiting temperature T^. Thus ■^' = ^'' ~ '^ Lw^+aw) ' ■ ■ ■ (461) T. = t. + 6.[^j^f^). . . . (461a) Since the maximum amount of heat that can be transmitted is (Ta — Tx) ChWh = {Tx — to) CcWc, the true efficiency is there- fore, in the ideal case, _ (Tg - Tb) ChWh _ (Tg - Tb) , . ^'^^'~ iTg-Tx)aW,~ (Ta-Tx)' ' ' ' ^402; T-Z?^ (^b — ta) CcWc tb — ta /.z:^\ As given in Eqs. (443) and (442) the comparative efficiency (for comparison with the other cases) is C£/* = ^^V^ (464) or CEf. = '±^ (465) depending on whether the object is to cool the hot fluid or to heat the cold one. HEAT TRANSFER 647 310. Case IV. Counter Flow, (a) This case is shown in Fig. 414, the directions in which the temperature curves are generated being shown by the arrows. Compared with the other cases it is a Uttle more difficult to develop usable equations for this ^ ^^^-^^^^^^i^^ sort of flow because, in general, only the initial temperatures Ta and th at ' opposite ends of the plate are known and both Ba and Qh are unknown. ^ (b) As in previous cases, however, hQ^hTCnWK = KB'hS . [a) = 8tCcWc .(b) Hence 1^ 8t/8T = ^5^ = Z, ic] CcWc the symbol Z being introduced as this ratio will be frequently used in the following development. From the figure it is seen that the change in temperature difference over any elementary area 8S is 80 = 01-02 = 8T - 8t* Substituting for dt in terms of 57" from Eq. (c) and solving gives 8T = 80/ (i - Z) (d) If this is substituted in Eq. (a) there results, after transforma- t^o^' 80 ^i-Z ChWh K'8S, which, being integrated between limits a and b, gives . . . (466) and rearranged. logeT^ = ^ T.. KS, CuWu which, after both sides are multiplied by {0a — CnWn KS{0a-t gives (467) "' I- Z loge {0a/ Bb) ' ' ' (c) From the figure it is further apparent that An + ^6 = ^ta + 0a; and from Eq. (c), by analogy \ta = Z^.Tb, {e) * The analysis given is for Z < i. If Z > i, then in Fig. 414 db > ^o and d2> di. For this case substitute (62 - di) for (^i - ^2), (5/ - 8T) for {5T - 5t), (Z - i) for (i - Z), db/da for Oa/db, and {db — da) for {da — db). 648 HEAT-POWER ENGINEERING substituting from which in the last equation and solving gives An= (^a-^6) - (I -Z). . ... . . (/) Now A(3 = iUkTbChWh and substituting the value of AT^ just ^Q = {ea-e,)^^• {g) found gives _ ^ _ ^^^^ (d) Returning now to Eq. (467) and comparing with Eq. (g), it is obvious that the left-hand member is equal to A (2, hence ^^ = loge {eje,) (4^'^ and a — a These expressions are evidently the same as in the other cases. However they are not of value until da and dt have been deter- mined, either by the methods which will now be given, or from actual experiment with existing apparatus. (e) From Eq. (466) it is evident that ea/dt = eC'^^^ =w, (470) in which n is the number whose Nap. log is ^ „r KS. Sub- ChWh stituting the value of dt from this equation in Eq. (J) gives * An = ^«(i-y-(i-z) (h) From Fig. 414 it can be seen that Ata = (Ta — k — 6a), substi- tuting which in Eq. (e) and solving gives An = (Ta - 4 - ea)/Z (i) Now subtracting Eq. (i) from Eq. (h) and solving gives \Z^ I -Zl by which the temperature difference at one end can be deter- mined in terms of known quantities. * For Z > I the footnote on p. 647 applies up to this point. Change (h) to be ATb = da {n — 1) -i- {Z — i) and in (471) substitute ( Z _^ ~^j]^^ ^^^ paren- thesis. HEAT TRANSFER 649 (f) With 6a known, the value of ^6 follows from Eq. (470) ; LQ and dm can be determined from Eqs. (468) and (469) ; and the final temperatures of cold and hot fluids are {Ta-da) (472) and ta n = {tb + di) (473) (g) It is important to note that the expressions in (f) can be used only to determine the conditions at the ends a and b or over Fig- 415- the entire length of area S. They cannot be used for interme- diate points, that is, for plotting the curves TaTb or tJb and the like. 311. Case V. (T = const. & t = const.) A Hot Substance Surrenders Heat at Constant Temperature to a Cold Substance whose Temperature is Constant, (a) This case is exemplified in vacuum pans in which steam at constant temperature (T) surrenders some of its latent heat to evaporate a solution at constant temperature (/). The type of apparatus which is known as a "single effect vacuum pan" is illustrated in Fig. 415 in one of its many forms and arrangements. (b) In such case dm = (T — t) and the heat transmitted through the heating surfaces is A(2 = KSdm from Eq. (437). 650 HEAT-POWER ENGINEERING Neglecting losses, the weight of steam condensed in unit time by an amount of heat equal to A Q is obviously W^ = AQ/r, (474) where r is the latent heat of steam at temperature T °F. ; and the weight of solution evaporated in unit time is W, = AQAK ~ (to - 32)\ (475) where Xc is the total heat (above 32°) per pound of the vapor formed at temperature t from the solution, and to is the tem- perature at which the solution enters the vacuum pan. (c) The vapor (at temperature ti) from the solution in one vacuum pan may be used, as in Fig. 416, to vaporize (at lower Condenses Fig. 416. temperature ^2) the solution in a second vacuum pan, the latter acting as condenser for the first element; the vapor from the second pan (at temperature ^2) may be similarly used to evapo- rate (at lower temperature ts) the solution in a third pan, and so on, the vapor from the last pan being carried to a condenser. When more than one pan is thus used the arrangement is termed "multiple efifect." Arrangements are called "double effect," "triple effect," "quadruple effect," and so on according to the number of pans in the series. In Fig. 416 the weak solution is admitted at / to the first pan from which it is fed at proper rate through valves Vi and V2 to the other ones. The strong solu- tion is withdrawn from the respective pans slI A, B and C. CHAPTER XXXVI. APPARATUS FOR HEATING FEED WATER. 312. Object of Heating Feed Water, (a) The principal advantages to be derived from heating the feed water suppHed a boiler are: (i) A decrease in the amount, of fuel required to generate the steam, hence an increase in the over-all efficiency of the plant; (2) less severe strains in the boiler metal, as there is less differ- ence of temperature between boiler shell and the fresh feed water ; (3) the partial deposition outside of the boiler of scale-forming impurities contained in the water; and (4) an increase in the steaming capacity of the boilers as less heat need be transmitted per pound of steam generated. (b) An idea of the saving of fuel derived from the use of hot boiler feed can be obtained by analyzing an average case. As- sume, for instance, that the water as received at the plant has an average temperature of 60° F. with g = 28.08 and that it is converted into steam at a pressure of 150 lbs. abs. (with X = 1 193.4), thus requiring the addition of 1 193.4 ~ 28.08 = 1164 B.t.u. (approx.) per pound. Assuming the specific heat of water as unity, every 11.64 (say 12) degrees by which the tem- perature of the water is raised before its introduction into the boiler means i per cent less heat to be added in the boiler, which would roughly correspond to a saving of i per cent of fuel. Expressed as a formula, the theoretical saving, due to using hot feed water at temperature //' instead of cold at temperature tfj in a boiler generating dry saturated steam is approximately: per cent saving = j^ _ X 100, . . . (476) in which ^^ q/ = sensible heat of the hot feed water above 32° F. = W - 32) approx., g/ = sensible heat of the cold feed water above 32° F. = {tf - 32) approx., X = total heat of steam above 32° F. at boiler pressure. 651 652 HEAT-POWER ENGINEERING If the steam is superheated in the boiler, the saving is 2/' - Qf per cent saving = CpD + X — 2/ X loo. . . (477) The savings in per cent resulting from different amounts of feed-water heating with different initial temperatures for the case of saturated steam are shown diagrammatically in Fig. 417. These are obtained by the method just given. (c) Inspection of these curves will show that if water at as low a temperature as 40° F. is raised to a temperature of 200° F., 160 -«150 fa" ^140 »120 •siio ~~ — 13^ S a.Wag. ~^ ^.J2l_ L_ ■ ~~M3(^ -— i^^ . \ H H 7^ ( ''or Stean I Pressur J at 175 L t)8. Gauge ) 40 60 80 100 120 110 160 180 200 Initial Temperature of Feed WaterC'F.) Fig. 417. i.e., through a range of i6o° F., the saving will be slightly over 13 per cent; and a change from 60° to 180° effects a saving of about 10 per cent of the fuel that would otherwise be needed. As the boilers do not have to transmit as much heat per pound of steam generated from preheated feed water as from cold water, smaller or fewer boilers may be used for a given output, when other considerations permit. 313. Feed- Water Heaters in General, (a) One method of heating the boiler feed water is by using for that purpose some of the latent heat in the exhaust steam from a steam-driven prime mover (as has already been explained in Section 297), the apparatus in which the transmission occurs being called a Feed- Water Heater, or an Exhaust Steam Feed -Water Heater. APPARATUS FOR HEATING FEED WATER 653 (b) If w pounds of steam are utilized for heating per pound of raw feed water which is at temperature //, then (t/ -If) =w[\- (//-32)]X£/, in which t/ = temperature finally attained by the feed water and condensed steam, X = total heat above 32° of I lb. of steam used for heating, and Ef = efficiency of heater. Then the temperature of the feed water, when w lbs. of steam are used per pound of feed, is , _ tf + w(\ + 32) Ef ^' i+wEf ' . . . • (478) and to attain a temperature of t/ the weight of steam required per pound of raw feed is "' [x-V-32)r ^^ (479) In the foregoing it has been assumed that the condensed steam is finally cooled in the heater to the temperature of the outgoing feed water. Any error which is thus introduced is corrected by the efficiency factor. (c) // the condensed steam is not returned to the boiler with the feed, this expression for w also gives the maximum propor- tion of the total steam generated which can be utilized for heat- ing an equivalent weight of feed water. For example, if feed water at 60° is heated to 212° F. by steam from an engine ex- hausting at atmospheric pressure, and if Ef = .90, the maximum possible weight of steam so utilized is found to be about 17 per cent, or about Jth of all that is available. It is, of course, de- sirable that the heat in the remaining portion (|) should be utilized in some other way as far as is possible. In plants in which the main units are operated condensing, the auxiliary engines, which generally use less than ^ of the total steam, are operated noncondensing and their exhaust steam is utilized for feed heating. This results in greater thermal effi- ciency of the plant as a whole than would exist if the auxiliaries were connected to the condenser, since all the heat of the steam not used for power is then theoretically returned to the boiler. vv^ 654 HEAT-POWER ENGINEERING (d) When the condensed steam (at t/) is returned to the boiler with the feed, the total weight of feed per pound of raw feed is (i + w), and the proportion of raw to total is 1/(1 + w), where w is the weight of steam condensed per pound of raw feed as givenbyEq. (479). Then the steam condensed per pound of total feed water is w' = w/{i -\- w) (480) which is the maximum proportion of the total steam generated that can be utilized for feed heating in such cases. (e) If the heater is located in the exhaust system between the prime mover and the condenser, it is called a (i) Vacuum Heater, and the maximum temperature which the feed water can theoreti- cally attain is that corresponding to the vacuum. When located in the exhaust system of a noncondensing unit, it is termed an (2) Atmospheric Heater y and the theoretical temperature attain- able with sufficient steam is 212°. Should the heater take steam from the auxiliary apparatus of the power plant it may be named an (3) Auxiliary Heater. If the condensate from the main units is not used as feed and there is not enough steam from the auxiliary apparatus to raise the temperature to the maximum otherwise attainable, the vacuum and auxiliary heaters are sometimes arranged in series — the water first passing through the former, which is then called a (4) Primary Heater, and finally through the latter, which becomes the (5) Secondary Heater. When the pressure of the steam used for heating is considerably above atmospheric, the apparatus is a (6) Pressure Heater. When the arrangement is such that the feed water and steam intermingle in the same chamber the heater is said to be of the (7) Open Type; and when the two substances are kept separate by heat-transmitting surfaces it is of" the (8) Closed Type. 314. Open Heaters, (a) Heaters of this type are generally in the form of rectangular boxes, or circular shells, fitted with coarse cascading or spraying devices to break up the water as it passes through and thus bring it into more intimate contact with the steam. They usually contain a filtering bed or settling chamber in which the solids carried in suspension or in solution are more or less completely removed after heating. When necessary, they are also fitted with oil separators in the steam APPARATUS FOR HEATING FEED WATER 655 inlet for removing the cylinder oil from the steam before it comes in contact with the water. This oil, if carried over to the boiler, would seriously reduce the transmission of heat in that apparatus 1 Water Outlet Fig. 418. — Open Heater. and might even cause overheating of the metal parts subjected to high temperatures. Two of the great variety of heaters of this type are shown in Figs. 418 and 419, the water level in the latter being automatically regulated by a float. Fig. 419. — Open Heater. (b) The main advantages of Open Atmospheric Heaters are: (i) the feed water can be heated nearly to 212° F. if sufficient steam is available, and surplus steam can be utilized for heating 656 HEAT-POWER ENGINEERING buildings and in industrial processes where conditions permit; (2) scale and oil do not affect the surrenderor the heat; and (3) the hot condensed steam is returned to the boiler with the raw feed, but should be purified of oil (if any is brought over from the engine cylinder by the steam). The open heater may be arranged, as in Fig. 419, to include in its structure (a) an oil separator, which is usually located in the exhaust pipe at entrance to heater, (b) a filter for removing sediment, part of which may be precipitate brought down by heating, and (c) a hot well, which may also receive the returns (condensate) from systems for heating buildings and such. As the feed water is hot and at pressure near atmospheric these heaters should be located above the feed pump and this latter Miscellaneous Losses H^at :;•.•■H^at'.•.■•:^_■■. Value of)- .Value-'of Useful Work Fig. 420. should be suitable for pumping hot water. If the raw water is not available under sufiicient head to flow into the heater, a second or cold-water pump must be added. (c) The proportion of the total steam generated that can be used for heating the feed water is obtainable from Eq. (479), being about ^th in ordinary cases, and the saving of fuel effected is given by Eq. (476) or (477), the maximum being about |th. Fig. 420 shows in full lines the energy stream for a power plant having all units exhausting to atmosphere but using as much waste heat as is possible in a feed -water heater; and in dotted lines it illustrates the same case when no heater is used. In the first case the over-all thermal efficiency is A /B and in the second A/B', the heat supplied to the prime mover being C in both cases. (d) If the main engines are condensing, and the steam from steam-driven auxiliary apparatus is used for feed heating, the APPARATUS FOR HEATING FEED WATER 657 Stream line is that illustrated in Fig. 421 by the heavy lines. A is the heat utilized, B is the heat value of the fuel used, C is the heat supplied to the main and auxiliary engines, and the ratio A/B is the over-all thermal efficiency. Miscellaneous Losses 1 Water Outlet ■Surface Blow-oflE Fig.''42I. But if the auxiliaries are power driven, the energy being fur- nished by the main units, then the case is shown in the same figure by the dotted lines; the useful output is A (as before), B^ is the heat value of the fuel used, and C[ is the heat furnished to the main units, its amount being less than C because the water rates of the larger units are lower than those for the small auxiliary engines. The over-all thermal efficiency in this case is A/B' which is less than when the auxiliaries are driven by steam and their exhaust is used for feed heating. 315. Closed Heaters, (a) Heaters of this type are so arranged that the steam does not come in contact with Expansioa Joint Steam Inlet Bottom Blow-ofE. the water. They are generally con- (ot.autiet)0 structed with straight or coiled tubes contained in a shell of some sort, with proper provision being made for in- equalities in expansion. The water generally passes through the tubes or coils and the steam fills the envelop- ing space, the condensation being drained off as it collects. The three most common of the many possible arrangements are shown in Figs. 422 to 424. Fig. 422. — Closed Heater. 658 HEAT-POWER ENGINEERING (b) Closed heaters are comparatively difficult to clean as a large part of the impurities in the water is deposited on the inside of the tubes and forms a coating similar to boiler scale. To counteract this effect, the water is often forced through the tubes at enormously high velocity, tending to keep them clean by "scouring." However the power required for pumping places a practical limit to the velocities used and the method is only partly successful. If the steam contains oil, and it is not removed before entering the heater, the tubes will become coated Outlet tor ^ Condensatioa Fig. 423. Coil Heater. Fig. 424. — Closed Heater. with this material, which is of low conductivity, and the rate of heat transmission will be greatly impaired. (c) These heaters are generally placed between the feed pump and the boiler, hence the former deals with cold water only and but one pump is required (not considering reserve ' pumps for emergencies) as against two with open heaters which do not receive the raw water under head. The feed water is free from oil, but the condensate is generally wasted. Figs. 420 and 421 apply equally well to this case except that the heater loss E includes the sensible heat of the condensate (measured above the temperature of the raw feed) unless there is more than enough steam to raise the feed temperature to the maximum possible value. The maximum temperature attainable is gen- APPARATUS FOR HEATING FEED WATER 659 Normally Closed S Exhaust Steam To Boiler Fig. 425. erally 2 degrees or more below the steam temperature, which latter depends on the pressure of the steam used. (d) In all such cases, the auxiliary apparatus, such as heaters, should be so piped that when out of commission the steam can be exhausted to atmosphere direct, and the feed water can be by-passed around the heater. The piping is therefore arranged somewhat as in Fig. 425, 5 and W being the steam and water by-pass valves which are nor- mally closed. (e) The saving effected by closed heaters can be found from Eqs. (476) and (477), the tem- perature attained by the feed water is given by Eq. (478), and the proportion of the total steam generated, that can be used for heating the raw feed, is given by Eq. (479). (f) The heat transmission falls under Case I of Sections (306) and (307). The mean temperature head is given by Eqs. (438) or (449) and the number of square feet of heating surface can be found from Eq. (440) when K is known. For feed-water heaters K varies widely with the kind of material, character of surface (scale, oil film, corrugations, etc.), with the velocity of flow of feed water and with other factors. It ranges ordinarily with copper, or brass, tubes from 175 with velocity of 12^ feet per minute and single pass, to 250 with velocity of 50 ft. per min. and multipass; with a velocity of 150 ft. per min. through coils it reaches 300 B.t.u. per square foot per hour per degree differ- ence in temperature, while under very favorable conditions much higher values are attainable. (g) Closed heaters with copper tubes are sometimes rated in terms of ^^ heater horse power,'' J square foot of surface being allowed per rated horse power. On this basis, if the steam pressure is atmospheric and UK = 192, the 30 lbs. (approx.) of feed water required per so-called boiler horse power will be heated from 60° to 194° (134° increase) by the \ square foot of surface — or i sq. ft. will heat about 90 lbs. of water (the amount required for 3 boiler h.p.) through this temperature range. 66o EEAT-POWER ENGINEERING 316. Economizers, (a) The function of the economizer is to abstract a portion of the heat from the flue gases, and to deliver it to the feed water on its way to the boiler, thereby somewhat reducing the large loss c in Fig. 3. The energy stream for this Economizer Loss F Beturned by /-V°' Economizer Miscellaneous Losses Heat / '. -Heat •'.-.• Valine of X-Yalueof -■ •.'-'. -rvReat Delivered/// ■■"" ■ * ■" ' iby.Boiler ■ 'MS^lM^^^MMEIEh^^'^ Energj F lei ;^;;I^^el;:-/;S. Boiler and Furnace Losses Fig. 426. case is shown by the full lines in Fig. 426, in which the case without the economizer is that with dotted lines, the boiler per- formance being assumed to remain unchanged. For the same boiler-output the fuel used is in the ratio oi B to B\ Ikixing Gear Safety Valve Remova'ble Lids Water O tlet Fig. 427. — Economizer. (b) One form of economizer is shown in Fig. 427. The appa- ratus usually consists of nests of staggered, vertical, cast-iron tubes fitted into top and bottom headers (with metal to metal APPARATUS FOR HEATING FEED WATER 66l To Stack Access Side Fig. 428. joints), each set of headers being connected together by longi- tudinal branch pipes having handholes which give access to the interior for washing out deposits. In the upper headers are located removable lids opposite the ends of the tubes in order to give access to the latter, and power-driven scrapers constantly move along the external surfaces of the tubes to remove the deposit of soot, the scrapings falling to a pit below, from which they are withdrawn from time to time. The water is preferably introduced at the end farthest from the boiler and discharged from the nearer end ; for its direction of flow is then counter to that of the flue gases, thus obtaining the counterflow of Case IV, discussed in Chapter XXXV. The setting is either of brick or of sheet steel lined with nonconducting material (magnesia or asbestos) ; the arrangement of flues is such (see Fig. 428) that the gases from the boilers can be by-passed direct to the stack when the economizer is out of commission, and the water can be delivered direct to the boiler. (c) In some instances the flue gases are cooled from ordinary stack temperature of 550° to 650° F. to as low as 240° F. and the water is heated to 270° or more; temperatures much higher than can be obtained with an atmospheric feed-water heater. But because the temperature of the stack gases is low and because of the additional resistance in the flues due to the presence of the economizer tubes, the natural draft must generally be assisted in some manner. Hence, in connection with the finan- cial problem involved, the cost of such draft apparatus and the annual expenses chargeable against it must be added to the charges against the economizer itself, including those for the space it occupies and the power required for driving the scrapers. As the economizer occupies a great deal of space it is frequently placed either above the boiler or outside of the building. (d) In addition to the four advantages accruing in all cases from heating feed water, as given in Section 312 (a), the econo- w» 662 HEAT-POWER ENGINEERING mizer has (5) a great reserve of hot water near the vaporizing point, ready to meet sudden demands. on the boiler; (6) its use may make it possible for the boiler itself to operate with higher efhciency, and (7) it is especially advantageous when the boilers are being forced, for then the flue gases are hottest and the stack waste is ordinarily the greatest. Owing to the higher tem- perature attained by the water, some scale-forming materials aresdeposited which are not precipitated in atmospheric feed heaters^ (e) If the counterflow principle is used in the economizer the equations of Section 310 apply. A simple approximation can be made however by assuming the two curves in Fig. 414 to be straight lines, then, at the middle of the curves, dm = (Ta - b.T^l2) - (4 + t^taU) =Ta-k-\{l^T^-\- Ma). (a) But CpGAn = wMa (b) where Cp = specific heat of gas (= 0.24), G = weight of gas per boiler h.p.-hr., w = pounds of water per boiler h.p.-hr. Solving (b) for ATb and substituting in (a) gives ■ dm= Ta-k- iAta (l + w/GCp), . . . (c) But the heat absorbed in the economizer by the water used per boiler horse power is Q = wAta, hence Eq. (437) becomes (per boiler h.p.) wAta = KSdm. ....... (d) Substituting the value of dm from (c) and solving gives the increase in the temperature of feed water as A/„ = ^F°_rJ'} ^ (approx.). ' . (481) H"^)' In practice S ranges from 2| to 5 square feet per boiler horse power. Corresponding to gas temperatures of 300° and 600° F. respectively K has values of about 2J and 3i B.t.u. per square foot per degree difference of temperature per hour. The weight of water (w) per boiler-horse-power hour is generally taken at APPARATUS FOR HEATING FEED WATER 663 about 30 lbs.; and the weight of gas (G) per boiler-h.p./br. as G = (I + ii.6x) Xi^, where x = excess coefficient, p = weight of combustible per boiler-h.p./hr. = 3 to 4 lbs. G is ordinarily from 80 to 120 lbs. per boiler h.p./hr. Then the final temperature of the feed water is tf = h + A4, •.'.... (482^ and the final temperature of the flue gas is n=Ta-An, (483) in which An = ^; (484) LrLp and if w = 30, G = 80, and Cp = 0.24 An = 1.56 A4. ..... (485) (f) The per cent saving effected by raising the feed temperature by the amount Ata may be obtained from Eqs. (476) and (477) by substituting Ata for the numerator. The actual saving of boiler and economizer taken together may be still more, since the boiler may have higher efficiency because of the better conditions of operation. v^ CHAPTER XXXVII. CONDENSERS AND RELATED APPARATUS. % 317. Advisability of Condensing. The principal advantages accruing from the use of condensers in connection with steam- driven prime movers are: (i) Improved thermal efficiency of the unit (except in the smaller sizes) ; (2) greater power from a given size of prime mover; and, when the condensate is used for feed water, there are the additional advantages of (3) the thermal gain from using hot feed water and (4) the freedom from deposits of scale in the boiler because the feed water is distilled. However, despite the apparent advantages, it is not always desirable to operate condensing, for financial and other reasons. The additional expense for the extra equipment, its installation, attention and upkeep, the expenditure for condensing water, for pumps and their operation, and the additional space required by the apparatus may in some cases wholly offset the advantages. It is generally not considered profitable to operate condensing with small engines, or with simple engines of the ordinary types (some special types, such as the unidirectional flow engine, operate to best advantage when condensing) ; nor should condensers ordinarily be used when a considerable part of the exhaust steam can be employed for heating or for industrial purposes. 318. Condensers in General, (a) The two main classes into which all types of condensers may be divided are: (i) Direct- contact Condensers and (2) Surface Condensers. In the former, the steam and condensing water mingle in the same chamber, while in the latter type they are kept separated by heat-trans- mitting surfaces. In each class there are many different arrange- ments possible and some of these will be considered in detail later. (b) Theoretically, the material handled by a condenser is low- pressure steam; actually it is a mixture of water, water vapor 664 CONDENSERS AND RELATED APPARATUS 66$ and air. Part of this air comes from the boiler, being carried into that vessel in solution in the feed water, and part of it leaks into the system through the stuffing boxes surrounding the piston and valve rods, through the joints of pipes and of such other parts of the equipment as are handling the material below atmos- pheric pressure. Also the water used for condensing carries air in solution when under atmospheric conditions, and in direct-con- tact condensers this air is released under diminished pressure and is added to that which enters in the various ways just outlined. ' (c) Then, according to Dalton's law, the total pressure within the condenser is the combination of the pressures of the air and vapor, i. e., it is the sum of their partial pressures. The import- ance of this fact is best appreciated from an example. Assume the temperature within a condenser to be 115° F. Then if the condenser contained only water and saturated steam at this temperature the pressure within the enclosure would be 2.99 inches of mercury, corresponding to a vacuum of 26.93 inches. If, however, every pound of steam has mixed with it one-quarter of a pound of air, which is not at all uncommon, the pressure due to this air can be found as follows: One pound of saturated steam at a pressure of 2.99'' Hg. occu- pies a volume of 231.9 cu. ft. This must also be the volume occupied by the 0.25 lbs. of air mixed with it, and the tempera- ture of this air is that of the steam (115°). Then from the law of ideal gases, the pressure of the air in the condenser is or p = 0.46 inches of mercury. Thus, the total pressure in the condenser will then be 2.99" -f 0.46'' = 3.45 in. Hg. and the vacuum will be 29.92 — 3.45 = 26.47 in. Hg. The back pressure on the prime mover is slightly higher than this, as a pressure drop must exist between that piece of apparatus and the condenser in order to cause the steam to flow through the exhaust pipe. With one pound of air per pound of steam, which is a possible condition, the pressure due to the air would be 1.84 inches of mercury, under the same circumstances, and the vacuum would only be 25.09 inches. The air is thus seen to have a very appreciable effect upon the ■■■■■■■■MHWII 666 HEAT-POWER ENGINEERING vacuum and every precaution should therefore be taken to prevent an excessive amount of it entering the apparatus. If allowed to accumulate it would gradually increase In pressure and destroy the vacuum. It must therefore be removed as rapidly as it collects. Before it can be discharged from the condenser, however, its pressure must be raised to that of the atmosphere (or slightly above) which is done by an air com- pressor or pump having terminal pressures sufficiently above atmospheric to effect a discharge. When this pump handles only the air it is called an ''Air Pump/' or ''Vacuum Pump.'' In some cases where the water is discharged from the condenser with considerable velocity, the arrangement is such that the air is ejected by the water, no separate air pump being needed. (d) Condensers in steam-power plants practically always use water as the condensing medium, but any liquid or gas that could be obtained cheaply, in sufficient quantities and at a low temperature, could be used; in fact air has been so utilized in a number of special instances. It is seldom that water is available under a head sufficient to cause it to flow into or through a condensing apparatus. It is therefore generally delivered to the condenser by a " Circulating Pump,'' which may be independently driven by steam, by electric motor or by belt, or may be operated by links driven by the prime mover. These pumps generally have comparatively low lifts and handle large volumes, hence the centrifugal type is commonly used, although there are many cases where the rotary or the reciprocating types have the advantage and are installed. In apparatus in which condensing water and steam mix and form a vacuum, the condensing water is often forced into the condenser by the atmospheric pressure acting on the surface of the water outside, no circulating pump being used. This is very common practice where the suction head is not oVer 15 feet, and it is used even with greater heads in some instances. (e) The removal of the water from the vacuum chamber of the condenser may be accomplished in several ways. If the hot well, which receives the condensate, can be located with water level at least 34 feet below the condenser, the water can be discharged by gravity through a "Tail Pipe," or " Barometric Tube," whose lower end is submerged in the hot well (the 34-foot column of water corresponding to a 30 inch column of Hg. CONDENSERS AND RELATED APPARATUS 667 on the barometer). In other cases it is necessary to have pumps which raise the water from condenser pressure to atmospheric. Such pumps are called "Tail Pumps,'' ''Hot-well pumps,'' etc., when they handle only water (and whatever air it happens to have entrapped). In many instances, however, the same pump plunger discharges both the water and the free air, in which case the one pump serves both as hot-well pump and as air pump, and is then called a " Wet Vacuum Pump " or *' Wet Air Pump." (f) Each prime mover may have its independent condenser or there may be a central condensing equipment for a number of units. In the former case the exhaust piping may be made short, direct and with few joints; in the latter, because of the greater length of pipe and larger number of joints, there is more opportunity for air infiltration and more resistance to flow, but larger and more economical auxiliaries may be used. In order to permit of operating noncondensing when the con- densing apparatus is out of commission, the exhaust pipe should contain a valve which can be opened to the atmosphere. This valve is usually arranged to open automatically when the con- denser ceases to operate. To permit of repairs while the engine is running there should be a shut-off valve in the exhaust pipe leading to the condenser; and should several condensers dis- charge to a common main there should also be shut-off valves between them and that pipe. 319. Contact Condensers, (a) There are several different kinds of contact condensers only a few of which will be described. That in Fig. 429 is known as the "Ordinary Jet Condenser." * In it the injection water entering at / and the steam entering at 5 mingle in the conical condenser head B and the resulting mixture of condensate, injection water and noncondensable gases is raised to atmospheric pressure and discharged by the wet air pump located below, the flow of injection water being regulated by handwheel H. At {a) in Fig. 429 is a diagram of the piping for such a condenser. It includes an atmospheric relief valve {A) which will automatically open to the atmosphere when the valve V is closed for making repairs to the condenser, or when the vacuum is "broken," as when the injection water fails. * The term "Jet Condenser" is also used as being synonymous with "direct contact condenser." 