1、NASA TECHNICAL NOTE NASA TN /- C.I D-4719 -c-F.-v o* h II P a z c 4 c/I 4 z LOAN COPY: RETURN TO KIRTLAND AFB, N MEX AFWL (WLIL-2) SUPERSONIC AERODYNAMICS OF LARGE-ANGLE CONES I . 4 . 4 ;. , c ” ri , f by Jumes F. Cumpbell und Dorothy T. Howell ;PA -, * these trends are adequately predicted by an in
2、tegral relations method. INTRODUCTION Use of an aeroshell device during unmanned atmospheric entry has been proposed to protect the payload from the severe loading and heating environments and to provide suf- ficient aerodynamic braking. One of the shapes considered as an aeroshell candidate is the
3、large-angle cone. This type of body provides a combination of the necessary high- drag characteristics with some degree of volume capacity. Several investigations (refs. 1 to 3) have been made to determine the aerodynamics of cones with semiapex angles up to (and including) 60. To make the conical a
4、eroshell optimum for a particular mission pro- file, however, it is necessary to determine the aerodynamics of cones with semiapex angles up to 900. Accordingly, an investigation has been conducted on a series of cone bodies with semiapex angles from 40 to 900 (disk) and the results of these tests a
5、re reported herein. For comparative purposes, results of tests on a 50 cone (from ref. 1) are included. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ii Static force and moment measurements and schlieren photographs were obtained at Mach numbers fr
6、om 2.30 to 4.63, at angles of attack from -4 to 24O, and at a Reynolds number based on model (base) diameter of 0.8 X lo6. SYMBOLS The results of the force tests are presented in coefficient form for both the body and staljility axis systems. base on the geometric center line of the cone as shown in
7、 figure 1. The pitching-moment reference center is located at the model cA Axial force axial-f orce coefficient, qs drag coefficient, lift coefficient, Lift force slope of lift-force curve with angle of attack, - per degree pitching- moment coefficient , Pitching moment slope of pitching-moment curv
8、e with angle of attack, - acm, per degree normal-force coefficient, Normal force slope of normal-force curve with angle of attack, - per degree aa Drag force qs qs aa qSD aa qs Pb - P base pressure coefficient, - q stagnation pressure coefficient behind normal shock base diameter of model sting leng
9、th, measured from base of model to sting flare free-stream Mach number free-stream static pressure static pressure at model base Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-local static pressure free-stream pitot pressure free-stream dynamic pres
10、sure radial coordinate base radius of model base area of model surface length axial coordinate angle of attack, degrees standoff distance of detached shock wave, measured along geometric center line from cone apex cone semiapex angle, degrees cone semiapex angle which corresponds to sonic flow condi
11、tions on cone sur- face, degrees Subscripts : 0 conditions at zero angle of attack 1 2 shock APPARATUS AND TESTS Models Dimensional drawings of the models are shown in figure 1. The models consist of right-circular cones with semiapex angles of 400, 600, 70, 80, and 900 (disk); they were 3 Provided
12、by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-constructed of polished aluminum and had pointed noses and flat bases. Diameter for all the models was 4.80 inches (12.19 cm). The 40 cone model was provided with an insert which could be removed to effect an in
13、dented-base configuration. Details of the 50 cone model are found in reference 1. Two lengths of model sting supports (see fig. 2) were provided to aid in investigating sting-length effects on base pressure; the ratios of sting length to model base diameter were 2.0 and 4.0. Mach number 2.30 2.96 3.
