1、NASA TECHNICAL NOTE NASA TN D-5204 L PRESSURE DISTRIBUTIONS ON 1400, 16009 AND 180 CONES AT MACH NUMBERS FROM 2.30 TO 4.63 AND ANGLES OF ATTACK FROM 00 TO 200 by James F. Campbell and Dorothy H. Tudor Langley Research Center Langley Station, Hampton, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
2、 WASHINGTON, D. C. MAY 1969Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NASA TN D-5204 PRESSURE DISTRIBUTIONS ON 1400, 1600, AND 1800 CONESAT MACH NUMBERS FROM 2.30 TO 4.63 ANDANGLES OF ATTACK FROM 0 0 TO 200By James F. Campbell and Dorothy H. Tud
3、or Langley Research CenterLangley Station, Hampton, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sole by the Clearinghouse for Federal Scientific and Technical InformationSpringfield, Virginia 22151 - CFSTI price $3.00Provided by IHSNot for ResaleNo reproduction or networking permitted with
4、out license from IHS-,-,-PRESSURE DISTRIBUTIONS ON 1400, 1600, AND 1800 CONESAT MACH NUMBERS FROM 2.30 TO 4.63 ANDANGLES OF ATTACK FROM 00 TO 200 By James F. Campbell and Dorothy H. TudorLangley Research Center SUMMARY An experimental investigation has been conducted to obtain surface-pressure dis-t
5、ributions on spherically blunted cones with apex angles of 140 0, 1600, and 1800 (flat disk) The 1400 and 1600 cones had a ratio of nose radius to base radius of 0.25. The studies were conducted at Mach numbers from 2.30 to 4.63 and at angles of attack from 00 to 200. Results of this study indicated
6、 that an increase in cone angle or angle of attack or both leads to an increase in pressure windward of the measured stagnation point; a decrease in cone angle or an increase in angle of attack leads to a decrease in pressure leeward of the measured stagnation point. Mach number has little effect on
7、 the pressure distributions for the cones at zero angle of attack. At angles of attack greater than zero, an increase in Mach number results in a decrease in pressure on the leeward side of all the configurations. A correlation parameter successfully correlates the stagnation-point locations for the
8、 entire range of test Mach number, cone angle, and angle of attack; an empirical representation of this correlation is in good agreement with the experimental results. Pressure distributions obtained on the cone models at zero angle of attack are in good agreement with a theoretical solution based o
9、n the one-strip method of integral relations. Circumferential pressure distributions on large-angle conical bodies are amenable to approximation by second-order polynomials. INTRODUCTION Vehicles with low ballistic coefficients (i.e., high aerodynamic drag) are being con-sidered for use as unmanned
10、probes to traverse planetary atmospheres. The function of this type of vehicle is to protect the payload from the severe loading and heating environ-ments associated with entry while providing sufficient aerodynamic deceleration. One particular body shape which appears to be amenable to this type of
11、 mission is the large-angle cone (ref. 1). Optimization of the conical shape for a particular mission profile is dependent on an adequate knowledge of local flow properties, local aerodynamic heatingProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-rat
12、es, and local structural loading. These criteria can be determined from surface-pressure distributions. The experimental investigations of references 2 and 3 provide pressure distributions on a 1200 cone. For the purpose of optimization, the acquisition of similar pressure data on cones with larger
13、apex angles is desirable. The present investigation was undertaken to obtain surface-pressure distributions on 1400, 1600, and 1800 cone configurations. The 1400 and 1600 cones had a ratio of nose radius to base radius of 0.25; the 180 0 cone was a flat disk. The data were obtained at Mach numbers f
14、rom 2.30 to 4.63 and at angles of attack from 00 to 200. Reynolds num-ber for these studies was 2.0 X 106 based on model (base) diameter. SYMBOLS A,B,C constants (see eq. (3)- pressure coefficient, p1 p00 q D base diameter M1 local Mach number M00 free-stream Mach number PL local static pressure alo
15、ng leeward ray (9 = 00) for a P1 local static pressure Pt free-stream stagnation pressure t,2 stagnation pressure behind a normal shock PW local static pressure along windward ray (U = 1800) for a 00 P.“ free-stream static pressure q00 free-stream dynamic pressure rb base radius rn nose radius 2Prov
16、ided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-s surface length (see fig. 1) total surface length (i.e., surface length from most forward station on model to shoulder corner) (see fig. 1) (S/S*) Sp stagnation-point location a angle of attack nondimensio