668 HEAT-POWER ENGINEERING If the suction lift for the injection water is not too great this water may be siphoned into the condenser by the vacuum after it has been estabUshed by priming and starting the pump. In such cases this Uft may be as much as 15 to 1 8 feet, provided the piping is short and not restricted. When the water is suppHed in this manner there is danger of flooding and wrecking the engine in case the pump ceases to operate before valve C is closed, or if it runs so slowly that it cannot discharge the water as fast as it collects. To prevent the possibility of such disaster various Fig. 429. — Jet Condenser. expedients are adopted, such as providing a float (F in Fig. 429) which, when the water level becomes dangerously high, will be raised and open a valve v to admit the atmosphere to the con- denser and thus "break" the vacuum and stop the flow of injection water. If a pump is used for the injection water the head against which it operates is the difference between the total head and that through which the water would be "drawn " by the vacuum. CONDENSERS AND RELATED APPARATUS 669 /ills' (b) The term ''Barometric Condenser " may be applied to any form of direct-contact condenser having the barometric tube. Fig. 430 shows one arrangement commonly called the ** Siphon " Typef^ The injection water entering the condenser head B from pipe / passes downward in a thin annular sheet around the hollow cone in the condenser head and unites with the steam which passes through the cone. The mixture is discharged through the neck or throat N with sufficient velocity to carry with it the noncondensable gases. A is an atmospheric relief valve and ^ is a handwheel for regulating the injection water. The water level L in the tail pipe depends on the vacuum maintained, but for safety the tail pipe is extended 34 feet above the water level in the hot well. If injection water is available at a head h (in the figure) of not over 18 feet, it may be "drawn in " by the vacuum after this has once been established by opening the lower valve shown dotted, or in some other manner, and in such case, the pump P can be dispensed with. At the foot of the exhaust pipe there should be either a drain, or an ''entrainer," the latter being so arranged that the exhaust steam impinges on the surface of the water which has collected in a pocket, and gradually picks it up in small particles and disposes of it by entrainment. Because of the great head room required by these condensers they are fre- quently located outside of the power house; and sometimes a Tail Pump is substituted for the tail pipe, as in Fig. 431. (c) Fig. 431 shows a direct-contact condenser somewhat simi- * All direct-contact condensers can be used to siphon the condensing water, but the term " Siphon Condenser " is generally applied only when there is the neck N shown in Fig. 430. Fig. 430. Siphon Condenser. PF 670 HEAT-POWER ENGINEERING lar to the one just discussed except that it uses a '^dry air pump " for removing the air. As the volume of air to be handled will increase with its temperature, and as the size of the dry air pump will increase with the volume of the air, the latter is usually cooled in some manner before it goes to the air pump. In the arrangement shown this is done by passing it through a spray of cold water, in the upper part of the condenser head, on its way to the discharge opening. Fig. 431. — Condenser with Dry Air Pump. (d) TheEjector Condenser, shown diagrammatically in Fig. 432, operates on the same principle as the steam ejector which is used for forcing water into boilers against the pressure of the steam. The injection water enters at / and passes through the neck of the combining tube B, where it rapidly condenses the exhaust steam which passes through small nozzles in the wall of this tube. Some of the heat surrendered by the condensed vapor is converted into kinetic energy of the steam jets flowing through these nozzles and the momentum acquired propels the water CONDENSERS AND RELATED APPARATUS 671 with high velocity through the neck. This velocity is reduced in the expanding tube below so that the pressure is raised to atmospheric when the end E is reached. To start the flow of injection water with the arrangement shown, boiler steam may be admitted through the starting valve C. This steam then issues through the check valve D and partly exhausts the atmosphere from the injection pipe, thus causing the water to rise and enter the condenser. The valve Starting Valve C [otiVVielh f Fig. 432. — Ejector Condenser. C may then be closed, the exhaust steam continuing the circu- lation of the water in the manner just described. The siphoning of injection water can also be started by admitting high pressure water through the starting valve C, in which case valve D can be omitted. The operation of the condenser ceases, of course, when the supply of exhaust steam is discontinued, hence this arrangement of condenser cannot be used for intermittent service, nor is it satisfactory if the load varies widely and frequently. With steady load the " suction lift " may be 16 feet; with variable loads it is limited to a smaller value. w^ 672 HEAT-POWER ENGINEERING The combining tube may be arranged with adjustable internal throttling device and external sleeve to permit the regulation of the water and steam openings to suit the load. Should the water contain foreign matter a strainer should be located in the injection pipe. If the condensing water is supplied under a head of 20 feet, or more, a slightly modified arrangement can be used and a more certain vacuum obtained even with wide variations in load. (e) With all types of contact condensers the weight of water required per pound of dry steam for any vacuum is ^^ X.-g X.--fa-3 2l* ^ ^ ^ (gm - qi) {tm - ti) where Xa; = total heat above 32° F. per pound of steam at ex- haust pressure, gi = heat of liquid of injection water, at temp. ti° F. q^rn = heat of liquid of mixture at temp. tm° F. {tm is from 5 to 15° less than the temperature of the exhaust steam.) The temperature of the water in the hot well is practically that of the mixture, and this water is available for boiler feed when the character of condensing water permits. The weight of water to be handled by the circulating pump per hour is w X weight of steam condensed in that time, and the weight delivered by the discharge pump is {w + i) X wt. of steam. (f) The principal advantages of direct-contact condensers are: (i) Their simplicity; (2) low first cost; (3) low cost of upkeep; and (4) small space required. They have, however, certain detrimental features which in some instances may partly or wholly counterbalance these advantages: {a) If the in- jection water is sea water, or has scale-forming impurities, or is otherwise unsuitable for boiler feed, none of the heat in the condenser discharge can be returned to the boiler; {h) the dis- tilled water resulting from the condensation of the steam is lost since it is mixed with the injection water, whereas with surface condensers it is available for boiler feed; {c) the temperature of the hot-well water used for boiler feed is lower than that from a surface condenser of proper design; {d) it is more difhcult to obtain a good vacuum than with surface condensers, because of * A correction of from 5 to 15 per cent must be made to allow for cooling the air and entrained moisture and for the inefficient heat absorption. CONDENSERS AND RELATED APPARATUS 673 the air introduced by the injection water; and (e) larger air pumps are therefore required. ^ 320. Surface Condensers, (a) A water-cooled surface con- denser is essentially an enlargement in the exhaust piping through which pass tubes which contain the flowing condensing water. If this water flows merely from one tube header to the other, the apparatus is called a "single pass" condenser, and "multipass condenser " is the general term applied when the water flows across the steam chamber two or more times. A double-pass condenser of the ordinary type is shown in Fig. 433, with cooling steam. Inlet Discharge |-|-- Fig. 433. — Double Flow Surface Condenser. water flowing from the lower part {A) of one head to the other head {B) and then back to the upper part (C) of the first one. The arrangement of piping for a surface condenser resembles that for the jet condenser in Fig. 429(a). In order to insure the flooding of all the condenser tubes at all times the condensing water is usually introduced at the bottom of the condenser and discharged at the top. (b) The surface condenser has certain advantages over the di- rect-contact type. The principal ones are as follows: If the con- densate is used as boiler feed, (i) substantially all of the available wr 674 HEAT-POWER ENGINEERING sensible heat of the exhaust steam is returned to the boiler; (2) the same water is used repeatedly, thus avoiding the ex- pense for new water (which is of importance only when suitable water is difficult to obtain or when its cost is high); (3) the feed water is distilled and free from scale-forming impurities; (4) less air is carried into the boiler by the feed water; and (5) sea water or any other water which is unsuitable for boiler feed can be used for cooling and yet the available sensible heat of the exhaust steam is returnable to the boiler; (6) better vacuums are generally obtainable with smaller air pumps and less power for same, because of (4) and because the air entrained in the condensing water is kept separated from the steam: and (7) there is no possibility of the circulating water flooding and wreck- ing the prime mover. The principal disadvantages are the relatively large (a) first cost, (b) space occupied, (c) upkeep expense (the latter being largely due to the corrosion and deterioration of condenser tubes and to the multitudinous joints which must be maintained free from leakage), and (d), in the case of steam engines, the presence of oil in the condensate. The latter item does not hold with turbines. The surface condenser requires at least two pumps (the wet air and the circulating water pumps) and may use a third (a separate dry air pump) when the best results are desired. In contrast, some direct-contact condensers have no pumps, and others only a wet or dry air pump. (c) The weight of condensing water required per pound of ex- haust (with quality unity) is evidently qd — qi {td — ti) where \x = total heat above 32° F. per lb. of exhaust steam. qc = heat of liquid of condensate leaving condenser at t°. tc = from 0° to 20° F. below the exhaust temperature 4- qi = heat of liquid of condensing water at inlet, at ti. qd = heat of liquid of condensing water at discharge, at td. td = from 5° to 10° F. below exhaust temperature tx. With from 25 to 26 inches of vacuum w is from 25 to 30 lbs. depending on the value of ti ; and with better vacuums w is from 45 to 55 lbs. and even more. (d) The heat transmission in Surface Condensers is according * See footnote on page 672. CONDENSERS AND RELATED APPARATUS 675 to Case I of Sections 306 and 367 and the amount of condensing surface required to condense Ws lbs. of exhaust steam per hour (quality unity) is from Eq. (437). 5 = A(3 -^ BmK = W,\K - {tc 32)} -^-0^, . (488) where the symbols in the bracket have the same meaning as in Eq. (487) ; and from Eq. (438) Bm = {ta ^-(logel^l) (489) The value of K depends on the surface coating on the tubes (scale and oil), on the velocity of the water, on the air present in the steam, on the material of the tubes (although, this is usually negligible) and on other items. It ordinarily ranges from 250 to 300 B.t.u. per square foot per degree F. per hour in the simpler types of condensers under ordinary conditions, but with the best designs, well drained, and with good air pumps, the rate of transmission may be from two to three times these values. For ordinary condensers with from 24 to 26 inches vacuum about 10 lbs. of steam are condensed per square foot of heating surface per hour. For small turbines with high vacuums from 2\ to 4 square feet of condensing surface are ordinarily used per kilowatt rating of the generator; and with large turbines from i to 2| sq. ft. are found with the best types of condensers. (e) The essentials which make Surface Condensers most effec- tive are: (i) All the tube surface should be available for heat transmission; none of it should be air-bound either on the steam or water side. (2) The falling condensate should not "drown " any tubes, for then {a) the surface is only about 10 per cent as effective, {h) the condensate is cooler, hence not so valuable as feed water, and (c) more condensing water is required. (3) The velocities of the steam and water should be high enough to break up the surface films. As the transmission is largely depend- ent on the heat-absorbing ability of the water, the more rapidly the latter is brought in contact with the tube surfaces, the greater the rate of transmission. (4) The air in Fig. 434. m^ 676 HEAT-POWER ENGINEERING the condensate should be cooled as much as possible to decrease the volume to be handled by the air pump and to reduce its par- tial pressure acting on the prime mover. (5) There should be suitably arranged baffles to so distribute the steam that all parts of the condensing surface are equally effective. (f) Fig. 434 shows one form of dry-tube condenser with ar- rangement for preventing the lower tubes of the condenser from Circulating d Water Fig. 435- being drowned and from serving as condensate coolers. This is accomplished by the baffles A, B, which are arranged to collect and draw off the condensate from the tubes immediately above as rapidly as it is formed. Baffle pans somewhat similarly arranged (with drains) are used in like manner in other con- densers of this type. (g) In some condensers the counter-current principle is used CONDENSERS AND RELATED APPARATUS 677 as regards the condensate. In such cases the exhaust steam enters the condenser at the bottom, hence the falhng condensate passes downward through this upflowing steam and becomes heated thereby, the feed water then being substantially at exhaust temperature. (h) As a cubic foot of air is heavier than a like volume of steam at the temperatures existing in condensers, and as it is coolest and most dense at the bottom of the shell, it tends to gravitate, hence the wet air pump placed below the condenser is correctly located for receiving the air as well as the con- densate. (i) Fig. 435 shows the piping of a condenser having separate dry air and hot-well pumps. The arrangement includes an air cooler through which the air passes on its way to the dry air pump, the condensed vapor from this cooler being passed through a water seal to the hot well where the condensate collects. t 321. Air Pumps, (a) As has already been seen a Dry Air Pump is an air compressor which receives the air (and its en- trained moisture) at condenser pressure and compresses it sufficiently to permit ~^lT Atm, of discharge to the atmosphere, the com- pressor card resembling Fig. 436 in the i^-7^ best instances. As the compression ratio i \ ^7~~" — ^ cona» is high, the clearance volume must be small, for no air can be received from the condenser until that in the clearance space is expanded to condenser pressure. To increase the volu- metric efficiency the three expedients most commonly used are : (i) The air may be compressed in two stages; (2) an equalizing passage (as a in Fig. 437) may be so arranged that at the end of the stroke the clearance air may at the proper time be moment- arily exhausted into the other end of the cylinder which is filled with air at condenser pressure, thus when the stroke begins the clearance space is under pressure nearly equal to the vacuum; and (3) the clearance space may be filled with water, as is the case in wet air pumps. Air pumps as well as the other pumps are usually steam driven, as the exhaust steam can ordinarily be advantageously used for feed-water heating. Fig. 436. W" 678 HEAT-POWER ENGINEERING (b) A Wet Air Pump of the ordinary horizontal reciprocating type is shown at the left in Fig. 433, 5 indicating the suction valves and d the discharge valves. One of the vertical types is illustrated in Fig. 438 with foot valves, bucket valves and dis- charge valves as shown. In the Edwards type, shown in Fig. 439, the foot and bucket valves are dispensed with, and whatever condensate collects in the base of the pump is displaced and forced into the pump cylinder by the conical end of the plunger as it approaches the bottom of its stroke. This water and the air above are then caught above the plunger when it ascends and are discharged in the usual manner. As in most pumps, there is a lip around the upper valve deck so that the valves will always To Eccentric Fig. 437. — Dry Air Pump with Equalizing Passage. be water sealed to prevent air leakage. Other single-acting vertical pumps and double-acting horizontal ones are somewhat similarly arranged to operate without foot and bucket valves. A wet air pump of the Rotary Type is shown in Fig. 440, it being so arranged that the water-sealed lobed wheels not only discharge the water but also carry along the air which is intro- duced at A below the wheels. (c) The Lehlanc type of dry air pump is shown in Fig. 441. Water in chamber A, ''drawn in " by the vacuum, is discharged at B and is projected downward by the vanes on the rotor R in a series of layers which, acting as pistons, entrap the air entering at C and force it through the neck N against the atmospheric pressure. To start the vacuum live steam may be temporarily admitted at S. CONDENSERS AND RELATED APPARATUS 679 (d) The volume of condensate (Vc) and that of condensing water ( Vw) used per minute can be readily estimated and the necessary size of pumps can then be determined if water alone is to be handled. If, however, air is to be pumped there is no exact method of arriving at the volume (Va) to be discharged per minute and the proportions of the pump are based on rough isc haige Fig. 438. —Wet Air Pump. Kaige Fig. 439. — Wet Air Pump, Edwards Type. Fig. 440. — Rotary Type of Air Pump. estim.ates. Surface water under atmospheric conditions may contain by volume from 2 to 5 per cent of air, and the leakages may increase the percentage of "atmospheric air" in the con- densers to from 7 to 10 per cent. Under partial pressure and higher temperature conditions the volume of this air is greatly increased and its value can be readily computed, and serves as a rough basis for determining the size of the pump. 68o HEAT-POWER ENGINEERING According to Gebhardt* single-acting wet vacuum pumps for jet condensers ordinarily have plunger displacements per minute of about 3 Vwj where Vw is the volume of the injection water pumped in that time, and double-acting pumps have displace- ment 3I Vw, the piston speeds being about 50 feet per minute. With reciprocating engines the wet air pump for a surface con- Air Fig. 441. — Leblanc Air Pump. denser ordinarily has a displacement of 10 Vc, where Vc is the volume of condensate, and for steam turbines it is about 20 Vc, these values being the average of two hundred plants. For dry air pumps the displacement of the plunger ranges from 20 to 30 Vc with vacuum below 27 inches, up to 50 Vc for 28 inches and over, these values being based on an investigation of fifty installations. * Gebhardt's " Steam Power Plant Engineering," published by John Wiley and Sons. CONDENSERS AND RELATED APPARATUS 68 1 322. Recovery of Condensing Water, (a) The amount of water required in a plant for condensing purposes is relatively very great, varying, as shown in Sec. 320(c), from about 25 to 55 pounds per pound of steam condensed. After being used this water is generally wasted, hence a continuous supply of fresh water is required in such cases. When a plant owns its own water supply or is situated near a large river, or other body of water, from which it can pump condensing watqr, the cost of the water is practically only that of pumping. Many plants are so situated, however, that the only source is the city mains and in such cases the continuous expenditure for condensing water may be far in excess of the saving effected by its use. Methods of cooling and storing condensing water have been developed, therefore, so that the same water can be used repeatedly and thus make it possible to obtain the benefit of condensing opera- tion in cases where the cost of a continuous supply of fresh water would be prohibitive. (b) For cooling the water, various evaporative cooling devices are in use. They all operate by exposing large surface of water (sometimes in thin sheets or in drops) to air currents, the cooling being effected both by the direct contact of the cooler air with the hot water and by the evaporation of part of the water. For this purpose (i) a pond having relatively large exposed surface may be used; or (2) the water may be sprayed into the air and allowed to fall into a pond; or, (3) it may be passed through a cooling tower, such as described in the following paragraphs. (c) Cooling towers are roughly divided into two classes: 1. Natural draft cooling towers, and 2. Fan towers or forced draft towers. In the natural draft type, a vertical, rectangular or cylindrical shell is filled with some material or structure (trays, slats, wire screens, etc.) adapted to spread the water into thin sheets or streams. The water is introduced at the top, gravitates over this filling to a reservoir in the base of the tower and is then returned to the condenser. Air enters at the bottom of the tower and passes upward through the filling so that cooling takes place on the counterflow principle. The upward motion of the air in the tower is due to the fact that its temperature and humidity are greater than JTT 682 HEAT-POWER ENGINEERING those of the outside air and it is therefore constantly displaced upward by fresh, cool air entering at the bottom. This effect (the "draft") is increased by lengthening the column of hot moist air by the addition of a "flue," or "stack," above the filhng. (d) A fan type of tower is essentially the same as one with natural draft so far as filling and cooling are concerned; the stack is omitted, however, and the draft is assisted by fans ^: M Fig. 442. which force air in at the bottom of the tower. Such a struc- ture, of which there are many arrangements, is shown in Fig. 442. This type of tower has the disadvantage of requiring an expenditure of power to operate the fans, but is independent of atmospheric conditions so far as draft is concerned. A combination of both types is occasionally used, the stack supplying draft when possible and being helped out by the fans when necessary. CONDENSERS AND RELATED APPARATUS 683 (e) Neglecting losses, the heat abstracted in a given time from the exhaust steam in condensing it equals the weight of the condensate (wx) times the latent heat (r^) of the exhaust steam at its partial pressure, and this, of course, is the amount of heat absorbed by the cooling water. Hence, if this water is used repeatedly, it must first be cooled by the surrender of this same amount of heat before its return to the condenser. This cooHng is accomplished principally by the evaporation of a portion of the water, the heat carried away in this manner being equal to the product of weight (w^,) vaporized in the given time, by the latent heat (r^,) at the partial pressure existing at the surface exposed to the atmosphere. Then, considering that the cooling is effected entirely by evaporation and neglecting losses, it follows that / \ / x / \ {wr)x = {wr)y\ (492) or, the weight of cooling water evaporated in a given time is approximately , . . Wv = w^r^lr^ (493) But, as Yx and r„ do not differ greatly, it is roughly true that Wv = Wx, — that is, under the conditions assumed, the weight of condensing water vaporized in the cooling device is about equal to the amount of condensate formed in the same interval of time in the condenser in which that water is used. Thus, if all the steam generated is condensed in a surface condenser and returned to the boiler, no new water (theoretically) is needed for boiler feed, but about an equal weight of make-up water must be constantly added to the supply of cooling water; and with surface condensers this water may, of course, be of quality unsuitable for use in the boilers. This is theoretically the maxi- mum amount that need be lost in the process of cooling. (f) If the air were so fully saturated that it could receive no more moisture, none of the water would vaporize and no cooling would be effected in the manner just described. In such case heat could still be abstracted from the water by bringing cooler air and its moisture in contact with it. The cooling media would then have their sensible heat raised by absorbing heat from the water, but it would take a great quantity of air to effect the cooling in this manner. (g) The actual case is intermediate between the two extremes just discussed. The atmospheric air is practically never fully iwr 684 HEAT-POWER ENGINEERING saturated but nearly always has some humidity. In the aver- age cooling tower from | to ^ of the heat is carried away by the increase in the sensible heat of the air and its vapor, and the rest by evaporation. The actual operation of the cooling de- vice is dependent on the humidity, temperature, amount and distribution of the air and on the temperature and extent of exposed surface of the water. Ordinarily, under unfavorable conditions, one cubic foot of air entering can be expected to remove at least 2 J B.t.u. as sensible heat of the air and latent heat of vaporized water ; from 2 to 4 per cent of the condensing water is all that need be lost by evaporation; and the condensing water can be readily cooled 40 to 50 Fahrenheit degrees. CHAPTER XXXVIII. . WATER PURIFICATION 323. Impurities in Natural Waters, (a) Waters available for power plant use are never the simple H2O of chemistry but always carry certain impurities in suspension and in solution. When taken from streams or lakes the water generally has large quantities of mud and silt in suspension at certain periods of the year; in some cases at all periods. Water taken from sources which receive large deposits of leaves, twigs and other vegetable and animal remains will always carry certain organic substances in solution and sometimes in suspension as well. Practically all waters found on, or below, the earth's surface contain inorganic salts and gases in solution and sometimes free acids as well. (b) All such impurities are liable to cause trouble in power plants, either (i) by clogging tubes and pipes, or (2) by corroding metal surfaces, or (3) by incrusting heat-transmitting surfaces, or (4) by causing foaming within boilers and similar apparatus. (c) When solid material in suspension is of large size it can often be separated by simple mechanical means, as by screening, by settling, or by filtering through beds of coke, broken rock, or sand. When fine it can be removed by first entangling it in a flocculent precipitate and then filtering, as is done with municipal supplies. In general, however, after such treatment average water will still contain in solution quite a quantity of material which will cause trouble if allowed to enter the apparatus of a power plant. The greatest difficulty is experienced in steam boilers and in the jackets of internal-combustion engines because of the deposition of such dissolved material upon the metal surfaces, thus forming a crust, or a scale, which materially decreases heat conductivity, clogs the passages, and may lead to the overheating of metal plates or surfaces. Acids in solution may cause corrosion of such surfaces. 