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Boundary-layer receptivity to unsteady pressure gradients: experiments and overview

Published online by Cambridge University Press:  21 April 2006

M. Nishioka  and
M. V. Morkovin
M. Nishioka
Affiliation:
College of Engineering, University of Osaka Prefecture, Sakai, Osaka, Japan
M. V. Morkovin
Affiliation:
Department of Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, U.S.A.
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Abstract

The experimental evidence on the mechanisms of forcing of unstable vorticity waves (the Tollmien–Schlichting–Schubauer or TS waves) of circular frequency ω and wavelength λTS in wall layers by unsteady pressure gradients of amplitude A and frequency ω is reviewed and found to be confused and contradictory. It is proposed that a likely effective receptivity mechanism rests on the fact that under realistic conditions A varies with distance x along any body of finite thickness, A(x), and introduces thereby additional characteristic lengths which can match λTS. Heuristic arguments suggest that through A(x) the pressure gradient infuses vorticity at the wall and forces spatial growth of the TS mean-square vorticity $\overline{\zeta^2}$, at a rate proportional to the real part of ΔAF(κTS), the contribution of A(x) between x−½λTS and x + ½λTS to the Fourier transform AF(κ) at κ = κTS. A second input into $\overline{\zeta^2_{\rm TS}}$ growth corresponds to the conversion of the steady boundary-layer vorticity into unsteady ζTS, through the action of vf, the normal velocity of the forcing field. The rate is given by $\int_0^{\delta}\overline{v_{\rm f}\zeta_{\rm TS}}U^{\prime\prime}(y)\,{\rm d}y $ and is proportional to the imaginary part of κTSΔAF(KTS).

The proposition is consistent in all currently verifiable respects with one numerical and a series of laboratory experiments. In the laboratory experiments, various configurations of a pulsating pressure source and shielding plates located in the free stream supplied the variable-amplitude pressure gradients over the nearby flat-wall boundary layer. Three of the cases presented here demonstrate that stationary unsteady pressure fields induce Stokes-like sublayers when the boundary layer is stable and self-excited vorticity waves when it is unstable. The results of a fourth experiment suggest that unsteady pressure sources in wakes near the boundary layer can force the growth of unstable wall waves at the wake frequencies even though their propagation speeds differ. Material is also presented on key Soviet experiments and views on receptivity. Finally, these experiments and ours are examined for consistency and complementarity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 171 , October 1986 , pp. 219 - 261
Copyright
© 1986 Cambridge University Press

