1、1 EXPERIMENTALLY DETERMINED LOCAL FLOW PROPERTIES AND DRAG COEFFICIENTS FOR A FAMILY OF BLUNT BODIES AT MACH NUMBERS FROM 2.49 TO 4.63 by Robert L. Stallzngs,Jr, Langley Research Center Ldngley Station, Hampton, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. OCTOBER 1967 Provide
2、d by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB, NM I llllll11lll lllll lllllllllllllllIIll1Ill1 EXPERIMENTALLY DETERMINED LOCAL FLOW PROPERTIES AND DRAG COEFFICIENTS FOR A FAMILY OF BLUNT BODIES AT MACH NUMBERS FROM 2.49 TO 4.63 By Robert
3、 L. Stallings, Jr. Langley Research Center Langley Station, Hampton, Va. NATIONAL AERONAUTICs AND SPACE ADMINISTRATION - - -For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTl price $3.00 Provided by IHSNot for ResaleNo reproduction or n
4、etworking permitted without license from IHS-,-,-EXPERIMENTALLY DETERMINED LOCAL FLOW PROPERTIES AND DRAG COEFFICIENTS FOR A FAMILY OF BLUNT BODIES AT MACH NUMBERS FROM 2.49 TO 4.63 By Robert L. Stallings, Jr. Langley Research Center SUMMARY Drag coefficients and local flow properties were experimen
5、tally determined for a family of blunt bodies at Mach numbers from 2.49 to 4.63 at a Reynolds number, based on afterbody diameter, of 1.88 X lo6. The family consisted of bodies of revolution having variable nose and shoulder radii (rn and rc, respectively) and cylindrical afterbodies 7.5 inches (191
6、 mm) in diameter (d). The geometry of the 18 models tested ranged from a hemisphere-cylinder to a flat-face cylinder. The Mach number effect on nondimensional pressure and velocity distributions of the hemispherical model decreased rapidly with increasing Mach number. These distri butions at Mach nu
7、mber 4.63 were essentially the same as previously published results for Mach numbers up to 11.4. Increasing the nose bluntness also decreased the Mach number effect on the pressure and velocity distributions. There was no effect of Mach number on these distributions for the zero-shoulder -radius mod
8、els for 3 0.707. Dragd coefficients determined from integrated pressures over the nose of the hemispherical model and by assuming the base pressure coefficient to correspond to -1/Mw2 (where M, is the free-stream Mach number) were in good agreement with previously published data for a sphere. These
9、results were also in good agreement with drag coefficients determined from modified Newtonian theory. A reduction in drag coefficients as indicated by both experiment and theory occurred for a decrease in bluntness obtained by an increase in shoulder radius. The maximum velocity gradient for all mod
10、els occurred either at or slightly downstream of the point of tangency of the nose and shoulder arcs, Stagnation-point velocity gradients determined from measured pressures were in good agreement throughout the range of variables of this investigation with theoretical esti mates based on Traugotts m
11、ethod and measured shock-standoff distances. A comprehensive presentation of these data in figure form is included for suffi ciently small intervals of nose and shoulder radii to enable the pressure distributions, velocity distributions, stagnation-point velocity gradients, shock-standoff distances,
12、 or drag coefficients to be determined - either directly or by interpolation - for any body of the general shape described. Since all these variables indicated only very small Mach number effects at the higher test Mach numbers, these results should be applica ble at a much higher range of Mach numb
13、er than that of this investigation. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-INTRODUCTION The advantages of blunt nose shapes for reducing the convective aerodynamic heating at the forward stagnation point of bodies moving at hypersonic flight
14、 speeds have been well established within the past decade. Unfortunately, the governing partial-differential equations for the subsonic flow field between the bow shock wave and nose of such bodies are of the elliptic type and, as yet, no exact analytical solutions are available. This condition has
15、led to what is generally referred to as the “blunt body problem.“ Some gains have been made in recent years toward the solution of this problem by various numerical and approximate methods - for example, see references 1 to 6; however, as discussed in reference 7, large discrepancies can exist betwe
16、en the pressure distributions determined by the different methods. Until the problems associated with these discrep ancies are resolved, experimental investigations are required to determine the local flow properties on all but the more basic nose shapes. A blunt nose shape that has received conside
