A Survey of Unsteady Hypersonic Flow Problems

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kM L2 From Fig. 3.2 of Ref. I9 5 0.50\ \ 040 ‘-z 0.30 ‘q--.- \. - - _ - - 420’ . - o-10 0 0 04 0.8 MB;‘2 1’6 0 0.4 0 0.4 0.8 l-6 - o*8M%J”2 ‘.6 - - 2nd order piston theory - ----- 3rd order piston theory Shock-expanse on Low frequency flutter derivatives for a biconvex airfoil - comparison of piston theory with shock-expanston method
I.0 / / / / ,: kMM; k&I M; A 2-o 0 0 0 0.4 O-0 I. 2 I.6 0 O-4 MeN kt4L; A kHH; A From Fig. 3.3 of Ret. Ig / 4 *o --.qgA-- O-20 N A N O-8 t-2 l-6- 0 0.4 0 aMe I.2 I.6 MeN N 2.0 2.0 0 ,/ M)‘I y-,,,,,,,gut / =$ . // / I.0\-A-’ I*o’“,,W,._,--.Y/-- N . \* 0 Exact steady-state result for 0 0 0.4 1, 0.8,,Nl*2 I.6 0 - 0 0.4 \ O-8Me 1.2~ I.6 f$=o-I, M=IO - - 2nd order piston theory N \ ----- 3rd order piston theory \ -Shock- expansion Low frequency flutter derivatives for a double wedgeairfoll -comparison of piston theory with shock-expansion method
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 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: 0.4 0 From Fig. 3.26 of Ref. 26 FIG
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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