68s 6S6 HEAT-POWER ENGINEERING (d) To prevent troubles of this character water is often "treated," "softened," or "purified," before use. The problem of water treatment is very large and by no means entirely solved as yet. In the following paragraphs the fundamental principles and the most common methods of treatment of boiler feed waters will be very briefly considered. 324. Troubles from Untreated Feed Water, (a) If untreated water is fed to a boiler the following troubles may ensue: (i) Corrosion may occur because of (a) Free acid, such as H2SO4 and HNO3, which will not only attack the metal of the boiler, but if present in larger quantities than 5 parts per 1,000,000 * will often corrode or pit the metal parts of the engine with which the steam comes in contact; and because of (b) Organic material, such as infusions of leaves, sewage and such, which acts as though acids were formed within the boiler. (2) Incrustation may occur because of (a) The deposition of suspended matter, such as mud, in parts of the boiler in which the circulation is not sufficiently rapid to maintain it in suspension; ih) The concentration of salts brought into the boiler with the feed water and left behind by the issuing steam; (c) The deposition of decomposed salts, such as the soluble bicarbonate of calcium, Ca{HC0z)2, which when heated loses one molecule of CO2 and one of H2O, leaving insoluble CaCOz; (d) The- deposition hy heating of salts which are less soluble in hot water than in cold, as calcium sulphate, CaSOi, the solubility of which at ordinary steam tempera- tures is only about one-fourth as great as at ordinary atmospheric temperatures; and (e) The deposition of soaps formed by the saponification of greases and organic oils by alkalies present in the feed water. * Parts per, 1000, 100,000 and 1,000,000 are the terms commonly used for expressing the results of water analyses. Since one U. S. gallon of water at 60 degrees F. weighs 58,335 grains, one part per 100,000 is equal to 0.584 grain per U. S. gallon. WATER PURIFICATION 687 (3) Foaming may be caused by (a) The decomposition or modification of salts to form floc- culent precipitates which collect as a scum on and near the surface of the water; and by (b) Organic matter, grease, soaps and such, which form similar scums. (b) By far the most troublesome salts commonly found in feed waters are those of calcium and magnesium. They are generally either the carbonates or the sulphates of these metals. The carbonates of calcium form a more or less granular scale which it is not very difficult to remove with the tools used for cleaning boilers. The sulphate of calcium forms a very hard, porcelain-like scale which is removed only with great difficulty. Magnesium carbonate generally gives rise to a scum, causing priming, and also forms a hydrate which serves to cement to- gether other scale-forming materials. The sulphate of this metal decomposes at high temperatures, liberating sulphuric acid which may cause corrosion and forming the hydrate which acts as a cement. 325. Methods of Treating Feed Waters, (a) A large quan- tity of the material carried in solution in boiler feed waters can often be precipitated by simply raising the temperature. This should be done in open type heaters using exhaust, or live steam, whichever is necessary to attain the necessary temperature. The impurities which are precipitated either remain fastened to the pans and other parts of the heater or are separated by filtering through a bed of coke, or other material, contained within the heater itself. (b) Where the use of live steam is not desirable or where the water contains salts that are not readily precipitated by simply raising the temperature, certain chemicals can be added to the water. These chemicals should be so chosen as to react with the majority, or with the most harmful, of the impurities to form insoluble precipitates, or to form less harmful, soluble com- pounds. By far the most common chemical in use for this purpose is soda ash (impure sodium carbonate) although various other inorganic and organic compounds are also utilized. Soda ash has the advantages of very low cost, small weight required, 688 HEAT-POWER ENGINEERING applicability to most waters and formation of compounds which are easily disposed of in the heaters and in the boilers. (c) In many cases, particularly where steam is not available, or where special conditions are to be met, cold methods are used. In such cases a solution of the proper chemical, or chemi- cals, is fed in measured quantities to the raw water, and any precipitates formed are settled or filtered out, after which the treated water passes to some sort of storage to await use. Apparatus of this type is generally made wholly or partly automatic. It is always of large size and therefore costly, and because of the low temperature many reactions which may be easily carried out in heaters are either entirely absent or are very incomplete. (d) Many " boiler compounds,'' some of secret composition, are in use. They are mixed with the feed water on its way to the boiler and are supposed to prevent or mitigate the formation of scale. It should be remembered that no solid material which enters the boiler can leave with the steam and hence it must all remain within the vessel unless removed by other means, such as blowing down, skimming, etc. This being the case, all that can be expected of a boiler com- pound is that it will react with the most troublesome impurities so as to change them to less troublesome ones which can be removed as sludge through the blow-off valve, rather than as a hard scale adhering to the metallic surfaces. In any event the amount of solid to be removed from the boiler will be greater when a compound is used than when the untreated water is vaporized, and it is merely a question of whether the greater amount of soft material permits of more economical and safer operation than does the smaller quantity of harder scale. It is therefore obvious that the impurities should, when possible, be removed from the water before it is introduced ' into the boiler. (e) There are some so-called " boiler compounds " on the market which are not supposed to react with the solids in the water but are intended to coat the water side of all heating sur- faces in such a way as to prevent the adherence of scale and scale-forming material. Besides the commercial compounds, kerosene and similar hydrocarbon oils have been more or less successfully used for this purpose. Oil so used should contain WATER PURIFICATION 689 no organic admixture as this may cause trouble by saponifying in the boiler and it should contain no heavy hydrocarbons which will form tar or pitch as these might cause overheating of plates to which they become attached. It has also been claimed that graphite acts in a way similar to kerosene in preventing the adherence of scale-forming material. wr CHAPTER XXXIX. POWER PLANTS. 326. General, (a) Only a very general discussion of the sub- ject of power plants as a whole can be attempted in this book and that must be given in the briefest manner possible. Plants having internal combustion engines and those having steam- operated prime movers will be the only types considered. (b) The choice between plants of these two types depends on many considerations, some of which are: (i) kind of fuel avail- able, (2) fuel economy, (3) first cost and other financial con- siderations, (4) reliability, (5) weight, (6) space occupied, (7) cost of water, (8) ability to secure properly trained attendants, (9) location, and (10) character of load. In general, where coal is very expensive, the producer plant will give better finan- cial returns than a steam plant unless the power requirements are such as to call for unusually large units (say, from looo to 4000 or 5000 horse power for the plant). 327. Internal Combustion Engine Plants. If the fuel is oil, or gas, the plant merely consists of the engine with means of I I supplying the fuel and for I transmitting the energy de- veloped, and with provision for jacket water. If solid fuel is used in a producer, the elements of the plant are those given in Fig. 443. ! Heater 328. Steam Power Plants, (a) The location of the plant is selected with respect to (i) railroad and dock facilities for receiv- ing coal and disposing of ashes, (2) supply of water suitable for feed and condensing purposes, (3) convenience for distribu- 690 Product (Electric Energy) Elements of a Producer Gas Power Plant. POWER PLANTS 691 tion of its products (electrical energy, exhaust steam for heating, belt delivered power, etc.), (4) cost of real estate, (5) suitability of ground for foundations, (6) space for storage of fuel, (7) char- acter of the surrounding neighborhood, and (8) allowance for increase in size of plant. (b) The building is generally divided by a fireproof and dust- Fuel from >^J^ f^ ct> fy i,"?}:^ Energy Supply Outside Source ^ ♦Transportation Fuel Storage Feed Pump Feed Water Purification Closed Heater Hot\ Well' Est. Auxiliary Engines Open Circulating Pump Cooling Tower Surface , , Condenser Outside Water Supply Coal and Ash Handling Forced Draft Fan Furnaces and Boilers Steam Header Engines Y Product (Electric Energy) Fig. 444. — Elements of a Steam Power Plant. proof wall into the boiler room and the engine (or turbine) room, and is provided with proper lighting and ventilating facilities and with doorways of sufficient size to admit the largest pieces of the equipment. In large plants the railroad track usually enters the building, the doors being large enough to admit box cars. The architecture of the building should be in harmony 692 HEAT-POWER ENGINEERING with its surroundings and the design should, in general, permit of enlargement of plant to meet increases in the demand for power. The scheme of the steam power plant equipment is illustrated in Fig. 444. This diagram is very general and includes pieces of equipment which are used only in special cases; it also shows apparatus which would not, in gen- eral, be used at the same time in ordinary cases. Several arrangements of steam power plants are shown in Figs. 445 to 449. (c) In the boiler room, besides the boilers, are lo- cated the feed pumps, fans, feed heaters (generally), economizers, etc. Car tracks are arranged to deliver the coal at such point as to reduce the manual labor to the minimum. Large plants usu- Fig. 445. — Small Engine Plant. Fig. 446.— Small Turbine Plant. ally have overhead bunkers, to which the coal is brought by cars or by mechanical conveyors of the bucket, belt, or other type, and from which chutes lead to the hoppers of the stokers, or, in case of hand firing, to the floor in front of the boiler ; and ash hoppers POWER PLANTS 693 are generally placed under the grates with dumps discharging to conveyors or cars below. In some instances- boilers are located on two or more floors (as in "double deck" plants) as in Fig. 447. — Large Turbine Plant. Fig. 448, or are fired from both ends (Figs. 367 and 449), to re- duce the ground area occupied. These special arrangements are more often adopted in turbine plants than in those having engines, w 694 HEAT-POWER ENGINEERING because the turbine room is generally much smaller than the boiler room, whereas an engine room is ordinarily of about the same size, (d) The larger engine rooms are usually provided with over- head traveling cranes of capacity at least sufficient to lift the heaviest piece of machinery. Surface and jet condensers and their pumps are usually located below the engine, in the base- Fig. 448. — Power Plant with Double Deck Boiler Room. ment; and barometric and siphon condensers are often placed outside the building. (e) In electric plants as much of the steam piping as is feasible is located in the boiler room to prevent liability of damage to the electrical apparatus by the steam in case of pipe failure. Where plant shutdowns are of serious consequence, the ideal arrangement of piping would permit (i) of running any prime mover from any boiler, (2) of any boiler, or engine unit, being isolated without affecting the rest, and (3) of making repairs to any portion of the piping without affecting any unit (or not more than one). This ideal case is approximated most closely POWER PLANTS 695 by the "loop or ring'' system of piping, a in Fig. 450, and by the ''double-header'' system, as b in Fig. 450. These systems call for an amount of piping and a number of joints and valves that is prohibitive in most cases. Ordinarily the connections from the boilers are merely led to a ''single header" from which other pipes lead to the prime movers, as c in Fig. 450. In large plants it is common practice to arrange each prime mover and Fig. 449. — Power Plant with Boilers Fired from Both Ends, and with Com- pound Steam Engines Exhausting to Low Pressure Turbines. the boilers which serve it, as an independent unit; but fre- quently cross-connections are provided between units for use in emergencies. There is almost an unlimited number of arrange- ments of piping possible, but they are generally modifications or combinations of those just given. The piping for the auxiliary apparatus is independent of the main system to permit that apparatus to be operated even though the other is not in use. 696 HEAT-POWER ENGINEERING The steam pipes from the boiler have hand-operated shut-off valves, and in some cases also include emergency valves which will close if abnormal outflow of steam occurs, as when a steam pipe is ruptured, and act as check valves preventing the inrush B B B ^ VtV, r \f W tfF B B B II 1 E • E E E E E ^ f^ ^ E E E (a) (&) Fig. 450. — Steam Piping Arrangements. (<'') of steam from other boilers if a tube fails. The engine feeders also have shut-off valves near the cylinders and sometimes there are also valves which will automatically close if the engine starts to run away. All steam piping should be lagged with non- -J By-pass Economizer Fire Pump Water Supply N0..3 , 5 Hot Well Water „(_ Water Supply No. 1 \ or Raw Feed Fig. 451- conducting covering; it must be properly supported; provision for expansion must be made by the introduction of slip or swivel joints, corrugated sections or flexible curved portions; and it must be so arranged as to be without undrained portions from which the collected water can be carried over in large quan- tities to the prime mover with disastrous results. The piping POWER PLANTS 697 should be properly drained by suitably arranged collecting pockets connected with "traps" or equivalent devices and at the engines there should be "steam separators." The traps (by float or other device) automatically discharge the accumulation of water from time to time. (f ) The boiler feed-water piping is preferably so arranged that any of several pumps (or injectors) can be used for supplying the feed water, and also so that there are several sources from which this water can be obtained. One of the numerous possible arrangements of piping is diagrammed in Fig. 451. (g) Each piece of auxiliary apparatus is preferably so arranged that it can serve any one of the sets of main units, and so that it can be isolated if out of commission and the materials which it ordinarily handles may be by-passed around and led direct to their final destinations. CHAPTER XL. CONTINUOUS FLOW OF GASES AND VAPORS THROUGH ORIFICES AND NOZZLES. 329. Introductory, (a) The thermodynamic transformations previously discussed in this book were assumed to occur in such manner that the change of kinetic energy (velocity energy) associated with the flow of the working substance from one part of the system to another was zero. In the usual cases of flow of gases or vapors through pipes and in cylinders this same assumption may be made without introducing serious error, because of the relatively low velocities prevailing. When, however, gases or vapors flow through nozzles or ori- fices both the changes in velocity and the corresponding changes in the kinetic energy of the working substance may be very large. In such instances much of the potential energy associated with the substance may be converted into the kinetic energy associated with the change of motion, or the reverse process may occur. (b) Let Fig. 452 represent a conduit through which the ma- terial flows in the direction of the arrow; and let Po and K be respectively the simultaneous poten- tial and kinetic energies associated with a pound of the working substance at any instant. Then Poi + Ki is the total associated energy per pound when the stream passes section i in Fig. 452 and P02 + K2. is its value when passing section 2. If the conduit is of such character that energy neither passes through, nor is stored by, its walls, it follows from the Law of Conservation of Energy, and from the First Law of Thermodynamics, that Poi + Xi = P02 + X2, (494) from which AK = K2 - Ki = Poi - P02 . . . . (495) where i^K is the Change in Kinetic Energy per pound of mate- rial. This equation shows that the changes in kinetic and 698 CONTINUOUS FLOW OF GASES THROUGH ORIFICES 699 potential energies between sections i and 2 are equal in amounts but opposite in direction. (c) For the purposes of analytical development it is desirable to examine more in detail the character of the potential energy which must be considered in connection with the flow of gases and vapors. One form of potential energy is that due to posi- tion, as exemplified by the familiar ''head" in hydraulics. In most engineering problems dealing with the thermodynamics of flow of the materials under consideration the magnitude of this form is so small that it may be neglected without serious error. A second form is that due to a substance's stored heat energy which was expended in raising the sensible heat of the material, or in doing internal work, or in both; and it is obviously composed of the A 5 and A J which have been used before. The only other form of potential energy is that stored in the enveloping media due to external work done upon them by the substance sur- rounded. Although stored in the surrounding media, it is con- venient to consider this potential energy as associated with the substance that did the work, because in all cases this energy would be returned if that substance were brought back to the original conditions. Evidently this stored external work cor- responds to the A£ used in previous discussions, but for subse- quent purposes it will be convenient to obtain a slightly different viewpoint regarding it. (d) For this purpose suppose the plug a (in Fig. 453), weighing one pound, and having a (specific) volume V, is injected its full length into a closed vessel h which is so large that the medium it contains may be assumed to remain at constant pressure P pounds per square foot during the process. Then, the external work done by the plug upon the medium is PV foot-pounds, or PV/778 B.t.u. This energy is stored in the surrounding medium, but as it will be returned when the plug is withdrawn, it may be considered to be associated with the plug. Obviously all ^^' ^^^' material, which is surrounded by media upon which it has done work which is stored as potential energy of this form, may be considered as having associated with it this returnable energy. 700 HEAT-POWER ENGINEERING (e) Now, summing up, the total potential energy which may be considered as associated with a pound of the material is Po = A5 + A J + PV/778 .... (496) measured above certain datum conditions which will be consid- ered later. This value of the potential energy may now be substituted in Eq. (494) giving, for the conditions of flow shown in Fig. 452, (A5i+A/i+PiVi/778)+i^i= (A52+A/2+P2V2/778)+i^2, (497) and Eq. (495) then becomes AK = (K2 - Ki) = (A5i + All + PiVi/778) - (A52 + A72 + P2V2/778) . (498) The change in kinetic energy AK, and hence the change in velocity, between sections i and 2 can thus be computed when the intrinsic energies {AS + A I) and the PV conditions of the material as it passes these sections are known. (f) li w pounds of substance are flowing per second with a velocity of v feet per second, the kinetic energy of the flowing material is wK = wv^ -^ (2 g X 778), or the kinetic energy per pound is 2 K= ^B.t.u (499) 2 g X 778 ^^^ If the velocity is increased from Vi to V2, the change in kinetic energy is, per pound of substance, Air=(ii:2-ifO=(f^-|^)/778B.t.u. . (500) But since {K2 — Ki) = (Poi — P02) this equation may be re- written / 2 „,2\ AX = P.i-P.2=(|^-y/778B.t.u., . (501) which may be used for determining the velocity changes when the changes in potential energy are known. 330. Flow of Saturated Steam in the Ideal Case, (a) Fol- lowing the general equation (498) , the kinetic energy change during flow, in terms of the change in potential energy, is AX=(A5. + AI. + f|f(A5. + A/. + |f). and as the right hand side of this equation represents differences between the various heat quantities, it is immaterial what is CONTINUOUS FLOW OF GASES THROUGH ORIFICES 701 taken as a datum. It is therefore convenient in the case of steam to use 32 degrees F, as such. With this assumption it is obvious that for saturated steam which is initially dry A^i and A 6*2 must equal qi and $2; A/i and A/2 must equal pi and X2P2; and -PiVi/778 and P2V2/778 correspond to {APu)i and {xAPu)2 if the volume of water be neglected, which is permissible since it is relatively insignificantly small. The general equation for saturated steam may therefore be written in the form AK = (g + p + APu)i — (2 + xp + xAPu)2- = (a + r)i- iq + xr)2 = A(2i- A(22, (502) in which A(2i and AQ2 are the total heats above 32 degrees per pound of steam at points i and 2 respectively. While the foregoing discussion considered only the case of dry saturated steam, it applies equally as well to any initial condition. Thus in the ideal case AQi is the total stock of heat per pound of steam entering the nozzle and AQ2 is that remain- ing when the lower pressure is reached by the process of ex- pansion. It is obvious that even though the initial and final pressures are known, Eq. (502) cannot be used for the solution of numerical problems until some means is found for determining the value of X2, or AQ2. But after they have been found Ai^can be deter- mined; then from Eq. (501) the change in velocity of flow can be computed. Methods of determining the values of X2 and AQ2 will now be considered. (b) Since the velocity of steam flowing through a nozzle or similar conduit is very high there is very short time of contact between steam and walls. And further, since the temperature of the steam in contact with any particular ring in the wall of the conduit is always the same so long as steady conditions are maintained, it follows that each part of the wall will acquire practically the same temperature as the steam in contact with it. As a result of these two facts there is in a real case very little transfer of heat between the walls and the steam and it is reasonable to assume no transfer in an ideal case, hence the flow may be considered an adiabatic process, or, since the pressure decreases as flow progresses, as an adiabatic expan- sion. 702 HEAT-POWER ENGINEERING It can also be shown that for ideal conditions this adiabatic expansion may also be treated without serious error as isen- tropic, consequently all the mechanism previously developed for such conditions can be used in this case. (c) Then, on the T0-diagram in Fig. 454, if the initial state point is I (the condition being Ti, Xi, A (2i), the ideal expansion in the nozzle would be along the isen- tropic line to point 2 where the condi- tion is T2, X2, AQ2. The heat AQi per pound of steam at the beginning of expansion is shown by the area sur- rounded by the heavy line; and the heat AQ2 at the end of the process, by the sectioned area ; hence the net work AK done is AQ1 — AQ2 and is shown by area ab 12. This area is seen to equal that surrounded by the lines of the Clausius cycle. Hence, in the ideal case the change of kinetic energy AK occurring in a steam nozzle is equivalent to the external work, AE = (A(2i — A (22), done with a Clausius cycle having the same expansion line and using the same weight of material. Thus AK {= AE = AQi - AQ2) can be computed by the methods given in Sect. 94 for determining the work of the Clausius cycle, or it can be obtained from the T0-diagram or from the Mollier Chart. (d) On the Mollier Chart, Fig. 455, the ideal (isentropic) process for one pound of steam is represented by the line 1-2. At the initial point the con- , dition of the steam is Xi, pu AQu and at point 2 it is X2, p2, AQ2. During the process heat equal to AK = (AQi -r AQ2), as shown by the length 1-2, is surrendered for producing the flow.* (e) Having found AK = (Aft — AQ2), the velocity of the stream passing point 2 is, from Eq. (501), ^X— -curve to the longitudinal section of the nozzle; — thus for discharge to atmospheric pressure (14.7 lbs.) the end diameter is seen to be dj^, the length of nozzle is /^, and the terminal velocity is i-^; for discharge to a pressure pn = .58 pi the corresponding values would be Jn, In and Vn ; and for terminal pressure equal to pB they would be ds, Ib and vb- Evidently a nozzle originally used with discharge pressure p2 will be theoretically correct for a case where the pressure is atmospheric, if its end is cut off sufficiently to have the final diameter beyond the neck equal to J^, and similarly for the other terminal pressures. Thus regardless of the exit pressures. Fig. 456 (c) is the horizontal section of all nozzles discharging the same weight of steam per second with same initial conditions, the only difference between the various nozzles being in the lengths and end diameters, which are made to correspond to the terminal pressures. (d) The reason the neck is present in all cases where the ex- pansion is to a pressure below .58 pi can now be easily explained: From Eq. (507) the area of the nozzle at any section, per pound of material flowing per second, is a = -^Xi44. / Now referring to the curves for xY and v in Fig. 456 {c) it will be seen that as the expansion progresses the numerator .vV at first increases much slower than does the denominator r, and hence the nozzle areas (a) must first diminish; but that later the conditions are reversed, consequently the areas must then * There will be slight variations with the initial conditions, but these are not great and will not be discussed in this elementarj' treatment. 706 HEAT-POWER ENGINEERING increase. Obviously there must be a neck where the converging and diverging portions of the nozzle join. (e) It has been seen that, corresponding to each cross section of the nozzle, the steam has a definite condition and velocity, as shown by the ordinates in Fig. 456 immediately above the sec- tion under consideration. If the cross sections of the nozzle were shifted or spaced differently, so as to alter the longitudinal section of the nozzle from that shown, the ordinates of the curves would be similarly shifted and the character of the curves would change. This shifting may be so done as to cause any one of the curves to become a straight line; thus the nozzle may be such as to cause a uniform drop in pressure throughout its length, or a uniform increase in velocity, or a uniform in- crease in volume, whichever is most suitable for the purpose in hand, or any line can be made to have any desired curvature. Usually nozzles are made with rounded entrance like that shown, but with straight conical divergence, as in Fig. 457, as this form is easiest to make and appears to be about as efficient as any. The stream lines of the jet issuing from such a nozzle are practically parallel, which is important if the jet is to act Fig. 457. on turbine blades. For such a nozzle it is only necessary to compute the areas of the neck and discharge end; the entrance is then made rounded and the diverging portion is conical, the length depending on the angle of divergence, which should not be too great. (f) With a given nozzle (ideal or approximately such) it is found that, accompanying a lowering of the pressure against which it discharges, the velocity of flow increases until that through the smallest section (or neck) reaches the criticaF value (the pressure then being the critical one) and that any further diminution of the pressure does not change the velocity and pressure at that section, nor does it increase the weight of mate- rial flowing per second through the nozzle. Hence, if the ter- minal pressure is below .58 pi, the area of the neck and the critical velocity will fix the amount of material flowing per second. If merely an orifice with rounded entrance is used the discharge velocity will be the critical regardless of the pressure against which the jet issues, provided it is below the critical. After the steam has once passed the neck it can further expand CONTINUOUS FLOW OF GASES THROUGH ORIFICES 707 in a properly proportioned nozzle and can acquire in the diverg- ing portion of the nozzle an increased velocity of any desired amount (theoretically), its value merely being dependent on the terminal pressure. ^ 332. Actual Steam Nozzles, (a) It will be remembered that adiabatic conditions are those under which the working sub- stance, while undergoing a thermodynamic change, neither re- ceives nor surrenders heat as such. It has already been shown that in the actual case of flow through nozzles the conditions are practically adiabatic, for the time of contact of each particle with the wall is infinitesimal and, with continuous flow in one direction, each portion of the nozzle wall becomes heated to the temperature of the contiguous fluid and remains at that temperature; hence, neglecting radia- tion and conduction, there is no temperature head to produce heat transfer. (b) But although the conditions are adiabatic the expansion process is not necessarily the equivalent of an isentropic one. In fact, it is possible to obtain adiabatic conditions of expansion, from the higher pressure to the lower one, under which none of the potential energy may be converted into kinetic energy of a flowing stream. For example, if the expansion is through a porous plug with pressure drop, the velocity of flow is negli- gible and, as has already been seen, the total heat A (22 per pound of working substance at the end of the process is equal to the amount AQi it had at the beginning, hence AQi — A (22 = o and ^K = o. This expansion from the higher to lower pressure is along the constant heat lines on the T^-diagram and on the Mollier Chart and is accompanied by increase in entropy. This is a case of resisted flow, and it can be considered that, for each slight pressure drop, some of the intrinsic energy (8S + 81) of the material is expended in producing velocity (dv) of flow through a short length of plug, but that the friction and eddy currents reconvert this energy (8K) of flow back into heat (8Q) which is returned to the fluid and brings its stock back to the original value. Throttling of steam is a similar process. (c) Between the constant heat expansion (with AK = o) and the isentropic one (with AK = AE) there may be an un- limited number of processes even though under adiabatic con- 7o8 HEAT-POWER ENGINEERING ditions. It is, of course, desirable to so proportion the nozzle that it will offer no resistance to expansion, and cause no eddying, also that it will deliver the material in parallel stream lines. If this is effected the ideal conditions exist and the expansion is equivalent to isentropic. (d) With resisted flow the velocity of the steam can be com- puted by using Eq. (505) and introducing the efficiency coeffi- cient Ef, the proper values of which depend on the character, extent and shape of the guiding walls, and on the velocity, density and quality, or superheat, of the steam. The values of Ef range from .85 to .97 in nozzles used in turbines. (e) The case of resisted flow is shown on the T(}>-diagram^m Fig. 458, the heat AQi initially associated with each pound of working substance being shown by the area surrounded by the heavy line. If the expansion were ideal, from i to 2, the heat AQ2, at temperature T2y remaining in the material after the process would be shown by the area below ah2. However, with resisted flow to the same lower tem- perature, T2, less heat than the ideal amount is abstracted ; hence more heat (of total amount ^Q^') remains associated with the material, its amount being shown by the sectioned area. The final state point is then at 2' \ the quality is X2', which is higher than X2 as would be expected, and <^2 is the entropy, which is greater than <^i. Evidently the heat available for accelerating the jet is i^K' = (A(2i — A(220 which may be used under the radicals in Eqs. (504) and (505) to obtain the velocity of flow for this case; after which Eqs. (507) and (508) may be used in the same manner as before. If Ef is the efficiency of conversion then AK' = AK X Ef, where AK is the energy theoretically available in the ideal case. In the T^-diagram there is no one area representing this available energy AK' ; it is merely shown by the difference be- tween the area surrounded by the heavy line and that which is hatched. (f) The Mollier diagram for resisted flow is shown in Fig. 459. With ideal expansion from state point i \to 2, the heat per pound of steam would change from AQi to AQ2, the heat Fig. 458. CONTINUOUS FLOW OF GASES THROUGH ORIFICES 709 surrendered would be /S.K = A(2i — A(22, and the final quality would be X2. With resisted expansion to the same terminal pressure, p2, more heat, ^.Q2 (> A(22), remains in the steam than in the ideal case (as less is abstracted) and the final state point is found at the intersection 2' of the constant heat line of AQ2 with the pressure line p2. The final quality X2 ( > X2) and en- tropy 4>2 {> i) are determined by the quality and entropy lines passing through point 2'. Fig. 459- The heat converted into kinetic energy is AK' — AQi — LQ2 (< Ai^), and as before AZ' = AXX Ef. This value of AK' is then used in the manner described at the end of the preceding paragraph.