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 NATIONAL ADVISORY COMMITTEE 
 
 FOR AERONAUTICS 
 
 TECHNICAL MEMORANDUM 
 
 No. r> 
 
 ON COMBUSTIGK IK A ITIPBULEKT FLOV/v 
 By K. J.. . >ielkin 
 
 Jourixal of Technical Physics (USSR) 
 Vol. XIII, Hob. 9-10, 19^*3 
 
 aciP^ 
 
 . IMIVFRSITY OF FLORIDA 
 Washington ^'^'^TS' tc nFPARTMENT 
 
 P.O.BOX 117011 ,o,njs^ 
 
 GAINESVILLE, FL 32611 fUii 
 
-::^ 
 
X ' - ' / /<f 
 
 MTIOI'JAL ATVISOEY COM/LETTEE FOR AEROMUTICS 
 
 TECMIC.AL MEMOEjyroUM WO. 1110 
 
 01 COIyEUSTIOS IN A TraBULElT FLOW^' 
 By K. I. SheH-cin 
 
 The characteristics Introdi'ced by the turbulence . in the process of 
 the fl£uiie propagation are considei-ed. .On the hajBas of geonie'trical and. 
 dimensional considerations an expression is obtained for the velocity 
 of "the flame propagation in a t'loy of large scale of tui'bulence. 
 
 IMSODUCTION 
 
 It has long been a well-Iinot-m fact that the motion of a gas very 
 greatly increases the rate of coiubustion of the gas mixture. The com- 
 bustion of fuel mixtures under practjcal conditions always occurs in a 
 flow existing either before the combustion (furnaces^ internal- combustion 
 engines) or arising in the process of combustion process as a result of 
 the propagation of the burning gases (the irjf lammation of mixtures at 
 rest in pipes, gas reservoirs, inflammation of methane in mines, etc.). 
 For this reason, it is very essential to study the laws of incr.ease. in 
 the rate of combustion as a function of the properties of the gas flow. 
 
 In connection with this problem, it is necessary to distinguish, the 
 effect of the motion of the gas mass with a certain definite velocity 
 whereby the combustion surface is expanded and thereby the combustion 
 rate increased, from the effect of the turbulent fluctuations, the veloc- 
 ity irregularities- of smaller scale. 
 
 In a gas at rest or in a laminar flow the velocity of propagation of 
 the flame in a direction perpendicular to the surface of combustion is 
 constant. This velocity is denoted as the normal or fimdamental flame 
 . velocity; it depends only on the physicochemical properties of the mix- 
 tui'e, and does not depend on the motion of the gas. The total rate of 
 combustion, the volume of gas burned per ^onit of time, is equal to the 
 product of the flame area by the normal combustion velocity. In a turbu- 
 'fc, lent flow; for example, in- a burner or pipe, the combustion surface is 
 not smooth as in a laminar flow, but there appear on it small disturb- - 
 -ances of the flame front produced by the turbulent fluctuations. 
 
 ijour. Tech. Phys. (USSE), vol. XIII, nos. 9-10, 19h3, pp. 520-530' 
 
KACA TM No. 1110 
 
 If there is considered a sufficiently large surfacae, the dimensions of 
 which are large in comparison with the scale of turbulence^ the rate of 
 combustion per imit surface will no longer he constant as in the case of 
 the laminar flow, hut will increase and will depend on the velocity of 
 the fluctuations. In this sense it is as though the normal velocity of 
 ccmDustion increased. In this ps-per an attempt will he made to arrive 
 at a quantitative estimate of this increase. 
 
 Qualitatively, the effect of turbulence on combustion has been 
 known for 60 years. Mallard and Le Chatelier (reference l) wrote in 
 1883 that turbulence (agitation) increases the heat transfer, increases 
 the surface of the flame, and forms new centers of inflammation. The 
 turbulence may increase the velocity of the flame 100 times compared with 
 its velocity in a medium at rest. The fact that the ignition of slowly 
 burning mixtures in mines may lead to catastrophic explosions was ex- 
 plained by Mallard and Le Chatelier as due to the effect of the turbulence. 
 
