ACA t'^'BZX^Hi ®- "• LEADON NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL MEMORANDUM 1328 CONCERNING THE FLOW ABOUT RING-SHAPED COWLINGS PART Vm - FURTHER MEASUREMENTS ON ANNULAR PROFILES By Dietrich K'uchemann and Johanna Weber Translation of ZWB Forschungsbericht Nr. 1236/8, March 25, 1943. Washingto^;^;,yppQ,p/ qf FLORIDA February 1952 . -•'- mLarY 1 20 MA^ iNOt LIBHAHY P.O.BOX ;i/'uii GAINESVILLE. FL 32611-7011 USA %U ^ 3 7T^y^_/ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL MEMORANDUM I328 CONCERNING THE FLOW ABOUT RING-SHAPED COWLINGS PART VIII - FURTHER MEASUREMENTS ON ANNULAR PROFILES* By Dietrich Kuchemann and Johanna Weber ABSTRACT: The measurements of part V (reference l) of this series of reports, which concerned comparatively long ring profiles, are supplemented by measurements on shorter rings as they are used for shrouded propellers and cowlings of ring-shaped radiators. Mass-flow coefficients and profile drags are given. Furthermore, it has to be determined how far the potential theory describes the flow phenomenon with sufficient accuracy and whether the present theory for the calcu- lation of thin annular profiles yields useful profile forms and is suitable for determination of the mass flow for thick profiles. OUTLINE : • I. STATEMENT OF THE PROBLEM II. THE ANNULAR PROFILES INVESTIGATED III. THE METHOD OF MEASUREMENT IV. RESULTS V. APPLICATION OF THE RESULTS VI. SYNOPSIS I. STATEMENT OF THE PROBLEM The measurements on annular profiles given in the present report serve as a supplement for part V (reference l) . However, whereas in part V (reference 1) the annular profiles had a relatively great length 2 referred to the ring diameter 2xq, namely Z/SrQ = 2, shorter profiles *Uber die Stromung an ringfc5rmigen Verkleidungen. VIII Mitteilung: Weitere Messungen an Ringprof ilen. Zentrale fiir wissenschaftliches Berichtswesen der Luftfahrtforschung des Generalluftzeugmeisters (ZWB) Berlin-Adlershof , Forschungsbericht Nr. I236/8, Gbttingen, March 25, 19'+3- NACA TM 1328 will be investigated now as they are used for shrouded propellers (compare part VII (reference 2)) and as cowlings of annular radiators. For both purposes of application, a profile form is desired for several operating conditions, preferably for start and climb, with the smallest possible profile drag and the greatest possible increase of the mass flow. The annular profile alone was to be investigated first for a preliminary clarification of these problems. In particular, the question was to be treated as to how far the existing theory of thin annular profiles (part III (reference 3)) enables the development of usable profile forms and permits predetermination of the mass flow. II. THE ANNULAR PROFILES INVESTIGATED According to the calculation method given in part III (reference 3), the mean camber lines of four profiles with different (negative) circu- lation and of equal length {i/2.Tq = O.5) were determined. The annular profiles 5 and 6, as well as 7 and 8, have, in every case, the same total circulation and are distinguished only by the facts that 5 and 7 have a curved mean camber line, while 6 and 8 have an additional S-curvature. The calculation parameters c^ of part III (reference 3) have the values : (Camber) (S-curvature) Annular profile 5 C2 = -0.05 Annular profile 6 C2 = -0.05 Annular profile 7 eg = -0.10 Annular profile 8 C2 = -0.10 The theoretical coefficients Cj. of the radial force which correspond to Ca for two-dimensional profiles are Cj, = -0.5 for the annular profiles 5 and 6, and c-p = -1.1 for the annular profiles 7 and 8. The influence of the finite profile thickness has, so far, not been treated theoretically. We were therefore obliged to assume a thickness distribution and to superimpose it on the mean camber lines. The modi- fication to the mass flow thereby produced may be calculated in first approximation according to the continuity equation which proved to be satisfactory for the profiles investigated in part V (reference 1), however, a certain error is connected with this assumption which takes effect particularly in the determination of the radial-force coeffi- cient Cp, as has been shown in part I (reference k) . The influence of the thickness manifests itself in making the c^-values negatively larger than those resulting for the mean camber line. ^^3 = ^3 = -0, .05 ^3 = c^ = -0, .10 NACA TM 1328 3 We used the same thickness distribution for all annular profiles (see fig. 1) as in part V (reference 1) with a maximum thickness of 20 per- cent of the profile length at 35 percent of the length counted from the leading edge. The profile forms produced by superposition of this thickness distribution along the mean camber lines may also be seen from figure 1 . Aside from these four annular profiles, a further shorter one (z/2ro = 0.25) was investigated which has a curved mean camber line with S-curvature and is related to the annular profile 6. The pertaining data are: Annular profile 9 C2 = -O.O5 Co == -0.05 