* (g) The values of AX' and X2 may also be found by compu- tation. First AK for the ideal case is determined by the methods given in Sect. 94 for the Clausius cycle. Then with Ef assumed, LK' is AX X Ef, and the heat remaining per pound of steam at the end of the process is A(2/ = AQi - (AX X £/) (509) Since AQ2 = X2r2 + §2, it follows that X2' = {IAQ2 - 22) -^ ^2, (510) where ^2 and Y2 correspond to the known terminal pressure. The final entropy is then 1 U- v= ^•^^ 3-1 720 HEAT-POWER ENGINEERING been usefully employed. Thus the volumetric efficiency of this ideal simple compressor must be y^f = yi- ■ ■ ^32) Obviously the piston displacement of the compressor with clearance must be to that of the compressor without clearance in the proportion V,/ Vet if both are to compress the same quan- tity of air per cycle, therefore the existence of clearance makes necessary a larger compressor to handle a given volume of air. Effect of Clearance upon Work. (c) In the ideal case it may be assumed that the expansion of the clearance air along da takes place according to the same law as the compression of the mixture of clearance air and cylinder charge along the curve he. Then, if the clearance air be imagined to be separated by a flexible diaphragm from the fresh charge, and to be used over and over again, it is evident that it will deliver just as much work when expanding from d to a as will subsequently be consumed in compressing it from a to d. Then the net work necessary per cycle will be only that required to compress the volume Ves of cylinder charge from pressure Pi to P^ and discharge it at P2. Therefore, in the ideal case the presence of clearance does not alter the net work which must be done per cycle. It should, however, be noted that since the compressor with clearance will be larger than that without, the friction losses and cost of the machine will be greater in the real case. 342. Real Single Stage Compressor Diagram, (a) The real compressor differs from the ideal in many respects, chiefly be- cause the cylinder and piston cannot be made of heat-resisting materials, because the valves cannot be made to operate per- fectly, and because of the inertia of the air being handled. A diagram obtained from a real compressor is shown in Fig. 466, superposed upon an ideal one for the same machine, the pressure of air being supposed to be raised from atmospheric (Pi) to a receiver pressure equal to P2. (b) The ideal card is drawn for isothermal compression of the clearance air and charge and with isothermal expansion of the COMPRESSED AIR 721 clearance air. In the real case it is never possible to obtain isothermal compression with a reciprocating air compressor; instead, the compression line falls between the adiabatic and the isothermal and is expressible by the equation PV"^ = constant, with values of n varying from about i .2 in extremely favorable cases to about 1.3 under rather unfavorable conditions. To obtain such a curve it is necessary to cool the air during com- pression, by the methods which will be considered later. For present purposes ^2 it is merely necessary to note that the air, and therefore the cylinder walls, will become heated during compression. (c) During expansion of the clearance air, this material will, in general, be in volume" contact with walls which are at a higher ^^' ^ temperature, hence it will receive heat during the process. Ordinarily the real expansion line for this air lies between an adiabatic and an isothermal, but in the average case it approaches more nearly to the latter. The real expansion line may then be assumed to have a shape and position similar to da' in the figure. (d) In the ideal case the admission valve would open as soon as the clearance pressure has decreased to atmospheric, but actually the pressure must drop somewhat lower to give an unbalanced pressure great enough to open the valve against its spring, its friction and inertia, and also to overcome the inertia of the air and the resistance to flow through the more or less restricted areas available. After the valve is open and the air is in motion there' are gen- erally several oscillations of the valve and the air column, as indicated by the wavy suction line, after which the pressure set- tles down to an average value sufficiently below the atmos- pheric pressure to cause the inflow. The oscillation of the valve is known as ''fluttering." (e) From the fact that the same machine has been assumed in both cases it is evident that the actual volume of air in the cylinder at the end of the suction stroke must be the same in each case. In the real case, however, the air has a lower pres- sure than it has in the ideal, and, in general, its temperature will also have been raised by the heated walls which are uncovered 722 HEAT-POWER ENGINEERING by the piston, thus the actual weight present will be less than the ideal. This effect will be considered more in detail in a later section. (f) Starting at the point b\ instead of b, the air in the real case will be compressed according to some law intermediate be- tween the adiabatic and isothermal and therefore steeper than the ideal, as shown by b'c^ in the figure. (g) The discharge valve does not open until the pressure attained is slightly above that in the receiver and it behaves much like the suction valve and for similar reasons. The dis- charge line actually obtained will then generally look something like c'd' instead of cd. (h) The discharge valve will obviously not close suddenly at the end of the stroke, consequently the corner at d' may be more or less rounded, the exact point at which expansion of the clear- ance air starts being rather difficult to determine. (i) The net result of the operation of the real compressor has been to compress a smaller weight of air than that handled by the ideal machine and to require the expenditure of work in excess of the ideal, as shown by the greater area enclosed. 343. Volumetric Efficiency, (a) The volumetric efficiency of the ideal compressor was shown to be Vea/Vg, the symbols refer- ring to Fig. 465. In a real case the determination of the volu- metric efficiency is not as simple as this and it is often very difficult, if not impossible, to obtain its true value. As a result several incorrect volumetric efficiencies easily obtainable from a card are often used in practice. True Volumetric Efficiency. (b) An ideal compressor should receive a charge equal to its total piston displacement and this charge should have atmos- pheric temperature and pressure. The^ weight of this charge would then be in which Vs = piston displacement in cubic feet, and Va = volume occupied by one pound of air under atmospheric conditions. COMPRESSED AIR 723 If, in any case, the weight of air actually received per suction stroke is W , the true volumetric efficiency is VEft = W'lW (533) VaW F. (533a) (c) To evaluate this efficiency it is necessary to determine W and this is generally very difficult to accomplish in any real case. It can be done by measuring the air actually received or discharged in a given time and then dividing this by the number of suction strokes occurring during that time period; but the accurate measurement of large quantities of air is generally difficult and therefore the true volumetric efficiency is seldom determined. Atmospheric Volumetric Efficiency. (d) In Fig. 467 is given in exaggerated form a real compressor diagram with the atmospheric line added. If there is no change of temperature of the working substance during charging and if the expansion of the clearance air and the compression of the mixture both follow the same law, the distance ej must measure the volume occupied by the clearance air, and jg is that occupied by the charge when compres- sion has progressed up to the point g. volume If it be further assumed that the ^^' ^ drop of temperature from / to a' and the rise from h' to g are negligible, it may be said that the distance fg is a measure, of the volume occupied by the charge when at atmospheric pressure and temperature. Then the volumetric efficiency, on an atmos- pheric line basis, would be ^'^ distance/^ , . VEja = —y;-^' (534) (e) This formula will probably give an incorrect result in all cases, because none of the assumptions made in its derivation are strictly correct. However, the error is generally not great in magnitude, hence, because of the simplicity of the method, the formula is commonly used in practice. d' of' i_ \ ^v ! a^^'~'~'~" '* 724 HEAT-POWER ENGINEERING Suction Line Volumetric Efficiency. (f) A still less perfect formula is often used for determining the volumetric efficiency from the diagram. The point a\ Fig. 467, is first determined by continuing the straight part of the suc- tion line backward to intersect the expansion line. The distance a'b' is then taken as the volume occupied by the charge and the distance from a' to the zero of volumes is taken as that of the clearance air at the same pressure and temperature. Neg- lecting the fact that the suction line is below atmospheric pres- sure the volumetric efficiency on a suction line basis is defined as T^T-/. distance a'b' , . y^u = — y^ — (535) (g) This method contains practically all the errors of that previously given with the added disadvantage of neglecting the difference of pressure, consequently it should never be used when the position of the atmospheric line can be obtained. 344. Cooling During Compression, (a) It has been shown in preceding sections that isothermal compression should, in general, prove more economical than adiabatic. It is practically impossible to attain isothermal compression in any real machine, but it can be more or less closely approximated and generally without involving excessive cost. (b) If a compressor fitted with a metal cylinder is operated very slowly, i.e., one or two cycles per minute, the heat gener- ated by compression will be conducted away by the cylinder metal almost as fast as generated and in such case the com- pression could be made to approach an isothermal process as closely as desired, but it would involve the use of enormously large machines because of the slow operation. Some method must therefore be used which permits of operation at the highest desirable speeds. (c) If any form of external cooling, such as radiation consid- ered above, is to be used the proportions of the cylinder are important. That cylinder which exposes the greatest surface to the external cooling agent, per cubic foot enclosed, will be the best so far as cooling is concerned. This would indicate the use of cylinders of small diameter and great length, i.e., "long stroke compressors," but such machines are always more COMPRESSED AIR 725 expensive than short stroke mechanisms, consequently a com- mercial limit is set to cylinder proportions adopted. (d) In practice a few types of compressors are cooled by radia- tion to the atmosphere, as, for instance, those used on locomotives for operating the air brakes. They are all comparatively small, are generally operated in strong currents of air and are at best rather inefficient. It is doubtful if the compression is appre- ciably better than adiabatic, the radiation serving simply to prevent overheating of the entire mechanism by storage of heat from cycle to cycle. (e) Most commercial machines are water cooled. There are three distinct methods of applying cooling water, two or more of which may be, and generally are, used on the same machine. They are: — (i) Injecting water into the cylinders; (2) water jacketing the cylinders; and (3) compressing in stages and using water jacketed vessels, called "intercoolers," between cylinders. Water Injection. (f) The injection of water into the compression cylinder has been rather extensively used in Europe but not in this country. If the water is introduced as a solid stream but little cooling is effected, the compression curve approximating the equation p^i.35 ^Q pyi.zi — constant; but with a very fine spray the cooling effect is much greater, and values of the exponent n as low as 1.26 to 1.28 may be obtained. (g) The introduction of water into the cylinder has the fol- lowing disadvantages: — It generally increases the wear of cyl- inder and piston; the feeding devices are an almost constant source of trouble; and the air leaves the cylinder practically saturated with water, some of which precipitates when cooled in the receiver, but much remains in the air and later may cause trouble by freezing when the air is expanded in doing work. Water Jacketing. (h) Jacketing the compressor cylinders with water does not introduce the difficulties considered above, but it is generally less efficient than water spraying unless it is very perfectly carried out. Values of the exponent n about equal to 1.25 to 1.28 are generally attainable. 4 hJ^K/\y^ 726 HEAT-POWER ENGINEERING Multistage Compression and Intercooling. (i) The raising of pressure from atmospheric to the desired receiver pressure need not occur entirely in one cylinder. The compression may be divided between as many cylinders as desired without changing the ideal process in any way. This is shown in Fig. 468 for the ideal case with three cylinders, i.e., compres- sion in three stages. It can be seen from the diagram that it is immaterial whether: — (i) Compression is carried out in one cylinder receiving the charge Vb and compressing it isothermally and discharging at a pressure P2', or (2) It is carried out in several cylinders, the first receiving a charge Vb at pressure Pi, compressing isothermally to / and d P2 c V h \ e \, ^-~^ft c- Volume Fig. 468. Fig. 469. then discharging along fe to a second cylinder which, receiving its charge along ef, compresses to g, and so on until the last cylinder compresses to and discharges at P2. (j) This method has the practical advantage of making it possible to use what is known as ''intercooling'' ; for the air dis- charged from one cylinder may be passed through a very effi- cient cooler on its way to the second, and so on. The practical advantage of this is shown in Fig. 469, which indicates the com- pression line which is thus made possible. The line be represents ideal or isothermal compression, be' shows an adiabatic, and the broken line befghe" the compression line which might be obtained with a jacketed, or spray cooled, multistage compressor fitted with intercoolers. The compression in the first cylinder brings the material to e COMPRESSED AIR 727 with a temperature higher than it had at h. An effective inter- cooler through which the air passes on its way to the next cyl- inder can reduce its temperature to the original value, so that compression in the second cylinder starts under the same con- ditions as though the process in the first had been isothermal. The work done in excess of that required in the ideal case is evidently measured by the small areas chc" , hfg and fbe, while without intercooling the loss would probably have been some- thing like that shown by the area cbc'^'. (k) The fact that the cooling water is often below the average atmospheric temperature suggests the possibility of cooling in the intercoolers to a value lower than that on the isothermal. This would give a com- pression line similar to that shown in Fig. 470 by befghc", which is sometimes approx- imated in practice when very cold water is available. Comparing this with the iso- thermal he shows that the latter may under these circumstances be very closely approx- imated. Some few machines have been operated with such effective intercooling that the sum of the work areas under the ^^' ^'^°' real compression lines in the several cylinders was less than under the ideal isothermal between the initial and final pres- sures. (1) Dividing the compression up into several stages and inter- cooling has a markedly beneficial effect upon the volumetric efficiency of a compressor for two reasons : — - First, since the temperature range in the low-pressure cylinder (ist stage) is reduced, the air is heated less during the suction stroke, hence greater actual weight will enter the cylinder than would be the case in a single cylinder operating between the ex- treme pressure limits. Second, less weight of air remains in the clearance of the low- pressure cylinder because the discharge pressure from that cylin- der is lower than with a single-stage compressor, which would be of the same size and have the same clearance volume. This will be made clear by Fig. 471 in which the idealized cards of a three-stage compressor with clearance are abed, a'b'e'd! and a"b"e"d" . It will be observed that the expansion of the 728 HEAT-POWER ENGINEERING clearance air in the low-pressure cylinder theoretically decreases the charge volume by the small amount equal to Va — Va; whereas if the compression had all been carried out in this one cylinder the clearance air at pressure P2 would have expanded from a volume Ve to a volume F/, theoretically decreasing the charge by the very large amount V/ — Vd. This serious loss is one worth preventing, if commercially feasible. (m) It is obvious from the diagrams and preceding paragraphs that the larger the total pressure range, the greater in every way will be the advantages of multistage compression. It thus happens in practice that machines for compressing to 25 or 50 pounds per square inch are generally built single stage, while Fig. 471. Fig. 472 those intended to compress to 100 or 150 pounds are generally made two-stage. Where exceptional efficiency is desired, or where extremely high pressures are to be attained, three-, and even four-, stage machines are sometimes used. (n) The differences between the actual cards and the ideal ones of each cylinder of a multistage compressor are similar to those which have been discussed for the single-stage cpmpressor. When superposed they look something like Fig. 472, in which the atmospheric, intercooler, and receiver pressures are indi- cated by horizontal dash lines. In each case the air is drawn into a cylinder at a pressure below that at which it exists out- side of the cylinder and is discharged at a pressure higher than that maintained in the vessel receiving the air. This results in an overlapping of the cards in the center of the diagram giving two loops, A and B, which very evidently represent lost work. COMPRESSED AIR 729 (0) The better the action of the valves and the larger the passages through ports, intercooler, pipes and such, the smaller will the areas of these loops become, the upper and lower lines tending to become coincident. In very well-designed compres- sors this lost work is so small as to be almost if not quite inde- terminate. 345. Blowing Engines. Blowing engines, or blowers, are simi- lar to air compressors in principle, but they are generally built to handle relatively very large quantities of air at comparatively low pressures, say 10 to 20 pounds per square inch above atmos- phere. Comparatively little attention need be given to cooling under such conditions because the pressure is so low that very little work can be saved by such means. Moreover, the com- pressed air is generally heated before being used, so that any cool- ing during compression would call for an expenditure of heat to raise the temperature immediately afterward. Because of the large volumes of air to be handled considerable difficulty is generally met in designing efficient valves, particu- larly if operated at high speeds. As a result there are many different types of both inlet and discharge valves in use, some operating automatically under the action of springs and air pressure, some mechanically operated, and some partly automati- cally and partly mechanically operated. 346. Turbine Compressors. Since the successful commer- cialization of the steam turbine, engineers have been trying to develop satisfactory "Turbo Compressors" or "Turbo Blow- ers." These compressors have a number of stages arranged in series, each impeller receiving its supply of air from the preced- ing stage and discharging into the one which follows, no valves being used. The stages are water cooled and intercoolers are em- ployed. These machines are just beginning to assume prominence for compressing to pressures from 10 to 20 pounds or more per square inch, but as yet few have been used in this country. 347. Compressed-air Engines, (a) Compressed air is used commercially in many different ways but most widely in engines for the production of power, the air serving as the working sub- stance. At first sight it seems an uneconomical method of producing power as the air compressor must be driven by an 730 HEAT-POWER ENGINEERING engine of some sort which apparently might better be used directly to produce the power desired, rather than to suffer the additional losses incurred during compression and utilization of the compressed air in a second engine. (b) Such reasoning is generally sound for conditions where the desired power can be conveniently generated at the point of utili- zation by any of the prime movers previously considered. There are, however, many cases where this cannot be done. Where a number of small engines are to be operated at widely scattered points and where electrical transmission is not suitable, com- pressed air engines find a field to which they are admirably suited. Compressed air can be transmitted for great distances without appreciable loss, and, as will be shown later, any loss can be more than made good at the point of consumption. Steam, on the other hand, cannot be efficiently transmitted over great distance because of the resulting condensation ; and more than this, steam engines of small size are very inefficient and the high temper- ature "at which they operate renders them unsuitable when han- dling is required. The working substance of internal combustion engines can be transmitted as easily, if not more easily, than compressed air, but the complicated valve and ignition mecha- nisms, the high temperature and the hot noxious exhaust gases make them less desirable than compressed air engines for a num- ber of purposes. (c) Thus compressed air engines are widely used in mining and quarrying operations and for the driving of small portable tools in shops and such. In Paris there is installed a central compressor station which distributes compressed air, much as gas is distributed in this country, and air is used by the con- sumers for operating small plants much as electricity is used here. 348. Compressed Air Engine Cycles, (a) Compressed air is sometimes used in engines without expansion, that is, according to the rectangular cycle. The work done per cycle in an engine without clearance is obviously work= VUP2-P1). (536) in which Vb is the volume displaced per stroke, P2 is the upper pressure, and Pi that of discharge. COMPRESSED AIR 731 Such use of compressed air is very uneconomical as no use is made of its associated heat and, as a result, better methods of utilization have been devised. (b) A cycle similar to the Clausius described under vapor cycles is generally considered to represent the ideal cycle for air. As shown in Fig. 463, it consists of two constant pressure lines, dc and ba, a constant volume line ad, and an adiabatic expansion line cb. The theoretical work made available by such a cycle can easily be determined from the formulas previously given. (c) In practice the air generally enters an engine at about atmospheric temperature and during the approximately adiabatic expansion it becomes cooled, in some cases to such an extent that the moisture in it freezes and leads to difficulties. The theoreti- cal temperature decrease can never be attained in any real engine because heat will be supplied to the engine cylinder from the sur- rounding atmosphere and will tend to make the expansion more nearly isothermal. If the engine were operated very slowly the expansion would very closely approach a true isothermal. (d) This approach toward isothermal expansion is advan- tageous for the following reasons: (i) It tends to prevent the deposition, in the form of ice, of the moisture accompanying the air, thus tending to prevent the resultant troubles with lubrication and stoppage of valves and passages. (2) It increases the work made available, as the area under an isothermal is greater than that under the steeper adiabatic between the same two pressures. (3) It lessens the range of temperature within the cylinder so that there is less tendency to cool down the entering air. Such cooling would result in a decrease of volume and therefore an increase in the weight required per cycle. (e) It is interesting to note that from the theoretical view- point isothermal operation is not as advantageous as adiabatic. The object of using expansion is to make use of some of the heat associated with the working substance as it enters the engine. If the expansion is isothermal no work can be done at the expense of such associated heat; on the contrary, heat equivalent in quantity to the work done must be supplied from an external source. With an adiabatic expansion, however, all work would 732 HEAT-POWER ENGINEERING be done at the expense of heat already associated with the gas as it enters the cyHnder. The discrepancy between theory and practice is due to the fact that in the assumed case heat suppHed from the atmosphere during the isothermal expansion costs nothing and may there- fore be freely used without decreasing the commercial efficiency of the process. (f) It was shown that it was uneconomical to use complete expansion in a reciprocating steam engine. The same thing is true in the case of a reciprocating compressed air engine, and as a result the toe of the card is cut off in practice. (g) Real engines are further found to operate more quietly, and therefore more satisfactorily, when the exhaust valve closes before the end of the stroke trapping some air which is then compressed into the clearance. Such operation causes a loss of diagram area and therefore a loss of work from a given size of cylinder running at a given speed. It may, however, result in a saving in the amount of air used per horse power in two ways: (i) When compression is not used the air admitted must first be mixed with that in the clearance until the full admission pres- sure is attained ; after that the entering air becomes available for driving out the piston, and (2) Compression tends to raise the temperature of the walls, cylinder head and piston and thus to decrease the cooling effect upon the incoming air. 349. Preheating, (a) In practical use, compressed air en- gines and the compressors supplying the working fluid are gen- erally widely separated. It has already been shown that so far as the compressor is concerned the cooler the air the better. A cool supply means larger capacity for a given machine and efficient cooling during operation means a smaller amount of work required. The same thing is true for the "receiver" or storage tank, and for the pipe line carrying the air to the engine, for the cooler the air the smaller can these parts be for a given quantity of air. (b) Conditions are, however, quite different so far as the engine is concerned. The warmer the air, within reason, the better. If the compressed air could be heated at constant pressure COMPRESSED AIR 733 before entering the engine, it would expand according to Charles' law. A given volume of heated air admitted to the engine would represent a smaller actual weight but would be able to deliver the same amount of work as a larger weight of colder air, and there would be the added advantage that there would be less danger of the moisture freezing at the end of expansion. (c) Such heating of the air is known as " preheating " and the devices in which it is effected are called "preheaters." It is actually used in places where the transmission piping is of great length and also where the engine units are few and of large size. It is found in practice that the running expense for the fuel supplied for preheating is less than the extra charges against the larger compressor and pipe line which would otherwise be used. I . . u /■^ CHAPTER XLII. REFRIGERATION. 350. Definition, (a) By refrigeration is generally meant the removal of heat from a body, or substance, to such an extent as to leave it, or maintain it,, at a lower temperature than that of its surroundings. This may be done commercially in moderate climates by the use of ice ; it may be accomplished in the labora- tory by the use of liquefied gases; it may be done in very hot climates by the naturally rapid evaporation of water. (b) In the ordinary engineering application of the term, how- ever, it is taken to mean the removal of heat by mechanisms, or systems, which will be described in later sections and which are grouped under the title of Mechanical Refrigeration. 