17、nalized parameter used to correlate stagnation-point location, a (see eq. (8) 12O-crc Y ratio of specific heats B meridian angle ac cone semiapex angle roll angleAPPARATUS AND TESTS Wind Tunnel Studies were performed in the high Mach number test section of the Langley Unitary Plan wind tunnel, which
18、 is a variable-pressure continuous-flow facility. The test section is approximately 4 feet (1.22 meters) square and 7 feet (2.13 meters) long. The nozzle leading to the test section is of the asymmetric sliding-block type, which permits a con-tinuous variation in the test-section Mach number from ab
19、out 2.30 to 4.63. Models and Instrumentation Details of the cone models with apex angles of 140 0, 1600, and 1800 are presented in figure 1. The models were constructed of polished aluminum and had sharp shoulders. The 1400 and 1600 cone models had spherically blunted noses, the radii of which were
20、25 percent of the magnitude of the base radii. Some amount of thickness was necessary for the 180 0 cone (flat disk) to facilitate the installation of the pressure orifices. A sharp shoulder was produced in the 1800 cone by the 15 0 bevel illustrated in figure 1(b). Base diameter of all the models w
21、as 8.00 inches (20.32 cm), and the sting utilized for the studies had a diameter of 1.50 inches (3.81 cm). The surfaces of the 140 0 and 1600 cone 3Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-models were instrumented with 49 pressure orifices, wh
22、ereas the 1800 cone model was instrumented with 45 pressure orifices. (See fig. 1.) Internal diameter for the pressure orifices was 0.050 inch (0.127 cm). The orifices were located along the meridians 9 = 001 9001 1800, and 2700. The pressures were recorded by using two 48-channel pressure-sampling
23、valves which sequentially transmit each pressure sampling to an electrical pressure transducer. The transducer transforms the pressure information into an electrical signal which is then recorded in digital form on punch cards. The two gages had a maximum range of 10.0 psia (6.89 N/cm2).Accuracy and
24、 Test Conditions The accuracy of the pressure-sampling values is within 1 percent of the full-scale range of the gage; this accuracy includes all errors of linearity, hysteresis, and repeat-ability. The stagnation pressure was measured with a precision mercury manometer, the accuracy of which is 0.5
25、 psf (23.94 N/rn2). The models were tested at free-stream Mach numbers of 2.30, 2.96, 3.95, and 4.63 for a Reynolds number of 2.0 X 106 based on model (base) diameter. The results of a test-section calibration indicated the following deviations in Mach number: For M., 2.30 . 0.02 For M., 2.96 . 0.02
26、 For M, 3.95 . 0.06 For M(, 4.63 . 0.05Tunnel stagnation temperatures were 150 0 F (338.70 K) at M = 2.30 and 2.96 and 1750 F (352.60 K) at Mac, = 3.95 and 4.63. Pressure data were obtained for the models at angles of attack from 00 to 200 for a zero sideslip condition. Circumferential pressure dist
27、ributions were obtained by rolling the model from 00 to 900 at constant angles of attack. Boundary-layer trips were not affixed to the models and base pressure measurements were not made. - TABULATION OF EXPERIMENTAL DATA The experimental pressure data obtained during the course of this investigatio
28、n are presented in tables Ito XH. Listed along with the measured static pressures are the pressure coefficients and Mach numbers. The values of Pt/Pt 2 and M1 are based on the computed stagnation pressure behind a normal shock, which was obtained from normal-shock relations, together with free-strea
29、m Mach number and stagnation pressure. The isentropic flow equation used to calculate M 1 is 4Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Ml=/21()1 (1) where the value y was taken to be 1.4. Each pressure listed in the tables is identified by an
30、orifice number (as defined in fig. 1) and the associated meridian angle and surface length. Surface length is presented nondimensionalized by both the base diameter D and the total surface length s *. For the spherically blunted cone, as illustrated in the sketch, the total surface length is found t
31、o bes* /Trb 5rn S = r(9O0 - ac) + csc ac - rn CO5 (2) ac. An index to the tabular data is as follows: Model Table(*) p2.30 I )2.96 II 1400 cone3.95 4.63 W 2.3O V 12.96 VI 1600 coneVII 4.63 .30 IX .96 X 180 cone (flat disk)41.6953 XIIEach table is divided into five parts with part (a) being for a = 0
32、0, part (b) for a = 50, part (c) for a 100, part (d) for a = 150, and part (e) for a = 200.5. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-It should-be noted that the data for orifice 29 on the 1400 cone were incorrect because of leakage and are n
33、ot presented in the tables. RESULTS AND DISCUSSION The discussion presented herein is limited to the effects of cone angle, angle of attack, and free-stream Mach number on the variation of local static pressure. Experimental Pressure Distributions The effect of cone angle on the pressure distributio
