A Survey of Unsteady Hypersonic Flow Problems

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No. Author(s) 12 Ashley, Holt and Zartarian, Garabed 13 Ashley, Holt and Zartarian, Gerabed 14 Lighthill, M. J. 15 16 17 18 19 20 21 22 23 24 Miles, J. w. Raymond, Joseph L. East, R. A. Mahony, J. J. Eartarian, Garabed Zartarian, Gerabed and Sauerwein, Harry Tobak, Murray and Wehrend, William R. Margolis, K. Reid, Robert C. Jr. and Mayo, Edward E. Van Dyke, Milton D. - 70 - References (Appendix II) Title. etc. Thearetioal hypervelocity unsteady aerodynamics. Proceedings of Symposium on Aerothermoelasticity. ADS TR-61-645. Thickness and boundary layer effects. AGARD Manual on Aeroelasticity, Vol.11, Chap.9. Oscillating serofoils at high Mach number. J.Ae.Sci. Vo1.20, pp.402-406, June, 1953. Unsteady flow at hypersonic speeds. Hypersonic flow. Proceedings of 11th Symposium of the Colston Research Sooiety, Bristol 1959. p.180 Butterworths Scientific Publications. Piston theory applied to strong shocks and unsteady flow. J.Fl.Meoh. Vo1.8, Pt.4. 1960. pp.509-513. A theoretical and experimental study of osoillating wedge shaped aerofolls in hypersonic flow. University of Southampton AASU Rep. No.228. A critique of shock expansion theory. J.Aero.Sci. Vo1.22, No.10. 1955. pp.673-680, Unsteady airloads on pointed airfoils and slender bodies at high Maoh numbers. Wright Air Development Center. WADC TR-59-583. Further studies on high speed unsteady flow. ASD-TDR-62-463. September, 1962. Stability derivatives of cones at supersonic speed. NACA TN 3788. September, 1956. Theoretical evaluation of the pressures, forces and moments at hypersonic speeds acting on arbitrary bodies ofrevolution undergoing separate and combined angle-of-attack and pitching motions. NASA TN ~-652. June, 1961. Equations for the Newtonian statio and dynemio aerodynamic coefficients for a body of revolution with en offset center-of-gretity location. NASA TN D-1085. June, 1963. A study of hypersonic smsll disturbance theory. NACA Report 1194. 19%. 25/
gg. Author(s) 25 Sychev, V. V. 26 Zartarian, Garabed and Hsu, Pao Tan - 71 - Title 1 etc. Three-dimensional hypersonic flow past slender bodies at high angles of attack. PMM Vo1.24, No.2, 1960. pp.205-212. Theoretical and experimental studies on airloads related to hypersonic aeroelastio problems of general slender oonfigurations. ASD Tech. Report 61-7. April, 1961. 27 Zartarian, Garabed, Hsu, Pao Tan Dynamic airloads and aeroelastio problems at entry Mach numbers. and Ashley, Halt Journal of Aerospace Sciences, Vo1.28, No.3. March, 1961. pp.209-222. 28 Eggers, A. J. Jr., A study of invisoid flow about airfoils at high Syvertson, Clarence A. supersonic speeds. and NACA Report 1123. 1953. Kraus, Samuel 29 Eggers, A. J. Jr. and Savin, Raymond C. 30 31 A unified two-dimensional approach to the . calculation of three-dimensional hypersonic flows, with application to bodies of revolution. NACA Report 1249. 1955. Eggers, A. J. Jr., The generalized shock-expansion method and its Sevin, Raymond C. application to bodies travelling at high supersonio and Syvertscn, Clarence A. speeds. J.Aero.Soi., Vo1.22, No.4 April, 1955. pp.231-238. Savin, Raymond C. Application of the generalized shook-expansion method to inclined bodies of revolution travelling at high supersonic speeds. NACA TN 3349. April, 1955. 32 Kennett, H. Some steady and unsteady inviscid hypersonic flows past bluff bodies. AFOSR 1031 MIT Fluld Dynamics Research Lab. Rep. 61-l. 33 34 35 Holt, Maurice A linear perturbation method for stability and flutter calculations on hypersonic bodies. Journal of the Aerospace Sciences, ~01.26, No.12. December, 1959. pp.787-793. Kawamura, Ryuma and Tsien, Fu-Hsing Lighthill, M. J. Aerodynamic stability derivatives of axi-symmetric body moving at hypersonic speeds. Presented at 3rd Int. Congress of Aero Sciences, August, 1962. Stockholm. The response of laminar skin friction and heat transfer to fluctuations in the stream velocity. Proo.Roy.Soo.(London), Series A, Vo1.224. July, 19%. 36/
Page 1:
MINISTRY OF AVlATlON AERONAUTICAL R
Page 4 and 5:
-2- CONTENTS Int~~duction . . . . .