14、95 4.63 Tunnel Total pressure Dynamic pressure Stagnation temperature lb/ft2 N/m2 lb/ft2 N/m2 OF OK 1532 73.352 X lo3 453 21.690 X lo3 150 338.7 2169 103.852 384 18.386 150 338.7 3863 184.960 298 14.268 175 352.6 5275 252.567 232 11.108 175 352.6 Data were obtained on the models mounted in the high
15、Mach number test section of the Langley Unitary Plan wind tunnel, which is a variable pressure continuous-flow facil- ity. The test section is 4.0 feet (1.22 meters) square and approximately 7.0 feet (2.13 meters) long. The nozzle leading to the test section is of the asymmetric sliding- block type
16、which permits a continuous variation in Mach number from 2.3 to 4.7. Test Conditions and Measurements The models were tested at Mach numbers from 2.30 to 4.63 through an angle-of- attack range from about -4O to 24O at zero sideslip. model (base) diameter was 0.8 X lo6; the corresponding test conditi
17、ons at the respective test Mach numbers are summarized in the following table: The Reynolds number based on Stagnation dewpoint was maintained below -30 F (239O K) to avoid significant condensa- tion effects in the test section. Aerodynamic forces and moments were measured by means of an electrical
18、strain-gage balance housed partially in the models. The aft end of the balance which extended behind the base of the models was enclosed in a sleeve so that it was protected from any flow gradients. For the largest angle cones Bc = 70, 80, and goo), which had little or no model volume in which to at
19、tach the balance, a permanent extension was affixed to the model base; this extension served as the attachment point and protective sleeve for the balance. (See fig. 1.) It is believed that this extension had no significant effect on the data presented in this paper. ( Chamber and base pressures wer
20、e measured on all the cone configurations, the base pressure orifice being located at a point 1.20 in. (3.05 cm) above the model center line 4 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-in the plane of symmetry. Because of the similarity exhibit
21、ed between the chamber and base pressures on all the cone configurations, the base pressures measured on the 40 cone are presented along with the chamber pressures obtained on all the cones. The axial-force measurements presented in this paper, however, are gross values and were not corrected for ba
22、se pressure. Angles of attack have been corrected for both tunnel- flow angularity and deflection of the balance and sting due to aerodynamic loads. Bound- ary layer trips were not affixed to the models. RESULTS AND DISCUSSION Aerodynamic Characteristics Experimental.- The basic aerodynamic characte
23、ristics in pitch for the test models are presented in figures 3 to 6; the modified Newtonian theory shown for comparison is discussed in a subsequent section. These data indicate that all the configurations are statically stable (-Cma), the pitching moment being nearly linear through the angle-of -
24、attack range. This stability is illustrated in the summary plots of figures 7 and 8 where pitching-moment slope at zero angle of attack is shown as a function of semiapex angle and Mach number, respectively. The stability of the 50 cone is highly dependent on Mach number, a decrease in stability occ
25、urring with increase in Mach number for Mach numbers less than that for shock attachment (about 3.2), and an increase in stability occurring with increase in Mach number for Mach numbers greater than that for shock attachment. This trend of stability with Machnumber applies to the other cone configu
26、- rations, where for the 40 cone the shock is attached in the test Mach number range and the stability increases with Mach number increase. Cones with semiapex angles equal to or greater than 60 have detached shocks regardless of Mach number so that their sta- bility decreases with Mach number incre
27、ase. It is interesting to note that the pitching moment of the flat disk (6“ = 90) is due solely to axial force, since normal force for this configuration is equal to zero. The variation of normal force with angle of attack for the cone configurations (figs. 3 to 6) is seen to be essentially linear.
28、 As cone angle is increased, there is a cor- responding decrease in normal force so that for the flat disk, normal force goes to zero. Similar trends of normal-force slope at zero angle of attack CN with cone semiapex angle are seen in figure 9. An increase in Mach number results in a corresponding
29、increase in CN greater than 600 are virtually insensitive to Mach number. 040) for the 50 cone (fig. 10); cones with semiapex angles equal to or a,o The basic aerodynamic data of figures 3 to 6 indicate that maximum axial force (and drag) occurs at angles of attack near zero for the cone bodies. Inc
30、reasing the cone semiapex angle results in increases in axial force throughout the angle-of-attack range, 5 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a maximum being approached for the flat-disk configuration. Of the cones tested, the largest r
31、ate of increase in axial force with increase in cone semiapex angle occurs between the 40 and 50 cones. (See summary plot of fig. 11.) Increasing semiapex angle from OC = 50 leads to a nearly linear increase in axial force, although at a rate not as great as that between Bc = 40 and 50. The effect o