 Unfortimately, since the publication of the work of Mallard and 
 Le Chatelier 60 years ago, the concepts with regard to this phenomenon 
 have undergone no essential change. The authors know of only one work 
 (reference 2) In which an attempt is made at a quantitative approach to 
 the study of this phenomenon; this work vrill be discussed in the presen- 
 tation which follows. 
 
 Eecall the fundamental characteristics of turbulent flow. The lat- 
 ter is characterized ty the degree, scale, and frequency of the turbu- 
 lence . The degree of turbulence, or siniply the turbulence, is quantita- 
 tively determined by the I^rman number K given by 
 
 .M 
 
 K = 
 
 77^ 
 
 where v v is the mean square value of the fluctuating component of the 
 velocity, denoted in what follows by v', and W is the mean velocity 
 of the flow. The turbulence depends on the geometric dimensions, the 
 configuration and degree of roughness of the pipe through which the gas 
 moves, and does not depend on the velocity of the flow and the EejTiolds 
 number Ee when the latter is above the critical and the turbulence is 
 measured at a sufficiently large distance from the entrance or turbulence- 
 producing screen. This assertion is based on turbulence measurements in , 
 aerodynamic wind tunnels. It possibly is also valid for chambers of 
 other shape as the combustion chamber of an engine. Thus the fluctuating 
 velocity, at least in pipes, increases proportionately with the mean flow 
 velocity. 
 
 The scale of turbulence may be determined by the expression 
 
MCA TM No, 1110 
 
 where 
 
 r 
 
 I = I Edx 
 
 Ml 
 
 is the coefficient of correlation and x the distance between two points 
 in the space in which there are simultaneously measured the fluctuating 
 components vi and v{. In the physical sense the scale of turbulence 
 is the distance for which there exists a relation between the fluctua- 
 tions. Roughly speaking, it is the distance penetrated by a turbulent 
 gas element in which the element mixes, with those surrounding it. In a 
 flow there is always observed an entire spectrum of scales starting with 
 the largest. 
 
 The frequency of the fluctuations ms.y be thought of as connected 
 with the scale and the velocity of the fluctuations, and hence is not an 
 independent magnitude characterizing the turbulence. 
 
 In all cases of combustion in turDulent flow, the most essential 
 property of the flow as regards combustion is the forced mixing of the 
 elementary volumes of the gas. The intensity of the turbulent mixing is 
 determined by the coefficient of the turbulent exchange Zv' which has 
 the dimensions of temperature conductivity, coefficient of diffusion or 
 of kinematic viscosity. 
 
 The turbulent exchange affects the process of the mixing of air with 
 the fuel if the latter were not previously mixed. This process, however, 
 will not be considered in what follows. The combustion of a homogeneous 
 fuel mixture leaving aside the stage of mixture formation will be consid- 
 ered. 
 
 ELHvffiSITAEY THEOEY 
 
 In considering combustion in a turbulent flow, it is necessary to 
 compare a magnitude having the dimensions of length and characterizing 
 the turbulence (i.e., the degree of turbulence) with a magnitude of the 
 same dimensions characterizing the combustion: namely, the width of the 
 flame front. On the ratio of the scale of turbulence to the width of 
 the front of the normal flame depends the nature of the effect of the 
 turbulence on the speed of propagation of the combustion. Two cases may 
 be considered: namely, when the scale is respectively small and large as 
 compared with the width of the flame front. 
 
MCA TM Wo, 1110 
 
 Th e scale of the turb ulence i a smal l with re spect t o the width of 
 the zone of normal coahust ion. This case was considered by Damkohler 
 (reference 2) who for the speed of the turbulent propagation obtained 
 the relation 
 
 where Ujj is the speed of noi«r2a,l combustion (according to Damkohler, ^ 
 the speed in the laminar flow), ^t the coefficient of turbulent ex- 
 change, and Xj^j the temperature conducbivitj. 
 
 A similar result was arrived at independently by Y. B. Zeldovich 
 (private communication to the author) . This typpe of relation is ob- 
 tained, since it is aasumed that the reaction time in the flsoue front 
 is determined by the speed of the chemical reaction but the process of 
 mixing in the flame front takes so little time in comparison wj.th the 
 reaction time that the mixing time may be neglected. This actiially oc- 
 curs when the scale of fluctuations Z is small in comparison with the 
 width of the front, and the coefficient of turbulent exchange cannot be 
 neglected in comparison with the temperature conductivity. 
 
