The Influence of Surface Waves on the Stability of a ... - aerade

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ROYAL AIRCRKFT ESTABLISHMENT C.P. No.161 Technical Note No. Aero 224.1 Uarch, 123 <strong>The</strong> influence <strong>of</strong> surface waves on the stablllty <strong>of</strong> a laminar boundary layer with uniform suctmn D. A. Sperm, B.A., Ph.D. I). G. Randall, B.Sc. In order to estmate the destab.bllxmg effect <strong>of</strong> the waves likely to be encountered on wmg surfaces whwh wxllbe used with boundary layer suction, calculations have been made <strong>of</strong> the effect <strong>of</strong> small sxwoldal surface waves on the stablllty <strong>of</strong> the asymptotic suction pr<strong>of</strong>lle. Curves are presented <strong>of</strong> the percentage increases m local suction flow 2 necegsary to mamtain the stablllty <strong>of</strong> the boundary layer at the s Le level as on a completely flat surface, for varwus values <strong>of</strong> the variables Vs F , helght:wavelength ratm L and Reynolds number based on wavelength, UL 7’ <strong>The</strong>se should provide quantltatlve estimates for more general cases. It 1s found, as might have been expected, that the lower "$ or the larger h , the larger the necessary percentage mcrease 111 % , espeolal 4 y for low ULI u . 10 per cent 1s a typical magm.tude for the necessary increase at a hq$Reynolds nmber. -I-
List <strong>of</strong> symbols 1 Introduction LIST OF CONTENTS 2 Stability theory for parallel flows 3 Outline <strong>of</strong> calculations 4 Numerical example 5 Discussion Referenoes LIST OF APPENDICES Calculation <strong>of</strong> velocity pr<strong>of</strong>iles on a wavy surface with asymptotic suction Calculation <strong>of</strong> (Rg*) from Lin's formula or <strong>Surface</strong> waves as a source <strong>of</strong> disturbance Typical neutral stability cmve Velocity pr<strong>of</strong>lles along wavy wall LIST OF ILTJJS!IPATIONS Extra suction required for stability on a wavy surface v Required increase in suction, for + = 0.0014, as function <strong>of</strong> k and $ ~ Appendix Page 3 4 4 5 7 7 a 9 17 19 Fig. 1 84 b)(c)(a) 3(a)(b)(c)(d)(e) Variation in form parameter on a wavy surface with suction 5 Vsriatlon <strong>of</strong> (Rg*)crit with H for suction pr<strong>of</strong>iles 6 -2- 4
Page 1: MINISTRY OF SUPPLY AERONAUTICAL RES
Page 5 and 6: 1 Introduction The
Page 7 and 8: The analysis 1s ca
Page 9: The fact that wave
Page 12 and 13: the equations are z+ (H+ 2) (8) Wit
Page 14 and 15: By differentmtmg (11) and puttug y
Page 16 and 17: For h = 1 , the equatmns (IT) to (2
Page 18 and 19: From Flg.6, for thrs value
Page 21 and 22: (R ff)CRlT R6” FIG. I& 2(a) FIG.1
Page 23 and 24: I PROFILE POSITION @ 0 FlG.2@). FRO
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Page 27 and 28: 10 15 “5. -4 0 u x ‘O FIG.3 (e)
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Page 31: Crown Copyr@t Reserved York House.

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