351. Thermodynamics of Refrigeration, (a) It was shown in Sect. 49 (h) that by the expenditure of energy (A£) a reversed j J I heat engine would remove heat from a body I at low temperature and would discharge to — I t pAQi=AQ2+AE another body, at higher temperature, that X — *L heat plus the heat equivalent to the energy L \ \ 'v-\ \ expended in the operation. That is, a re- V \ \~yT — versed heat engine shown diagrammatically j4-(^ as R in Fig. 473 can receive a stream of heat i tr^^^ AQ2 from the low temperature body T2 and discharge the larger stream AQi, made up of ' ^ ,* AQ2 and AE, to the high temperature body Ti. ^^' ^'^^V (b) This is a process of refrigeration because heat can be. removed from the low temperature body even if its temperature be far below that of its surroundings. It thus appears that the reversed heat engine, which has been called a heat pump, is what may now be called a refrigerator, or refrigerating machine. (c) Imagine the Carnot cycle, shown in Figs. 18 and 21 to PV- and T0-coordinates, to be carried through in the direction 734 REFRIGERATION 735 dcha for purposes of refrigeration. Heat will be absorbed along the line dc at temperature T2, and in quantity as shown on the T<^-diagram by the area dcef. The work expended in driving the machine will be shown by the area ahcd on the PV-diagram, if measured in foot-pounds, or by the similarly lettered area on the T0-diagram, if measured in thermal units. Heat will be dis- charged along the line ha at temperature Ti and its quantity will be the area, feba on the T<^-diagram, equal to the sum of two areas previously considered. (d) The expenditure made in order to abstract the heat AQ2, shown in Fig. 21 by area dcef, is obviously the energy AE used in driving the machine as shown by the area abed. If the heat removed, AQ2, be taken as the result obtained, the efficiency of the process is t-» 1^ a ^ ^ Result ^ Ag2 -^ ~ Expenditure ~ AE ' (e) It is obvious from the T-diagram of Fig. 21 that for the case for which this figure was drawn AQ2 is considerably greater than A£, hence the ratio which has just been given as the effi- ciency will be greater than unity. This is a very common property of refrigerating processes. Since engineers are not ac- customed to speak or think of efficiencies greater than unity it is common practice to call this ratio the Coefficient of Performance (Co. P.), or the Figure of Merit, rather than the efficiency of the process. Then the C.o.P.=|| ....... (537) for refrigerating machinery of this kind. (f) The apparently remarkable attainment of an efficiency greater than unity is meaningless. The work expended and the heat removed from the cold body are really not connected in any such way as are heat supplied and work done in the case of an engine. This can best be seen from the T(^-diagram of Fig. 21. Assume the line dc to be moved upward while the line ab maintains its position. Then the heat removed (A (22) will obviously increase while the area of the cycle, representing AE, will decrease, that is, it takes less work to remove larger amounts of heat. (g) That this should be so can easily be seen by carrying the ^■u 736 HEAT-POWER ENGINEERING assumptions to the limit. If dc rises above ab the previously cold body has attained a temperature greater than the previ- ously hotter one and work can actually be obtained by allowing heat to flow from it to the latter. Obviously the coincidence of the lines dc and ab would indicate that the two bodies are at the same temperature, that no work is attainable by heat flow, and that no work is necessary to cause heat flow. Requirements for Maximum Coefficient of Performance. (h) Inspection of the T0-diagram will show that anything which brings the two lines ab and dc, that is, the temperatures Ti and 7^2, closer together will increase the value of the coeffi- cient of performance. This can be done by dropping Ti or by raising T2^ Dropping Ti will decrease A£ but will not change AQ2. Raising T2 will decrease A£ and increase AQ2 by the same amount. It is therefore evident that raising the lower temperature is more effective for attaining a high coefficient than lowering the upper temperature; but this results in a higher temperature in the cold body and hence may not be desirable. Obviously with given upper temperature Ti, the lower the tem- perature {T2) of the cold body is maintained the smaller will be the Co. P.; and, with given lower temperature (T2), the lower the temperature of the hot body receiving the heat, the larger will be the value of the Co. P. Theoretical Values of Coefficient of Performance. (i) For purposes of comparison with real refrigerating ma- chinery the ideal reversible refrigerator already described is very useful although its theoretical performance ca^n never be even closely approximated by a real machine. The case is very similar to that of engines where the perfect Carnot engine is used as a measure of perfection although practically unattainable. (j) In order that numerical comparisons may be made later, several values of the coefficient of performance will now be obtained for a Carnot cycle refrigerator. The formula pre- viously given can be put in more convenient form for this pur- REFRIGERATION 737 pose in the following way. It was shown on page 82 that for a Carnot engine the net work is A£ = RTi loge r - RT2 log« r = {Ti-T2)R\oger, and that AQz = RT2 loge r. Then, for this case, Aft RTiXogeT T2 C.o.P. = AE {Ti-T2)R\oger T, - T^ (538) Values of the C.o.P. can be easily obtained by substitution of assumed temperatures in the last term. A very common case would be a machine which theoretically withdrew heat from a cold body at 18° F. and discharged it to 50r 10 20 30 40 Temperature, \ in Fah. Degrees Fig. 474. a hot body (cooling water) at a temperature of, say, 50° F. coefficient of performance in this case would be Aft ^ T2 ^ 18 + 460 A£ " Ti - Ta ~ (50 + 460) - (18 + 460) The 15, approx. (k) The results obtained by varying the two temperatures are shown by the curves in Fig. 474, in which each curve is drawn for a certain upper temperature Ti and shows by its rise toward the right the increase in the value of the coefficient of performance with rise of the temperature T2. 738 HEAT-POWER ENGINEERING Expansion Cylinder L ^■'■'M Compression Cylinder 352. The Air Refrigerating Machine, (a) Any gas, not lique- fiable at ordinary temperatures, may be used as the working substance, or refrigerant, in commercial refrigerating machines, but air is the gas most commonly used. This material has the advantages of being readily procurable, non-poisonous and can be brought into actual contact with food stuffs and such, which are to be cooled or kept cool without detriment to the latter. (b) In the ideal machine the same charge of air would be used continuously and the entire operation would be carried out in a single cylinder. In practice it is found more convenient to use separate organs to perform different functions during the cycle and it is generally found best to discharge the air used in each cycle and to draw in a fresh supply for the next. It will be noted that this parallels the conditions met with in most real engines. (c) An idealized refrigerating machine using a unit weight of air as a working substance is shown diagrammatically in Fig. 475, the apparatus consisting of a compression cylinder, an air cooler and an expansion cylinder. The compression cylinder (without clearance) draws cold air from the cold-storage room at atmospheric pressure and at a constant temperature T2, according to the constant pressure line ab in Fig. 476. The air is then compressed adiabatically, as shown by be, and discharged at the higher pressure Pi with a temperature Ti, higher than T2, and specific volume dc. If the delivery pressure is sufficiently high, the temperature attained may be greater than that of available cooling water so that the air may be cooled by discharging it into the cooler through which this water is circu- lated. By assuming the volume of the cooler to be very large, the reduction of temperature may be assumed, without sensible error, to take place at constant pressure; hence, the delivery to Fig. 475- Fig. 476. REFRIGERATION 739 the cooler is shown by the Une cd in the figure, but when cooled the volume of the air is de at this same pressure. Continued operation of the compressor cylinder would result in continued duplication of the cycle ahcd. (d) The expansion cylinder running at the same speed as the compressor can be imagined as receiving from the cooler exactly the same weight of air per cycle as is delivered by the com- pressor. This air will be admitted according to the constant- pressure line de, in Fig. 476, and its adiabatic expansion will be according to line ef, bringing the material back to the initial pressure P2 but with a temperature lower than the original temperature T2, for, according to Charles' law, Tf/n = Tf/T, = Vf/V,, from which Tf=T-,{Vf/V^) (539) This cooled air at temperature Tf can then be discharged to the cold-storage room to balance heat leaking into 'it through the walls or brought in by fresh produce. It is only necessary to properly regulate the quantity of air handled and the tem- perature at which it is returned, to maintain any desired tem- perature (within limits) in the cold-storage room. Power Required. (e) The work consumed by the compressor is obviously shown by the area ahcd and that made available in the expansion cylinder is similarly shown by the area defa. The net work required per cycle is then only Jhce if the expansion and com- pressor pistons be connected together. This work can be ex- pressed in terms of temperatures, pressures and volumes by the equations given in Chap. VIII. Refrigerating Effect and Coefficient of Performance. (f) The net refrigerating effect, that is, the heat A(22 removed from the cold room per cycle, is obviously the difference between the heat in the air as it leaves and that in the same air when it returns. That is, in which LQ, = WCAn-T,), ..... (540) W = weight of air per cycle, Cp = specific heat of air at constant pressure, Tb = temperature of air leaving cold room, and Tf = temperature of air returning to cold room. 740 HEAT-POWER ENGINEERING (g) In a similar way the heat rejected to the water must be A(2i = WCATc- Te).- ..... (541) Since A£ = A(2i - Aft, it follows that ^E = wc, (n - Te) - wc, (n - r^), . . (542) and from these values ~ (r, - Te) - (n - Tf) ^^^^^ This value may be further simplified as follows: Inverting both sides of the equation gives 1 _ {Te - Te) c.o.p. n - Tf and since from the adiabatic relation Tc^Te^ Te- Te n Tf n-T/ 1 Te-T, Te - 1, and C.O.P. . n Tf C.O.P. = ^ J'^ - ^ ^^ .... (544) Comparison with the Reversed Carnot Cycle. (h) A Carnot cycle refrigeration would work between the temperatures T^, which is the highest temperature of the cool material, and Te, which is the lowest temperature of the warm material. Its coefficient of performance would therefore be C.o.P.=^^. Since {Te — Tb) is less than {Te — Tb) in Eq. (544), it follows that even in the ideal case the real refrigerating machine de- scribed must have a lower coefficient of performance than that obtained with the reversed Carnot cycle. The difference is due to the use of two irreversible, variable- temperature, constant-pressure processes which in the real case increase the temperature range. The temperature of the air REFRIGERATION 741 discharged to the cooler must be so high that the water used can remove heat from it, finally bringing the air down to a value approaching that which it had when entering the compressor cylinder. Similarly, the air is cooled during expansion to a temperature considerably lower than that of the cold room, and when intro- duced into that room it is heated irreversibly until it finally attains the temperature existing there. Practical Modifications. (i) In a real machine operating on the cycle just discussed, there will be clearance and valve losses in both cylinders, fric- tion throughout the mechanism, and heat losses to and from the working substance as it passes through the apparatus with temperatures different from those of surrounding bodies. These will all increase the size of machine and the amount of work necessary to produce a given amount of refrigeration. (j) In practice it is customary to water jacket the compressor. This makes the compression line less steep, i.e., intermediate between the adiabatic and the isothermal, and proportionally reduces the amount of work required. It also leaves less heat to be removed in the cooler and makes possible the use of a smaller vessel for that purpose. It is therefore decidedly ad- vantageous. Actual Coefficient of Performance. (k) Both in the ideal and actual cases, the coefficient of per- formance of air refrigerating machines is very poor in compari- son with machines using vapors such as ammonia. The use of air machines is therefore dictated by convenience rather than by economy of power. For average cold-storage conditions, in temperate climates for instance, the coefficient of performance of a Carnot cycle refrigerator is about 9 to 10. The coefficient of the ideal air machine (Eq. (544)) is only about 1.5 to 2 ; and in the real machine it is generally, if not always, below 0.75, as determined by test. 353* Vapor Compression Process of Refrigeration, (a) It was shown in the previous section that the air machine there described was considerably handicapped by the cycle on which 742 HEAT-POWER ENGINEERING it operated, its theoretical coefficient of performance being necessarily much lower than that of the ideal Carnot cycle refrigerator because the constant pressure reception and rejec- tion of the heat are not reversible processes with gases. (b) By using a liquid and its vapor as the working substance, instead of a gas, a much better performance can be obtained because the constant-pressure processes for saturated vapors and their liquids are reversible isothermal ones. It therefore follows that with such working substances the same sort of machine as that just described would in the ideal case operate on a Carnot cycle which would give the best performance possible. (c) Fig. 477 can be used for the purpose of developing this cycle by assuming the discharge pipe of the expansion cylinder and the inlet pipe of the compressor con- nected by a coil, as shown dotted by C in Fig. 475, so that the entire system is "closed." This coil may be regarded as immersed in the material to be cooled. Imagine the ideal compression cylinder to draw in a charge of mixed saturated vapor and its liquid, at temperature T2 from this coil, as shown by the line ab in Fig. 477. The return stroke of the piston will result in adiabatic compression to the point c, and, with a properly chosen quality at b, the material can be brought to the condition of dry saturation at c. From c to d the working substance is driven into the cooler which now acts as a condenser reducing all of the vapor to the liquid form with volume de'. The liquid may then be admitted to the expansion cylinder, as shown by the line de, expanded adiabatically to / and discharged along the line fa into the assumed coil C, where it may be vaporized wholly, or partly, at temperature T2, at the expense of heat in the material surrounding the coil. After this it may be readmitted to the compressor and the cycle repeated. (d) So far as cycle is concerned the operations outlined have resulted in the generation of the reversed Carnot cycle fbce. So far as heat is concerned they have resulted in the removal of heat A (22 from the cooler substance during vaporization at tern- Fig. 477. REFRIGERATION 743 perature T2 and In the surrender of a larger amount of heat A(2i to the warmer substance (condensing water) at the tempera- ture Ti. T-Diagram of Vapor Process. (e) The T0-changes of ammonia vapor and its Uquid, in an ideal case, are shown in Fig. 478 in which points are lettered to correspond with those of Fig. 477. The liquid line and the saturation line have been added to the diagram. From this diagram it can be seen that the heat absorbed from the cooler body is ^2 {xh — Xf) and that discharged to the warmer body isri. The work required in » B.t.u. per pound of substance is therefore § e c 1 1 \ 1 1 1 1 h ^•/' \ \ \ Entropy A£ = n - fsfe - :x:/). . (545) Fig. 478. The mixture of liquid and vapor is cooled during the expansion ej by the giving up of heat to cause partial vaporization as indicated. Practical Modifications of Vapor Compression Process. (f) In any real case the expansion cylinder would be very small in comparison with the compression cylinder, and the work done by it would be practically negligible. It has come to be regarded as more of an incumbrance than a benefit and is commonly omitted In real machines. In its place Is substi- tuted an " expansion valve'' as X in Fig. 479. This Is merely a throttle valve through which the working substance can flow from the high pressure of the condenser to the low pressure of the coil. (g) This flow is an adiabiatic process but Is not reversible and hence Is not isentropic. It is not represented by the line ej of Fig. 478, but by some line starting at e and terminating on the line jh at some point /' to the right of /. The entropy increases and the possible refrigeration effect decreases because the energy which would have been given up as external work during isen- tropic expansion here remains associated with the substance giv- ing It the higher quality x/, instead of Xf. The heat which can be absorbed from the body to be cooled Is then only ^2 {xh — x/^ instead of Yi {xh — xf). 744 HEAT-POWER ENGINEERING In real cases the difference is so small that it is negligible in comparison with the increase in mechanical efficiency and ease Wate r Out Compression Cylinder Cold Storage Room Fig. 479. of operation, and with the decrease in first cost and operating expense. Actual Coefficient of Performance. (h) The great majority of vapor compression machines oper- ate with ammonia vapor for their working substance. Such machines give a coefficient of performance of from 5 to 7 under conditions which give a coefficient of 9 to 10 for the ideal Carnot cycle. In comparison with the values given for air machines these performances are very much higher and it is doubtful if the ammonia machines can be greatly improved. 354. Relative Advantages of Different Vapors, (a) While most vapor refrigerating machines use ammonia this material is not the only one available. For plants used aboard ship carbon dioxide is often preferred and many stationary machines have been operated with this substance and with sulphur di- oxide. Other materials, including water, have been used. (b) The choice of ammonia as the common working substance is decided largely by practical considerations, though it so hap- pens that certain thermodynamic properties would lead to the same choice. The most important considerations are probai^ly those of volume and pressure. REFRIGERATION 745 (c) The actual volume of working substance required to cause a given amount of refrigeration determines the size of machine required. The larger the machine, the greater the friction losses if other things are equal. Since all friction must even- tually result in the generation of heat the refrigerating efifect will be diminished thereby. Bulk is therefore undesirable be- cause of cost of machines, cost of power to operate and loss of refrigerating effect by friction. The pressure is important in two ways. Some available substances have vapor pressures below atmospheric when at the temperatures common in refrigeration. Their use would mean the maintenance of a vacuum within the refrigerating machine which is by no means a simple matter because of difficulty with air leakage. Other substances have vapor pressures so high that they can be used only with great difficulty. (d) Ammonia is quite satisfactory both as regards bulk and pressure. More than twice the bulk of sulphur dioxide is re- quired for the same refrigerating effect, and between 300 and 400 times the bulk of water vapor. Carbon dioxide requires only about one-quarter the bulk of ammonia vapor but, as will be seen, is handicapped by enormously high pressures. The pressure of water vapor is entirely below atmospheric at refrigerating temperatures, while that of sulphur dioxide is below for the lowest temperatures and only slightly above for the highest temperatures. The pressure of ammonia vapor varies from about 20 or 25 pounds to something below 200 pounds, while that of carbon dioxide varies from about 300 to 1000 pounds per square inch. It is obvious that the best commercial balance is struck when ammonia is adopted, excepting in cases where an ammonia leak might cause very serious difficulties. (e) In the case of real machines there is also another point which must be considered and which is more of a thermodynamic nature. Where an expansion valve is substituted for the expansion cylin- der, the working substance brings into the refrigerating coil heat which in the ideal case would have been converted into work and used in driving the machine. Obviously any heat brought into the coil by the working substance itself means just so much less, heat to be abstracted from the surroundings to cause evapor- ation, hence there will be an equal reduction in the refrigeration. 746 HEAT-POWER ENGINEERING That material which brings in relatively the smallest amount of heat in this way will be the most desirable if other things are equal. The amount of heat under consideration is that in the liquid at the end of the liquefaction process, that is, it is the quantity when the working substance is at the higher temperature Ti which is above that in the same liquid at the lower temperature T2. It is therefore equal to C (Ti — T2) in which C is the specific heat of the liquid. The larger this value in proportion to the latent heat of vaporization at the temperature Ti, the poorer the material for use in a vapor compression machine having an ex- pansion valve. From this point of view, water is the best of the materials cited as possibilities and ammonia comes next, carbon dioxide being the worst of all; thus, ammonia forms a good commercial ycompromise. 355. The Ammonia Absorption Process, (a) The vapor compression machine operates (i.e., refrigerates) because the process of vaporization requires a supply of heat from external sources and the process of liquefaction yields heat to external media. Any device or machine which can bring about such alter- nate liquefaction/ and vaporization can be used as a refrigerating machine. (b) The so-called absorption refrigerating machine carries through these two processes in a manner analogous to that of the compression machine but by entirely different means. It is illus- trated diagrammatically in Fig. 480 and operates in the following way: (c) The generator contains a strong solution of arnmonia in water, and the ammonia is driven off from this solution at high temperature and pressure, by the heat supplied by the steam coils shown at S. The vapor, under this pressure, enters the condenser K in which it is liquefied, as in the previous case. It then passes through the expansion valve X and evaporates in the refrigerating coils C as before. Leaving the refrigerating coils as vapor, it enters the absorber A at low pressure and low temperature and is absorbed by water to form a strong solution which, by a pump P, is delivered to the generator to displace that which has given up ammonia REFRIGERATION 747 vapor under the action of heat, and which is then returned to the absorber. (d) The absorber, pump and generator together correspond to the compressor of the previous type. The action in the ab- Cooler or Condenser r Ammonia "Vapor (H^ Bj «»^ Expansion Yaly.e "W Steam Liquor CWeakJ Water Fig. 480, sorber corresponds to the charging operation of the compressor; the action of pump and generator corresponds to the compression and discharge. Coefficient of Performance of Absorption Machines. (e) No mechanical power, except the small amount for pump P, is supplied such a machine, the absorption of heat at a low temperature following from the supply of heat at a high tem- perature. The coefficient of performance cannot therefore be obtained as in previous cases. If, however, it is considered as the quotient found by dividing the heat absorbed by heat sup- plied to cause that absorption, a ratio is obtained which may be used in the same way as the coefficient of performance. Comparing such ratios with those for ideal refrigeration oper- ating on a reversed Carnot cycle it is found that the absorption machine has a coefficient of performance of about one-eighth to one- tenth that of the ideal. (f) It was shown in Sect. 353 (h) that for the compression process the coefficient is about seven-tenths of the ideal and it would seem from this that the absorption machine should give a very poor commercial result. It should, however, be observed 748 HEAT-POWER ENGINEERING that the coefficient for the compression machine was based upon the energy suppHed the compressor and not upon the heat suppHed the plant which generated that energy. To make the two results comparable the value of 0.7 for the compression machine must be multiplied by the thermal effi- ciency of the plant on the basis of developed horse power. When this is done the two types are more nearly on an equal footing, with the absorption machine giving the better perform- ance for wide temperature ranges, excepting when a very efficient plant is used to drive the compression machine. 356. Rating of Refrigerating Machines, (a) Refrigerating machines are generally used in practice for the purpose of main- taining a cold atmosphere in "cold-storage rooms" or for the making of ice. The ammonia machines generally achieve both results indirectly by cooling brine and pumping the brine to the point at which heat is to be absorbed. (b) No matter what use is made of the refrigerating machine or how it operates, it is rated on ice-melting capacity in pounds, or tons, per unit of time. To melt one pound of ice at 32° F. to water at the same temperature requires approximately 144 B.t.u. A machine which could absorb from the cold body a quantity of heat equal to 144 B.t.u. per hour would have an ice-melting capacity of one pound per hour. The capacity is generally ex- pressed in tons per twenty-four hours, thus this machine would have an ice-melting capacity of (i X 24) -^ 2000 = 0.012 ton, approximately. Ice-melting capacity has no direct connection with ice-making capacity. When making ice the water from which it is made must first be cooled to freezing temperature, the ice then formed, and generally reduced to a temperature considerably below 32° F. As a result, the ice-making capacity of a machine is generally only about one-half of its ice-melting capacity. - PROBLEMS. CHAPTER II. 1. Assuming the specific heat of water constant and equal to unity, how many B.t.u. are required to raise the temperature of i lb. of water from 32° F. to 212° F.? 2. Under the same assumptions as above, how many B.t.u. must be ab- stracted to lower the temperature of 20 lbs. of water from 212° F. to 32° F.? 3. If 33,000 ft. -lbs. of mechanical energy are completely converted into heat energy, how many B.t.u. result? 4. If mechanical energy is made available at the rate of 33,000 ft. -lbs. per minute for i hour it is said that i horse-power hour has been made available. What is the energy equivalent of i horse-power hour in thermal units? 5. Find the weight of water (specific heat = 1) which will have its tem- perature doubled by the addition of 180 B.t.u., the final temperature being 120° F. 6. Find the change of temperature of 12 oz. of lead (specific heat = 0.0314) when 4 B.t.u. are added. 7. Assuming no loss by radiation, how much electrical energy in terms of thermal units would be required to raise the temperature of a copper wire one mile long and weighing 0.3 lb. per foot through a range of 10 degrees? The specific heat of copper is 0.095. 8. If 130 B.t.u. raise the temperature of 10 lbs. of cast iron 100 degrees, what must be the specific heat of this material? 9. Assume the specific heat of wrought iron as 0.113, the specific heat of water as i.o and the weight of water as 62.5 lbs. per cu. ft. Find the increase in temperature of 2 cu. ft. of water when a common temperature of 45° re- sults from putting into the water a piece of iron weighing 10 lbs. and at a temperature of 1000° F. 10. A winch is used in lowering a load of two tons a vertical distance of 50 ft. The load is lowered by means of a friction brake which prevents the attainment of too high a speed and which brings the load to rest just as it reaches the end of the 50-ft. drop. It takes one minute to lower the load. Neglecting friction of bearings and similar losses, how much heat must be radiated by the mechanism of the brake and winch? How many horse power must be absorbed by the brake? 11. An electric motor receives electrical energy, converts part of it into heat within itself and delivers the remainder at the pulley as available me- chanical energy. A certain motor delivers, in this way, 20 horse power (i h.p. = 33,000 ft. -lbs. per min.) and converts into heat 15 per cent of all the energy supplied it. How much heat must this motor dissipate per hour? How many ft. -lbs. of energy must be supplied it per minute? 12. Assume yourself called upon to investigate the claims made for a piece of mechanism with the following characteristics. It receives no energy of any kind excepting that given it by a driving belt which supplies 250,000 ft.- Ibs. per minute. It is claimed that the mechanism gives out or makes avail- able 400 B.t.u. per minute. Would you make the investigation? Why? 13. What is the largest amount of heat energy which the mechanism oper- ating as in problem 12 could make available per minute in an ideal case? Could it do this in practice? Why? 749 750 HEAT-POWER ENGINEERING 14. Assume yourself called upon to investigate the claims made for a piece of mechanism with the following characteristics. It is supposed to receive no energy of any kind excepting 300 B.t.u. per minute and is supposed to make available 240,000 ft. -lbs. of mechanical energy in the same time. Would you make the investigation? Why? y 15. Assume that the mechanism in problem 14 above is supposed to receive only 300 B.t.u. as before and that in the ideal case (neglecting friction, radia- tion, conduction and similar losses) it is supposed to deliver 233,400 ft. -lbs. in the same time. Would you make the investigation? Why? 16. Assume that the value of the variable specific heat C of a subtance is given for temperature t by the equation C = 0.5 + 0.02 /. Find the total heat required to raise the temperature of 12 lbs. of the material from 50° to 100° F. 17. An engine receiving 300 B.t.u. per minute and no other energy of any kind rejects to a cold body an amount of energy equal to 150 B.t.u. per minute. If there are no friction or similar losses, what would be the amount of mechanical energy in ft. -lbs. made available per minute? ./' 18. If the engine operating as in the first part of prob. 17 above loses in friction and radiation 10 per cent of the energy which would otherwise be made available, what will be the amount of mechanical energy in ft. -lbs. made available per minute? ' 19. A factory building is being designed. Calculations from the radiating surface of the building, character of that surface, location, direction of winds, etc., indicate that about 400,000 B.t.u. per hour must be liberated within the building to keep the temperature up to 65° F. The heating engineer desires to keep the cost of the heating equipment down to a low figure and believes that he can do so by allowing for heat generated by friction of the moving mechanisms within the factory. He discovers that 100 horse power (i h.p. = 33,000 ft.