 Consider the flame front under these conditions. On figure 1 is 
 shown echematically the temperature distribution in the flame. Accord- 
 ing to the theory of normal flame propagation (reference 2) the velocity 
 of the flame, independent of the mechanism of the reaction, is of the 
 order of the square root of the temperature conductivity divided by the 
 reaction time: 
 
 u ~ 
 
 The reaction time t ^ in the normal flame is detenained for a tempera- 
 ture near the combustion temperature and depends on it according to 
 the law of Arrhenius: 
 
 E/RT 
 
 X ® 
 
 Where t^ is given with an accuracy up to a factor having the dimen- 
 sions of time. 
 
 Let the temperature T at the section B determine the reaction 
 time. In the case of the absence of turbulence the temperature will be 
 the same at all points of the section. It is assumed that the same 
 
MCA TM No. 1110 
 
 temperature distribution is also established in the presence of turbulent 
 exchange. In that case, at a mean temperature T In section B the 
 temperature at various points of this section will be different; it will 
 
 dT dT 
 
 vary approximately from T - I -r- to T + Z f-. It is recalled that I 
 
 dx dx 
 
 is the scale of turbulence. The turbulent fluctuations will bring the 
 gas into section B from the neighboring layers included between sec- 
 tions A and C and at a distance from B equal to the scale of tvirbu— 
 lence. It is evident that the scale of the elementary areas lying in 
 section B the temperature of which differs from T will be of the 
 order of Z^. In such a distribution of the temperature over the section 
 the reaction time over the entire section will no longer be determined 
 by the mean temperature T, To a rough approximation it will be of the 
 order 
 
 E E 
 
 .^ — (., 
 
 T - T 
 The order of magnitude of the temperature gradient is ~ -, where 
 
 K 
 
 Tc and To are the combustion temperature and the initial temperature, 
 respectively, and X, is the width of the flame front. In the case where 
 
 dT Z / \ 
 ^ dx "^ '^ °^ Xv^ ~ '^o)<T, there is obtained on neglecting second- 
 order quantities 
 
 e/rt 
 
 T - e = Tx 
 This condition is realized if Z «; X. 
 
 Suppose that Z increases for a constant turbulence exchange coef- 
 ficient Zv» . The tenrperature distribution and the gradient depend on 
 Zv' and hence remain unchanged, and A, likewise does not change. The 
 
 ratio z/a,, however, increases and in the end Z t— cannot be neglected 
 
 dx 
 
 in comparison with T. The reaction time in section B for the same 
 mean temperature T will be determined by the exponential curve 
 
 E 
 
 ^ ^ ^BCT - l/\ (Tc -To)] 
 
 For some value of Z it will become so large that an element of the gas 
 with a temperature T - l/X (Tc - To) mixes with the neighboring ele- 
 ments rather than reacts. The combustion will be determined by the rate 
 of mixing of the element of gas (with subsequent rapid combustion 
 
UACA TM Ko. 1110 
 
 at a higher temperattire and a corresponding concentration of reaction 
 products). For large values of I therefore the determining factor 
 will be the mixing time of an order of magnitude to z/v. It may be 
 noted that for constant 2v', l/x increases with Z but the reaction 
 time depends on the temperature exponentially, and therefore increases 
 more rapidly. 
 
 Thus it may be stated that for scales of turbulence of the order of 
 the width of the combustion zone the reaction time will be determined not 
 by the speed of the reaction at a given section but by the speed of mixing 
 of the elementary volumes of the gas. This is wha.t constitutes the nev/ 
 factor introduced by the turbulence in the mechanism of the propagation. 
 
 Bearing in mind what has been said previously, the following resume 
 may be made. For turbulence of small scale (KX) , the speed of propa- 
 gation of the turbulent flame depends on the ratio of the coefficient of 
 turbulent exchaiige to the teirperatin-e conductivity. If it is assumed 
 that the molecular and turbulent (diffusive) flows combine (k^Xt+Xm) 
 
 UT ~ /-Xll = uj,^ / i + _i. (la) 
 
 The above formula has the advantage as compared with (l) that in the 
 limit for X t = C) it gives wj; = ujij. 
 
