A Survey of Unsteady Hypersonic Flow Problems

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-2- CONTENTS Int~~duction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Surrey and Conclusions ........................ 1. Hypersonic Flight Conditions ..................... 2. The Analysis of Unsteady Hypersonic Flows ............ 3. The Dynamic Stability of Hypersonic Vehicles ........... 4. Flutter of Hypersonic Vehicles ................... 5. Discussion and Conclusions ..................... APPENDXES Detailed Reviews APPFxDlxI: Review of Hypersonic Flight Conditions ........... 1.f Characteristics of Hypersonic Flows ......... 1.2 Hypersonic Vehicles .................. I .3 Flight Envelopes for Hypersonic Vehicles ...... APFmDIx II: Review of Theoretical Analysis of Unsteady Hypersonic Flows .............................. 2.1 Methods of Analysis ................... 2.1.1 Piston theory and Newtonian impact theory . . 2.1.2 Hypersonic small disturbance theory ...... 2.1.3 The variational method ............. 2.1.4 The shock-expansion method ........... 2.1.5 Small perturbation analyses .......... 2.2 The Influence of Real Gas Effects and Vzscosity ... 2.3 The Experimental Verification of Theoretical Analysis ......................... 2.4 Discussion and Conclusions ............... APPENDIX III: Review of the Dynamic Stability of Hypersonic Vehicles . 3.1 The Longitudinal Behaviour of Hypersonic Vehicles . 3.1 .I Steady flight at constant altitude ...... 3.1.2 Be-entry flight .................. 3.1.3 The effects of aerodynamic non-linearities . 3.2 The Lateral Behaviour of Hypersonic Vehicles .... 3.3 Discussion and Conclusions ............... APPENDIX IV: Review of Flutter of Hypersonic Vehicles ......... 4.1 Types of Flutter, and Values of Flutter Frequency Parameter ........................ 4.2 Flutter Investigations .................. 4.2.1/ a 3 4 4 5 6 7 9 10 10 10 11 13 13 13 17 23 25 27 30 2 37 37 37, z E 46
-3- C 0 N T E N T S (Co&L) 4.2.1 Bending-torsion flutter of wings . . . . . . 47 4.2.2 The flutter of slender configurations . . . 4.2.3 Panel flutter . . . . . . . . . . . . . . . . . 4.3 Discussion and Conclusions . . . . . . . . . . . . . 56 2 Nomenolature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Acknowledgements . . . . . . . . . . . . . .i. . . . . . . . . . . . . . . . 68 References: CoverFng Appendix Review I (Refs. 1 to 11) . . . . . . . 13 I, 11 Review II (Refs. 12 to 40) . . . . . . 70 1, ,I Review III (Refs. 41 to 54) . . . . . . 1, II Review IV (Refs. 55 to 78) . . . . . . :: This report is concerned with hypersonic flows around bodies undergoing pitching and plunging oscillations and around bodies or parts of bodies undergoing flutter. It brings together information on the methods of analysis sppllcable to these unsteady flows, and on the practical problems of dynamic stability and flutter of hypersonx vehicles where an understanding of such flows may be needed. It is intended that the report should give a basis for the planning of research and some conclusions are drawn from the information presented about the kind of work which would be of value or of interest. The report is divided into a general survey and four Appendices, which give detailed information and references. The first of the Appendices gives some background information on hypersonic flows, flight conditions, and vehicles, and the other three are reviews of particular fields of work - the theoretical andys~ of unsteady hypersonic flows; analytical studies of the dynamic stability of hypersonic vehicles in level flight, and the oscillatory behaviour of vehicles in re-entry or exit trajectories; and information from experimental and analytical studies of flutter at hypersonic speeds. The general survey, which forma the first part of the document, summarises the information given in the Appendices, and presents general conclusions about the kinds of research work that should be considered. If detailed information, and evidence for the conclusions are not required, only the first part needs to be read (i.e., pp. 3-V). CenerBl/
Page 1: MINISTRY OF AVlATlON AERONAUTICAL R
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 72 and 73:
No. Author(s) 12 Ashley, Holt and Z
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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A Survey of Unsteady Hypersonic Flow Problems

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