^CATM'^SJ^, 
 
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 NATIONAL ADVISORY CQMMITTEE 
 
 L 
 
 FOR AERONAUTICS 
 
 TECHNICAL MEMORANDUM 1329 
 
 , f 
 
 CONCERNING THE FLOW ABOUT RING-SHAPED COWLINGS 
 
 PART DC - THE INFLUENCE OF OBLIQUE ONCOMING FLOW ON TH^ 
 INCREMENTAL VELOCITIES AND AIR FORCES AT THE 
 FRONT PART OF CIRCULAR COWI^ 
 By Dietrich Kuchemann and Johanna Weber 
 
 Translation of "ZWB Forschmigsbericht Nr. 1236/9, 
 
 June 10, 1943 
 
 NACA 
 
 Washington 
 February 1952 
 
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7 ^ ' '• • ^ 1^-75 'jO ^ 
 
 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
 
 TECHNICAL MEMORANDUM 1329 
 
 CONCERNING THE FLOW ABOUT RING-SHAFED COWLINGS 
 
 PART IX - THE INFLUENCE OF OBLIQUE ONCOMING FLOW ON THE 
 INCREMENTAL VELOCITIES AND AIR FORCES AT THE 
 FRONT PART OF CIRCULAR COWLS^ 
 By Dietrich Kuchemann and Johanna Weber 
 
 ABSTRACT: The dependence of the maximum incremental velocities and air 
 forces on a circular cowling on the mass flow and the angle 
 of attack of the oblique flow is determined with the aid of 
 pressure-distribution measurements. The particular cowling 
 tested had been partially investigated in reference 1. 
 
 OUTLINE: I. THE PROBLEM 
 
 II. THE METHOD OF MEASUREMENT 
 
 III. RESULTS 
 
 IV. SYNOPSIS 
 
 V. REFERENCES 
 
 I. THE PROBLEM 
 
 As a supplement to former measurements (compare reference 1 and 
 reference 2) where the main stress was laid on the development of usable 
 forms of circular cowls in the case of purely axial flow, the measurements 
 presented here are to give a s\irvey of the phenomena in case of flow at 
 an oblique angle of attack. The occurring forces in the vertical direc- 
 tion to the axis of the cowl are of interest not only in aerodynamical 
 respect but also for the structural stress on the propulsion unit. It 
 was to be assumed that the magnitude of these transverse forces will be 
 a fimction not only of the geometrical dimensions of the entire engine 
 
 *Ober die Str6"mung an ringformlgen Verkleidungen. IX Mitteilung: 
 Der Einfluss der Schraganblasung auf die Uebergeschwindigkeiten vmd 
 Luftkrafte am vorderen Teil von Ringhauben. Zentrale fiir wissenschaftliches 
 Berichtswesen der Luftfahrtforschung des Generalluftzeugmeisters (ZWB) 
 Berlln-Adlershof, Forschungsbericht Nr. 1236/9, Gottingen, June 10, 19^3- 
 
2 . NACA TM 1329 
 
 nacelle and of the angle of attack but also of the mass -flow coefficient 
 and hence the strength and direction of the leaving jet, and of the 
 position of the engine with respect to other airplane parts. Of all 
 these interrelated questions, only a single one has been investigated 
 which could be answered the fastest with the means at disposal and which 
 is of fundamental importance for all further problems. What influence 
 does the oblique flow exert on the front part of the inlet of such an engine 
 cowling? In detail, it had to be determined for a characteristic example} 
 in what manner the transverse force depends on the angle of attack and 
 the mass-flow coefficient, where, approximately, lies the center of 
 gravity of these forces, and how strongly the maximim incremental veloc- 
 ities on the outside of the cowl increase in case of oblique flow. 
 