 In a flow of small scale of turbulence the flame propagation is 
 determined by the coefficient of turbulent exchange. Hence, within 
 certain limits (as long as 1<X) it depends on the scale of turbulence. 
 
 For turbulence of large scale, as will be seen l8.ter, the scale of 
 turbulence does not affect the flame speed.; the determining factors are 
 orii^f ^the velocity of the fluctuations, the degree of turbulence and the 
 Karm.an number. In the intermediate range (Z~X,) a transition occurs 
 when, at least for strong turbulence ('v'~>uh), the mixing being begins to 
 
 affect not only the heat transfer (as for small scales) but also the time 
 of chemical reaction in the flame. Thus are presented the laws of flame 
 propagation at a small scale of turbulence, and the properties that appear 
 as the scale increases are showed. 
 
 It should be pointed out that the case where the scale of turbulence 
 is small by comparison with the width of the flame front is rarely met 
 with in pure form. Under normal conditions for homogeneous gas mixtTuree 
 the width of the flame front is of the order of 0.1 millimeter. Under 
 real conditions (gas furnaces, engine combustion chamber) scales of order 
 of magnitude less than 0.1 millimeter can only accompany larger scales 
 and occupy only a certain extreme position in the scale spectrum. Howevsr, 
 
NACA ™ Wo. 1110 7 
 
 immediately on passing to slowly burning mixtures (e.g., lean mixtures) 
 the width of the front may considerably exceed the above-mentioned order 
 of magnitude^ and the probability of existence of the case discussed 
 increases. 
 
 Bext, consider the case where the scale of tui'bulence is large in 
 comparison with the width of normal combustion zone. An analysis of this 
 case in its general foiia on the basis of dimensionality considerations 
 permitted Y. Zeldovich to conclude (unpublished work) that the speed of 
 turbulent propagation of the flame does not depend on th$- scale of turbi>- 
 lence and can be represuntsd by a formula of the type 
 
 UT = Ui^ f (ufl/v ' ) 
 
 where f (uj^/v') is a function of the ratio of the velocities to be 
 determined. In the case of large-scale tarlRalence the flame surface is 
 cui'ved. As the velocity of the fluctuating components increases the 
 curvature increases^ and finally the flame front begins to break away. 
 At strong turbulence the elementai'y volumes of gas^ both burning and 
 fresh,, move chaotically with respect to one smother. In the flame there 
 remain "islands^ " centers of unbui-ne-d mxture, broken off by the fluctu- 
 ations into pai'ts and annihilated by the flame. If the effect of the 
 curvatiire on the speed of flame propagation is neglected^ the normal 
 flame speed may be considered as constant. The surface of combustion, 
 however, increases and hence also the total rate of combustion. 
 
 Before determining the speed of turbulent combustion over the flame 
 surface^ consider the limiting case of a strong large-scale, turbulence 
 when the combustion zone is filled with islands of imburned mixture. 
 
 In figure 2 the sppce between the sections AA and BB may be con- 
 sidered as the reaction zone of the turbulent combustion. In front of 
 the plane AA is the fresh mixture, and behind the plane BB are the 
 products of combustion. From A to B the mean concentration over the 
 cross- sectional areas of the products of combustion Increases, and the 
 concentration of the fresh gas decreases. The distance betvreen the 
 sections may be considered as the width of the t^jrbulent f lomo front. 
 As was mentioned previously, the speed of the flame, from dimensional 
 considerations independent of the mechanism of the reaction is a magni- 
 tude of the order of 
 
 u~ JxT^ (3) 
 
 In a turbulent flame the p.art of the temperature conductivity is taken 
 by the coefficient of exchange Zv* and the part of the reaction time 
 by the mixing time Z/v', and this gives for the velocity:. 
 