34、ns can be seen in figure 2, in which the local static pressures, nondimensionalized by stagnation pressure behind a normal shock, are plotted as a function of local surface length, nondimensionalized by total surface length. These results are presented for a free-stream Mach number of 2.96 and for a
35、ngles of attack of 001 100, and 200 and are typical of those results obtained at the other test Mach numbers. Experimental data for a 120 0 cone (ref. 2), having the same percentage of nose bluntness as the 1400 and 1600 cone models of the present investigation, are included for comparison. As shown
36、 in figure 2, at zero angle of attack, an increase in cone angle results in an increase in pressure over the entire face of the cone, and the stagnation point (indi-cated by the maximum measured pressure) is located, as expected, at the apex of the cones regardless of cone angle. At an angle of atta
37、ck of 100, the stagnation point shifts to the windward side of the cones, and the pressures in the direction of the windward shoulder become noticeably greater than those for the a = 0 0 condition. Further increase in angle of attack accentuates this shift in stagnation-point location and increase i
38、n pressure. Similarly, for angles of attack greater than 00, an increase in cone angle leads to a further shift in stagnation-point location toward the windward shoulder. Increasing cone angle also results in increases in the pressures located between the stagnation point and the windward shoulder;
39、however, the greatest pressure increase for an increase in cone angle occurs at zero angle of attack. For the cones at an angle of attack greater than 00, the expanded flow around the spherical nose results in decreases in pressure from the maximum value at the stagna-tion point; this decrease in pr
40、essure toward the leeward side becomes more significant with decrease in cone angle and increase in angle of attack. The data indicate the exist-ence of an adverse pressure gradient near the sphere-cone juncture on the leeward sides of the 1200 cone at a = 100 and the 1200 and. 1400 cones at a = 200
41、. Increasing cone angle from 1200 decreases the strength of the expansion and adverse pressure gradient, so that a uniform pressure distribution exists on the flat disk (1800 cone). 6Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-The experimental re
42、sults presented in figure 2 for the models at a = 00 and Mac, = 2.96 are compared in figure 3 with the results from the one-strip method of integral relations described in reference 4. The pressures predicted by the integral-relations method are in good agreement with the experimental values for all
43、 the cone models. A maximum deviation in agreement occurs at a value of /* of about 0.8, where the theoretical predictions are approximately 3 percent less than the experimental values. The effect of angle of attack on the pressure distributions of the three cone models is more clearly illustrated i
44、n figures 4 to 6 for all the test Mach numbers. The curves faired through the pressure data are extrapolated to the sonic condition which theoreti-cally exists at the shoulder. As previously indicated, an increase in angle of attack results in higher pressures on the windward side and lower pressure
45、s on the leeward side. A progressive shift in the stagnation point toward the windward shoulder is noted as angle of attack is increased to the highest test value. The adverse pressure gradient located near the sphere-cone juncture on the leeward side of the 1400 cone (mentioned previously) is seen
46、in figure 4 to increase with increased angle of attack. Similar trends in pressure distribution exist for the 1600 cone, as shown in figure 5, though to a lesser degree than exist for the 1400 cone. Increasing cone angle and decreasing angle of attack have similar effects on the pressure distributio
47、ns on the leeward side of the models; increasing cone angle and increasing angle of attack have similar effects on the pressure distributions on the windward side. The data presented in figures 7 to 9 illustrate the effect of free-stream Mach num-ber on the pressure distributions for the cone models
48、 at angles of attack of 00, 100, and 200. At a = 0, only small effects of Mach number are seen for the different cone con-figurations. The small differences in pressure between the 00 and 1800 meridians noted at the highest test Mach numbers are probably due to slight data acquisition inaccuracies.
49、At angles of attack greater than 00, the pressures windward of the stagnation point are relatively insensitive to increase in Mach number, whereas the pressures leeward of the stagnation point decrease with increased Mach number. This decrease in pressure is particularly obvious near the sphere-cone juncture. An increase in angle of
