1、NASA TECHNICAL NOTE o* m m N I n I + 4 r/l 4 I CORRELATION GRAPHS FOR SUPERSONIC FLOW AROUND RIGHT CIRCULAR CONES AT ZERO YAW IN AIR AS A PERFECT GAS by Mitchel H. Bertrum Lungley Reseurch Center Lungley Stution, Humpton, Vu. r, x NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, 0. C. 0 JUN
2、E 1964 J 1 c Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB. NM CORRELATION GRAPHS FOR SUPERSONIC FLOW AROUND RIGHT CIRCULAR CONES AT ZERO YAW IN AIR AS A PERFECT GAS By Mitchel H. Bertram Langley Research Center Langley Station, H
3、ampton, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sale by the Office of Technical Services, Department of Commerce, Washington, D.C. 20230 - Price $0.75 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CORRELATION GRAPHS FOR SUPERSONIC FLO
4、W AROUND RIGHT CIRCULAR CONES AT ZEBO YAW IN AIR AS A PERFECT GAS By Mitchel H. Bertram Langley Research Center SUMMARY Concise accurate graphs of cone flow properties at zero yaw in air as a perfect gas are presented in correlation form. density, temperature, shock angle, and Mach number may be obt
5、ained both at the cone surface and immediately behind the shock, for free-stream Mach numbers from that for shock detachment to that approaching infinity and for cone semi- apex angles up to 50. is given for the same range of conditions. From these graphs the pressure, In addition, the initial slope
6、 of the normal-force curve INTRODUCTION Knowledge of the flow about flat plates and cones in supersonic flow is basic to understanding the flow about more complex shapes as well as being important for its own sake. In reference 1 generalized correlation parameters were found to be useful tools for c
7、onstructing concise accurate graphs describing the two-dimensional oblique shock. For the conical shock no really satisfactory graphs for air exist. For example, the graphs of reference 2 extend only to a Mach number of 4 and those of reference 3 cannot be read accurately at low cone angles and high
8、 Mach numbers. There are tabular results for cones available in references 4 and 5. In the present paper these tabular results have been plot- ted in correlation form to provide accurate readily used graphs for the inviscid flow about cones at zero yaw in air. These charts allow both accurate interp
9、o- lation and extrapolation. wherever possible the entire range of tabulated Mach numbers has been presented. In addition, for usefulness in aerodynamic work these charts have been supple- mented by the initial slope of the normal-force-coefficient curve from refer- ences 6 and 7. The hypersonic Mac
10、h numbers have been favored but Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SYMBOLS “he following sketch is presented to clarify the symbols defined in this section. CL L lift-force coefficient, normal-force coefficient, N CN ($ !- however, in on
11、e plot of shock-angle parameter, presented as figure 2(c), it had a significant effect and the results in this figure only apply for Approximate solutions have been used to obtain the proper form for y = 1.405 and those in references 5 and 7 are for In most cases this difference in specific-heat rat
12、io was not impor- Y = 7/5. Figure 1 presents the similarity cone-surface-pressure coefficients as a function of the hypersonic similarity parameter. Good correlation is evident beginning at the higher supersonic Mach numbers (generally to 4). is insensitive to the value of 7 for which the calculatio
13、ns are made. Com- parison with exact calculQtions for cones in helium (from ref. 10) indicates this to be true. Figure l(b) allows extremely accurate values to be obtained in the hypersonic range and comparison with the hypersonic cone theory from reference 8. thus, 2- ( y + 7 PS 8 ) TS so that the
14、asmyptotic relation for the ratio of gas surface density to free- stream density (fig. 3(a) is The initial slope of the normal-force-coefficient curve in correlation form is given in figure 5. Figure ?(b) allows accurate values to be obtained in the Provided by IHSNot for ResaleNo reproduction or ne
15、tworking permitted without license from IHS-,-,-hypersonic range. can be obtained as follows The initial slope of the lift-coefficient curve (inviscid) where CL is in degrees. Langley Research Center, National Aeronautics and Space Administration, Langley Station, Hasnpton, Va., March 24, 1964. 5 Pr
16、ovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1. Bertram, Mitchel H., and Cook, Barbara S.: The Correlation of Oblique Shock Parameters for Ratios of Specific Heats From 1 to 5/3 With Application to Real Gas Flows. NASA TR R-171, 1963. 2. Dailey, C.