8 ■ MCA OM Eo. 1110 
 
 Thus the conclusion is reached: for large turbulence when the velocity 
 of fluctuation v' is large 'by corrparison with the normal velocity v^ 
 (only in this case will the combustion front have a form like that in 
 fig. 2), "the velocity of tiu'hulent flame propagation is proportional 
 to the nean fluctuating velocity and does not depend on the chemical 
 nature of the gas mixture. 
 
 The reaction time in a turbulent flame may be computed .in a differ- 
 ent mannei". Tlie combustion time of an elementary volume l'^ may be 
 determined as 
 
 T - 
 
 
 (P) 
 
 where £5% -^^ ^^^ volume rate of combustion, the product of the flame 
 
 area by the normal velocity. It should be taken into account that an 
 elementary volume with area of the order I- on entering the combustion 
 front is broken up into parts by the fluctuations. The breaking up will 
 continue as long as the flsme with normal velocity xx^i passes over a 
 distance equal to the scale of turbulence I, this time is equal to Z/iN. 
 During this time the total path traversed with the fluctuating velocity 
 reaches the value L = l/n-^ v*. 
 
 The ratio l/z shows how many times during the combustion of the 
 volume Z'^ the latter is traversed by fluctuations. Each such traversal 
 leads to the formation of a new fLnme area of the order to Z^. The 
 mean area of combustion of an element Z"^ will be proportional to the 
 magnitude 
 
 Z^ vVujj (6) 
 
 The averaging of this quantity with respect to the combustion time affects 
 only the constant factor. The time required for burning the volume Z^ 
 id found eaual to 
 
 (7) 
 
 ■Ug 
 
 The same result is attained; namelj^, that the combustion tinie is propor- 
 tional to the mixing time. 
 
NACA TM Wo. 1110 
 
 The case where v'» ujj has heen eonsidered. Tlie case of small 
 tTjrhulence may he approached only geometrically. It is in this meinner 
 that the problem is considered by Damkohler. Rightly seeing the reason 
 for the increase in velocity of combustion in the increased area of the 
 flame surface, he schematically represents the flame surface as consist- 
 ing of conical surfaces with their bases at right angles to the directicn 
 of flame propagation (fig. 3)» Taking the areas of the cones proportional 
 to v' he arrives at the expression 
 
 Urj] ~ v' 
 
 The considerations of Damkolrler are not accurate and for small v' are 
 not true. According to Damkohler, the absence of turbulence (v'.=0) leads 
 to zero velocity of the flame. Actually a relation like (k) as shown 
 above is obtained only for strong turbulence v'>ui^, and not for weak 
 
 turbulence which is the case considered by Damlcohler. 
 
 Consider this problem more in detail. The ratio of the speed of 
 turbulent propagation of the flame to the normal speed will be equal to 
 the ratio of the lateral area of the figure a (fig. 3) to its base. 
 The height of the figure, which is assvmied as a cone, will be of the 
 order Zv'/ujj. For an element of the flame front will be carried away 
 
 by the fluctuation from the general flame front only during the time re- 
 quired for the noi'mal of the flame to traverse the distance Z. This time 
 is eaual to Z/ujj. The height of the cone will therefore be of the order 
 of Zv'/uj,j. The lateral area is 
 
 Slat - AZ2/1 + B(v'/uij)2 
 
 where A and B are nondimensional coefficients of the order of imity. 
 The ratio of the velocities of propagation is 
 
 }n ^ Slat ^ Ai/ 1 -H B(vVuii)^ (8) 
 % ^ase 
 
 For strong turbulence v' > u,^ (equation (8)) leads to the known relation 
 
 Uij V • 
 
 The absence of turbulence v' = should lead to the condition u^p = Uj^. 
 This gives the value Ai = 1. 
 
 For any tiirbulence, including small turbulence, the criterion shouii 
 hold 
 
10 HACA TM No. 1110 
 
 ■ (ld''.=- l-^B(^) (9) 
 
 The value of the fluctuating component of the velocity is thus found to 
 vary hypertoUcally vith the velocity of turhulsnt flame propagation 
 (fig. h) . If v' is replaced by the product of the Karmaii munher by 
 the mean flow velocity, the formula is obtained 
 
 '-^-) - 1 + BK2 (10) 
 
 
 in which all magnitudes are subject to direct measurement. 
 