 II. THE METHOD OF MEASUREMENT 
 
 We shall use pressure-distribution measurements on a selected inlet 
 device in oblique flow. The pressirre-distribution measurements in refer- 
 ence 1 and elsewhere-'- have proved to have many applications to our present 
 problem. It is necessary to select a circular cowl where the results 
 may, to some extent, be regarded as generally valid for the tests, thus, 
 extreme forms are a priori excluded. The cowling 1 with hub 2^ investi- | 
 
 gated in reference 1 is such a circular cowl which satisfies these require- ^ 
 ments for all operating conditions with respect to its construction (ratio ; 
 
 between free entrance cross section F^ and maximum outer cross sec- 
 tion Fa, ^sAa ~ 0«27] with respect to its maximum incremental velocities 
 and with respect to the loss-free flow about it (compare reference 2). 
 The model of this cowling described in reference 1 could be used directly. 
 Thus, it was only necessary to expand the former program of measvurements i 
 
 in reference 1 insofar that more detailed and more finely subdivided § 
 
 series of angles of attack are tested and that the measurements for 
 oblique flow are extended to include smaller mass-flow coefficients. 
 These new measurements are desirable because we had to assume that the 
 locally greatest stresses appear for such states of flight ('which, it is 
 true, are extraordinary) where the mass flow is very small or in the 
 extreme case zero. 
 
 ■'-Among others, measurements by M. Schirmer (reference 3) on airship 
 bodies show that the forces and moments obtained from pressure distribu- 
 tions for nonseparated flow agree well with the results from a balance. 
 
 '^his cowl differs only slightly from the circular cowls of class I 
 indicated in reference 2 by a somewhat greater slenderness (the cylindrical 
 piece begins at a distance 3Ra fi'o™ the leading edge). 
 
 t 
 
NACA TM 1329 
 
 Because of the disturbed rotational symmetry, an evaluation of 
 pressure-distribution measurements for transverse forces requires the 
 placing of test points over the circumference of the cowl since the 
 pressure p depends - besides being a function of the space coordi- 
 nates X and r in axial and radial direction - on the angle 9 (com- 
 pare fig. 1). The entire air force, N, that acts vertically to the 
 axis of rotation for a circular cowl of the axial length Z is obtained 
 by integration of the respective corresponding component of the local 
 pressure p(x,r,cp) 
 
 p(x,r,cp)ds — cos q)r(x)d9 
 ds 
 
 (1) 
 
 with s as arc length along the body contour. A simple estimate can 
 be made with the assumption that the difference between the local pres- 
 sure for oblique flow and the corresponding value without oblique flow 
 (a = 0) is distributed over the circumference of the cowl according to 
 a cosine law3. Thus, 
 
 p(x,r,cp,a) - p(x,r,a = 0) = lp(x,r,cp = 0,a) - p(x,r,a = O) 
 
 = p - p „ cos cp 
 
 cos cp 
 
 (2) 
 
 Under this assumption of the cosine relationship for oblique flow, one 
 pressure-distribution measurement in the upper part of the meridian 
 section (cp = 0) is sufficient and the integration over the periphery of 
 the circle can be performed. Equation (l) becomes 
 
 f r^" 2 
 
 N = [p^ - P^^q]cos cpr(x)dx dcp 
 
 = « I [p - P rir(x) dx 
 Jo L°^ ^=^ 
 
 (3) 
 
 Theoretically, more complicated relations may be assumed as was the 
 case in a report by J. Lotz (reference h) on airship bodies in oblique 
 flow. 
 
NACA TM 1329 
 
 If one would, instead of the assumption of equation (2), make the extreme 
 presupposition that the press\ire has on the entire upper side of the body 
 (-It/2 "^ cp "S +J1/2) the same value as for cp = and on the entire lower 
 side the same value as for cp = n, a factor h instead of the factor n 
 would result in equation (S)- Thus, the values given later would, at 
 the worst, have to he multiplied by h/n = 1.27. 
 