-lbs./min.) are to be continuously supplied the factory by means of an electric motor and that all of this power will be consumed within the factory. The motor has an efficiency of 85 per cent. What allowance can the heating engineer make on theoretical grounds? /^ 20. In the manufacture of a certain chemical compound it is necessary to stir and mix a rather heavy liquid in a large vat. If the temperature of the liquid rises above a certain value it is apt to cause a violent explosion. The formation of the compound causes the absorption of 20,000 B.t.u. per hour and the vat is so arranged that 25,000 B.t.u. can be carried away per hour under all conditions by means of a water jacket and loss to the surrounding atmosphere. How many foot-pounds of energy could be supplied the stirring apparatus per hour without causing a dangerous rise of temperature? CHAPTER IV. i.^An ideal gas occupies a volume of 17 cu. ft. at a pressure of 1500 lbs. per sq. ft. and a temperature T. What will be its volume at a pressure of 2000 lbs. per sq. ft. and at the same temperature? 2.' A gas has its volume halved by an increase of pressure at constant tem- perature. The initial pressure was 3000 lbs. per sq. ft.; what is the final pressure? 3. A gas with an initial pressure of 4500 lbs. per sq. ft. is contained in a water-jacketed cylinder, the jacket being so connected with a water system that the temperature within it is always 60° F. The cylinder is fitted with a frictionless piston which can be moved in or out as desired. The piston is moved very slowly so that the gas is maintained at the same temperature as the water jacket. At the end of a certain time the pressure of the gas within the cylinder is found to be 14.7 lbs. per sq. in. Was the piston moved in or out? What is the ratio of the final volume to the initial? PROBLEMS 751 4. A balloon is filled with hydrogen gas at atmospheric pressure (14-7 lbs. per sq. in.) and at atmospheric temperature. The balloon then ascends to a point where the atmospheric pressure is only 12.7 lbs. per sq. in. but the temperature is the same as at the lower level. If the balloon is made of non- extensible material, what will be the pressure of the hydrogen gas within it? If the balloon is made of perfectly stretchable material (stretching with appli- cation of only infinitesimal forces), what will be the pressure within it? In the latter case what expansion of volume must have occurred? 5. The inner tube of a certain tire has a capacity of 854 cubic inches. How many pounds of air will it contain when filled with air at a pressure of 70 lbs. per sq. in. and a temperature of 32° F.? (One cubic foot of air at 14.7 lbs. pressure and 32° F. weighs 0.0807 lbs.) 6. What will be the increase of pressure of air in problem 5 if the tempera- ture rises to 70° F. and the tire does not stretch during the process? 7. A closed metal tank is designed to be safe when subjected to an internal pressure of 100 lbs. per sq. in. It is used to hold compressed air and is filled with this material at a temperature of 60° F. and a pressure of 80 lbs. per sq. in. The tank stands in the sun and its contents may attain a temperature of 125° F. Assuming that the tank does not expand with temperature and pressure changes, will the designed pressure be exceeded? What temperature would have to be attained to raise the pressure of the air to tiie 100 lbs. for which the tank was designed? 8. A submarine boat is closed at the surface, with air content at a tempera- ture of 80° F. and a pressure of 14.5 lbs. per sq. in. After sinking beneath the surface the temperature of the air drops to 40° F. If the hull has not changed size during the temperature change what must be the pressure of the air under the submerged conditions? 9. Assuming that the men and machinery in the boat of problem 8 radiate enough heat to maintain a temperature of 60° within the boat what will the air pressure be? 10. A quantity of gas occupies a volume of 10 cu. ft. at a pressure of 5000 lbs. per sq. ft. and a temperature of 70° F. What will its volume be at a pressure of 7000 lbs. per sq. ft. and a temperature of 100° F.? 11. A quantity of gas occupies a volume of 15 cu. ft. at a pressure of 40 lbs. per sq. ft. and a temperature of 60° F. What will be its volume at a temperature of 70° F. and a pressure of 30 lbs. per sq. ft.? 12. A quantity of gas occupies a volume of 10 cu. in. at a pressure of 7000 lbs. per sq. ft. and a temperature of 50° F. What will be its volume at at- mospheric pressure (14.7 lbs. per sq. in.) and a temperature of 70° F.? • 13. The value of R for a certain gas is 55. One pound of this gas occupies a volume of 12.8 cu. ft. at a pressure of 14.7 lbs. per sq. in. What is the tem- perature of the gas? What will be the volume of two pounds of this gas if pressure and temperature (ordinary Fahrenheit scale) are doubled? 14. Three pounds of air are enclosed in a nonexpansible vessel. The pres- sure is 20 lbs. per sq. in. and the temperature is 80° F. The value of R is 53.34. What is the volume content of the vessel? What will be the pressure of the air if its temperature is increased to 180° F.? 15. One-half pound of nitrogen gas is contained in a cylinder fitted with a piston. The temperature of the gas is 8g° F. and its pressure is 40 lbs. per sq. in. The piston moves out until the volume of the gas has doubled and it is then found that its pressure is 20 lbs. per sq. in. What must the tempera- ture have become? {R for nitrogen = 55.16.) 16. A certain gas is collected over mercury and measured. It is found to have a volume of 10 cu. in. at a pressure of 14.6 lbs. per sq. in. and a tem- perature of 60° F. The gas is then passed through a reagent which absorbs part of it and the remainder is collected over mercury and measured. It measures 6 cu. in. at the same pressure as before but the temperature has changed to 70° F. between the two measurements. What percentage of the original volume was absorbed by the reagent? 17. The products of combustion from a boiler reach the base of the stack 752 HEAT-POWER ENGINEERING at a temperature of 500° F. At the top of the stack their temperature is only 200° F. Neglecting the slight pressure change which would occur during the ascension, determine the relative values of the cross-sectional areas at top and bottom of the stack to give equal gas velocities at the two points. 18. An air compressor draws into its cylinder a charge of air at a pressure of 13.5 lbs. per sq. in. and a temperature of 60° F. It compresses this air to a volume equal to one-quarter of its original value and the pressure attained is 60 lbs. What must be the final temperature of the air? 19. A diving bell is to be used for executing certain work under water. It is made in the form of a flat-ended cylinder open at the bottom. The inside diam- eter is 12 ft. and the inside height is 14 ft. The men and tools accommodated within the bell occupy a cubical content of 120 cu. ft. If the bell is lowered into the water when atmospheric pressure is 14.7 lbs. per sq. in. and tempera- ture is 60° F., how far below the surface can the bottom of the bell be lowered if the water has a temperature of 40° F., weighs 62.5 lbs. per cu. ft., and is not to rise to a height of more than 4 ft. from the bottom of the bell? Assume that men and tools remain entirely within the air space, that they do not change volume with pressure change; that the air within the bell acquires the same temperature as the surrounding water. 20. A quantity of heat equal to 1000 B.t.u. (= AQ) is given to an ideal gas maintained at constant volume. What are the numerical values of the several terms in the equation AQ = AS + A/ + AE? 21. Two pounds of a gas with Cv = 0.1662 and Cp = 0.2317 are heated at constant volume from a temperature of 60° F. to a temperature of 80° F., and then at constant pressure to a final temperature of 100° F. (a) How much heat is supplied to the gas? (b) What is the value of A^" for each part of the process? (c) What is the value of AE for each part of the process? 22. The true specific heat of a certain gas is 0.1733 in thermal units. The value of R is 55.16, what is the value of Cp for this gas? 23. Three pounds of an ideal gas are heated until 200 B.t.u. per lb. have been supplied it. During the process the gas expands and 133,038 ft. -lbs of work are done by it. . Find the value of AS. ^ 24. A balloon is filled with hydrogen gas at a pressure of 14.7 lbs. per sq. in and a temperature of 60° F. The balloon is spherical in shape and has an internal diameter of 25 ft. At a later time it is found that the pressure of the gas within the balloon is only 0.95 of the original value but that the tempera- ture is the same as before. What fraction of the original weight of gas must have escaped if the dimensions of the balloon have not changed? How much heat would have had to be removed to cause the pressure to fall to the same extent if no leakage occurred? (i lb. of hydrogen at 32° F. and 14.7 Ibs./sq. in. occupied a volume of 178 cu. ft. R = 766.5; Cp = 3.41.) What would be the final temperature? 25. Ten pounds of air (specific volume at 32° and 14.7 lbs. = 12.387 cu. ft.) - are contained in a receiver at a temperature of 55° F. and a pressure of 100 lbs. per sq. in. Air leaks out until at a later time the pressure in the receiver is found to be only 40 lbs. per sq. in. with a temperature of 50° F. What weight has leaked out? 26. An air receiver has a factor of safety of 5 when filled with air at a pres- sure of 200 lbs. per sq. in. and a temperature of 100° F. What amount of heat would have to be supplied the air to reduce the factor of safety to 2.5 on the assumption that the cubical content of the receiver remains constant with changing temperatures. (Cp = 0.2374; y = 1.4037.) Assume vol. = 20 cu. ft. ^, 27. The value of R for a certain gas is 34.9. How much external work will be done by five pounds of this gas if its temperature is raised from 50° F. tp 150° F. at constant pressure? ^28. The value of Cp for a certain gas is 0.23 and the value of 7 is 1.39. What volume must this gas occupy when at a temperature of 60° F. and sub- jected to a pressure of 150 lbs. per sq. in.? Assume 5 lbs. of gas. 29. A certain gas with molecular weight equal to 28 occupies a volume of ^PROBLEMS 753 12.8 cu. ft. per lb. What volume will another gas with molecular weight of 32 theoretically occupy when at the same temperature and pressure.-* 30. A certain gas with molecular weight of 44 weighs 0.1224 lbs. per cu. ft. at standard conditions. Another gas has a molecular weight of 26. What is its theoretical density under the same conditions of temperature and pressure? 31. A water pump running at 50 strokes per minute delivers i cu. ft. of water per stroke. An air chamber is to be fitted to this pump of such size that the discharge pressure on the pump shall vary from 100 lbs. per sq. in. at the beginning of the stroke to 150 lbs. per sq. in. at the end of the stroke if all the water delivered during one stroke must be accommodated in the air chamber. The temperature of the water and of the air in the chamber re- main constant at 60° F. and no air is absorbed by the water, (a) What must be the volume of the air chamber if R for air is equal to 53.3? {h) Would there be any economic advantage in using a gas with i? = 96? 32. Assume that gas is to be used for the doing of external work by being heated at constant pressure through a certain temperature range. If a large number of gases are available but only one pound of any one gas can be used, would you select the gas having the lowest or highest value of R if maximum amount of work was a consideration? Why? What other property of the gases would you consider if size of machine was also of importance? Why? Assuming that it is desired to determine the gas which would give the maxi- mum amount of work with the smallest machine, how would you proceed? CHAPTER V. I. (a) How much work can be done by two pounds of air expanding at a constant pressure of 50 lbs. per sq. in. to twice the original volume if the initial temperature is 50° F.? {h) What will be the final temperature? (c) How much heat will have to be supplied the gas? {Cp = 0.2374.) 1^2. One-half pound of nitrogen is inclosed in a cylinder fitted with a fric- tionless piston. When the gas has a temperature of 100° F. the pressure upon the piston is 25 lbs. per sq. in. It is desired to abstract 20 B.t.u. from the gas without changing its pressure. What will be the temperature drop and how much must the volume be decreased? (Cp = 0.2438.) -i 1/ 3. A vessel with a capacity of 5 cu. ft. is filled with air at a pressure of 125 lbs. per sq. in. when at a temperature of 60° F. It is desirable to lower the pressure to 50 lbs per sq. in. What amount of heat will have to be abstracted and what will be the final. temperature of the gas, assuming that the vessel , ... ^. does not change in size with change of temperature? (-^ = 53-34; 7 = 1.4037.) ^_^. ^ 4. A cylinder permanently closed at one end is fitted with a frictionless f^" 2^S2-. < piston and stands vertical upon its closed end in a vacuum. It holds a volume of I cu. ft.'of gas at a temperature of 75° F., and a pressure of 20 lbs. per sq. in., the pressure being maintained by the weight of the piston and superposed discs of metal. The temperature is raised to 150° F. and the piston is pre- vented from rising by additional weights placed upon it. (a) What per- centage of the original weight of piston and discs must be added? (b) If no additional weights had been added how much external work would have been done by the expanding gas? 5. How much work must be done to compress 100 lbs. of air isothermally from a pressure of 13 lbs. per sq. in. at a temperature of 70° F. to a pressure of no lbs. per sq. in.? (Spec. vol. at 32° F. and 14.7 lbs. = 12.387.) 6. How much heat must be absorbed during the process assumed in prob- lem 5 above? ^ 7. One pound of air expands isothermally in a cylinder behind a frictionless piston. The initial pressure is 100 lbs. per sq. in., the initial temperature is 50° F., the ratio of expansion is 5. (Spec. vol. at 32° F. and 14.7 lbs. = 12.387.) (a) What amount of work will the gas do upon the piston? (b) How much heat will have to be supplied the gas during the expansion? 754 HEAT-POWER ENGINEERING 8. Find the work done by 0.5 lb. of carbon dioxide expanding isothermally at 100° F. from an initial pressure of 'lOO lbs. per sq. in. to a final volume of 10 cu.ft. (Spec. vol. at 32° and 14.7 lbs. = 8.1 cu. ft.) 9. Air is compressed at constant temperature from a volume of 60 cu. ft. and a pressure of 14.7 lbs. per sq. in. to a volume of 12 cu. ft. Find (a) final pressure, (b) heat removed, and (c) work done upon the gas. 10. Find the work done by 4 lbs. of air expanding isothermally from a pressure of lOO lbs. per sq. in. to 20 lbs. per sq. in., the final volume being 80 cu. ft. 11. Five pounds of air expand isothermally from a pressure of 120 lbs. per sq. in. to a final pressure of 20 lbs. per sq. in., the work done being 248,500 ft.- Ibs. (R = 53.3.) Find (a) initial volume, (b) final volume, (c) initial tem- perature, and (d) heat supplied. 12. The volume of i lb. of air at 32° F. and 14.7 lbs. per sq. in. = 12.387 cu. ft. (a) Find work done during the isothermal expansion of one pound of air from 100 lbs. per sq. in. to 20 lbs. per sq. in. at 100° F. (loge 5 = 1.61.) (b) Find initial and final volumes, (c) Find value of R. 13. A given weight of gas occupies 3.09 cu. ft. and is under a pressure of 200 lbs. per sq. in. It expands isothermally, the ratio of expansion being 3. Find (a) final volume, {b) ft. -lbs. of work done, and (c) B.t.u. necessary to do this work. 14. Atmospheric pressure at sea level on a certain day is 14.7 lbs. per sq. in. and on a certain mountain it is 12.5 lbs. per sq. in. An air compressor at each place compresses isothermally 100 cu. ft. of air per minute (measured at existing atmospheric pressure and same temperature in each case) to a pres- sure of 80 lbs. per sq. in. How much work is done upon the gas in each case? What is the difference, and what per cent of the smaller quantity is used in excess in the less favorable location? 15. If, in the preceding problem, each compressor had raised the pressure to five times atmospheric pressure at its own location, how would the quantities of work compare? 16. A gas with 7 = 1.4 expands adiabatically from an initial volume of 10 cu. ft. and an initial pressure of 100 lbs. per sq. in. to a terminal pressure of 15 lbs. per sq. in. What is the final volume? 17. A gas with 7 = 1.35 expands adiabatically from an initial volume of 0.4 cu. ft. and an initial pressure of 80 lbs. per sq. in. to a final volume of 4 cu. ft. What is the final pressure? 18. A gas with 7 = 1.41 is compressed adiabatically from an initial volume of 5 cu. ft. and an initial pressure of 15 lbs. per sq. in. to a final volume of I cu. ft. What is the final pressure? 19. A gas with 7 = 1.33 is compressed adiabatically from an initial volume of 2 cu. ft. and an initial pressure of 15 lbs. per sq. in. to a final pressure of 85 Jbs. per sq. in. What is the final volume? \po. One pound of air expands adiabatically in a cylinder fitted with a frictionless piston. The initial pressure is 100 lbs. per sq. in.; the initial temperature is 50° F.; the ratio of expansion is 5. (Spec. vol. at 32° and 14.7 lbs. = 12.387; 7 = 1.4037.) (a) What amount of work will the gas do upon the piston? (b) How much heat will have to be supplied the §^^s during the expansion?rNj (c) Compare with results of problem 7. ' "• 'l^i^ ', .. 21. Five pounds of gas with 7 = 1.4 expand adiabatically from a volume of 0.2 cu. ft. and a pressure of 90 lbs. per sq. in. to a final pressure of 18 lbs. per sq. in. (a) What is the final volume? (b) How much external work is done by the gas? 22. How much work must be done upon two pounds of gas to compress them adiabatically from a volume of 2 cu. ft. and a pressure of 14 lbs. per sq. in. to a final pressure of 80 lbs. per sq. in.? The value of 7 is 1.4. 23. What will be the difference in the amounts of work required to com- press 5 cu. ft. of free air (air at 60° F. and 14.7 lbs. per sq. in.) to a pressure of 90 lbs. per sq. in. when the compression is adiabatic and when it is isothermal? (7 = 1.4037.) PROBLEMS 755 -" 24. Assume that an air compressor can be so arranged as to compress air either isothermally or adiabatically. If receives air at a pressure of 14 lbs. per sq. in. and compresses to a pressure of 75 lbs. per sq. in. (7 = 1.41.) (a) How much work would be done in compressing an initial volume of i cu. ft. of air by each method? ih) What would be the percentage of saving when using the more economical method? 25. Five pounds of gas have an initial pressure of 300 lbs. per sq. in. and occupy an initial volume of 20 cu. ft. {Cp = 0.238; R = 53.3.) (a) Find Cv and Ti. (b) If this gas is expanded adiabatically to a pressure of 150 lbs. per sq. in., what. will be the numerical value of V2, T2 and work done? 26. One-quarter of a pound of gas with Cp = 0.238 and Cv = 0.169 is ex- panded adiabatically from Vi — 0.2 cu. ft. and pi = 300 lbs. per sq. in. to p2 = 150 lbs. per sq. in. (a) What are the numerical values of R, T, V2, T2? (b) What is the numerical value of work done? y 27. One-quarter of a pound of air is compressed adiabatically from 13 lbs. per sq. in. and 60° F, to a pressure of 100 lbs. per sq. in. After compression its temperature is decreased to 60° F. while the volume is maintained constant. (a) How much heat will have to be abstracted to bring this about? (b) What will be the final pressure? (c) If the gas is now allowed to expand adiabati- cally to a pressure of 13 lbs., how much work can it do and how does this compare with that required in the original compression? (d) What will be the volume and temperature at end of expansion as in (c) above? (Spec. vol. at 32° and 14.7 lbs. = 12.387; 7 = 14037; Cp = 0.2374.) 28. Using logarithmic cross-section paper determine the pressure exerted by a gas for each cubic foot of volume increase when expanding according to the law PF^-^^ = constant, from an initial pressure of 100 lbs. per sq. in. and an ini- tial volume of one and one-half cu. ft. to a terminal pressure of 15 lbs. per sq. in. ^ 29. Air is drawn into an air compressor at a temperature of 61° F. and at Atmospheric pressure (14.7 lbs. per sq. in.). The flash point of the oil used to lubricate the compressor piston is 350° F. If compression is adiabatic, what pressure could be attained in the compressor if the maximum allowable temperature is 50 degrees below the flash point of the oil? (Assume 7 = 1.41.) 30. An air compressor compresses adiabatically 100 cu. ft. of air per min- ute measured at initial conditions of 15 lbs. per sq. in. and 60° F. The final pressure is 90 lbs. per sq. in. (a) Find work done on air per minute, (b) Find final temperature, (c) Find weight of air compressed per minute. (Spec, vol. = 12.387 at32°F. and 14.7 lbs.; R = 53.3; and t = 141.) 31. The initial conditions of two pounds of gas are pi = 100 lbs. per sq. in. and /i = 60° F. (R for this gas is 53.3 and 7 = 1.41.) (a) How much work will be done by the gas if it expands isothermally to a final pressure of 15 lbs. per sq. in.? (b) If the expansion is adiabatic? (c) What is the percentage gain by the former method? (d) How is this gain purchased? (e) How do the final temperatures compare? v-'32. Power is obtained by expanding air adiabatically in an engine cylinder. It is found that when the temperature of the air drops below 32° F. the mois- ture which is carried by the air freezes and impairs the action of the engine. Air is received by the engine at a temperature of 60° F. and a pressure of 100 lbs. per sq. in. (Assume 7 = 1.41 and assume further that the quantity of moisture present in the air is so small as to have no thermodynamic effect, i.e., all formulas may be used as though dry air only were present) (a) What is the lowest pressure to which the air can expand if its temperature is not to drop below 32° F.? (b) To what initial temperature would it be necessary to heat the air in order that it may be possible to expand to 15 lbs. per sq. in. without dropping below the minimum allowable temperature? 33. Air is available for use in a compressed air engine at a temperature of 65° F. and at a pressure of 125 lbs. per sq. in. It is desired to preheat it at constant pressure to such a temperature that it will not drop below a tempera- ture of 35° F. when expanded to a final pressure of 16 lbs. per sq. in. according to the equation PV^-^^= const. How much heat will be required per pound if Cp = 0.237? 756 HEAT-POWER ENGINEERING 34. How much work will be required to compress two pounds of gas from Vi = 25 cu. ft. and pi = 13.5 lbs. per sq. in. to p2 = 75 lbs. per sq. in. accord- ing to the equation PF^-35 = const.? What will be the final temperature if the initial temperature is 55° F.? CHAPTER VI. 1. Is the following process thermodynamically reversible? Why? Gas in contact with a hot body with the same temperature as the gas, receives heat from that hot body while expanding isothermally and doing work. • 2. Is the following process thermodynamically reversible? Why? Gas expands isothermally and does a certain amount of work at the expense of heat received from a hot body at temperature 10 degrees higher than that of the gas. 3. Is the following process thermodynamically reversible? Why? A gas is made to expand at constant pressure by being brought into contact with a hot body. 4. Is the following process thermodynamically reversible? Why? A gas maintained at constant volume has its pressure decreased by being brought into contact with a cold body. 5. Is the following process thermodynamically reversible? Why? Gas is compressed adiabatically in a nonconducting cylinder. 6. Is the following process thermodynamically reversible? Why? Gas is compressed in a cylinder with metallic walls. 7. Is the following process thermodynamically reversible? Why? A blacksmith strikes his anvil forcibly with his hammer. 8. Is the following process thermodynamically reversible? Why? The hot gases resulting from the combustion of fuel within a boiler furnace flow up a smoke stack because their density is less than that of the atmosphere surrounding the stack. Is the process going on in the stack reversible? 9. Is the following process thermodynamically reversible? Why? A car- penter bores a hole in a piece of wood by means of a brace and bit. 10. Is the following process thermodynamically reversible? Why? A machinist cuts a thread upon a bar of metal which is rotated in a lathe. The bar and cutting tool are kept cool by a stream of soap solution. Outline the energy changes occurring and tell whether the process is reversible so far as these energy changes are concerned. 11. Assume two vessels of equal cubical content arranged as in Sect. 35 (b), one containing one pound of air at a temperature of 60° F. and a pressure of 100 lbs. per sq. in., the other absolutely void. (Spec, volume of air at 32° F. and 14.7 lbs. = 12.387). Assume that it is possible to open the cock between the two suddenly, to allow gas to flow from the high-pressure to the low-pres- sure vessel until both have the same pressure of gas, and then to close the cock suddenly so as to isolate the two bodies of gas. Assume further that the material "of which the two vessels and fittings are made is absolutely impervious to heat, (a) At the end of the process what will be the tempera- ture of the gas contained in the vessel originally charged with high-pressure gas? (b) At the end of the process what will be the temperature of the gas contained in the vessel originally void? CHAPTER VII. 1. Find the change of entropy of 4 lbs. of a gas heated at constant pressure from a temperature of 60° F. to a temperature of 1000° F. (Cv = 0.192; R = 45-3-) 2. If 6 lbs. of air are cooled at constant volume until the final pressure is one-fourth of the initial, find the change of entropy. {Cv = 0.169.) 3. If 10 lbs. of air are heated at constant pressure until k = 2 ti, thereby adding 1185 B.t.u. to the gas, find the change of entropy, (Cp = 0.237.) PROBLEMS 757 4. Find the entropy change of gas which is compressed isothermally from a pressure of 14.7 lbs. per sq. in. and a volume of 60 cu. ft. to a volume of 12 cu. ft. The gas is maintained at a temperature of 80° F. 5. If 25 lbs. of carbon dioxide, having R = 35.1, are compressed from a volume of 50 cu. ft. to a volume of 10 cu. ft., the pressure remaining constant, find the change in entropy. {Cp = 0.2008.) 6. If 5 lbs. of air expand isothermally from a pressure of 100 lbs. per sq. in. to a pressure of 20 lbs. per sq. in. and a temperature of 60° F., find the change in entropy. (R = 53.3-) 7. If ^ lb. of air is allowed to expand isothermally at a temperature of 70" F. until its final volume is 4 times its initial one, find its change in entropy. (R = 53.3-) 8. Find the entropy change of 5 lbs. of a gas which expands isothermally at 60° F. until the ratio of its final volume to initial volume is 14.8. {Cp = 0.2008; Cv = 0.1548.) 9. Find how much heat would be required to heat 4 lbs. of air at constant volume so that it would experience an entropy change of 0.468, its initial temperature being 60° F. (C^ = 0.169.) 10. 3 lbs. of air are compressed isothermally from a volume of 36 cu. ft. and pressure of 15 lbs. per sq. in. to a volume of 9 cu. ft. Find the change in entropy. (R = 53.3.) 11. At the end of the compression stroke in a gas engine cylinder, the tem- perature is found to be 970° abs. and the entropy change from 32° F. is 0.55. After combustion at constant volume (pressure rise at const, vol.) the entropy has increased to 0.96. (Cv = 0.16.) (i) What is the final temperature at the end of combustion? (2) How much heat has been added? 12. Imagine 0.4 lb. of an ideal gas to expand in a cylinder which prevents any heat flow to or from the gas, initial pressure being 100 lbs. per sq. in. and initial volume ^ cu. ft., find the work done when its volume has become 3 cu. ft. Find change in temperature. Find the change in entropy. {Cp = 0.124. Cv = 0.093.) CHAPTER VIII. 1. A Carnot cycle is performed with gas as a working substance. The temperature of the hot body is 1000° F, and that of the cold body is 60° F. How much work is done per cycle if the heat supplied per cycle is 10 B.t.u.? 2. In the case of the Carnot cycle as above with higher temperature 1000° F. and lower temperature 60° F., how much work would be done per cycle if the heat rejected per cycle equals 10 B.t.u.? 3. A Carnot cycle with gas as working substance is used for the develop- ment of power. It is desired to obtain 100 ft. -lbs. of work per cycle. The heat supplied per cycle equals 0.3 B.t.u. and the temperature of the hot body is 500° F. What must be the temperature of the cold body? 4. A Carnot engine is to be used as a heat pump to remove 10 B.t.u. per cycle from a body at a temperature of 32° F. and discharge to a body at a temperature of 100° F. (a) How much energy will be required per cycle to operate this heat pump? {b) How much will be required if the upper tem- perature is 200° F.? (c) How much heat will be discharged to the hot body in each case? 5. An engine using air as a working substance, receiving heat from a hot body at temperature 1000° F. and rejecting at temperature 100° F., operates on a cycle composed of an isothermal expansion, an adiabatic expansion, an isothermal compression, and an isovolumic. Is this a reversible cycle? Why? 6. Draw cycle described in 5 above and determine: (i) Heat supply (positive or negative) during each process. (2) Work done (positive or negative) during each process. (3) Efiiciency of cycle. (4) Carnot efficiency with same temperature limits; 7 = 1.41; R = 53-3; W = i lb.', r = 2 for the isothermal expansion. 758 HEA T-POWER ENGINEERING 7. One-half of a pound of air is enclosed in a cylinder fitted with a move- able piston. It occupies a volume of 3 cu. ft., exerts a pressure of 100 lbs. per sq. in., and the area of the piston is i sq. ft. The gas is expanded at constant pressure to a volume of 6 cu. ft.; the pressure is then dropped at constant volume to a value of 15 lbs. per sq. in.; the gas is then compressed at constant pressure to a volume of 3 cu. ft.; lastly the pressure is raised to 100 lbs. per sq. in. at constant volume. (a) Draw the cycle to PV coordinates and indicate values of pressure, vol- ume and temperature at the four corners. (&) Find the net work done by the gas during one cycle. (c) Find the heat supplied or rejected during each process and the net heat change. {d) Find the efficiency of the cycle. {e) Assuming the use of one hot and one cold body is this cycle reversible? Why? 8. (a) Draw the Carnot cycle to PV and T^ coordinates for the following con- ditions. Two pounds of nitrogen are used as working substance. The maxi- mum temperature is 1500° F. and the maximum pressure is 200 lbs. per sq. in. The ratio of isothermal expansion is 2. The minimum temperature is 50° F. {h) Find the heat supplied, the heat rejected and the work done. (c) Find the efhciency of the cycle, or of an engine using the cycle. 9. (a) Determine the efficiencies of Carnot cycle engines using gaseous working substances when the hot body and the cold body have the following temperatures respectively: Hot Body Temperature Cold Body Temperature (1) 3000° F. (2) 1500° F. (3) 1500° F. 500° F. o°F. 500° F. {h) Which is the more effective method of increasing the efficiency, raising T\ or lowering 7"2? Why? 10. If the maximum and minimum temperatures and pressures are both given, what must be the ratio of isothermal expansion in a Carnot cycle engine using gas as a working substance? 