 It is of importar,Ge to note that in the finite expression (9) or 
 (lO) the scale of turbulence dees not enter. Hence, the obtained rela- 
 tion will be valid for any scale, provided the latter does not exceed the 
 width of the normal combustion front. 
 
 BOMa Pli^CTICAL REMARKS 
 
 From formii.la (9) it follows that for lax^e ratios v*/ujj (or by 
 formula (lO) Y^^j-x-^) unit y may bo neglected undei- the root sign. The 
 
 conibuEtion velocity is then independent of the noriual flame velocity and 
 therefore of the phyEicocheraical properties of the nixture, and is pro- 
 portional to the fluctuating velocity. For a given value of the latter 
 (large in comparison with \x.^) different fuels will burn at the same I'ate. 
 If the I'atio v'/u (J?///ui}) is of the order of 1 or less, the x-ate of coar 
 bustion will depend on Utj. V.'ithin increasing fluctuating velocity the 
 
 rate of combustion increases hyperbolically. For very small v' the 
 effect of the turbulence may be neg3.ectod as a second- order magnitude. 
 By comparing v'/% with unity, it should be remembered that the val;ie 
 of B is equal to 1 only in. order of magnitude. Fuj^-thermore , it will 
 evidently depend on the structure of the turbulence. For exeonple, in 
 pip;es with roughness of various shapes determ-inlng the structure of the 
 turbulence, different values of B may be expected. 
 
 Examination of formula (9) permits drawing the conclusion that if 
 the velocity of fluctuation is not very large in comparison with ujf 
 the effect of the turbulence on the speed of propagation characterized 
 by the relative increase in the combustion velocity (urp/ujj) will be 
 
 greater the slower the combustion of the mixture of the same composition 
 at rest. The lower the value of u^ the greater the given v' (gi-wen 
 turbulence), the numerical value of the root in formula (9). 
 
MCATM No. 1110 
 
 11 
 
 This conclusion is confirmed "by the published tests on the effect 
 of swirling and turbulence on the speed of comhustion (reference 3)- 
 Swirliiig always moi^e greatly increases the speed of combustion of lean 
 and rich mixtures than stochiometric mixtures. The conditions of the 
 experiment do not permit a quantitative analysis of these data but 
 qualitatively they correspond in any case to these results. To evalu- 
 ate the possible effect of turbulence on the flame propagation, it is 
 necessary first of all to know the normal speed of combustion Uj^ and, 
 
 of course, the speed of the fluctuations or, if the turbulence is known 
 (the Karman number), the mean flow velocity. In table 1 are given the 
 normal flame speeds for certain fuel-air mixtures taken from the book 
 of Jost (reference h) (the speeds correspond to the coiiiposition of the 
 mixture of maximum combustion rate). As an exeoaple, there are also 
 given the mean flow speeds for 5--percent turbulence (K - O.O5), the 
 mean fluctuating speed of which is equal to the corresponding normal 
 speed of the flajne. 
 
 Table 1 
 
 Fuel 
 
 (cm/sec) 
 
 w 
 (m/sec) 
 
 Hydrogen 
 
 267 
 
 53. i^ 
 
 Acetylene 
 
 131 
 
 26.2 
 
 Ethylene 
 
 63 
 
 12.6 
 
 Propylene 
 
 i^3.5 
 
 8.7 
 
 Methane 
 
 37.0 
 
 7.4 
 
 n— pentane 
 
 35.0 
 
 7.0 
 
 n— hexane 
 
 32.0 
 
 e.k 
 
 Benzol + O.5 per- 
 cent Ha 
 
 38.5 
 
 7.7 
 
 Carbon monoxide +1.2 
 percent water 
 
 41.5 
 
 8.3 
 
 Table 1 gives an indication of the order of flame speed at 5- 
 percent turbulence when there is to be expected a hyperbolic depend- 
 ence of urp on ¥ or when this dependence may be considered as linear. 
 