The theoretical coefficient of the radial force also is c^ = -0.5- III. THE METHOD OF MEASUREMENT The rings were turned from wood and had the dimensions shown on figure 2. They were attached with a sting to the drag balance as described in part V (reference 1). The profile drag, W, was measured for various free-stream velocities Vq and plotted against a Reynolds number, formed with the profile length I, Re = Vq — in the form of a V coefficient ^w = w/: I ^o\ with Fm signifying the generating surface of the annular profile which is identical with the surface area of the wing that is obtained by cutting open the annular profile and developing it into a plane. Thus, Re and Cv may be compared directly with the values customary for two-dimensional wings . The mass flow was determined by a survey at the exit area of the wing. The total-pressure measurement shows the regions where kinetic energy of the flow is lost and thus forms a supplement of the drag measurements. NACA TM 1328 IV. RESULTS The theoretical mean velocities v^^j^ in the narrowest inner cross section F^ and the corresponding measured values Vj^ are indicated in the following table: Annular profile Fa/fi vithK Vi/vo ^a/vq 5 1.3^^ i.kk 1.35 1.01 6 1.39 i.kk 1.37 0.99 7 I.U2 1.70 1.1+6 1.03 8 1.5^+ 1.70 l.i+O 0.91 9 1.17 1.22 1.21 1.04 The deviations between the theoretical and the measured values are seen to be slight in most cases. The theoretical presuppositions are satisfied best for the annular profiles 5^ 6, and 9 where insignificant losses in mass flow occur. For the annular profiles 7 and 8, the theo- retical value of the circulation obviously is too large and does not materialize in practice j this phenomenon was thoroughly discussed in part V (reference l). The numerical table gives the ratio between the exit area F^ and the smallest inner area Fi and, additionally, the mean measured velocity v^ in the exit plane. It may be erroneously assumed that approximately the undisturbed external pressure Po and hence the Undisturbed free-stream velocity Vq prevail in the plane of the exit which would justify a calculation of the flow on annular profiles under this presupposition in a simple one -dimensional manner. However, the measurements of the velocity distribution in the exit plane do not confirm this assumption, as is shown by the measured results indicated in figure 3- First, one recognizes that the boundary layer on the inside of the annular profile brings on a loss of flow. The limit of the range where the total pressure does not reach the full undisturbed value is characterized by a dashed line. In the entire adjoining inner space, however, there prevails according to the measurements preeminently a negative static pressure and therewith a velocity increased compared to Vq. This fact, also to be expected theoretically (see part 7 (refer- ence 2))f is what causes the increase of the mass flow mentioned. The fact that in some cases this velocity increase is on the average exactly NACA TM 1328 cancelled by the reduction in velocity in the boundary layer, is incidental. The theoretical value of the increase of the mass flow was not attained for annular profiles 7 and 8 (fig. 3)- This discrepency is caused by the relatively large regions with energy loss; one may speak of distinct separation phenomena particularly for profile 8. The measured drag coefficients for all profiles are plotted in figure k. The c^ values lie, for the annular profiles 5, ^) and 9, in a range which is usable for the practical application of such rings. Moreover, a noticeable dependence of the c-^ value on the characteristic Reynolds number appears so that one may assume even lower drags in practical applications such as shrouded propellers because of the increase in Re. In general, the drags are in a range which lies only slightly above the one customary for two-dimensional profiles of corresponding thickness and circulation. A certain increase of the profile drag due to the influence of the ring is to be expected as was shown in part V (refer- ence 1) . V. APPLICATION OF THE RESULTS The measurements, which are to be valued as spot checks for clarification of the properties of annular profiles, show that a note- worthy increase of the mass flow by a negative circulation is possible for relatively short annular profiles without the profile drag becoming excessive. One may expect, particularly for shrouded propellers, a further increase of the effectiveness and an increase in static thrust over those so far attained for short profiles since the additional velocity &o = Vi/vq - 1 caused by the present rings was considerably increased compared to the value of 5q = 0.12 in part VII (reference 2). For ring-shaped radiators it will in many cases be possible to design the cowling of the radiator so that the mass flow in climb need not be increased by more than 30 to to percent by auxiliary means such as small additional profile drags on the ring. This is particularly conceivable in the case of drum