A Survey of Unsteady Hypersonic Flow Problems

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a a, A b c cD CL %l %I c% C Q% C mq C P d E Ez f fi - 62 - Nomenclature (Some terms are not included III this index if they are used only locally) local speed of sound free-stream value of speed of sound aspect ratlo of wing (span/mean chord) representative length of a body($ for a wing, 8 for a body) mean chord of a wing drag coefficient of a body [Drag&@S] lift coefficient of a body [Lift/&U'S] rate of change of lift coefficient with angle of attack: X+/&x pitching moment coefficient rate of change of pitching moment coefficient with angle of attack: acdaa rate of change of pitching moment coefflczsnt with time irb %I rate of change of angle of attack parameter, - : U eoJ) rate of change of pitching moment ccefflclent with pitching Ob a% velocity parameter, - : IJ a(db/b) pressure coefflcvent maximum body diameter Young's Modulus P - P, &JJ" effective stiffness based on frequency of second elastic mode frequency of oscillation frequency of natural mode : i = 1 for first mode, etc. gravitational constant structural damping factor altitude
h iB IB k X x crit x Y c c Lb Li'Li m m m m Y % % Idi’M! . I n % P &.a - 63 - displacement of section in plunge (flutter) non-dimensional form of I B :pSbs pitching moment of inertia of a body about its centre of gravity frequency parameter - I U convergence factor for pitching oscillations of a vehicle flying on a re-entry path defined by equation (3.12) critical value of X in equation (3.14) CL m -+- 2 PSR pitching radius of gyration of B body about its oentre of gravity body length panel length - in flutter studies ratio of lift to drag see definitions of derivatives (i = 1 to 4) mass of vehicle - Appendix III mass per unit span of two-dimensional section mass of wing or cone mass/unit area Of panel free stream or flight Mach number U/s, flutter Mach number Mach number of boundary layer in approximate calculation of boundary layer damping in Figs. 64 to 65. see definitions of derivatives (i = 1 to 4) I Appendix IV number of circumferential nodes in the flutter of a cylindrical shell mid-plane stress in panel (Fig. 63) local pressure . free-stream static pressure
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 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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