 Thus, for hydrogen-air mixtures of stochiometric composition a linear 
 
12 KACA TM Ko. 1110 
 
 dependence (and independence of the speed of propa(i;atlon on the normal 
 flame speed) may "be expected at f lov speeds exceeding approximately 
 seven to eight times the speed giving this dependence in pentane or 
 benzol - air mixtures. For hjdrogen these will ha speeds of the order 
 of himdreds of meters per second; for benzol, methane, pentane, hexane, 
 of the order of tens of meters per second. If the t-orbulence is in- 
 creased tivo times, up to 10 percent, then to attain the same result half 
 the flow speed would be required, and so forth. 
 
 The practical independence of the speed of f Lsme propagation on the 
 physicochemical properties of the fuel in the engine was also observed 
 by Marvin (reference 5) • On figure 5 are given the curves of the flame 
 path against the crank angle degrees obtained at constant engine speed. 
 The slope of the curves gives the fl/me speed. In the center part of the 
 combustion cBamber where the flame front is sufficiently developed the 
 flame speed cksnges little over a large distance of the chamber, and for 
 various fuels is approximate!^'- the saiae while the nomial combustion 
 speeds of these fuels differ considerably/ from one another (table l) . 
 Different speeds in the engine are observed onlj in the initial stage 
 of the flame propagation. 
 
 The results of Marvin cen readily be explained. The velocities of 
 the fluctuations of che gas in the engine are large in comparison with 
 the normal velocities so that the flame propagation is described by 
 expression (U)^that is, the rate of combustion is proportional to the 
 speed of the fluctuation, and does not depend on the normal flame speed. 
 It is very probable that under the same conditions for hydrogen or 
 acetylene the speeds would be different. It is possible that for these 
 gases the same speed of the fluctuations would not be large by compari- 
 son with ujf. These considerations ai'e in the nati^re of suppositions 
 since the true value of the speed of the fluctuations under the test 
 conditions of Marvin is not knoi/n. 
 
 The absence of an accelerating effect of the tujrbulence in the 
 initial phase of the combustion (well icnown from the engine literature) 
 may from the author's point of view be explained by the fact that at 
 the start of combustion when the dimensions of the flame are small in 
 comparison with the scale of the turbulence the latter does not affect 
 the rate of combustion. A center of combustion is displaced as a whole 
 by the fluctuation, .and its surface therefore does not become branched. 
 The rate of combustion is determined only by the normal flame speed. 
 In this way it is assumed that the tiu:'bulence in the engine is of 
 relatively large scale. 
 
 Certain results for comparison of the theorj'^ with experiment are 
 given also by other investigations conducted on engines. There are, 
 however, fuaidamental difficulties, in applying the theory previously 
 presented, to combustion in the engine. Consider a few of these. 
 