17、rable attention in the past and that has been used on numerous reentry configurations (e.g., Mercury, Gemini, and Apollo) con sists of a hemispherical segment nose with a shoulder region having a circular cross section, Experimentally obtained stagnation-point velocity gradients for bodies of this t
18、ype with a shoulder radius of zero have been reported in reference 8 and with a limited range of shoulder radius, in reference 9. Although the stagnation-point velocity gradi ents are extremely important for determining the stagnation-point heating, it is well known that for extremely blunt bodies t
19、he maximum heating occurs off the stagnation point. Therefore, in order to assess accurately the level of heating over such a family of bodies, detailed pressure and velocity distributions must be determined over the com plete nose. Pressure distributions for such bodies have been reported in refere
20、nces 8, 10, and 11; however, the models used in these investigations provided only a limited range of geometrical variables and, being small, were limited in the amount of instrumentation. The present investigation was therefore initiated to determine the effect of nose and shoulder radii on the loc
21、al pressure and velocity distributions for a family of 18 blunt bodies. The models, which were 7.5 inches (191 mm) in diameter, ranged from a hemi spherical nose to a flat-face cylinder at intervals of nose and shoulder radii sufficiently small to enable the results from this investigation to be app
22、lied - either directly or by interpolation - to any shape of the general type. The tests were conducted through a range of Mach number from 2.49 to 4.63. The flow properties presented and discussed for the complete range of geometrical variables consist of pressure distributions, veloc ity distribut
23、ions, stagnation-point velocity gradients, and shock-standoff distances. Drag coefficients obtained by integrating the local pressures are also discussed. Limited comparisons are made with approximate theories. 2 I Provided by IHSNot for ResaleNo reproduction or networking permitted without license
24、from IHS-,-,-SYMBOLS a* A CD cP cp,max D d M P b IC rn S s1 s2 T U U e 81 Y free-stream sonic velocity area drag coefficient pressure coefficient maximum pressure coefficient, based on total pressure behind normal shock drag force afterbody diameter Mach number pressure afterbody radius shoulder (co
25、rner) radius nose radius surface length, measured from forward stagnation point (see fig. 1) nose surface length from forward stagnation point to point of tangency of nose and shoulder arcs (see fig. 1) nose surface length from forward stagnation point to shoulder -afterbody juncture (see fig. 1) te
26、mperature velocity stagnation-point velocity gradient, du/ds angle between normal to model surface and axis of symmetry (see fig. 1) value of 8 at s1 ratio of specific heats, 1.4 for air 3 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 shock-stand
27、off distance P density Subscripts: m free-stream conditions 1 local static conditions at outer edge of boundary layer t free-stream stagnation conditions t, 2 stagnation conditions behind normal shock at free-stream Mach number b pertaining to model base h pertaining to hemisphere APPARATUS AND TEST
28、 CONDITIONS The investigation was conducted in the high Mach number test section of the Langley Unitary Plan wind tunnel described in reference 12. This variable-pressure, continuous flow tunnel has an asymmetric sliding-block nozzle that permits a continuous variation in the test-section Mach numbe
29、r from 2.30 to 4.63. The deviations in Mach number in the entire 4- by 4-foot (1.22- by 1.22-meter) test section for the test Mach numbers are as follows: For M, = 2.49 kO.018 For M, = 3.51 kO.048 For Ma= 4.06 *0.061 For M,=4.63 *0.045 The effects of nonuniform Mach number were minimized in this inv
30、estigation by testing all models at essentially the same location in the test section. The effect of flow angularity associated with this nonuniform Mach number was also minimized by an adjust ment of the models for each test point relative to the free-stream velocity vector. This step was accomplis
31、hed by monitoring pressure differentials from the stagnation point to orifice locations equidistant and diametrically opposite the stagnation point and adjusting the model in both angle of attack and angle of yaw until these pressure differences equalized. 4 Provided by IHSNot for ResaleNo reproduct
32、ion or networking permitted without license from IHS-,-,-The pressure measurements were obtained for the model at an angle of attack of Oo. The free-stream stagnation temperatures at the test Mach numbers were as follows: Tt IM, OR 2.49 610 3.51 610 4.06 635 4.63 635 - . The test Reynolds number, ba
33、sed on afterbody diameter, was 1.88 x lo6. MODELS, INSTRUMENTATION, AND ACCURACY The general shape of the axisymmetrical models (see fig. 1) consisted of a hemispherical segment nose (of radius rn) faired into a circular-arc shoulder (of radius rc)which faired into a cylindrical afterbody (of diamet
