A Survey of Unsteady Hypersonic Flow Problems

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ft . c 0 40016 a FIG.6.5. Fig. 18 for Ref. 74 % = O-5 n = 22 5 =o A\ M 4 / Effect of boundary layer thickness on the shell thickness required to prevent flutter in scallop mode. Copper cylinder at 50,000 ft. altitude.
A.R.C. C.P. No.901 Harch. 1%5 Wood, B. M. A.R.C. C.P. NO.901 March, 1965 W o o d , 8. U. A SURVEY OF UNSTEADY HYPERSONIC FL&’ PRoBUM A SURVEY OF UNSTEADY HYPERSONIC FWW PRXUXB Arter glv,ng general lnronnatlo” on hypersonic rl”ws, rllghc condltlons lircer giving general im~ati0n on hypersonic riws. night .20”dltl0”3 and Vehicles. the repolZ ~‘evlews work on the analysis Of “nvteady hypersonic and vehicles. the report revlwa woe on the analysis of unsteady hypenonlc fldws, analytical studies or the dy”e,!Mc stablllty or hypenO”lc vehicles, riw.9. a”alyt1ca1 studies 0r the dynamic stablllty or hypeno”lc PehlCl.%, Bnd experlmentel and analytical work on rl”tter at hypersonic speeds. 0” and arperlmmtal and analytlcalwork on rlutter at hypersonic speeds. On this bsSls it then examines the need r”r research and suggests lines that thls basis lt then examines the need ror research end su&ests lines that research should rollow. research shollld r0lloA. The chief conclusion 1s that the qwsl-steady analysis of unsteady hypersonic fl‘ws may be adequate ror the practical purpOse.3 Of dynamic stablllty and flutter analyals. ,It is s”&?zsted that research should be directed to rlndlng the degl’ee or lnacc~recy involved I” quesl-Steady estimates or the unsteady aemdynamlc forces. and the se”sltlvlty or dynamic stablllty alYf rlurter analyses t” lnaccuracles I” these io,.Xs. The tiler concl”slon 18 that the quasi-steady analysis or ““ste*dy hypersonic rlows may be adequate rcr the practical purpcees or dy”amlc .m.b*lity and riutm- analysis. It 1s suggeSted that research should be directed to rlndlng the desee Or l”XCUIXCY Involved 1” quasi-Steady estlmtes or the ““steady ae~le Iores. znd the 9elsltlrlty or dynsmlC stablllty and rimer mlalyses to l”aCCuraCleS I” these rorce.9. P.T.O. P.T.O. A.&C. C.P. No.901 uamh. 1965 Wood, 8. U. A SUIWEY OF UNSTEADY “YPERBONIC Fu;w PROEUHB The chief conclusion 18 that the quasi-steady enalysls or unsready hypersonic rim may be adsquare r0r the pl-act&J purposes or dynamic stablllcy end riutter a”alys1s. It 1s suggested that research should be directed to rl”dlng the degree or l”wcw.wy Involved 1” quesl-stesdy estim.ma or the unsteady aerodynami0 r0me3, md t h e ~e~ltl~lty 0r dynamic stablllty and rlutter analyses t” l”a”curscles in these rorces. P.T.O.
Page 1:
MINISTRY OF AVlATlON AERONAUTICAL R
Page 4 and 5:
-2- CONTENTS Int~~duction . . . . .
Page 6 and 7:
General Surves and Conclusions -4-
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-6- and values of M6 < 1) and shock
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-a- have been ~0nce171ed with the f
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- to - APPENDICES Detailed Reviews
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- 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
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- 24 - minimum are that its variati
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- 26 - This simple form of the meth
Page 30 and 31:
t - 28 - and r “” + u’ i + (1
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- 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
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- 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.
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- 50 - The thcorctlcal deduction th
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- 52- frequcnoy. Theoretical calcul
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-%- 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
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a a, A b c cD CL %l %I c% C Q% C mq
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AP 9 P r 'b F a B % R % Be Rex s 9
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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
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&. Author(sl 36 Moore, F. K. 37 Oli
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- 74 - No. Author(s) Title, etc. 52
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No 65 66 67 68 69 70 . 71 72 73 Aut
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FIG. I (a) Slender wing/body combin
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h ft x From Ref.5 and calculation b
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FIGS.5-7 FIG 5 Axis system for thin
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%‘8 Ro (-X/R; e- -0 \t I FIG. 9 R
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-0.02 0 ’ 0.02 cP 0.04 0.06 O-08
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O- I- 2 - 3 - 4 - ,5- / , / / / /
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FIG. 15 (a) I
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CP (C) of5 = o rrom Flg.ZJof R 19.9
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O-/ 0.12 . 0 OS08 1. CP 0.04 0 -0.0
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O-16 CP o-12 From Ref.29 ;c) M = 6.
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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: 0.00 o-00 FIG. 64 FImm -... Fio~ =
Page 160: 0 Crown copyright 1966 Prmted and p
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