radiators. If one ass\imes, for instance, that the mass-flow coefficient for such an arrangement (that is, the ratio between the mean velocity Vj; at the radiator and the flight velocity Vq) is to be modified by the cowling between ^Y./^o = 0-1 (liigh-speed flight) and 0.28 (climb), one would have to attempt, by suitable shaping of the hub and the cooling block, to make ^yi/^o = 0.2 without cowling. The cowling then has the function of either reducing this mass-flow coeffi- cient to one-half (for high-speed flight) or to increase it to l.k times its value (for climb) which, in an appropriate design, ought to be possible by flaps without much additional drag. However, any increase NACA TM 1328 in the mass -flow coefficient caused by the ring by more than about kO percent (at the i/2ro proportions considered here), is accompanied by very considerable additional drags since the flow then certainly will separate at the ring. (See measurements, particularly those of part V (reference 1). The measurements show further that a usable annular profile may be designed according to the methods of part III (reference 3) where the influence of the thickness of the ring on the mass flow is taken into consideration with sufficient accuracy by the continuity condition. The magnitude of the circulation up to which the flow at the profile does not separate also may Tae estimated from the existing measurements. For the design of a propeller shroud, one has to consider, additionally, the slipstream and the influence of the propeller hubj this is discussed in more detail in part VII (reference 2). Analogous requirements apply to cowlings of ring-shaped radiators. VI. SYNOPSIS The profile properties of annular profiles as they are used for shrouded propellers, cowlings of ring-shaped radiators, and similar flow problems had been investigated for comparatively long profiles j in the present report, the profile properties are clarified for shorter profiles as well, In a first survey. All measurements are made on four different annular profiles with I/^Tq = 0.5 and on one with i/^Tq = 0.25 with respect to the increase of the mass flow by the circulation about the ring and to the profile drags appearing. It is found that the theory yields useful profile forms and that, moreover, the air quantity flowing through may, by means of the present approximation theory, be determined beforehand with sufficient accuracy up to certain values of circulation, the magnitude of which can be estimated. The profile drags in the nonseparated flow region are insignificantly larger than the corresponding values for two-dimensional wings. For the rings with I/'^.Tq = 0.5, it was shown that the mean velocity in the narrowest inner cross section can be about 30 to to percent higher than the free-stream velocity with- out the profile drag becomdng excessive. For the shorter profile with 1/'2.Vq = 0.25, the increase of the mass flow is correspondingly smaller and amounts, at the most, to about 20 to 25 percent. The conclusions to be drawn from these results as to the application of annular profiles for shrouded propellers and ring-shaped radiators are briefly discussed. Translated by Mary L. Mahler National Advisory Committee for Aeronautics NACA TM 1328 REFERENCES 1. Kuchemann, Dietrich, and Weber, Johanna: Uber die StrSmung an ringformigen Verkleidungen. V. Mitteilung. Forschungsbericht Nr. 1236/5, 19^2. (Available as Tech. Intelligence Trans. F-TS-62O-RE, AAF, Air Materiel Command, Wright Field.) 2. Kilchemann, Dietrich, and Weber, Johanna: Uber die Stromung an ringformigen Verkleidungen. VII. Mitteilung. Forschungsbericht Nr. 1236/7, 19^12. (Available as ATI 27053, Air Materiel Command.) 3. Kuchemann, Dietrich, and Weber, Johanna: Uber die Stromung an ringformigen Verkleidungen. III. Mitteilung. Forschungsbericht Nr. 1236/3, 19^1- (Available as Tech. Intelligence Trans. F-TS-683, AAF, Air Materiel Command, Wright Field.) k. Kuchemann, D.: Uber die Str'dmung an ringfSrmigen Verkleidungen endlicher Dicke. I. Mitteilung. Forschungsbericht Nr. I236, 19^0. (Available as NACA TM 1325-) NACA TM 1328 CO o o u a, 1) x; -♦-> c =3 .5 o ::3 £1 W C a; o he tu3 .<-H o NACA TM 1328 S B w o M G 0) Q -a 1) O) o 0) o CM 10 NACA TM 1328 Annulor profile 6 Re = 3.5 X 10' -^ 1 1 TTi p oA ae 1 .ii_ Jjv a/vo ^ ^= = 5 5-^ rm "■ — . »■ — ' "TTTT 2 c ) 0.4 0.8 Annular profile 8 Re^ 3.5x10* -^A^ f _ _ _ _ T _ - — — -5- f Annulor profile 9 Re=l.8xl0' Figure 3.- Measured velocity distributions in the ring exit plane. NACA TM 1328 11 0.03 0.02 0.01 » P ^^ k -2~ ^0 Generating surface Re = v.l IxlO* 2x10^ 3x10- 4x10= Figure 4.- Drag coefficients of the rings investigated as functions of the characteristic Reynolds number. NACA-Langley - 2-18-52 - inoo a O ^ C^J CO ^bSS: aa -^ -H . a o i£ ^ Z, ti 11 111 5 > Sii?.o?^^ ^ 3 J= O m CO -M Qj ra a s rt rt ^ '■ » 9 - ■ o ^l-o > s Q> H M E !>. 5P O 0) •a.5 2 D. « m <« „ a -o be c *j -^ •S 2 S ■" " I, o 2 ■= « ■o ^ « t. t. 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