 If one makes the normal force N dimensionless by means of the 
 free -stream dynamic pressure 
 
 P 2 
 ^0 2° 
 
 and the maximum cross sectional area nR^ , one obtains from equation (3) 
 
 N 
 
 q TtR 2 
 ^o a 
 
 w 
 
 This evaluation method can be improved by measuring with each 
 positive angle +a at the same time the corresponding negative angle -a 
 which, for reasons of symmetry, represents a second series of pressure 
 test points for cp = l80°. If our above assumption were justified, the 
 corresponding value of the integral, equation (^), would equal, except 
 for the sign, that for the positive angle. In the evaluation of the 
 measurements, it was found that these two values were no longer equal 
 for larger angles of attack (a = 9° and more); however, the deviations 
 were such that the use of the simple arithmetic mean between the two 
 values appeared justified. 
 
 Aside from the total force normal to the axis which was thus obtained, 
 equation (k) , the point of application of this force in the x-direction, 
 or the moment of these forces for instance referred to the point x = Zj 
 r = 0, are of interest. These are obtained by the further integration 
 
 M / a Pc, - Pa=o r(x)/ Z x\jx 
 
 qnEr 
 
 q. Ra VHi " rtJIr:' ^^^ 
 
NACA TM 1329 
 
 III. RESULTS 
 
 Figiires 2 through h show the wall pressure distributions for three 
 different mass flow coefficients.^ The resulting dependence of the 
 pressure minimum on the angle of attack was evaluated with respect to 
 the maximum excess velocities v„^^ (compare fig. 5)- The known char- 
 acteristic variation of Vjjjajr/vQ against the mass-flow coefficient "v^/vq 
 (with v-p = mean velocity in the entrance cross section Fg) is repeated 
 for the different angles of attack; the incremental velocities increase 
 considerahly with angle of attack. The increase of the incremental 
 velocities which is expressed by the quotient 
 
 <i(^max/^o) 
 
 da 
 
 depends^ aside from being a function of the mass-flow coefficient, on 
 the constriction and, to a high degree, also on the nose form, particu- 
 larly the nose radius. For the cowling investigated here which is 
 equivalent to a circular cowl of class I in reference 2, the following 
 equations are approximately valid: 
 
 dl^max, 
 
 da 
 for vj; = and 
 
 ^ = 2.7 
 
 <^(^max/^o) ^ -, . 
 da ^^ 
 
 for vg = v^ 
 
 For the circular cowls of class II with more pronounced rounding of 
 the nose, a lesser degree of dependence of the incremental velocities on 
 the angle of attack of the oblique flow is to be expected. Thus follows, 
 for instance, from measurements here not described in detail that for 
 circular cowl of the class II with Fg/Fg^ = 0.3 for ve/Vq =0.27 
 approximately 
 
 d(vmax/vo) ^ -^j 
 
 da 
 applies whereas for the corresponding cowl of class I 
 
 d(vmax/vo) ^ 
 
 = 2-2 
 da 
 
 Vlorres-Donding results for larger v-r. /v. are to be found in reference 1. 
 
 Corresponding results for larger '^e/'^o 
 
NACA TM 1329 
 
 For comparison, we further consider the measurement (reference 5)' on a 
 Ruden nose inlet of minimum constriction with a much more pointed nose. 
 For equal constriction and equal mass-flow coefficient, here 
 
 d(^max/^o) , „ 
 
 da ' 
 
 is foiond. The dependence discussed Just now also appears in two- 
 dimensional profiles and is in the same direction. For customary profiles, 
 for instance, of the NACA series with standard nose rounding, one finds 
 gradients of the same order of magnitude as for the cowls of the classes I 
 and II in the range of small angles-of-attack. 
 
 These measurements prove that the dependence of '^max/^o °^ ^^^ 
 angle of attack has the same significance as the dependence of '^max/^o 
 on the constriction (compare reference 2). It is therefore very important 
 as to how such an engine cowling is installed in the airplane. Particu- 
 larly, one problem therein is still unsolved: how far the flow direction 
 at the entrance is influenced, for instance, by a wing or other airplane 
 parts close by. 
 