11. An engine operating on the Joule cycle has the following conditions at the end of compression Va = 0.5 cu. ft.; pa = 70 lbs. per sq. in.; Ta = 1800° abs. After constant pressure expansion the volume is 0.75 cu. ft.^ For the gas used Cp = 0.26 and Cv = 0.19. Temperature at end of expansion is 900° abs. and at the beginning of compression is 600° abs. Find y(i) Net work of cycle. (2) Efficiency of cycle. 12. A gas engine operating on the Otto cycle uses 0.15 lb. of gas per cycle having Cp = 0.2056, and Cv == 0.1457. The pressure at end of compression is 75 lb. per sq. in. and the temperature is 1000° abs. At end of explosion line the temperature has risen to 2500° abs.; at the end of expansion the temperature is 1800° abs. and at the beginning of compression it is 720° abs. Find: .^^^ j ■ ^ ^^ *7^ jo V 13. A gas engine operating on the Diesel cycle uses an oil, the products of y^i v-' (i) Work during expansion and compression. 1 > • ^ i iJ •^-^^^^y^A^W) The heat sent into, and the heat sent out of, the system. .^ ^M *» ^ ""r^ /(3) ^^^ efficiency of the cycle. *1S io V i^. A gas engine operating on the Diesel cycle u combustion of which have a gamma value of 1.41. The weight of gas used is 0.15 lbs. The temperature at end of compression is 1800° abs. and at end of constant pressure expansion is 2000° abs. The clearance is 8 per cent and the piston displacement is 2 cu. ft. (Cp = 0.2056, Cv = 0.1457.) Find: (a) Heat added. 80, 125, 175 and 300. 2. Determine from the steam table the space filled by 10 lbs. of dry satu- rated steam under an absolute pressure of 200, 175, 135, 100, 80 and 10 lbs. per sq. in. 3. By means of the steam table determine the number of pounds of steam that will be required to fill 10 cu. ft. when under an absolute pressure of 200, 115, 40 and 5 lbs. per sq. in.: (a) If the quality is 100 per cent; (b) If the quality is 80 per cent. 4. Determine by means of the steam table the entropy of the liquid, and PROBLEMS 761 the entropy of vaporization for i lb. of steam under the following absolute pressures: 15, 50, 80, 125, 175, and 300 lbs. per sq. in. {a) If the quality is 100 per cent, {b) U the quality is 90 per cent. 5. Assuming the specific heat of water to be unity, compute the entropy of the liquid for a pound of water heated to the point of vaporization for an abso- lute pressure of 100 lbs. per sq. in. Find the per cent error by comparison with steam table values. 6. Compute the entropy of vaporization for a pound of steam having the following temperatures: 400, 300 and 200° F., the corresponding latent heats being 827.2, 909.5 and 977.8 B.t.u. 7. (a) Determine from the steam tables the amount of heat required to make a pound of steam, having a pressure of 100 lbs. per sq. in. abs., by heat- ing the water to the temperature of vaporization from a temperature of 100° F., and then vaporizing until the quality is 80, 90 and lOO per cent. {b) Draw the T^-diagram for (a). 8. With the same data as in (7) find; (a) The amount of heat required to superheat the steam 100°, 200°. Take Cp = 0.50. {b) Draw the T^-chart for (a). 9. Determine by means of the steam table the quality of steam containing 1029 B.t.u. of intrinsic heat and having a pressure of 125 lbs. per sq. in. abs. 10. Determine by means of the steam table the intrinsic heat added to I lb. of water in heating it from 90° F. to 444° F., if the pressure is keot con- stant at 120 lbs. per sq. in. abs. 11. Heat is added to i lb. of steam at a constant pressure of 80 lbs. per sq. in. abs., thereby increasing the quality from 0.4 to 0.9. Find by means of steam tables: (a) How much heat is added, {b) How much internal heat is added. {c) How much external heat is added. {d) How much work in ft.- Ibs. is done, {e) How much the volume of the steam is increased. 12. Find by means of the steam table the heat required to evaporate 50 lbs. of water having a temperature of 102° F. when pumped into a boiler, the steam pressure in which is 125 lbs. per sq. in. abs. 13. If the temperature of the feed water is 200'', find by means of the steam table the amount of heat required to make 100 lbs. of steam having a quality of 95 per cent, the pressure being constant at 175 lbs. per sq. in. abs. 14. By means of the steam table determine the volume occupied by the steam in the previous problem. 15. Compute the external work performed in vaporizing 4 lbs. of water into dry steam under a constant pressure of 100 lbs. per sq. in. abs. Com- pare with tabular value. 16. Find the pressure equivalent to the internal force which must be overcome in vaporizing i lb. of water under a pressure of 100 lbs. per sq. in. abs. 17. Steam in a boiler is under an absolute pressure of 100 lbs. per sq. in., and is superheated 150.6°. (a) Find by Tumlirz equation the specific volume of this steam. {b) Find the total heat of this steam if its specific heat is 0.51, (c) Show part {b) on a T0-chart. 18. Find the heat of superheat, and the total intrinsic heat energy for the steam in the previous problem. 19. Sketch on a T^-chart the water curve and saturation curve for a pound of water vapor between the pressure limits of 2 and 200 lbs. per sq. in. abs. showing the intermediate values for the following pressures, 10, 50 and lOO. (o) Mark on the sketch the value of the temperature and the entropy for each point, estimating the distances as closely as possible. ib) Give the numerical values for, and show what areas represent, the heat of the liquid, and the latent heat for the two limiting pressures given above. (c) If you had drawn the above sketch to the following scale: i" = 100° of temperature and i" = | unit of entropy, how many sq. in. would represent the total heat of the steam for the pressure of 200 lbs. per sq. in. abs.? Indicate this area on your sketch. 20. Find the volume of a boiler containing 1000 lbs. of water and 6 lbs. of 762 HEAT-POWER ENGINEERING dry saturated steam under a pressure of 135 lbs. per sq. in. abs. What per cent of this volume is occupied by each.? What per cent of the total heat energy above 32° is contained in each? 21. How much water having a temperature of 60° F. will be required to condense 3000 lbs. of steam per hour, the quality of the steam being 90 per cent and the pressure within the condenser being i lb. per sq. in. abs..? How much, if the condenser pressure is 5 lbs. per sq. in.? Assume the cold water to be thoroughly mixed with the steam. 22. Four pounds of steam having an absolute pressure of 125 lbs. per sq. in. are condensed by flowing into 200 lbs. of water, the temperature of which is thereby raised from 60 to 80° F. Find the initial quality of the steam. 23. Find the total heat necessary to change 500 lbs. of water from a feed pump temperature of 80° F. into superheated steam having a temperature of 1000° F., the boiler pressure remaining constant at 125 lbs. per sq. in. abs. Take the specific heat of superheated steam for this range to be 0,50. 24. One pound of water at a temperature of 60° F. enters a boiler and is vaporized under a pressure of 115 lbs. per sq. in. abs. until it becomes dry and saturated steam. How many pounds of water might have been vaporized if the same amount of heat had been added to the water at a temperature of 212° and changed into dry steam at this temperature? 25. How much steam with a quality of 90 per cent and an absolute pressure of 3.00 lbs. per sq. in. is condensed in a surface condenser using 14,500 lbs. of circulating (or condensing) water per hour, the water entering the condenser at 55° F. and leaving it at 115° F.? 26. An engine develops 15 horse power using 28 lbs. of steam per horse- power hour. If the engine exhausts its steam with a quality of 85 per cent and pressure of 15 lbs. per sq. in, abs. to the atmosphere, find the amount above 32° F. discharged per minute. What would be the maximum amount of heat that could be abstracted per minute from this exhaust steam by means of water which is to attain a temperature of 200"^? 27. For each pound of coal having a heating value of 14,300 B.t.u., a certain boiler evaporated 10 lbs. of water into steam, with quality of 95 per cent, the pressure being constant at 145 lbs. per sq. in. abs., and the temperature of the feed water being 188° F. Suppose that another boiler, using this same kind of coal, evaporated 9 lbs. of water into dry steam, under constant pressure of 125 lbs. per sq. in., from a feed water temperature of 121° F. Find the heat given water and steam by each boiler, and the boiler efficiencies (efficiency = heat supplied water and steam -^ heat supplied boiler). 28. Determine by means of the T0-diagram the pressure at which steam will become dry and saturated by expanding reversibly and adiabatically from a pressure of 100 lbs. per sq. in. and a superheat of 50° F. 29. Determine by means of the T^-diagram the final condition of steam which expands reversibly and adiabatically from an initial superheat of 150° F. at a pressure of 150 lbs. per sq. in. to a final pressure of 15 lbs. per sq. in. 30. Determine by means of the T^-diagram the volume of 10 lbs. of 80 per cent steam at a pressure of 75 lbs. per sq. in. 31. By means of the values given in the steam table draw- a T4 «^^ i- : qf9 IJTIO e, - 1 ,*i.|^f 1 ^>^ d-^ 't.i-?. a - : VO"?© K- . -^cj.e^^o ' 766 HEAT-POWER ENGINEERING 17. Find the heat supplied, heat rejected, work done and the efficiency of an engine working on the Clausius cycle receiving steam with a pressure of 140 lbs. per sq. in. abs. and 150° of superheat, if the exhaust pressure is 15 lbs. per sq. in. abs. Show the PV- and T^-charts. 18. Find the heat supplied, heat rejected, work done and efficiency of an engine working on the Rankine cycle in which the initial steam pressure is 130 lbs. per sq. in. abs. with 150° of superheat; and the temperature at the end of adiabatic expansion is 240.1° F. while the exhaust pressure is 15 lbs. per sq. in. abs. Show on PV- and T - i«^ , "? v^ ^^ of the various products of combustion? (&) What is the percentage compo- iT'Jjt/ sition of the products of combustion on a volume basis? (c) What quantity ^' w , of heat is liberated? H^N 13. The analysis of the gases obtained by burning carbon in air shows C (Xa ^,/; >0M'^ oxygen, 2 per cent; nitrogen, 80 per cent. ^^ ^-' CHAPTER XXX. 1. During the test of a certain boiler it is found that when fired with coal with a heat value of 14,000 B.t.u. per pound the ash contains 0.2 of a pound of carbon per pound of coal fired, (a) What is the heat value of the ascend- ing combustible per pound of carbon? (6) What is the grate efficiency? 2. If each pound of coal fired as in problem i causes the generation of 8 lbs. of dry and saturated steam at a pressure of 150 lbs. abs. from feed )). ^\'^ H V 776 HEAT-POWER ENGINEERING water at a temperature of 120° F., what is the value of the boiler efficiency according to the A.S.M.E. definition? 3. What is the over-all efficiency of the boiler considered in problems i and 2 above? 4. If a boiler generates 9 lbs of steam with a quality of 97 per cent at a pressure of 125 lbs. abs. from feed at a temperature of 70° F., what is the equivalent evaporation? 5. A certain boiler generates steam at a pressure of 160 lbs. abs., and superheated 100 degrees from feed at a temperature of 200° F. What is the factor of evaporation? 6. How many pounds of water at a temperature of 70° F. should be con- verted into dry saturated steam at 125 lbs gauge per hour by a loo-h.p. boiler when operating at normal load? What is the factor of evaporation for this case? How many pounds of material would leave the boiler per hour if it gave steam with a quality of 97 per cent? CHAPTER XXXII. 1. (a) Using Fig. 326 and Table XXIV, how much draft through the boiler will probably be required to burn 20 lbs. of anthracite pea coal per square foot of grate per hour? (&) With 50 ft. of flue and two 90° bends, what will be the draft probably required at the base of the stack? (B. and W. Boiler.) 2. (a) With flue temperature 550° F. and air at 60°, what would be the theoretical height of stack for case given in problem i ? (b) What would be the actual height? (c) What would be its diameter in inches for a 2000 boiler h.p. plant? CHAPTER XXXV. 1. Determine the quantity of heat which will flow per hour between two planes i ft. apart and of 6 sq. ins. section with a temperature difference of 100° F., the material being commercial copper and no allowance being made for variation of specific conductivity with temperature. Determine the "heat resistance" of the material between the two planes. 2. Determine the same quantities as called for in problem i, but for a case in which soft steel is the conducting material. 3. Determine the same quantities as called for in problem i, but for cases in which water and air are the conducting materials. 4. Tabulate the values obtained for quantity of heat transmitted in above cases and tabulate values as percentage by calling that transmitted by copper 100 per cent. 5. Taking values from Table XXVI, determine the specific conductivity of yellow brass at a temperature of 200° F. 6. Assuming values given in the text as correct, determine the amount of heat lost by radiation in i hour from the black surface of a sphere of i ft. radius and at a temperature of 1000° F. Do the same for a temperature of 2000° F. 7. (a) If the temperature difference at end a of the heating surface is 2000° and at end b it is 200°, what is the mean temperature difference with flow? (b) U K = 3.7, how many square feet of heating surface will be re- quired to transmit per hour 33,463 B.t.u. (= i boiler h.p.)? 8. A surface condenser receives exhaust steam at temperature 115° F., the initial temperature of the condensing water is 60° F. and its final temper- ature 105° F. (a) What is the mean tenperature difference? (b) With K = 300, what weight of dry steam will be condensed per square foot of sur- face per hour? (c) What is the efficiency of the surface (neglecting losses)? 9. In a boiler the furnace gases are cooled from 2500° F. to 550° F. and the temperature of the steam is 350° F. (a) Neglecting losses, what is the mean temperature difference? (b) If 3I lbs. of steam from and at 212° is evapo- rated per square foot of heating surface, what is the value of K? PROBLEMS 777 10. With parallel flow the initial and final temperature differences are 500° and 203. (a) What is the mean temperature difference? (6) With K = 2> B.t.u. how much heating surface is required for heating 30 lbs. of water per hour from 60° to 192°? 11. (a) With counter-current flow, with a temperature difference of 322° at one end of the heating surface and 357° at the other end, what is the mean temperature difference? (&) With K = 2> B.t.u. how much heating surface is required for heating 30 lbs. of water per hour from 60° to 192° F.? 12. In a feed water heater 90 lbs, of water per hour are heated by i sq. ft. of heating surface, K being 220. (a) If the initial temperature difference da is 142°, what is the final value dh, neglecting losses? {h) What is the effi- ciency? (c) Compute the efficiencies corresponding to different extents of surface and plot curve showing its variations. 13. In a boiler the initial temperature difference between gas and water is 2000° F. (a) If one boiler horse-power hour is equivalent to 33,479 B.t.u. and K is 3.7, what will be the final temperature difference (neglecting losses) if 100 lbs. of flue gas (with Cp = 0.24) are generated per boiler h.p. hour, {h) What is the efficiency? (c) Compute the efficiencies corresponding to differ- ent extents of surface and plot curves showing its variation. 14. In an economizer with parallel flow, i- CO M M 5 CS 00 H 00 lONO CO -^ ^ >OvO - On .00 i>. CO H 00 t^ 01 CO H CONO On CO M CO !>- -nO VO MMMMM i i > ■^ CN - 00 00 t^vo VO CO CO CO CO CO M M HHHMM MMMMM 3 < f^ 1^ t^ 10 ro ^ uovo f^OO CN » r^NO NO t^ t^ t^ t^ VO NO VO On vo On "^ VO 01 ■^ '^ rj- CO CO t-» j>. t^ !>. t^ CS CM CM M M X>. !>. i>. t^ t^ Cj lJ k-ll-IMI-IM HUt-ll-ll-l < 1 X w * 00 Tt H 'd-OO . t^ t~^ t^ t^ •^ -^ Tf VO VO t^ f^ t^ r^ t^ Q < < CO 1 d 1 1— 1 Q. ■* - vo VO t^ r^ M M M H 00 00 ^ t^ covo CO 00 On On On MMMMM M CS CN| » 10 M H On 10 "^ '^ r^ H C) CN) CN< H 00 VO Tt PONO OV IH fO ro CO PO rt- ■^ ThNO 00 On '^ rl- 't '^ M M H M VO M VO M M 04 CO -^ lOvO VO VO VO VO VO MMMMM t^OO 00 On VO 10 VO vovo M M H M M -4-> 100 r^ CN 00 00 - ONOO 10 8 CO tJ- rt CS VO H VOOO M NO CN) 00 fO r^ j>.oo 00 On t^ M 10 On M CO VO On W 1000 M M CN< CM (N «N CN| ID M VO t^oo M M M M -i y^ CN CN M M O O On onoo CO 00 t^ r^ i>- t^ i > 5 '^ ^ '-< O O M (N -^ (N M O OnOO CO CO CO CN C-J On m r-^O 00 lOOO O (OnO f^NO NO lO "^ CN (N .00 00 On (O CO CO i^O CO ~ CO CO '^ '^ '^ -^ t^ O CS M M CS CN (N '^ '^l- -^ ^ -"t o o o o o o o o o o o o o o o o o o o o o -6- < r^ t^ r>. j^o 00 W NO CJ H CO On Tf O NO Onoo 00 00 r^ NO NO NO NO NO M CO r^ CO H oo r^ r^ t^ t^ t^ NO NO NO r^ t^ t^ {-. r^ r^ j>. t^ t^OO 00 00 r^ t^ j>. t^ !>. 00 00 00 On On C u s Q. M lo O lo O . lO lO to tJ- -^ -"^ 00 00 00 00 00 CO H On t>. to ■^ Tj- CO CO CO 00 00 00 00 00 e2 3 vO . On CN to On O On t^O to On 0\ On On On CN o r^ lo CO Tt -^ <0 fO CO On On O^ On On H On f^ to CO CO CN CN CN . "* O M M 00 o\ o CO CO '^^ -^ ""I- APPENDIX 787 Pres. Abs. Lbs. Sq. In. O. sSv^SSR fl^^'Rcg CO 00 00 00 O^ Sp. Vol. Cu. Ft. > lo lovo 00 O 0\ r^ lo po cs Tj- On -"t O t^ O 00 r~*NO ^ ^ (N (N . . rf CO CO CO CS H H M M H < o) O 00 lo M O oo uooo M ro ro <~0 <~0 '^ '* '^ ^ •^ '^ CO NO 00 M CO ^ ^ ^ to lO ^ rl- Tl- Tt- rt- 1^ o H CO T^ to i^ O o) 'vf to tONO NO NO ^ -=*■ '^ -^ '^ ^ '^ ^ rj- CO NO 00 O cs Tt NO NO t^ t^ t^ Tj- T^ Tt rl- Tt- O O o O O O O O o o o o o o o o o o 'c3 o g -e- < O oo >o CO O "sf oo CO OO CO ^ vO O O O VO CO CNl H O 00 NO ^ .00 Os O CNq ro -^ lO NO t^OO On On O M Of CO -^ 0\ 0\ 0\ o o c^ r^ j>^ !>. x-» O O O O O 00 00 00 00 00 o o o o o 00 00 00 oo oo M M tH H H 00 00 00 00 00 o3 G ■ 1— ( a. O ■ t^ [l^^'Rcg 00 00 00 00 o\ s.3;s^8 * Gauge Pressure. Lbs. d cr in CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO t^ On M CO lO tJ- ""^J- vo lo lo r^ On M CO lO to »OnO NO NO t^ On H CO to NO NO t^ X>. t^ t^ On H CO to t^ t^OO 00 00 788 APPENDIX Pres. Abs. Lbs. Sq. In. Oi g-gK-S!? ^JJ?^l^g, l^vgv^RK (gcj?a^§ Sp. Vol. Cu. Ft. > O r-« O vo PO PO ;^00 X 4 M 00 O Tt O 0\ O CO 1^00 M M O OsOO H M M O O 0^ - M lo t^OO 00 Ov Ov -^ ^ '^ '^ -^ 00 10 . 'Jj- On H H tJ- 10 10 10 10 H C^ CM CM CM to to to to to 00 Nb^rt- t-» CM tooo M CO CO CO CO -"^ Tt to to to to to O o o o 00000 00000 00000 1 g -e- < O cvi t^ CO On 00 "^ O t^ CO On On OnOO 00 VO lO lO lO lO r^ t^ r^ O^ c^ t^ -^ M On 00 r^ t^ t^NO lO vo 10 10 10 •^ On to t-^ NO CO M OnnO NO NO NO to to to to to to to CO 00 NO NO ■<^ CM On r-^ to 10 to -"^f '^ ■<:1- 10 to to to to H M H H M in 1 E § 1 4J G 0) +-> 03 * NO 00 On O H CO "^vo r^oo 0^ • i^ c^i O ON On On 00 00 ir^ t^ f^ r^ to c^ ONOO 00 00 00 r^ f^ j>. r^ t>. 00 to CO H On t^ f^ r-^ r^NO fN. ^^ 1^ t^ x^ f^ to CO M On o 3 cq lOOO cs t^ CO On NO ■* • "^ 00 00 r^ t^ t^ 00 00 00 00 00 (N ON J>. 10 CO r^NO NO NO NO 00 00 00 00 00 M 00 NO Tt- 01 \0 to to to to 00 00 00 00 00 00 NO to CO 00 00 00 00 00 u cu 03 -Si O lO O CO lO NO r-^NO -^ (N OnnO cs t^ . t-^ r>.00 CO CO CO CO CO CO Abs. Lbs. Sq. In. 04 lO O lO O ID O M M N (S ^J^^^S, I^^nSn^RK cSc^a^s * Gauge Pressure Lbs. — ( CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO 8nS8 0^2 10 to 10 M CM C^ CO CO to to T^ ^ to too to to to NO t^ t^oo 00 . APPENDIX 789 i cm Abs. Lbs. Sq. In. Oi S>888888 r^ oOTMOO N Sp. Vol. Cu. Ft. to > M 10 10 t^ tr> 10 00 10 H -^ CN H M H I a, > ^1^ 1000 > M 00 \0 00 CN -^ <^e\- r>-. 66066 r^ -. •a a> 1 1 13 * rj- ri- 10 rfoo O 00 00 00 00 ir^vO cu 1— ( Q. 00 (N \0 H 00 t^ •<+ -. t^ CN ^ CO CO CO ^ ^ vo en g 10 H M A-. 0-. . 10 vo H T^'O ■* <* ^ ^ '^ ■* 1^0 J>- t3 Abs. Lbs. Sq. In. 04 5,888888 M CO Tj-UJ N M = total entropy above 32° F. Absolute Pressure. Lbs. Sq. In. Degrees of Superheat. Sat. Temp. op 50 100 150 200 250 300 ^5 1 (213) 1 Sp.V. AQ A(j> 26.27 I150.7 I • 7549 28.40 1174.2 I . 7886 30.46 1197.6 1. 8199 32.50 1221.0 1.8492 34-53 1244.4 1.8768 36.56 1267.7 1.9029 38-58 1291.1 1.9276 50 1 (281) Sp.V. AQ A(f> 8.51 1173.6 I. 6581 9.19 1198.8 I . 6909 9.84 1223.4 1.7211 10.48 1247.7 I. 7491 II. II 1271.8 1.7755 11.74 1295.8 1.8002 12.36 1319-7 1.8237 100 (327.8) Sp.V. AQ A0 4.43 1186.3 1.6020 4-79 1213.8 1.6358 5.14 1239.7 1.6658 5.47 1264.7 1-6933 5.80 1289.4 I. 7188 6.12 1313.6 1.7428 6.44 1337.8 1-7656 no (334.8) Sp.V. AQ A 3-73 1189.6 1.5873 4.04 1217.9 I. 6216 4.33 1244. I I. 6517 4.62 1269.3 1.6789 4.89 1294. I I. 7041 5.17 1318.4 I. 7280 5-44 1342.7 I . 7505 130 (347 4) Sp.V. AQ A(j> 3.45 1191.0 1.5807 3.74 1219.7 1.6153 4.02 1246. I 1.6453 4.28 1271.4 1.6724 4-54 1296.2 1.6976 4.80 1320.6 I. 7213 5.05 1344.9 1-7437 140 (353. I)| Sp.V. AQ Acf> 3.22 1192.2 1.5747 3-49 1221.4 1.6096 3.75 1248.0 1.6395 4.00 1273.3 1.6666 4.24 1298.2 I. 6916 4.48 1322.6 I. 7152 4-71 1346.9 1.7376 150 (358.5) Sp.V. AQ A 3.01 1193.4 I . 5692 3.27 1223.0 I . 6043 3.51 1249.6 I . 6343 3-75 1275.1 I. 6612 3.97 1300.0 1.6862 4.19 1324.5 I . 7097 4-41 1348.8 1.7320 160 f (363.6)1 Sp.V. AQ A 2.83 1194.5 I . 5693 3.07 1224.5 I . 5993 3.30 1251.3 1.6292 3-53 IP76.8 I. 6561 3.74 1301.7 I. 6810 3.95 1326.2 I • 7043 4.15 1350.6 1.7266 170 f (368. 5) 1 Sp.V. AQ A 2.68 1195.4 1-5590 2.91 1225.9 1.5947 3.12 1252.8 1.6246 3.34 1278.4 I. 6513 3.54 1303.3 1.6762 3-73 1327.9 I . 6994 3-92 1352-3 I. 7217 180 f Sp.V. AQ A0 2.53 1196.4 1.5543 2.75 1227.2 I . 5904 2.96 1254.3 I. 6201 3.16 1279.9 1.6468 3>-2>S 1304.8 I. 6716 3.54 1329-5 I . 6948 3-72 1353.9 I. 7169 190 j (377. 6)| Sp.V. AQ A(f> 2.41 1197.3 I . 5498 2.62 1228.6 1.5862 2.81 1255.7 I. 6159 3.00 1281.3 1.6425 3.19 1306.3 1.6627 3-37 1330.9 1.6904 3-55 1355.5 I. 7124 200 (381. 9) 1 Sp.V. AQ A(t> 2.29 1198.1 I . 5456 2.49 1229.8 I. .5823 2.68 1257. I I. 6120 2.86 1282.6 1.6385 3.04 1307.7 1.6632 3.21 1332.4 1.6862 3-38 1357-0 I . 7082 (4i7.5)[ Sp. V. AQ A 1.55 1204. I I. 5129 1.69 1240.3 1.5530 1.83 1268.2 1.5824 1.96 1294.0 1.6082 2.09 1319.3 1.6323 2.21 1344.3 1.6550 2.33 1369-2 1.6765 500 f (467.3)1 Sp. V. A^ A0 0.93 1210.0 1.470 1.03 1256 I. 519 1. 113 1285 1.548 1.22 1311 1. 573 1.31 1337 1.597 1-39 1362 1. 619 1.47 1388 1.640 CM £/, 190; rZ^E/A-, 365; TIEf, 190; T.U.E., 561; t, 30, 638; ^a499; ^c, td, 674; //, 499, 653; tf', 653; ^i, U, 672; tv, 105. U.E., 561; w, 107, 133, 140, 371. F, 32, 286, 462; V, 33, 133; Fc, 680; Ves, 719; Vs, 137; F^, 680; F£/, 720; V, 286, 371. TF, 8, 14, 197, 258; Wc, 239; Wd, 191, 363; W^dA-, 3^3\ Wi, 191; PF/, PF/^, 363; W], 239; w, 206, 372, 496, 653, 672; w', 654; Wc, 638; w/, 205; wf', 228; Wfc, 205; W/i, 638; Wh, 496; W7V, 496. X, 481; a;, HO, 479; xf, Xk, 220. :y, 108, 476, 481. Z, 647; z, 575; a, 277, 625; /3, 627; y, 38. A (finite change); AE, 11; A£p, AE5, 158; AEsx, 159; ^■?', A^, n; A^^?, A^s, m; AQxp, 110; AQxs, hi; AQj/p, 109; A5, 11; A0, 66; A(/>z), A0z, 119; A<^s, 120; A, 137, Appendix. Chemical combination, heat from, 3-5. equilibrium (prod.), 594. Chimneys, area of, 581, 583. draft of , 579- INDEX 8oi Chimneys, height of, 580, 581, 583. Kent's formula for, 582. Kingsley's experiments on, 583. types of, 584-585- Circulating pmnp, 666. water (condenser), 672, 673. Circulation, boiler, 542, 546. convection, 629. Clapeyron's equation, 133. Clayton's analysis of expansion, 351. Clearance, definition, 203. effect on compression, 203. effect on cyl. condensation, 231. in air compressors, 719. in internal comb, eng., 404. measurement of, 323, 351. radial (turbine), 386. Clinkers from coal, 511, CO2 recorders, 505. CO2 {see Carbon dioxide). Coal, analysis of, 460-462, 509. anthracite, 457, 458, 465. "as received," 461. bituminous, 456-458, 465. briquets, 466, 514. caking, 465, 512, 598. calorific value of {see Cal. value). Cannel, 465. classification, 456. composition, 456, 459, Diederich's formula for, 462. "dry," 459. Dulong's formula for, 462. dust, use of, 466. fieldsof U. S., 458. firing of, 519, 520. formation of, 455 . fuel value of, 462-466. geology of, 445. graphitic, 457. Mahler's curve for, 463. Marks' curve for, 461. moisture in, 464. noncaking, 465. rate of combustion of, 512, 513, 6cx3* selection of, 515-517. semianthracite, 457, 458. semibituminous, 457, 458, 465. sizes of, 465, 466. soft, 456-458. sub-bituminous, 457. value as furnace fuel, 508-515. Coefficient of contraction and discharge, 715. of excess air, 480, 481, 498, 504, 505- of governor regulation, 257. of performance (refrigeration), 735, 739-741, 744, 747. Coil, induction, 434. intensifier, 434. trembler, 437. Coke, 466-467. Coking arch, 524. Cold body, 80. Combined diagram, multiple-exp., 349. Combustible, 459, 472. Combustion, 472-502. actual, 503-532. air for, 476-482, 503-505- carbon, 472-486. complete, 472, 506-508. data, 473. hydrocarbons, 490-491. hydrogen, 486-490. line (int. comb, eng.), 411. mixtures, 491. oxygen for, 476. rate of, 508, 512-513, 600. recorders, 505. smokeless, 506-508. sulphur, 491. surface, 532. temperature of, 482-485. Combustion in furnaces, 503-532. air for, 503. complete, 472, 506-508. rate of, 508, 512-513, smokeless, 506-508. Commercial considerations, 622. value of coal, 508-516. value of heating surface, 539. Composimeter, 505. Composition of {see Analyses of). Compounds, boiler, 687, 688. Compressed air {see Air compressor). Compression, 44, 203. adiabatic, 50. constant pressure, 44. isothermal, 47. pressures in int. comb, eng., table of, 419. quaUty during, '214. steam engine, 275, 286, 288, 293-295- Compressors, turbo, 729. {See Air comp.) Condensate, 20. Condensation, cylinder, 229. fraction, 229. initial, 212. reduction of, 123, i230-243. Condenser, advantages, 673. air in, 665 . barometric tube, 666. electric (ignition), 437. essentials, 675. piping, 667, 677-680. pressures, 665. pumps, 666, 677. steam, 620, 664-677. surface of, 674. tail pipe, 666. types, 664-667. 802 INDEX Condensing, advisability of, 664. gains from, 235, 367. surface, 675. water, 20, 672-674. water recovery in, 681. Conduction, cyl. losses by, 214, 223. theory of, 624. Conductivity (heat), 625. specific (Table), 628. total, 635- Conjugate events, 275. Conservation of energy, 6. Constant entropy changes, gas, 70. vapors, 153-159- Constant heat curves (steam), 142. Constant pressure changes {see Isobaric changes.) Constant quality curves (steam), 140. Constant temperature changes {see Isother- mal changes). Constant volume changes {see Isovolumic changes.) Constant volume curves, steam, 140. Constants for flue gas, 479, 481. ideal gas, 32. real gases, 38-41 . Consumption {see Performance). Contact resistance, 634. Continuity of state, 121. Convection (heat), 627. {See Boiler circ.) Conventional indicator diagram: for int. comb, engine, 406. for steam engine, 323-351. Cooling of condensing water, 681-684. of internal comb, eng., 407. of producers, 601. of valves (int. comb, eng.), 439. ponds, 681. towers, 681-684. Cost, depreciation, 622. fixed charges, 623. operating, 623. St. Eng. vs. Turbine, 393. Counterflow, boiler, 541, 558. defined, 541. heat transmission, 641, 647. Cracking of oil, 427. in producers, 608. Crank end, 271. Critical conditions, 122. Critical pressure, gas, 122, 714. steam, 705- Critical teinperature, gas, 122. Critical velocity gas, 714. steam, 705. Critical volume, gas, 122. Crosshead, slotted, 272. Crude oil, 467-469- Culm, 466. Cushioning, 286. Cushion steam, 205. Cut-oflf, 275. changing in multi-exp. eng., 331, 340-342. early, 288, 293, 295. governing int. comb, eng., 429. steam eng., 256, 352. influence on cyl. condensation, 232. in marine engines, 338. in simple engines, 233. in stationary engines, 337. limit of (Corliss), 312. range, 292. valve, 297, 300, 303. Cutting out of nozzles (turbine), 382. Cycle, available work of, 79. Beau de Rochas, 94-98. Brayton, 98-100. , Carnot, gas, 78-79. reversed, 84, 740. steam engine, 194. vapors, 161. Clausius, 167-173, 200-202. closed, 77. Diesel, 100. Ericsson, 93-94. four stroke, 403-414. gas, 76-102. Joule, 98-100. losses, 181. open, 77. Otto, 94-98. four stroke, 403-414. two stroke, 414-417. rectangular, 177. regenerative, gas, 90-93. steam, 199. Stirling, 90-93. two stroke, 414-417. vapor, 161-179. Cylinder arrangement, 420-421. condensation, defined, 229. reduction, 230-243. efficiency, 188, 208, 370. feed, 205, indicated, 228. high pressure, 234. lagging, 240. losses, 23, 181. low pressure, 234. ratio, 334-340. surface in clearance, 231. Dalton's law, 116. and condensers, 665. Dash pot, 311. Deficiencies of air, losses from, 499. Degree of regulation, 257. Degree of superheat, in. determination of, 227. Delivered power, 185. INDEX 803 Delivered power, measurement of, 186. Density, specific, air, 477. gases, 40. steam, 134, Appendix, Deposits (scale), 686. Depreciation, 622. Diagram {see also Valve diagram). adiabatic changes of vapor on, 157. entropy, 119, Appendix. factor, 325-327, 351- of cycle, PV, 78. of energy stream {see Energy stream) . of gas curves, PV, 43, T0, 73. of gas cycles, 89-102 . of heat flow {see Energy steam) . of producer plant, 25, 690. of steam plant, 18, 691. of T changes of vapors, 119. of vapor cycles, 162-179. of vaporization (heat changes), 112. steam, 227. water rate, 227,. 229. Diederich's equation (coal), 462. Diesel cycle, 100-102. efl&ciency, 447. engine, 417, 427. Displacement of valve, 273. Distillate, 468. Double deck boiler plant, 693, Draft, amount of, 578. apparatus, 574-589. artificial, 585. balanced, 587, 589, 615. chimney, 579. down, 522, 610. forced, 587, 588. friction head, 575, 576. furnace, 517-518. induced, 587, 589. mechanical, 587. natural, 579. pressure drop, 517, 574, 578, 581, 582. resistance, 574, 577. steam jet, 587, 588. Dry vacuum pump, 677. Dvdong's formula, 462, 463, 492. Dutch oven, 522. Dynamics, of flow in nozzle, 371. of steam turbine, 371. Ebullition, 118. Eccentric, action of, 274. defined, 272. for int. comb, eng., 440. relative, 304. rod angularity, 272, 284. Econometer, 505, Economizer, boiler element, 559. fuel, 619, 660-663. producer, 606. surface, 662. Economy {see Performance). Effective power, 186. Efl5ciency, air compressor, 720. apparent (boiler), 537. boiler, 535-538. boiler and grate, 538. Brayton, 100. Carnot, gas, 82. general, 187. int. comb, eng., 445. steam engine, 194. vapors, 164, 165. Clausius, 170, 172. cold gas (producer), 593. combustion space (boiler), 536. CO2 and furnace, 505. cycle, 188. cylinder, 188, 208, 355, 370. Diesel, 102, 447. Ericsson, 94. furnace, 523, 536. grate, 523, 536. heat transmission, 639-649. hot air engine, 400-402. indicated, 188, 208, 355, 370. internal comb, eng., 445-447. mechanical, 189, 224, 413, 446. nozzle, 369, 708. Otto, 96, 410, 443-447. over-all, 190, 211. boiler, 538. internal comb, eng., 447. steam turbines, 363, 366, 370. producer, 592-594- Rankine, 176, 177. rectangular PV, 178, 179. refrigeration {see Coef. of per- formance) . regeneration, gas, 92. steam, 199. relative, 188, 445. shaft, 370. steam engine, 355-358. Stirling, 92. thermal, 190, 209, 210, 395, 443, 446. thermodynamic {see Carnot). turbine, 365-370. voltunetric, 411, 720-724. Electric energy (heat), 3; ignition, 434-438. EUenwood Chart, 145, 793, 794, 795. Endothermic reaction, 472. Energy, associated heat, i, 9, 15. change of intrinsic, def., 11. of gases, 35. 