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k Pt TM 19
5 L . H' . :. ..ABiRACT: OUTLINE: CONCERNING THE FLOW ABOUT RINGSHAPED 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 Kichemann and Johanna Weber 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 pressuredistribution measurements. The particular cowling tested had been partially investigated in reference 1. I II III IV, V THE PROBLEM THE METHOD OF MEASUREMENT RESULTS SYNOPSIS 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 survey 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 function not only of the geometrical dimensions of the entire engine *Ober die Strfimung an ringf6'rmigen Verkleidungen. IX Mitteilung: Der Einfluss der Schriganblasung auf die Uebergeschwindigkeiten und Luftkrafte am vorderen Tell von Ringhauben. Zentrale fUr wissenschaftliches Berichtswesen der Luftfahrtforschung des Generalluftzeugmeisters (ZWB) BerlinAdlershof, Forschungsbericht Nr. 1236/9, Gottingen, June 10, 1943. ,I f I )' 1 __7 it 1 '5 f V ff  NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL MEMORANDUM 1329 I II * IV V .* * nacelle and of the angle of attack but also of the massflow 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 massflow coefficient, where, approximately, lies the center of gravity of these forces, and how strongly the maximum incremental veloc ities on the outside of the cowl increase in case of oblique flow. II. THE METHOD OF MEASUREMENT We shall use pressuredistribution measurements on a selected inlet device in oblique flow. The pressuredistribution 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 22 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 FE and maximum outer cross sec tion Fa, FE/Fa = 0.2 with respect to its maximum incremental velocities and with respect to the lossfree 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 measurements 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 massflow 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. 1Among 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. 2This 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 from the leading edge). : I '" *:" ;: ;'  ~ ~ c ". ':. l{.: NACA TM 1329 ::. 1! ,NACA TM 1329 3 Because of the disturbed rotational symmetry, an evaluation of pressuredistribution 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 p (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 2 is obtained by integration of the respective corresponding component of the local pressure p(x,r,p) N = p(x,r,cp)ds dx cos cpr(x)d(p (1) 0i JO ds 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,p,a) p(x,r,a )= = p(x,r,q = 0,a) p(x,r,a = 0 cos P = [ Pa cos q (2) Under this assumption of the cosine relationship for oblique flow, one pressuredistribution 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 (1) becomes N = p a cosC2pr(x)dx dq = p P 1r(x) dx (3) tEheoretically, more complicated relations may be assumed as was the case in a report by J. Lotz (reference 4) on airship bodies in oblique flow. 4 NACA TM 1329 If one would, instead of the assumption of equation (2), make the extreme presupposition that the pressure has on the entire upper side of the body (n/2 < cp < +n/2) the same value as for p = 0 and on the entire lower side the same value as for p = n, a factor 4 instead of the factor a would result in equation (3). Thus, the values given later would, at the worst, have to be multiplied by 4/n = 1.27. If one makes the normal force N dimensionless by means of the freestream dynamic pressure P=2 qo = v 2 % 2 0 and the maximum cross sectional area nRa2 one obtains from equation (3) N 1/Ra Pa Pa=o r(x) (4) 2 J0 q d (4) o ao R 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 (p = 1800. If our above assumption were justified, the corresponding value of the integral, equation (4), 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 = 90 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 (4), the point of application of this force in the xdirection, or the moment of these forces for instance referred to the point x = 2; r = 0, are of interest. These are obtained by the further integration M '/Ra Pc Pa=o r(x) ia \d( (5) qoiRa3 JO Ra a a NACA TM 1329 5 III. RESULTS Figures 2 through 4 show the wall pressure distributions for three different mass flow coefficients.4 The resulting dependence of the pressure minimum on the angle of attack was evaluated with respect to the maximum excess velocities vmax (compare fig. 5). The known char acteristic variation of Vmax/Vo against the massflow coefficient VE/Vo (with vE = mean velocity in the entrance cross section FE) is repeated for the different angles of attack; the incremental velocities increase considerably with angle of attack. The increase of the incremental velocities which is expressed by the quotient d (Vma/Vo) da depends, aside from being a function of the massflow 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: d(vmax/o) 2.7 do for vE = 0 and d(vmax/o) . da for vE = vo. 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 FE/Fa = 0.3 for VE/vo = 0.27 approximately d(vmax/v) = 1.6 da applies whereas for the corresponding cowl of class I d vmax/vo) 2.2 da Corresponding results for larger are to be found in reference .orresponding results for larger vE/vo are to be found in reference 1. 6 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 massflow coefficient, here d(vmax/o) _ da is found. 