17、L., and Wood, F. C.: Computation Curves for Compressible Fluid Problems. John Wiley & Sons, Inc., c.1949. 3. Ames Research Staff: Equations, Tables, and Charts for Compressible Flow. NACA Rep. 1135, 1953. (Supersedes NACA TN 1428.) . 4. Staff of the Computing Section, Center of Analysis (Under Direc
18、tion of Zdengk Kopal): Tables of Supersonic Flow Around Cones. Tech. Rep. No. 1, (NOrd Contract No. 91-69), M.I.T., 1947. 5. Sims, Joseph L.: Supersonic Flow Around Right Circular Cones - Tables for Zero Angle of Attack. NASA SP-3004, 1964. 6. Staff of the Computing Section, Center of Analysis (Unde
19、r Direction of Zdenzk Kopal): Tables of Supersonic Flow Around Yawing Cones. Tech. Rep. No. 3 (NOrd Contract No. 9169), M.I.T., 1947. 7. Sims, Joseph L.: Supersonic Flow Around Right Circular Cones - Tables for Small Angle of Attack. NASA SP-3007, 1964. 8. Lees, Lester: Hypersonic Flow. Fifth Intern
20、ational Aeronautical Conference (Los Angeles, Calif., June 20-23, 1955), Inst. Aero. Sei., Inc., 1955, pp. 241-276. 9. Grirmninger, G., Williams, E. P., and Young, G. B. W.: Lift on Inclined Bodies of Revolution in Hypersonic Flow. Jour. Aero. Sei., vol. 17, No. 11, Nov. 1950, pp. 675-690. 10. Hende
21、rson, Arthur, Jr., and Bra.swel1, Dorothy 0.: Charts for Conical and %-Dimensional Oblique-Shock Flow Parameters in Helium at Mach Numbers From About 1 to 100. NASA TN D-819, 1961. 6 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.4 .2 .1 .08 .06 .0
22、4 .oi M, sin 0, = K, (a) Vdues of & from 0.06 to 12. Figure 1.- Cone-surface-pressure coefficient in similarity form, applicable to 7 = 7/5 and 1.405. 7 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-0 0 Lo w i I v h i I I i/ I 1 I I/ t/l r I 4 A 1
23、I I 1 I 4 I I t I I I I I I 0 0 .vi r so : conc .I .L .Y .4 1 - 1 I M, sin 8, K, I I I I I 1 1 I I I I .5 i I 1 I I ! I I / 1 I I I I I I I ! .- (b) Values of Kc from 1.7 to a. Figure 1.- Concluded. 8 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-M
24、, sin 0, = K, .2 I .6 .8 1 40 20 10 8 6 44 I b? II T+ 21 I) a3 d I) .4 1 9 .8 .6 .4 .2 1 2 4 6 810 20 Mm sin 0, = K, (a) Difference between shock angle and Mach angle, y = 7/5 and 1.405. Figure 2.- Cone shock angle in similarity form. 9 Provided by IHSNot for ResaleNo reproduction or networking perm
25、itted without license from IHS-,-,-V Y I v) Y c v) .- (b) Difference between shock angle and cone angle, 7 = 7/5 and 1.405. Figure 2.- Continued. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. _.- .24 -22 .2( .1 m m .!i rn .1 .10 .OE ersonic c .i
26、.2 -3 .4 (c) Ratio ok shock angle to cone angle, y = 7/5 only. Figure 2.- Concluded. 11 I Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-M-sine- =K, 1 (a) Density ratio. Figure 3.- Ratio of density, temperature, and Mach number at the cone surface t
27、o free-stream values, y = 7/5 and 1.405. 12 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Moo sin 8, = K, , .04 J. .8 .6 .4 .2 .1 .08 -0 6 rl I .Of .o 3 .OOE .oo t .OOL 06 .1 2 4 Moo sin 0, = Kc 6 10 20 (b) Temperature ratio. Figure 3.- Continued.
28、Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1.0 .9 .8 .7 .6 MC Mm - .5 .4 .3 .2 .1 0 .1 .4 .6 .8 1 -04 .06 .08 .I I I I I I 2 4 Mm sin 0, = K, (c) Mach number ratio. Figure 3.- Concluded. 14 Provided by IHSNot for ResaleNo reproduction or network
29、ing permitted without license from IHS-,-,-_13 _ _.-_. I A-_l_._-. Pc PS - .04 .06 .1 .2 .4 .6 1 2 4 6 10 20 Moo sin 6, = K, (a) Pressure ratio. Figure 4.- Ratio of pressure, density, temperature, and Mach number at cone surface to value immediately behind the shock, applicable to 7 = 715 and 1.405.
30、 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-(b) Density ratio. Figure 4.- Continued. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1.09 1.06 1.03 1.00 (e) Temperature ratio. Figure 4.- Continue
31、d. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-(a) Mach number ratio. Figure 4.- Continued. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-_- M, sin 8, K, (e) Mach number ratio, K, from 1 to m. F
32、igure 4.- Concluded. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-0 3 z u a v .04 .06 .08 .1 .2 .4 .6 .8 1 2 4 6810 20 M, sin Bc = K, (a) K, from 0.04 to 20. Figure 5.- Initial slope of normal-force-coefficient curve in correlation form, applicabl
33、e to 7 = 715 and 1.405. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.035 ,031 .1 = %sin Bc K, , .4 Kc from 1.5 to 1 J I m. Figure 5.- Concluded. 21 NASA-Langley, 1964 L-3972 Provided by IHSNot for ResaleNo reproduction or networking permitted wit
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