Page 6 and 7:
General Surves and Conclusions -4-
Page 8 and 9:
-6- and values of M6 < 1) and shock
Page 10 and 11:
-a- have been ~0nce171ed with the f
Page 12 and 13:
- to - APPENDICES Detailed Reviews
Page 14 and 15:
- 12 - where W is the weight of the
Page 16 and 17:
- 14 - In practice, equation (2.1)
Page 18 and 19:
- 16 - nsteady Newtonian theory is
Page 20 and 21:
- 18 - Then the transformed velocit
Page 22 and 23: - 20 - of a disturbance is of order
Page 24 and 25: - 22 - u cot cl ucota = . . . (2.35
Page 26 and 27: - 24 - minimum are that its variati
Page 28 and 29: - 26 - This simple form of the meth
Page 30 and 31: t - 28 - and r “” + u’ i + (1
Page 32 and 33: - 30 - The cut-of-phase component o
Page 34 and 35: - 32 - indication of their reliabil
Page 36 and 37: -34- between theory and. experiment
Page 38 and 39: - 36 - will no longer apply and a s
Page 40 and 41: - 38 - where m is vehicle mass; p i
Page 42 and 43: - I+0 - vehicle. (The difference be
Page 44 and 45: -4z- where C . is the rate of chang
Page 46 and 47: -44- is to reduce further the range
Page 48 and 49: 46 - APPENDIX IV Review of Flutter
Page 50 and 51: where z.2 = ll& *.. (4.1) . . . (4.
Page 52 and 53: - 50 - The thcorctlcal deduction th
Page 54 and 55: - 52- frequcnoy. Theoretical calcul
Page 56 and 57: -%- wiierc h and au are the flutter
Page 58 and 59: - 56 - mean incidence case; but, fo
Page 60 and 61: - 58 - pressure both for divergence
Page 62 and 63: - 60 - .h = -. q/MA-1 w3 12(1-l?) E
Page 64 and 65: a a, A b c cD CL %l %I c% C Q% C mq
Page 66 and 67: AP 9 P r 'b F a B % R % Be Rex s 9
Page 68 and 69: Y Y yi 6 F A K - 66 - instantaneous
Page 70 and 71: Dcfmitions of derivatives "B L, = -
Page 74 and 75: &. Author(sl 36 Moore, F. K. 37 Oli
Page 76 and 77: - 74 - No. Author(s) Title, etc. 52
Page 78 and 79: No 65 66 67 68 69 70 . 71 72 73 Aut
Page 81 and 82: FIG. I (a) Slender wing/body combin
Page 83 and 84: h ft x From Ref.5 and calculation b
Page 85 and 86: FIGS.5-7 FIG 5 Axis system for thin
Page 87 and 88: %‘8 Ro (-X/R; e- -0 \t I FIG. 9 R
Page 89 and 90: -0.02 0 ’ 0.02 cP 0.04 0.06 O-08
Page 91 and 92: O- I- 2 - 3 - 4 - ,5- / , / / / /
Page 93 and 94: FIG. 15 (a) I
Page 95 and 96: CP (C) of5 = o rrom Flg.ZJof R 19.9
Page 97 and 98: O-/ 0.12 . 0 OS08 1. CP 0.04 0 -0.0
Page 99 and 100: O-16 CP o-12 From Ref.29 ;c) M = 6.
Page 101 and 102: Inviscid theory - - - - Theory with
Page 103 and 104: I ‘6 2 FIG. I 9 From Fig.3.8 of R
Page 105 and 106: 1.2 O-8 0.4 0 -0 *4 -0.8 -1.2 0.8 A
Page 107 and 108: 0.4 0 From Fig. 3.26 of Ref. 26 FIG
Page 109 and 110: I.0 / / / / ,: kMM; k&I M; A 2-o 0
Page 111 and 112: k M Mq I.4 O-8 0.6 0.4 0*2 0 -0.2 F
Page 113 and 114: From Ref. 38 -0.16 (a) Details of m
Page 115 and 116: IO'4- 5 x 101J- IO' J- 5 x10; 2- 2-
Page 117 and 118: kit From Fig. 2 of Ref. 48 FIG. 31
Page 119 and 120: . 2.4 2.0 l-6 K crit l-2 0.0 0.4 0
Page 121 and 122: M 4 3 2 (,t”, 10-4) Tern OF I Fro
Page 123 and 124:
From Fig.8 of Ref. 56 FIG. 36 50 10
Page 125 and 126:
“f,o 5 I From Ref. 56 I I 0 IO FI
Page 127 and 128:
From Fig.2 in Ref. 57 FIG. 39 ----L
Page 129 and 130:
From Ref 57 0.7 6 0 - - - - - 3% --
Page 131 and 132:
From Ref. 57 o-7. 0.61 0 - - - - 3%
Page 133 and 134:
6 I i 1 nbol 6 = From Ref.61--/ Tip
Page 135 and 136:
. b 0 oao b FIG .44 c) 0 N 0 N . 0
Page 137 and 138:
FIG. 46 From Fig. 5.1 of Ref. 26 0
Page 139 and 140:
From Ref. 57 n.Al I 0.5 FIG. 48 I I
Page 141 and 142:
From Ref. 57 14 IZ- FIG.50 c - 3% t
Page 143 and 144:
(“f Iaxp w Ah (“f )axp (“f )t
Page 145 and 146:
I From Ref. 65 Modes as in FIG.53 P
Page 147 and 148:
q 5 0 7 6 5 4 From Fink 73 nf Rrf~
Page 149 and 150:
2.1 2 -0 Data taken from Ref. 63 o-
Page 151 and 152:
$3 i I a( I.2 (Ib/sq 1 in.) ’ ‘
Page 153 and 154:
I From Ref.71 FIG. 62 0 5 IO M 15 2
Page 155 and 156:
0.00 o-00 FIG. 64 FImm -... Fio~ =
Page 157 and 158:
A.R.C. C.P. No.901 Harch. 1%5 Wood,
Page 160:
0 Crown copyright 1966 Prmted and p
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