34、er d). A total of r18 models were tested and they had geometries ranging from a flat-face cylinder (2= 0, 3= a) to a hemisphere (F= 0.5, 3= 0.5). Values of rc/d and rn/d for eachd d model are shown in the table presented in figure 1. Also included in this table are values of sl/d and s2/d, where s1
35、is the value of s at the point of tangency of the nose and shoulder arcs and s2 is the value of s at the shoulder-afterbody juncture. The afterbody for all models consisted of a cylindrical section 4 inches (102 mm) long and 7.5 inches (191 mm) in diameter. The model instrumentation consisted of app
36、roximately 80 pressure orifices of 0.050-inch (1.27-mm) inside diameter. Locations of these pres sure orifices for a typical model are shown on the sketch in figure 1. Photographs of each model tested are shown in figure 2, and a typical model installation in the test section is shown in figure 3. I
37、n the forward stagnation region of blunt bodies, the pressure magnitudes are gen erally quite large; however, the pressure gradients can be very small. Such a combina tion makes it extremely difficult, if not impossible, to measure the magnitude of the pres sure decrease with surface length within t
38、his region with an absolute-pressure gage to the precision required for accurately determining local velocity gradients. This problem was minimized in this investigation by using a sensitive differential-pressure gage, full-scale deflection of 1psi (6895 N/m2), to measure the pressure differential f
39、rom the for ward stagnation point to a select number of locations. The magnitudes of the pressures at 5 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-0.050-in. (1.27-mm) i. d. 1! Model Model -n shape d d 1 - 1 II Figure 1.- Model geometry. -d 0.126
40、 0.728 0.524 0.524 0.384 0.622 0.290 0.674 _ 0.167 0.729 0.555 0.555 0.448 0.635 0.605 0.605 _ -I 0.785 0.785 6 52 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-r,/d = m r,/d = 1.933 r,/d = 1.000 r,/d = 0.707 r,/d = 0.577 Model 1 Model 6 Model 11 M
41、odel 15 Model 17 (a) rc/d = 0. r,/d = 0 r,/d = 0.100 r,/d = 0.200 r,/d = 0.300 r,/d = 0.400 r,/d = 0.500 Model 1 Model 2 Model 3 Model 4 Model 5 Model 18 = 0.400r,/d = 0 r,/d 0.100 r,/d = 0.200 r,/d = 0.300 r,/dModel LO Model 6 Mod61 7 Model 8 Model 9 (c) r,/d = 1.933. r,/d = 0 r,/d = 0.200 r,/d = 0
42、.300 r,/d = 0.400 Model 11 Model 12 Model 13 Model 14 (d) rn/d = 1.000. r,/d = 0 r,/d = 0.200 Model 15 Model 16 (e) rn/d = 0.707. Figure 2; Model photographs. L-67-1073 7 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Figure 3; Typical mode1 insfall
43、ation in test section. L-65-7350 these locations were obtained by subtracting the pressure differentials from the stagnation-point pressure which was measured with a precision mercury manometer. The pressures at all remaining locations were measured with an absolute transducer having a full-scale de
44、flection of 10 psi (68 950 N/m2). Both the 1- and 10-psi (6895 and 68 95O-N/m2) transducers were used in conjunction with a multichannel scanning system so that only a total of four transducers were required. The output from each electrical transducer was recorded with a digital self-balancing poten
45、tiometer. The tunnel free-stream static and total pressures were measured with precision mercury manometers. The accuracy of the precision mercury manometers is within 0.5 psf (23.94 N/m2); therefore, the accuracy of the pressure measuring system is lim ited to that of the electrical transducers. Th
46、e accuracy of the electrical transducers is within 1percent of full-scale deflection, which corresponds to a pressure increment of 1.44 and 14.4 psf (69 and 690 N/m2) for the 1- and io-psi (6895- and 68 950-N/m2) gages, respectively. Pressure Distributions The effect of Mach number on the hemisphere
47、 pressure distributions is shown in figure 4 for the test range of Mach number from 2.49 to 4.63. The local measured pres sures have been normalized by the measured pressure at s/d = 0. The effect of Mach number, as expected, consists of a decrease in the magnitude of the normalized pressure 8 Provi
48、ded by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1.0 .a .6 .4 I.2 pt, 2 .I .08 .06 a 2.49 ) I 3*51 Present data IA 4.06+ 4.63 J 4 1.8-9.6 Ref. 13 L m 11.4 Ref. 14 .1 .2 .3 .4 .5 .6 .7 .8 s/d Fioure 4.- Comoarison of oressure distributions obtained on hemisoherical model with oreviouslv published results. distributions; the extent of this effect decreased with increasing Mach number. Also shown in this figure are experimental data from references 13 and 14 for Mach numbers up to 11.4. The data obtained from reference 13, indicated by the hatched