 We determined the normal forces according to equation (k) from the 
 pressure -distribution measurements. The integration was carried out 
 only over the front part of the cowl up to the cylindrical part so that 
 Z/Rq^ was set equal 3- For small mass-flow coefficients, the main 
 
 contribution to the transverse forces is made by the outside of the 
 cowling, whereas the share of the inside becomes significant only for 
 larger Vg/v . The pressiure distribution at the hub shows a very minor 
 dependence on a and, therefore, contributes practically nothing to the 
 transverse force. This fact is a renewed confirmation of the rule dis- 
 cussed in detail in reference (2) that the flow in the interior is almost 
 independent of the flow outside. Figure 6 shows the result of this 
 evaluation) aside from the linear variation with the angle of attack, 
 the slight degree of dependence on the mass flow is noteworthy. This 
 phenomenon probably is interrelated with the fact that for larger mass- 
 flow coefficients, the outside experiences less normal forces but, on 
 the other hand, the inside gets a larger share. How far this result 
 repeats itself for arbitrary forms as well is still undecided. Certainly 
 deviations will result if the flow separates at any location along the 
 cowl which, for the cowl investigated here, was the case to a slight 
 extent at v-g = and a = 12°, but is otherwise avoided. The evalua- 
 tion of the moments of these air forces, according to equation (5)^ 
 showed that the center of gravity of the air force distribution lies, for 
 all mass-flow coefficients and angles of attack, approximately in the 
 same plane x/R^ =0.8 (x being counted from the entrance plane). The 
 
NACA TM 1329 
 
 air-force moment of the noncylindrical front part of the inlet referred 
 to the point x = 3Ra then is vith 
 
 2.2a 
 
 %^a^ 
 
 (compare fig. 6) 
 
 M 
 
 qo^^a^ 
 
 2.2a(3 - 0.8) = U.8a 
 
 The independence of the moment of the internal mass flow becomes under- 
 standable by means of the following deliberation: An arbitrary body, 
 immersed in a flow approaching at the angle of attack a referred to 
 the X, z-plane with the velocity Vq parallel to the x axis, experi- 
 ences a longitudinal moment of the magnitude 
 
 P 
 
 2 'o V^z '^x 
 
 M = - v^2^K^ _ K^lsin 2a 
 
 (compare F. Vandrey (reference 6)). Therein pK^ or PK2 are 
 apparent additional masses of the body for oncoming flow in x or 
 z direction. For elongated bodies K-^ is, in general, considerably 
 smaller than K^, (for instance, for a spheroid of the axis ratio ^:1, 
 the value of K^ is 10 times that of Kx) • If we have, as in our case, 
 a body through which the flow passes in the direction of the x-axis, Kx 
 only is important, not K2;. Furthermore, the mass flow Q also is small 
 in the cases considered, since 
 
 so that the mass to be deflected may be neglected compared to P^^z' ■^°^ 
 larger mass-flow coefficients, however, a modification of the moment is 
 to be expected. It is true that even for Vg/v^ up to 1 no significant 
 
 C/^O 
 
 iblis 
 
 deviation from the given values could be established. These larger mass- 
 flow coefficients are of less interest in practice since the transverse 
 forces and moments, taken absolutely, become significant only in case of 
 larger Vq, that is, of smaller v^/Vq. 
 
 Our simple result suggests a comparison with the instability moment 
 of nacelle bodies calculated by, among others, F. Vandrey in reference 6. 
 
8 NACA TM 1329 
 
 This report gives the moments of ellipsoids. If one selects a semi- 
 spheroid shown as the dashed line b in figixre 7 with the same semiaxis R^ 
 and length I, as the investigated circular cowl, a, there results 
 according to reference 6, a moment5 
 
 M 
 
 ^o^^a^ 
 
 2.8a 
 
 This is a smaller value than the one measured at the circular cowl; 
 however, a comparison of the forms makes this understandable. The 
 spheroid c in figxare 7^ which yields the same moment as the circular 
 cowl, fits the latter very well. Thus, there exists the possibility for 
 rough calculations of replacing in this manner a prescribed cowl by a 
 spheroid. Our simple result subsequently justifies the used method of 
 investigating only the front part of the cowling. It furthermore opens 
 up the possiblity of separate treatment also for the processes at the 
 exit and in the jet. 
 