32、f Mach number on axial force for the family of cones is shown in figure 12. The 40 cone shows a significant reduction in CA 0 with Mach number increase and the 50 cone decreases slightly, whereas axial force for the other cone semiapex angles is essentially constant in the test Mach number range. Ex
33、perimental frontal surface pressure distributions on a 60 semiapex angle cone are shown in figure 13. As seen in the basic data of figures 3 to 6, the lift-curve slope is negative for cones with semiapex angles equal to or greater than 50. This effect, of course, is due to a larger contribution of a
34、xial force than of normal force in generating lift force. (See expression below.) An increase in cone semiapex angle results in a decrease in lift- curve slope, a maximum negative value being obtained for the flat disk. The magnitude of the lift-curve slope at zero angle of attack (see fig. 14) is o
35、btained from the expression CL, = CN, - CA,O and is equal to the axial force (in radians) in the case of the flat disk where CN = 0. Theoretical.- The basic aerodynamic characteristics in pitch predicted by the modi- fied Newtonian theory using Cp,max) are shown in figures 3 to 6 superimposed on the
36、 experimental data. This theory predicts the trends in aerodynamic characteristics resulting from changes in cone semiapex angle and/or angle of attack, but generally does not accurately predict absolute magnitudes. ( The agreement between experimental pitching moment and that predicted by modi- fie
37、d Newtonian theory is seen in figures 3 to 6 to be dependent on cone semiapex angle; this dependence is best illustrated by the pitching-moment slope data of figure 7. Pitching-moment slopes predicted by modified Newtonian theory and by exact theory (ref. 4) are little different in the range of cone
38、 semiapex angles where both theories are applicable. Modified Newtonian theory is seen to predict a maximum stability level for a particular cone semiapex angle; this semiapex angle is calculated in the appendix to be 58.8O. Another interesting point concerning the modified Newtonian theory is that
39、it pre- dicts pitching-moment slope to be zero for the flat disk. Comparison of experiment and theory indicates that the pitching-moment slope for the 40 cone is adequately predicted by theory throughout the Mach number range, and that the value of Cm,O for the 50 cone approaches theory at the highe
40、st test Mach numbers. Because of inherent assumptions in modified Newtonian theory, the value of Cm predicted by this theory is not susceptible to shock-detachment conditions, in contrast to the 50 cone experimen- tal data discussed previously. a,O 6 Provided by IHSNot for ResaleNo reproduction or n
41、etworking permitted without license from IHS-,-,-Modified Newtonian theory predicts a lower normal-force slope than does exact cone theory (ref. 5) as shown in figure 9. A continual decrease in CN increases in cone semiapex angle for each test Mach number, fied Newtonian theory approaching zero as B
42、c approaches 90. This trend agrees with that established by the experimental data. Modified Newtonian theory generally under- predicts normal-force slope for cones with attached shocks and overpredicts normal- force slope for cones with detached shocks. Normal-force slope for the 40 cone is generall
43、y predicted by exact theory throughout the test Mach number range, whereas the value of CN number. Use of the coefficient of 2.0 instead of Cp,ma in the Newtonian theory would provide better agreement between theory and experiment for cones with attached shocks and greater disagreement for cones wit
44、h detached shocks. occurs with %O predicted by modid cNCY,O for the 50 cone is predicted by exact theory at the highest test Mach Theoretical methods available for predicting axial force of conical bodies at zero angle of attack represent only the pressure drag due to the frontal surface of the cone
45、. To compare these theories with the axial-force data presented in figures 3 to 6, it is necessary to adjust these theories to account for base drag. Accordingly, the theoretical methods shown in the summary plots of figures 11 and 12 were adjusted by the values of base drag measured during the test
46、s with the exception of the 40 and 50 cones whose base pressures were influenced by sting effects (see subsequent discussion); the theoreti- cal methods for these cone configurations (and those with smaller semiapex angles) were adjusted by base pressures measured on the 60 cone. It will be shown in
47、 a subsequent discussion that these measured values are closely approximated by the empirical expres- sion, Cp,b = -. 1 Modified Newtonian theory predicts lower values of axial force than does exact theory (ref. 6) in the range of cone semiapex angles where both theories are applicable (fig. 11). Th
48、e experimental data show that modified Newtonian theory predicts the trends of CA,O with cone semiapex angle, but is inherently poor in estimating absolute magni- tudes. A combination of exact cone theory with an integral relations method (ref. 7) ade- quately predicts the magnitudes of axial force
49、for all cone semiapex angles. The exact cone theory is utilized when supersonic flow conditions exist on the cone surface, and the integral relations method when mixed flow conditions exist. The point where the integral relations method fairs into exact theory at M = 2.30 is seen to be at that cone semiapex angle which supports sonic flow on its surface, test Mach numbers. A