8o4 INDEX Energy, change of intrinsic, of steam, 156- 158. of vapors, 108. electric (heat), 3. intrinsic, total, 4. kinetic (flow), 698-702, 708, 709. kinetic (molecular), 10. latent heat, 10-13. latent mechanical, 107 . potential, during vaporization, 13. (flow), 698, 699. radiant, 630. stream, boiler, 534. economizer, 660. feed water heater, 656, 657. general case, 187. internal comb, eng., 445. producer, 604. producer power plant, 25, steam power plant, 18. turbines, 369. Engine economies {see Performance). Engine {see Air engine, Blowing engine, Hot air engine. Internal combustion engine, and Steam engine) . Engine performance {see Performance). Engine room, 694. Entropy, absolute quantity of, 72. change, 68. constant, 70. of ideal gases, 67-72. of liquid, 119. of steam, 132. of superheating, 119. of superheated vapor, 120. of vaporization, 119. total, of steam, 137, Appendix. Equalizing pipe (turbine), 389 Equilibrium, chemical, 594. Equilateral hyperbola, 54, 324. Equivalent, evaporation, 561. molecular weight, 495. Ericsson cycle, 93-94. hot-air engine, 397-401. Ether vapor, T<^-diagram, 154. Evaporating pan, 620, 649. Evaporation, definition, 115. equivalent, 561. factor of, 562. rates (boiler), 563. unit, 561. Events, valve, 274, 275, Excess air (combustion), 478-481, 504, 505. coefficient, 480, 481, 498, 504. percentage, 497. Exhaust lap, 273. lap circle, 282. lap line, 276. losses, int. comb, eng,, 448. pipe area, 711. ports, auxiliary, 439. Exhaust valves, int. comb, eng., 439. valve timing, 441. Exhaust steam, in contact with walls, 232. turbine, 367, 390, 396. Exhauster, induced draft, 588. producer, 614. Exothermic reaction, 472. Expansion, adiabatic, gas, 50-53. in nozzles, 701. in steam engines, 196. vapors, 153-159- constant pressure {see Expan- sion, isobaric). constant temperature {see Ex- pansion, isothermal), constant volimie {see Expansion, isovolvunic). definition, 44. free, 63-64. general curves of, 54, 55. incomplete, 213, 732. in steam engines, 195, 196. . isobaric, of gas, 44. vapors, 146. isothermal, of gas, 47. vapors, 146. isovolvimic, of gas, 46. vapors, 159, 160. line (real int. comb, eng.), 412 piping (of), 696. ratio, 48, 330-340- valve (refrigerator), 743. Explosions, boiler, 544. producer, 614. External combustion engine, 397-402. - latent heat, 10, 13, 107. work, 10, 13, 107. valve, 273. Extractor, tar, 616. Factor of evaporation, 562. Fan (draft), 588. Feed water heaters, 651-663. advantages, 651, 655. economizer, 660-663. heating surface, 659. heat saving, 651- horse power, 659. saving, 651, 655. size, 659. surface (extent), 659. temperature increase, 653. types, 654-658. water saved, 654. Feed water impurities and treatment, 685. Figure of merit {see Coef . of performance). Financial considerations, 622. Firing of coal, hand, 519. stoker, 520. First law of thermodynamics, 6. Fixed carbon, 456, 459. INDEX 805 Fixed charges, 623. Flame length, 507, 522. Flexible shaft (turbine), 376. Floor space, boiler, 547, 555. engine vs. turbine, 392. Flow, Bernoulli's theorem, 575. counter (theory), 641, 647. gas and vapor, 698-715. Grashof's formula, 710. ideal gas, 712. imperfect gas, 715. Napier's formula, 710. parallel, 640, 644. pipes (in), 710. saturated steam, 700. unidirectional (engine), 242. velocity of gas, 713. of steam, 703. Flue gas analysis, 477-482, 493-502. loss {see Stack losses). Flues, 574- Fluid friction loss, int. comb, eng., 413. Fluttering of valve (air), 721. Foaming, 685, 687. Foot pound (unit), 180. Forward stroke, 271. Free expansion, 63-64. Friction, fluid (in int. comb, eng.), 413. head (flue gas), 575. horse power, 186. losses, 181. mechanism, int. comb, eng., 413. steam engine, 358. steam turbine, 370. valve, 291. Fuels, alcohol, 469. artificial gas, 471. charcoal, 467. coal, 455-467. coke, 466-467. consumption of {see Performance). culm, 466. definition of, 455 . fuel oil, 468. gasoUne, 468. graphitic coal, 457-458. industrial wastes, 467. kerosene, 468. lignite, 456-458, 465. municipal waste, 467. naphtha, 468. natural gas, 470. oil, 467-469. peat, 456, 464. petroleum, 467-469. prepared, 455. producer gas, 471, 590, 602. wood, 467. Fuel calorimeter, 492. Fuel oil, 468. Fuel oil, atomizing, 530. burning, 529-532. Fuel values {see Calorific values). FuU peripheral discharge, 385. Furnace efficiency, 505. capacity, 513. fittings, 521. grates, 520. length, 522. losses, 533. oil burning, 529, gas, 532. operation, 517-520. rate of combustion in, 513, size for coal, 513, for oil, 530. stokers (automatic), 523-529. types, 521-523. volume, 507. Fusible plugs, 560. Gain from decreasing back pressure: in steam engine, 235. in steam turbine, 367, 394. Gain from superheating: in steam engine, 236, 354. in steam turbine, 367, 394. Gamma, 38. value of, 41. Gas analyses {see Analysis). analyses (flue), 477-483, 493-S02. artificial, 471. constants, ideal, 32; real, 38-41- cycles, 76-102. defined, 28, 123. expansions, 43-58. from oil, 617. furnace (boiler), 532. ideal, 29. laws, 28-42. natural, 470. producer, 471, 590, 602. , specific densities of, 40. specific heats of, 33-38. specific volumes of, 41. Gas engines {see External combustion en- gine. Internal combustion engine, and Performance) . Gas producer, apparatus (general), 590. carbon monoxide method, 603. cooUng, 601-607. cleaning apparatus, 615. efficiency, 592. fuels for, 607. hydrocarbons, effect of, 607. limitations, 598. mechanical charging, 615. oil, 617. size, 600. 8o6 INDEX Cas producer, temperature control, 603. theory, advanced, 594. simple, 590. types, 608-615. balanced draft, 615. double zone, 610. downdraft, 609-610. grate bottom, 612. pressure, 613. suction, 614. updraft, 608. water bottom, 612. Gaseous state, region of, 123. Gasoline, 468. {See Performance.) Gauge pressure, 182. Gay Lussac's law, 29. Gears, turbine, 376. valve {see Valve gear). Governing, constant speed, 255, cut-off, 256. internal combustion engine, 427-431, 441-442. isochronous, 260-261. methods, 255. quality, 429. quantity, 429. resistance, 255. stable, 263. steam engines, 256. throttling, 256, 342, 352, 429. turbines, 376, 382, 389. unstable, 260. Governors, 255-270. adjustment of, 264, 270. Armstrong, 269. centrifugal, 266. characteristics of , 264. conical, 257. flyball, 257-262. inertia, 267. isochronous, 260, 261. loaded, 257. pendulum, 257-262. Porter, 259. Rites, 267. shaft, 262-270. speed limitations of, 258. speed variation of, 256. Sweet, 266. theory, flyball type, 257. shaft type, 262. Watt, 257. weighted, 259. Grain alcohol, 469. Graphitic coal, 457-458. Grashof's formula, 710. Grates, area of, 518. boiler, 520-523. efficiency of, 536. producer, 612. Half time shaft, 406. Hammering (of engine), 287. Head end, 271. Header (boiler), 554. Heat, associated, i, 15, 19. balance, boiler, 534. int. comb, engine, 447-449. steam engine (Hirn's), 219. changes of intrinsic, definition, 11. gases, 35. steam, 156, 158. vapors, 108. latent, 10, 13, 106-108. specific {see Specific heat). total, steam, 130, 137. vapor, 108. Heat changes during: isobaric changes of gases, 45. vapors, 147, 149. isothermal changes of gases, 49. vapors, 152. isovolumic changes of gases, 46. vapors, 159, 160. Heat conduction (theory), 624. Heat conductivity, 625. Heat consumption {see Performance) . Heat flow diagram {see Energy stream). Heat from chemical combination, 3-5. electrical energy, 3. mechanical energy, 3. sun, 2. Heat interchange with cylinder, 214-217. Heat of, combustion, 492. liquid, 105, 129. area for, 138. meaning of term, 108. steam, 130. area for, 139. superheat, in, 136, 137. vapor, total, 108. vaporization, latent, 106, 108. Heat resistance, 626. Heat transmission, actual, 632. boiler, 538, 540-544. cases of, 639-650. condenser, 675. conduction,. 624. convection, 627. economizer, 662. feed water heater, 659. heating surface, 636. radiation, 632. superheater, 572. {See Rate.) Heat unit, i, 6, 561. Heat utilization, evaporating pans, 620. heating, 621. industrial processes, 620. Heat value, calorimeters, 492. higher, 462, 487-490, 492. INDEX 807 Heat value, lower, 462, 487-490, 492. Heat value {see Calorific value). Heater {see Feed water heaters. Econo- mizers). Heating surface, boiler, 538, 563. commercial value of, 539. economizer, 662. effective, 636. extent, 639. feed heater, 659. mean temperature, 637- 639- superheater, 572. Heavy oils in internal comb, eng., 426-427. Height of chimney, 581-583. High pressure cylinder, 234. High pressure, effect on cylinder condensa- tion, 241, 354. on turbines, 394. Higher heat value, 462, 487-490, 492. Hirn's analyses, 219-223, 235, Horse power, boiler, 582. brake, 186. defined, 180. delivered, 186. effective, 186. -■ friction, 186. heat equivalent, 180, 191. heater, 659. indicated, 183, 184. Hot air engine, 397-402. Hot body, 80. Hot bulb (head) engine, 426. Hot gas eflSciency (product), 594. Hot well, 20. Humidity, effect on stack losses, 502. Hydraulic inches, 575. Hydrocarbons, 490-491. Hydrogen, available, 486. combustion of, 486-490. higher heat value of, 487. lower heat value of, 487. Hyperbola, equilateral, 54, 324. Ice machine {see Refrigeration). Ice making capacity, 748. Ice melting capacity, 748. Ideal gas, 29. mechanism, 7. vs. real engine, 180. Ignition, internal comb, engine, 433-438. Impurities (feed water), 685. Incomplete combustion in furnace, 472, 481, 501. losses in gas engine, 448. Incomplete expansion, 213, 732. Incrustation, 686. Indicator, 181. Indicator diagram, area of, 184. conventional, 323-351, 406. Indicator diagram, four-stroke cycle, 406- 412. meaning of, 182. multiple-exp. eng., 349. scales, 182-187. two-stroke cycle, 415-417. Indicated cylinder efl&ciency, 188, 208, 446. cylinder feed, 228. horse power, 183, 184. steam consumption, 227. work, 183, 413. Induction coil, 434. Initial condensation (definition), 212. Injection water (condenser), 672, 673. Injectors, 712. Inlet valve, internal comb, engine, 439. timing, 441. Insulating film (gas), 635. Intensifier coil, 434. Intercooling (air compressor), 726. Interest, 623. Interchange heat in engine cyl., 214-217. Internal combustion engine: actual, 403-454. advantages and types of, 403. after burning, 409. air card, 406. cam shaft, 406. cams, 440. classification of, 421-423. clearance space, 404. combustion in, 412. combustion line, 411. compression pressures, 418. cooling, 407. cylinder arrangements, 420. definition of, 397. diagrams (indicator), 406-412. Diesel, 417, 427, 447. double-acting, 420. eccentrics, 440. efficiency, 412, 443-454. four-stroke cycle, 403-414. fuel consumption of {see Performance). fuels, 418. fuels, modification for, 418. governing, 427-431. guarantees, 450-454. heat balance, 447. heavy oil in, 426, 427. hot bulb (head), 426. ignition methods, 433-438. indicator diagrams, 406-413. indicated work, 413. Koerting, 416. losses in, 410, 447-449. mechanical efficiency of, 413. mechanical features of, 420-442. oil engine, 454. Otto efficiency, 413. 8o8 INDEX Internal combustion engine: Otto type, 403. performance {see Performance), power per cylinder, 420. scavenging, 412. size of, 420. single- and double-acting, 420. suction line, 409. tandem, 422. turning effort of, 420. twin, 422. two-stroke cycle, 403, 414-417, valve gears, 438-442. vertical vs. horizontal, 421. working substance of, 403. Internal latent heat, 10-13, 108. Internal valve, 273. Intrinsic energy, 4, 11, 35. change of, 11. Intrinsic heat change, 11. gases, 35. steam, 145, 156-158. vapors, 108. Irreversible process, 59-64. Isentropic changes of gases, 70. vapors, 153-159- Isentropics, 70. Isobaric changes of gases, 44-45- steam, 142. vapors, 146-149. Isochronous governing, 260-261. Isothermal changes of gases, 44-49. vapors, 146-151. Isothermal compression (steam engine), 19 Isothermal expansion (steam engine), 196. Isovolumic changes of gas, 44-47- steam, 140. vapors, 1 5 9-1 61. Jacket losses, 447. Jackets, air compressor, 725. internal combustion engine, 407. steam engine, 238-240. Joule's experiment, 63. Junction box (boiler), 559. Kent's formula (chimney), 582. Kerosene, 468. Kingsley's experiments (chimneys), 583. Kinetic energy of flow, general, 698, 700. steam, 702. Labyrinth passage, 387. Lagged cylinders, 240. Lap, 273, 280, 276, 282. - Latent heat, 106-108. energy, 10, 13. internal, 10, 13. Latent heat of vaporization, external, 107. internal, 108. Latent heat of vaporization, total, 108. Latent mechanical energy, 107. Law, Avogadro's, 38. Boyle's, 29. Charles', gas, 29, 31. superheated vapor, 150. conservation of energy, 6. Dalton's, 116. gases, 28-33. Gay Lussac's, 29. Marriotte's, 29. partial pressures, 117. Stefan's, 630. thermodynamics, first, 6. second, 8. Willans', 352. Lead (valve), 276. Leakage, steam engine, 214, 230. turbines, 369. Lignite, 456-458, 465. Limitations of simple valve, 288. producers, 598. Line of transference, 329. Liquid and gaseous states (continuity of), 121. Liquid, ebullition, 118. entropy, 119. heat of, 105, 129. pressure within, 117. region of, 123. specific volume of, 113. Liquid fuel, burning, 529-532. Load, distribution of (compound eng.), 338-341- effect on water rate, 233. factor, 354. range of (high-speed engine), 292. Logarithm, tables. Appendix, use of. Appendix. Logarithmic cross-section paper, 55. Loops (combined diagrams), 342, 413. Losses, boiler, 534. bucket, 370. chimney {see Losses, stack), cycle, 181. cylinder, 23, 181, 214, 223, flue gas, 498. friction, 181. furnace, 533-536. grate, 533-536- int. comb, eng'., 410, 413, 447-449. jacket (int. comb, eng.), 447. mechanical, 181. nozzle, 369, 708. producer, 592-594, 604, 606. radiation, 447. stack, 498-502. steam engine, 194. turbine, 369-370. impreventable (boiler), 534. INDEX 809 Low-pressure cylinder, 234. Low-pressure turbine, 390, 396. Lower heat value, 462, 487-492. MacFarlane-Gray's formula, 315. Mahler's curve (coal), 463. Marine propulsion by turbines, 391. Marks' curve (coal), 461. Marriotte's law, 29. Maximum thrust (compound engine), 332. Maximiun valve opening, 286, 295. Mean effective pressure, 184. referred, 328. Mean hydraulic radius, 576. Mean specific heats of gas, 484-485. of superheated steam, 136. Mean temperature head, h.eat transmission, Cases I-IV, 639-649. Mechanical energy, heat from, 3. latent, 107. Method of ordinates (area), 185. Mixture of elements (combustion of), 491- 492. Moisture in coal, 459, 464, 509. loss in flue gas, 502. Mollier chart, 144, Appendix. Motion, perpetual, ist type, 7, 88. 2d type, 7, 9, 87, 88. 3d type, 7, 85, 88. Mud drum, 543, 555, 556. Multipass, boiler, 554. condenser, 673. Multiple effect, 650. Multiple-expansion engine, 234. changing cut-off in, 340-342. combined diagrams, 349. conventional diagrams, 327. cylinder ratios, 336-340. distribution of work, 338. expansion ratios, 336-340. indicator diagram, 340. PV-diagram, 348. Mtmicipal waste (fuel), 467. n, SI, 184, 257. n, value for air compressors, 721, 725. gas adiabatics, 52. steam adiabatics, 156. Napier's formula (flow), 710. Naphtha, 468. Natural fuels, 455. gas, 470. oil, 467-469. Neck of nozzle, 704, 714. Grashof's rule, 710. Napier's rule, 710. Negative work, area, 46. definition, 79. Network, 79. Non caking coal, 465. Nonconducting materials, 240, 241. Normal power, 353. Nozzle, applications, 712. area, 703. gas, 712-715. Grashof's formula, 710. loss, 369, 708. Napier's formula, 710. neck, 704, 714. steam, 703, 709. Oil, burning of, 529-532. distillates, 467. feeding systems, 250. kinds, 467. petroleum, 467. producer gas from, 617. Opening, diagram, 278. early, 287. valve, 273. Operating costs, 623. Overload capacity of boiler, 563. Overload, effect on water rate, 233. valve, 366, 389, 394. Oxygen for combustion, 476-482, Parallel flow, 640, 644. Parr's classification, 458. Partial pressures, 117. in condensers, 665. Passes, boiler, 554. condenser, 673. Peat, 456, 464. Perfoririance, boiler, 538, 561. coefficient of, 735-736, 739, 741, 744, 747. comparison of (true), 191,354. defined, 191. heat basis, 191. ice machines (see ■ Refrigera- tion), int. comb.eng., 449-454. refrigeration, 735-736, 739, 741, 744, 747. steam engine, 223, 352-358. steam turbine, 393-396. Periods of valve operation, 274. Perpetual motion, ist tj^pe, 7, 88. 2d type, 7, 9, 87, 88. 3d type, 7, 85, 88. Petroleum, 467-469. burning, 529. Pipes, steam flow in, 710. Piping, boiler, 697. condenser, 667, 677. expansion of, 696. feed water heater, 659. power plants, 694. steam, 694. Piston, balance (turbine), 389. 8io INDEX Piston speed, 245, 246. Pitch in producer, 607, Planimeter, 184. Plant {see Power plant). Pond, cooling, 681. Port, areas, 285. auxiliary, in valves, 289. auxiliary exhaust, 439. openings, 285. Positive work area, 46. definition, 78. Potential energy (flow), 698, 699. of vaporization {see Latent heat). Potential heat, 537. Power, 180. air refrigeration, 739. boiler, 562. brake, 186. delivered, 186. effective, 186. external comb, eng., 397, 399. friction, 186. horse, 180. indicated, 184. internal comb, eng., 413, 414. normal, 353. per cycle, 420. producer gas, 24. rated, 353. Power plant, 16, 24, 690-697. choice, 690. heat flow diagram, 18, 25. internal comb, eng., 25, 690. piping {see Piping), steam, 16, 690-697. Preheater, compressed air engine, 732. producer, 606. Preignition, 412, 418. Prepared fuels, 455. Pressure, Ijack, steam engine, 214. turbine, 367. compression, int. comb, eng., 418, 419- constant {see Isobaric). critical, gas, 714. steam, 705. drop in flue, 574, 578. effect on economy, 241, 354, 394. gauge, 182. heating system, 621. mean effective, 184. m.e.p., 184. of mixture, 117. referred m.e.p., 328. stages (turbine), 381. usual steam, 241. within a liquid, 117. Pressure-volume diagram (area), 47, 74, 79. Price of coal, basis of, 509. Prime mover, 16. Process, irreversible, 59-64. reversible, 59. Producer gas, 590-618. analyses, 602. oil, 617. plant, 24. Producers {see Gas producers) . Progressive distillation of vol. matter, 525. oil, 468. Progressive specific heat (steam), 130. Properties of air, 477. gases {see Gas constants), steam, 126-145, Appendix, sources, 127. Propulsion by turbine, 391. Proximate analysis of coal, 460-462. Pumps, air, 667, 677-680. circulating, 666. dry vacuum, 677. feed, 697. tail, 667, 669. vacuum, 666, 677-680. wet vacuum, 678. PV-quantity, 345-347- q, 105. Q,8. Quadruple expansion engine, 234, 339. Quality, no. curves, 139, 154, 206, 351. during compression, 214. factor, no. Quality governing, 429. Quantity governing, 429. Quintuple expansion engine, 234. r, 49, 131, 334- R, 32, 38, 40, 41, 334. Racing, 427. Radial clearance (turbine), 386. Radiant energy, 630. Radiation (heat), 629. losses, in int. comb, engine, 447. in steam engine, 214, 223. in turbine, 370. misuse of term, 632, Range, angle, 301. of cut-off, 292. Rate of combustion of coal, 512-513. combustion and smoke, 508. consumption of working substance, 191- fuel consumption, 191. See Performance, Heat Trans- mission. Rated power, 353. boiler, 563. Rating of boiler, 563. refrigeration mach., 748. INDEX 8ll Ratio of expansion, 48. in multiple exp. eng., 334, 340. in simple eng., 234. Reaction, endo thermic, 472. exothermic, 472. reversing, 476. Real and ideal engines, 180. Receiver, air, 732. infinite, 330. line, 329. reheating, 240. steam engine, 240, 251. Receiver pressure, formula for, 335. selection of, 331. with no clearance, 332. Reciprocating parts, 244. cushioning of, 286. Rectangular PV-diagram, 177-179. Referred m.e.p., 328. Refrigeration, air machine, 738. absorption process, 746. ammonia, 746. coefficient of performance, 735, 739, 741, 744, 747- materials for, 744. mechanical, 734. rating, 748. thermodynamics of, 734. vapor compr. machine, 741. vapors, kinds, 744. Regenerator, 90. turbine, 391. Region of gaseous and liquid state, 123. saturation, 114. superheat, 11 4-1 23. Regulation coefficient, 257. Reheating receiver, 240. Relative eccentric, 304. velocity, 371. Release, 275. early, 288, 293, 295, 347. Resistance, contact, 634. governing, 255. heat, 626. surface, 634. Resistance to flow (flue gas), 574. Reversed Carnot cycle, 84. refrigeration, 740. Reversed chemical reaction, 476. Reversible adiabatics, 70. isentropics, 70. processes, 59. Reversibility, 59-64. Revolutions per minute, 246. effect on cyl. cond., 241. Rider hot-air engine, 398, 400. Ripper's experiment (sup. steam), 237. Rites' inertia governor, 267. Rotary air pump, 678. engines, 248. Rotating parts of st. eng., 244. Rotative speed, effect on cyl. cond,, 241 of CorUss engines, 246. Rotor, 359. Running over and under, 250. Safety cam, 313. valve, 560. Saturated steam, properties, 126-135, Appendix. Saturated vapors, 109, in. defining condition of, 115. properties of, 103-110. Saturation curve, 113. for mult. exp. eng., 351. steam, 139, 206. Scale, boiler, 686. of indicator diagram, 182-183. Scavenging engine, 412. Scotch yoke, 272. Scrubber, dry, wet, 616. Second law of thermodynamics, 8, 9. Sensible heat, 1 1 . change of, 36. flue gas, SOI. producer gas, 593, 601. Sentinel whistle, 560. Separator, steam, 697. Shaft for high-speed turbine, 376. half time, 406. Shroud ring, 376. Simple engine vs. compound, 233. Single effect vacuum pan, 649. Sleeve motors, 438. Slide valve {see Valves) . Slotted crosshead, 272. Smoke, composition of, 508. prevention of, 506-508. Soft coal, 456-458. Solar heat, 2. Spark plug, 436. Specific density of gases, 38-41. steam, 134, Appendix. Specific heat, 14. conductivity, 625, 628. gases, 484-485. ideal gas, 33-35- mean, 14. progressive, 130. ' steam, 130. superheat, 135-136. true, 15-34- variable, 15. Specific volume of gases, 38-41. steam, 133, Appendix, super, steam, 137. vapors, 113. Speed, piston, 245, 246, 286. rotative, effect on cyl. cond., 241. of low-speed engines, 246. 8l2 INDEX Spontaneous ignition, 418, 434. Stack {see Chimney), losses, 498-502. Stagnant film, 635. State, continuity of, 121. Steam data, 127. properties of, 126-145, Appendix, saturated (table), Appendix, specific heat of, 130-136. superheated, 13S-137, Appendix. Steam, behavior of, in cylinder, 208-229. Steam calorimeter, 224-227. Steam consumption {see Performance). Steam distribution chart, 344. Steam engine {see Steam engine types) : action of steam in, 208-229. Carnot cycle and, 194. classification of, 245-254. compared with turbine, 360. comp. and exp. lines, 195-196. consumption, 197-202, 352-358. cycles, 161-179, 194-207. cylinder condensation, 230-243. diagrams (indicator), 323-351- efi&ciencies, 186-19 1. data, 356-358. governors, 255-270. jackets, 238-240. losses, 194. parts, 244. performance, 353-358. data, 354-358. determination, 223. steam consimiption, actual, 205, 352-358. indicated, 227. theoretical, 194-207. types, 245-254 {see Steam engine types), valves and gears, 271-322. water rate, actual curves, 232. data, 354-358. defined, 224. diagram, '229. Steam engine types: angle compound, 252. center crank, 250. compound, 233, 234. Corliss, 247. cross compound, 251. double acting, 248. duplex compound, 252. high speed, 245, 292, 293, 308. inclosed, 250. lokomobile, 240. left hand, 249. low speed, 246. marine, 253, 338. medium speed, 246. multiple expansion, 335. oscillating, 249. quadruple expansion, 234, 339. quintuple expansion, 234. Steam engine types: reciprocating, 24.8. reversing, 254. right hand, 249. self oiling, 250. side crank, 249. single acting, 248. steeple compound, 251. straight flow, 242. tandem, 250. triple expansion, 234, 336, 338. vmidirectional flow, 242. Woolf, 328. Steam heating, 621. Steam injector, 712. Steam jacketing, 238-240. Steam jets, 587, 588. blowers (producer), 613. Steam nozzle {see Nozzle), 703. Steam pipes {see Pipes), 711. piping, 694. Steam power plants, 16, 690-697. Steam properties {see Steam). Steam turbine, 359-396. accumulator, 391. advantages, 392. Allis-Chalmers, 389. appHcations, 390. back pressure (efiect), 367. BUss, 384. Branca's, 359. classification. clearance, 386. Curtis, 375, 380. defined, 359. De Laval, 373. dynamics, 371. double flow, 386. efficiency, 363-365. Electra, 382. energy stream, 369. exhaust steam, 367, 390, 396. flexible shaft, 376. gears, 376. governing, 368, 382, 389. heat supplied, 364. Hero's, 359. impulse, 359, 360. Kerr, 379. labyrinth, 387. leakage, 367. losses, 369-370. low pressure, 367, 390, 396. marine propulsion, 391. multi-stage, 361, 379, 390. nozzle, 359-361. losses, 369. theory, 697-715. overload, capacity, 366. valve, 366, 394, INDEX 813 Steam turbine, Pelton, 379. performance of {see Performance). Parsons, 375. 387- pilot valve, 382. pressure stage, 381. Rateau, 374, 379» 394- reaction, 360, 384, 387. Riedler-Stumpf, 383. rotor, 359. shroud ring, 376. single-stage, 379- small vs. large, 395. Sturtevant, 384. superheated steam with, 367. Terry, 383. tests, 395. thermodynamics of, 362, 369. velocity compounding, 380, 382, water rate, 363, 365. water seal, 379. Westinghouse-Parsons, 389. windage, 365. Zoelly, 374, 380. Stefan's law (radiation), 630. Stokers, 520, 523-529- Stoking {see Firing). Stratification, furnace gases, soy- Stroke, back, 271. forward, 271. Suction line, 409. p]3t)ducer, 614. Sulphur, combustion of, 491. dioxide refrigeration, 745. in coal, 464, 511. Superheat, degree of, in. determination of, 227. Superheated steam {see Steam), effect on, cylinder cond., 236-238, 354. steam turbine, 367, 394. Superheated vapor, in. Charles' law for, 150. properties of, 111-115. region, 123. Superheater, 127, 565-573- advantages, 236-238, 367, 565. arrangements, 567. protection of, 571. surface, 572. types, 566. Surface, boiler, 538, 563. combustion, 532. condenser, 675. economizer, 662. effect of clearance, 231. feed water heater, 659. resistance, 634. superheater, 572. water in boiler, 546. t, 30- T, 30. T<^-diagram, chart. Appendix. derived from PV, 217, 218. Table I, 40; II, 58; III, 102; IV, 241; V, 325; VI, 325; VII, 355; VIII, 358; IX, 358; X, 395; XI, 419; XII, 443; XIII, 457; XIV, 458; XV, 460; XVI, 465; XVII, 466; XVIII, 470; XIX, 473; XX, 477; XXI, 479; XXII, 481; XXIII, 491; XXIV, 578; XXV, 602; XXVI, 628. Tables, air, properties of , 477. coal classification, old, 457. Parr's, 458. sizes, 465, 466. coal, ultimate analyses, 460. combustion data, 473. compression pressures, 419. conductivities, 628. diagram factors, 325. draft through boilers, 578. efficiencies, steam engine, 358. Otto engine, 443. flue gas constants, 479, 481. formulas, volume changes of gases, 58. gas constants, 40. cycles, 102. expansions, 58. hydrocarbons, 491. . logarithms. Appendix, natural gas, 470. Parr's classification (coal), 458. performance, steam eng., 355, 358. turbines, 395. pressure drops, flue gas in boiler, 578. producer gas, 602. steam, saturated. Appendix. superheated. Appendix, steam pressures, usual, 241. symbols, Appendix, volimie changes (gas), 58. (i +loger) -i-r, 325. Tail pipe, 666. pump, 669. Tar extractor, 616. in producer, 607. Temperature, absolute, 30. control (producer), 603-605. from combustion, 482-485. head, mean, 639-649. range (comp. eng.), 331. vaporization, 105. Temperature-entropy, changes of, gases, 72. vapors, XI 8. chart, 138, 143, Ap- pendix. Tests {see Performance). Thermal equilibrium, vapor and liquid, 109. Thermal value {see Calorific value). Thermodynamics, defined, xvi. Throttled steam, 211, 212. 8i4 INDEX Thrust bearing (turbine), 389. maximum (comp. eng.), 332. Time element (cyl. condensation), 231. Timer (ignition), 436. Timing opening, 441. valves, 434. Transmission of heat {see Heat trans.) Traps, 697. Travel, valve, 273. Trip cut-oflf, 309. Triple effect (vacuum pan.), 650. True comparison of performance, 354. Try cocks, 560. Tubes (boiler) exposed, 549. replacing, 547, 548. submerged, 549, Timilirz's equation, 137. Turbines {see Steam Turbine). Turbo- compressors, 729. Turf, 456. Turning effort, int. comb, eng., 420. uniformity of, 332. u, 107, 133, 140. Ultimate analysis (coal), 460. Un combined hydrogen, 486. Underload, effect on water rate, 233. Unit of evaporation, 561. heat, I, 6. work, 180. Uptakes .(^ec Flues). Upton's Curves (sp. ht.), 484, 485. U. S. coal fields, 458. v, 286, V, 32, V, 2>3, 133, 286. Vacuum, effect on steam eng., 235, 354. on turbine, 367, 394. Valve {see Valve types) . action, 274. balancing, 291. definition, 272-273. diagrams, 274-288. {See Valve gear diagrams.) events, 274. fluttering, 721. friction, 291. gears, 271-322. {See Valve gears.) lead, 276, limitations, 288. opening, 273, 285-287, 295. steam velocity through, 286. travel, 273. types {see Valve types). Valve gears, Allan link gear, 316. Buckeye, 302. cam, 322. Corliss, H. S., 293, 308. L. S., 307-314- crossed rod, 315. Valve gears, diagrams {see Valve gear dia- grams), double eccentric Corliss, 313. floating lever, 322. Gooch, 316. high speed, 292, 293. independent cut-off, 297. int. comb., eng., 438-442. Joy, 319- link, 314-317. low speed, 307-314. McIntosh-SeymoUr, 306. Marshall, 318. Meyer, 304. open rod, 315. oscillating, 307. poppett, 321. Porter-Allen, 317. radial, 317-321. riding cut-off, 297, 302-307. Russell, 304. single eccentric Corliss, 309. Stephenson, 314. trip cut-off, 309. Walschaert, 320. Valve gear diagrams, Bilgram, 280, 299. elliptical, 277, 299. oval, 285. polar, 275. rectilinear, 275. Sweet, 278,^99. valve openings, 278. Zeuner, 279, 285. Valve types, Allen, 289. auxiliary air, 425. auxiliary ported, 289. balanced, 291. blow off, 560. carburetting, 424. cooled (gas), 439. Corliss, 308, 309. cut-off (riding), 297, 302-307. double ported, 289. D-valve, 271. exhaust, 439, 441. external, 273. gas, 431. gridiron, 306. inlet, 439, 441. automatic, 439. main, 297. marine, 289. mixing, 423, 431, 432. multiport, 289. mushroom, 438. oscillating, 307. overload, turbine, 366. pilot, 382. piston, 288. poppet, 321, 322, 438. INDEX 8iS Valve types, proportioning (gas), 431. relief, 292. riding cut-off, 297, 302-307. safety, 560. sleeve, 438. slide, gas, 438. stop, 560. Sweet, 290. Trick, 289. trip cut-off, 309. Woodbury, 291. Van der Waal's equation, 123. Vapor, cycles, 161-1 79. defined, 103, 123. dry, 109. ether, 154. expansion, 114. formation, 103. heat, 108. properties, 111-115. region, 123. saturated, 109, in. superheated, in. table (discussion), 113. wet, 109. Vaporization, heat of, 106-108. Vaporizer (producer), 606. Velocity, absolute, 371. bucket, 360. chimney gases, 582. compounding, 380, 382. critical (nozzle), gas, 714. steam, 705. diagram (turbine), 360. flow, flue gas, 576. gas, 713- steam, 702. jet, 360, 373. piston, 246, 286. relative, 371. steam through ports, 286. Volatile matter (coal), 456, 459, 506-510. Volume changes, gas, 53, 58. vapors, 146-160. Volumes, gases {see Gas constants). gas (from comb, of C), 477-482. steam, saturated, 133, Appendix, superheated, 137, Appen- dix, water, 113. Water, condensing, 20, 672-674. colimm, 560. curve, 138. gauge, 560. injection (air comp.), 725. jacket, 40s, 407, 725. Water, legs, 555- purification, 685-689. rate {see Water rate), seal, turbine, 379. producer, 612. specific heat, 130. treatment, 685-689. volume, 113. Water rate, 224. steam eng., 198, 201, 355, 358. steam turbine, 363, 391, 393- 395- Water rate curves, steam engine, 232. turbine, 363, 365, 392. Weight, air, 477. flue gas, 495, 497-499, 501. gases {see Gas constants). See Air for combustion. See Oxygen for combustion. Wet vacuum air pump, 678. Wet vapor method (producer), 605. Wetness factor, 206. Whistle, sentinel, 560. Willans' law, 352. Windage, 365. loss, 370. Wiredrawing, 211. Wood (fuel), 467. Work, areas (positive and neg.), 46. positive and negative, 78-79. Work done on and by piston, 23. area for, 47, 49, 74-79. Work, equalization (multi. exp. eng.), 332, 335, 341, 342. Work during changes, adiabatics, gas, 51. vapor, 156. isobarics, gas, 45. vapor, 149, 151. isothermals, gas, 48. vapor, 151. isovolxmiics, gas, 47. Work of cycles. Bray ton (Joule), 99. Carnot, gas, 79-82. vapor, 162, 165. Clausius, 169, 172. Diesel, loi. Ericsson, 93. Otto (Beau de Rochas), 95. Rankine, 175, 176. rectangular PV, 178, 179. Stirling, 92. Working substance, 76, 397, 403. X, no. Zero, absolute, 30,