MCA TM Wo. 1110 13 
 
 In the first place, with regard to the effect of the rotational speed 
 on the combustion rate, it is not known whether the Karman number re- 
 mains constant when the speed chsjiges. This can only be assumed on 
 analogy with pipes and special determinations : of K, for engines are 
 lacking.- In the second place, the true effect of the motion of the 
 entire mass of the gas in the engine chamber on the combustion rate is 
 not clear-. It may be supposed that owing to the small length and the 
 strong turbulence -producing effect of the intake valve, the degree of 
 turbulence of the flow diaring intake and then in the chamber will be 
 very strong, and the pajrt pla^'ed by the regular motion of the gas is 
 small. Flnal3-y, photographs give the flame speed with respect, to the 
 walls of the chambex' and not with respect to the gas, which is of inter- 
 est in the latter speed. In the latter case, however, the picture is 
 not clear. It may, moreover, be supposed that rotational flows are pre- 
 doiulnant in the engine. This is indicated, for example, by Marvin's 
 photographs in which a curbing of the f.lame front is noted, explained by 
 the circular motion of the gas in the cylinder head. These consideratioaa 
 are confirmed also by the fact that generally over a considerable distance 
 of the combustion chamber the photographs of the flame in the engine show 
 an only slightly varying flame speed. In the case of the presence of a 
 strong flow along the chamber 'from one end to the other) there should 
 exist also a return flow. It would then be possible to expect large ir- 
 regularities in the flame propagation. There is, therefore, some basis 
 for supposing that the principa.1 cause for the increased rate of combus- 
 tion in the engine is the turbulence and not a mass movement of the gas 
 in the engine head. In this respect the opinion of engine specialists 
 may be s^^scribed to; for example, Bouchard, F. Taylor, and E. Taylor, 
 who write, "the rapid increase in the maximum combustion rate with ro- 
 tational speed is due primarily to an increase in the small-scale in con- 
 trast to the organized motion of the gas in the engine head but not in 
 the sense of comparison with the width of the flame front of normal com- 
 bustion, of higher gas velocities through the intak;e system." (See 
 reference 6. ) The same authors investigated the dependence of the flame 
 speed on the rotational speed. The curve of flame speed against rota-r 
 tional speed is given in figure 6. The speed of the mixture on intake, 
 and therefore the speed of the gas in the chamber, increases in propor- 
 tion.',t.o the rotational speed. Hence, in figure 6 on the axis of ab- 
 scissae' instead of the rotational speed there may "be laid off a magnitude 
 proportional to the speed of the gas or under the assumptions made to the 
 speed of the fluctuations. The shape of the curve corresponds strongly 
 to the theoretical relation obtained (fig. h) . Unfortimately, for small 
 rotational speeds the experimental curve is extra-polated (dotted) . 
 Bouchard, F. Taylor, and E. Taylor drew this part of the curve on the 
 basis of measurement of the time of combustion of 95 percent of the 
 charge. The tests of these authors confirm (though indirectly with 
 account taken of the assumptions made) the conclusions as to the effect 
 of the speed of the flame propagation. An acciurate check of the theory 
 requires, of course, special tests with parallel measurement of the 
 speed of combustion, Karman nxanber and flow speed. 
 
ll; . ■ KACA TM Ho . 1110 
 
 COWCLUSIOKS 
 
 1. With strong tiirbulence as the scale of the turbulence in- 
 creases to a value comparable with the width of front of normal com- 
 "bustion, the rate of the combustion reaction begins to depend on the 
 mixing. 
 
 2. For turbulence the scale of which exceeds the width of the 
 front of normal combustion (I >\) , the speed of the flame propagation 
 increases hyperbolically with the speed of the fluctuations. For 
 large fluctuation speeds (v' > ujj) the dependence may be considered 
 
 linear, and for small values (v' <U]}j) the effect of the tui^bulence 
 
 is of second-order smallness. 
 
 3. The data presented in the literature ou the measiarement of 
 the flame speeds of various fuels in the enaiiie and the a-easui'ement of 
 the dependence of the flame speed on the rotational speed confirm the 
 theoretical conclusions, if it is aesn-^ied that the increase in the com- 
 bustion rate in the engine is determiiied by the turbulence. 
 
 Translation by S. EeisS; 
 Nations 1 Advisory Committee 
 for Aeronautics. 
 
KACA TM No, 1110 15 
 
 KEiS'EHmCES 
 
 1. Mallard and Le Chatelier: Ann. de Ifines, I883. 
 
 2. Damkohler, 5.: Ze-'tschr. fm' Elektrochemie, vol. kS, no. 11, Nov. 
 
 19^+0, pp. 601-626. 
 
 3. Lafitte, P. : La Propa£'at3on des Flsam.es dans lee Melanges Gaseux. 
 
 Paris, 1939^ p. 72. 
 Levis, B., and von Elbe, G. : Combustion, Flames, and Explosions 
 of Gases. 1938, p. 192. 
 
 k. Yost, W. : Explosions and Verbremiungs Vorgange in Gasen. Julius 
 Springer (Berlin), 1939- 
 
 5. Marvin, Charles F. Jr. : Observations of Flame in an Engine. SAE 
 
 Jour., 193^ p. 391. 
 
 6. Bouchard, C. L., Taylor, C. F., and Taylor, E. S. : Variables 
 
 Affecting Flame S-oeed in the Otto-Cycle Engine. SAE Jour., 
 vol. in, 1937, p." 515. 
 
 BIBLIOGEAPHT 
 
 1. Zeldovich, Y. B. : Jour. Experimental and Theoretical Physics. (USSS), 
 vol. 11, 191+1, p. 159. 
 
NACA TM No. 1110 
 
 Fige. 1,2,3,4,5,6 
 
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