 IV. SYNOPSIS 
 
 The previously published measurements made on circuleir cowls are 
 herein supplemented by detailed ones for oblique flow. With reference 
 to the maximum incremental velocities on the outside, a considerable 
 dependence on the angle of attack manifests itself which can be kept 
 within tolerable limits only by a sufficient rounding of the nose. The 
 transverse forces acting on the front part of the cowling are determined 
 from pressure-distribution measurements on a circular cowl characteristic 
 for the general case and result, for small mass flow, as almost indepen- 
 dent of the mass-flow coefficient and increasing linearly with the angle 
 of attack if the flow does not separate. For the circular cowl investi- 
 gated, a flow free from separation may still be realized for zero mass 
 flow up to an angle of attack of the oblique flow of about 10°. Since 
 the aerodynamic center of the transverse forces is, furthermore, almost 
 independent of the angle of attack and the mass flow, a linear relation 
 between the air -force moment about an arbitrary point of reference and ■ 
 the angle of attack results. A simple rule of thumb for the magnitude 
 of this moment may be given by replacing the circular cowl by a suitable 
 semiellipsoid. 
 
 Translated by Mary L. Mahler 
 National Advisory Committee 
 for Aeronautics 
 
 -'since, of the ellipsoid as well, only the front part is considered, 
 the moments indicated in reference 6 are to be divided by 2. 
 
 '^Measured air force moments of other body forms may be found in 
 reference 3- 
 
NACA TM 1329 
 
 REFERENCES 
 
 1. Kuchemann, D., and Weber, J.: Uber die Stromung an ringformigen 
 
 Verkleidungen. IV. und VI. Mitteilung: WindkanaLraessungen an 
 Einlaufgeraten. Forschungsbericht Nr. 1236/if, 19^1. (Available as 
 ATI 505^5^ Air Materiel Command.) Forschungsbericht Nr. I236/6, 
 I9U2. (Available as NACA TM 1327.) 
 
 2. Kuchemann, D. and Weber, J.: Das Einlauf problem bei Tri6bwerksver- 
 
 kleidungen. Erscheint demnachst in den Mitteilungen d.dt.Akad.d. 
 Luftf ahrtf or schung . 
 
 3. Schirmer, M. : Aerodynamische Modellversuche an deutschen und 
 
 auslandischen Luftschiff-Baumustern. Forschungsbericht Nr. l647^ 
 19^2. 
 
 k. Lotz, J. : Zur Berechnung der Potent ialstromung um quergestellte 
 Luftschiffkorper. Ing. Archiv., 2, 507, 1931- (Available as 
 NACA TM 675 . ) 
 
 5. Ruden, P.: Windkanalmessungen an einem rotationssymmetrischen 
 
 Fangdiffusor. Forschungsbericht Nr. lij-27/l, 19^1, oder: 
 Fangdiffusoren. LGL-Bericht ikk, 19^+1. (Available as ATI i+0320. 
 Air Materiel Command.) 
 
 6. Vandrey, F.: Abschatzung des Rvimpf e inf lus se s auf das Langsmoment 
 
 eines Fliigzeugs. Jahrb. 19^0 d.dtsch. Luftfahrtforschg. I 367' 
 
10 
 
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MCA TM 1329 
 
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12 
 
 NACA TM 1329 
 
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 Figure 3.- Wall pressure distributions. 
 
NACA TM 1329 
 
 13 
 
 Figure 4.- Wall pressure distributions. 
 
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 NACA TM 1329 
 
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 as functions of the oblique angle of attack a. 
 
NACA TM 1329 
 
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 Figure 6.- Coefficient of the transverse force perpendiciolar to the axis 
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 flow coefficient. 
 
16 
 
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