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 TI in the range of small anglesofattack. These measurements prove that the dependence of vmax/vo on the angle of attack has the same significance as the dependence of vmax/' 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 (4) from the pressuredistribution measurements. The integration was carried out only over the front part of the cowl up to the cylindrical part so that I/Ra was set equal 3. For small massflow 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 vE/vo. The pressure 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 vE = 0 and a = 120, 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 massflow coefficients and angles of attack, approximately in the same plane x/Ra = 0.8 (x being counted from the entrance plane). The .', * ");.:. .. * NACA TM 1329 7 airforce moment of the noncylindrical front part of the inlet referred to the point x = 3Ra then is with N = 2.2a q 0Ra (compare fig. 6) M S = 2.2a(3 0.8) = 4.8a a3 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,zplane with the velocity vo parallel to the x axis, experi ences a longitudinal moment of the magnitude M = vo2(K, Kx)sin 2a (compare F. Vandrey (reference 6)). Therein PKx or PKZ are apparent additional masses of the body for oncoming flow in x or z direction. For elongated bodies Kx is, in general, considerably smaller than Kz (for instance, for a spheroid of the axis ratio 4:1, the value of Kz 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 xaxis, Kx only is important, not Kz. Furthermore, the mass flow Q also is small in the cases considered, since Q/ta2Vo = (vE/Vo)(FE/Fa) = 0.27(vE/o) so that the mass to be deflected may be neglected compared to PKz. For larger massflow coefficients, however, a modification of the moment is to be expected. It is true that even for vE/vo up to 1 no significant 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 vo, that is, of smaller VE/Vo. 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 figure 7 with the same semiaxis R, and length 1, as the investigated circular cowl, a, there results according to reference 6, a moment5 M = 2.8a qonRa 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 figure 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 possibility of separate treatment also for the processes at the exit and in the jet. IV. SYNOPSIS The previously published measurements made on circular 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 pressuredistribution measurements on a circular cowl characteristic for the general case and result, for small mass flow, as almost indepen dent of the massflow 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 100. 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 airforce 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 5Since, of the ellipsoid as well, only the front part is considered, the moments indicated in reference 6 are to be divided by 2. 6Measured air force moments of other body forms may be found in reference 3. ." : .. ... .' .. .. NACA TM 1329 9 REFERENCES 1. Kichemann, D., and Weber, J.: Uber die Str6mung an ringf6rmigen Verkleidungen. IV. und VI. Mitteilung: Windkanalmessungen an Einlaufgereten. Forschungsbericht Nr. 1236/4, 1941. (Available as i' ATI 50545, Air Materiel Command.) Forschungsbericht Nr. 1236/6, j 1942. (Available as NACA TM 1327.) 1 2. Kichemann, D. and Weber, J.: Das Einlaufproblem bei Triebwerksver Skleidungen. Erscheint demnachst in den Mitteilungen d.dt.Akad.d. Luftfahrtforschung. 3. Schirmer, M.: Aerodynamische Modellversuche an deutschen und ausllndischen LuftschiffBaumustern. Forschungsbericht Nr. 1647, 1942. S, 4. Lotz, J.: Zur Berechnung der Potentialstrimung um quergestellte Luftschiffkirper. Ing. Archiv., 2, 507, 1931. (Available as NACA TM 675.) 5. Ruden, P.: Windkanalmessungen an einem rotationssymmetrischen Fangdiffusor. Forschungsbericht Nr. 1427/1, 1941, oder: Fangdiffusoren. LGLBericht 144, 1941. (Available as ATI 40320, Air Materiel Command.) 6. Vandrey, F.: Absch'atzung des Rumpfeinflusses auf das Langsmoment eines Flugzeugs. Jahrb. 1940 d.dtsch. Luftfahrtforschg. I 367. 10 NACA TM 1329 .* "? 100 uo II0 o o a) C, .0 0 I .c 0 / '4  c 'K C~*,i) NACA TM 1329 1.0 PP Inside l 6" Throttle position I 0.6 v/vu0 IUE/U0: 0 0.4  0.2 02 X CC12I " Ra 0 2 _03 0.4 0.5 06 O7 0O8 09 1. 1.2 I 1.4 09 0.6/ 3/ 0.8 9^*S^^y!'de 1.0 1.4 1.8  2.0 2.2  Figure 2. Wall pressure distributions on the arrangement 121 of reference 1 for different angles of attack a in the extreme meridian section. ...r a .. :~ , .m NACA TM 1329 .1 / *. Figure 3. Wall pressure distributions. ia * l PPo qo f NACA TM 1329 13 IACA TM 1329 13 Figure 4. Wall pressure distributions. NACA TM 1329 Figure 5. The incremental velocities to be expected for various mass flow coefficients on the outside of a circular cowl with FE/Fa = 0.27 as functions of the oblique angle of attack a. NACA TM 1329 15 Figure 6. Coefficient of the transverse force perpendicular to the axis of rotation acting on the noncylindrical part of the cowl of the length i = 3R, as a function of the angle of attack and the mass flow coefficient. I.. 16 NACA TM 1329 o T3 vi 0 00 I. 1i I=1 U, E S1 o \ 5 i Q3 0 \I 1 / *a i xI / %, , N, NACALangley 2153 1000 Nm = g w^ c9. ,i( i So4o >^ i" . s 0 NI q .ow r rr N ... . o' ^B Si i to I* Nt~ '.S 601 N I i N i '..... Wa .3s *a ) l a is i ~ IA a IUDb o. 0 0 A 0 l0 I~~~' ;~~s~lss~ i,^~gis i 3u 3  N v caBdI  c4 i ;atiB Q z jj t o u ? 0 zuU U 0 > 40.i=ga1 2i g q ws F U SR: 09 Elg gll ep 0 ca m L4 = m ma O 9 ub U haS a N , 0 a t a o 5 0 An I *' c C _m I ~ .mha 1~ 0 Lzz ooso '2I G t'i 0 UO M mm 5 C cis0 goa < = w C' z z u 0o o k E 6 ,6 i*5 Oc (zuuom ^s ^ >SSacnf 0 C 00 Na. .03 N 5 0  .3 N N N 5. c 5. 00 is l to iss L Z z 0 IX S .Lm '0 i s s 2 lsC la ^02 oi, ^fc ^^ ^Si^ t C l ^ w u / i~~~~o 'ala5^.~mm m .o u E O : L* 0P SPU N j, a V NNo 4 S c~ S 1 4. 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