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References

Aizin L. B.1974 On the stability of weakly nonuniform states with small perturbations of white noise. Prikl. Mat. Mekh. 38, No. 6 (in Russian).Google Scholar
Aizin, L. B. & Maksimov V. P.1978 On the stability of flow of weakly compressible gas in a pipe with model roughness. Prikl. Mat. Mekh. 42, 650–655Google Scholar
Aizin, L. B. & Polyakov N. F.1979 Acoustic generation of Tollmien—Schlichting waves over local unevenness of surfaces immersed in streams. Preprint 17, Akad. Nauk, USSR, Siberian Div., Inst. Theor. & Applied Mech., Novosibirsk (in Russian).
Bar Sever A.1984 Boundary layer transition over rough surfaces. MS thesis, Illinois Institute of Technology, Chicago, IL 60616.
Bechert D. W.1982 Excited waves in shear layers. DFVLR Rep. FB 82–83. Inst. Exper. Fluid Mechanics, Göttingen, condensed in AIAA Paper 83–0724.Google Scholar
Corke T. C., Bar Sever, A. & Morkovin, M. V. 1986 Experiments on transition enhancement by distributed roughness. Phys. Fluids (to appear).Google Scholar
Dovgal A. V., Kachanov Yu. S., Kozlov V. V., Levchenko, V. Ya. & Maksimov V. P.1979 Origin of perturbations in boundary layers. Development of Perturbations in Boundary Layers, Inst. Theor. & Applied Mech., Siberian Div. Akad. Nauk, USSR, pp. 4–22, Novosibirsk (in Russian). (Transl. in NASA TM-77986, 1986.)Google Scholar
Dovgal, A. V. & Kozlov V. V.1981a Generation of Tollmien—Schlichting waves by sound on blunt-nosed bodies. Preprint No. 21–81, Akad. Nauk, USSR, Siberian Div., Inst. Theor. & Applied Mech., Novosibirsk (in Russian).
Dovgal, A. V. & Kozlov V. V.1981b Influence of acoustic perturbations on the flow structure in boundary layers in adverse pressure gradients. Preprint 8–81, Akad. Nauk, USSR, Siberian Div., Inst. Theor. & Applied Mech., Novosibirsk (in Russian).
Dovgal A. V., Kozlov, V. V. & Levchenko V. Ya.1980 Experimental investigation of reactions of a boundary layer to periodic external perturbations. Izv. Akad. Nauk. SSSR. Mekh. Zhid. i Gaza 4, 155–159. (Transl. Fluid Dyn. 1981, 602–606.)Google Scholar
Fasel H.1976 Investigation of the stability of boundary layers by a finite difference model of the Navier—Stokes equations. J. Fluid Mech. 62, 249–261.Google Scholar
Gaster M.1975 A theoretical model of a wave packet in the boundary layer on a flat plate Proc. R. Soc. Lond. A 347, 271–289.Google Scholar
Gaster M.1977 Series representation of the eigenvalues of the Orr—Sommerfeld equation. Paper 2 of Laminar—Turbulent Transition, AGARD Conf. Proc. 224.Google Scholar
Gaster, M. & Grant I.1975 An experimental investigation of the formation and development of a wave packet in a laminar boundary layer Proc. R. Soc. Lond. A 347, 253–269.Google Scholar
Gedney Ch. J.1983 The cancellation of a sound-excited Tollmien—Schlichting wave with plate vibrations. Phys. Fluids 26, 1158–1160.Google Scholar
Ginevskii A. S., Vlasov, E. V. & Kolesnikov A. V.1978 Aeroacoustic Interactions. Moscow: Mashinostroenie.
Goldstein M. E.1983 The evolution of Tollmien-Schlichting waves near a leading edge. J. Fluid Mech. 127, 59–81.Google Scholar
Goldstein M. E.1985 Scattering of acoustic waves into Tollmien—Schlichting waves by small streamwise variations in surface geometry. J. Fluid Mech. 154, 509–529.Google Scholar
Goldstein M. E.1986 Proc. ICASE/NASA 1985 Workshop on Stability of Time Dependent and Spacially Varying Flows. Springer (to be published).
Goldstein M. E., Sockol, P. M. & Sanz J.1983 Evolution of Tollmien—Schlichting waves near a leading edge. Part 2. Numerical determination of amplitudes. J. Fluid Mech. 129, 443–453.Google Scholar
Hama F. R., Williams, D. R. & Fasel H.1980 Flow field and energy balance according to spatial linear stability theory of the Blasius boundary layer. In Proc. IUTAM Symp. on Laminar—Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 73–85. Springer.
Kachanov Yu. S., Kozlov, V. V. & Levchenko V. Ya.1975 Generation and development of small disturbances in laminar boundary layers under the action of acoustic fields Akad. Nauk, USSR. Seria Tekhn. Nauk, Novosibirsk, 13, 18–26 (in Russian).Google Scholar
Kachanov Yu. S., Kozlov, V. V. & Levchenko, V. Ya. 1978 Origin of Tollmien—Schlichting waves in boundary layers under the influence of external disturbances Izv. Akad. Nauk. SSSR. Mekh. Zhid. i Gaza, 5, 85–94 (in Russian). (Transl. Fluid Dyn., 1979, 704–11.)Google Scholar
Kachanov Yu. S., Kozlov, V. V. & Levchenko V. Ya.1982 Initiation of Turbulence in Boundary Layers. Novosibirsk: Nauka Publ. Siberian Div.
Kachanov Yu. S., Kozlov V. V., Levchenko, V. Ya. & Maksimov V. P.1979 Transformation of external disturbances into the boundary layer waves. In Proc. Sixth Intl Conf. on Numerical Methods in Fluid Dynamics, pp. 299–307. Springer.
Kegelman J.1982 Experimental studies of boundary-layer transition on a spinning and non-spinning axisymmetric body. Ph.D. thesis, Notre Dame University IN 46556, USA.
Kegelman, J. T. & Mueller T. J.1986 Experimental studies of spontaneous and forced transition on an axisymmetric body. AIAA J. 24, 397–403.Google Scholar
Kendall J. M.1984 Experiments on the generation of Tollmien—Schlichting waves in a flat plate boundary layer by weak free-stream turbulence. AIAA Paper No. 84–0011.Google Scholar
Knapp, C. F. & Roache P. J.1968 A combined visual and hot-wire anemometer investigation of boundary layer transition. AIAA J. 6, 29–36.Google Scholar
Kozlov, V. V. (ed.) 1985 Proc. 2nd Symp. on Laminar—Turbulent Transition, pp. 233–248, 283–320. Springer.
Leehey P.1980 The influence of environment in laminar boundary layer control. In Proc. 2nd Symp. on Viscous Drag Reduction (ed. G. R. Hough), AIAA Prog. in Astro & Aero., vol. 72.
Leehey, P. & Shapiro P.1980 Leading-edge effect in laminary boundary layer excitation by sound. In Proc. IUTAM Symp. on Laminar—Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 321–331. Springer.
Lemcke L., Naysmith A., Picken, J. & Thomann H.1970 Comparison of heat transfer measurements in free flight and in wind tunnel at M = 7 at similar Reynolds numbers and temperature ratios. Proc. 7th Congress Intl Council Aeron. Sci., Rome.
Liepmann H. W., Brown, G. L. & Nosenchuck D. M.1982 Control of laminar-instability waves using a new technique. J. Fluid Mech. 118, 187–200.Google Scholar
Lighthill M. J.1963 Boundary layer theory. In Laminar Boundary Layers (ed. L. Rosenhead). Oxford University Press.
Lin C. C.1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Loehrke R. I., Morkovin, M. V. & Fejer A. A.1975 Review: Transition in nonreversing oscillating boundary layers. Trans. ASME I: J. Fluids Engng 97, 534–549.Google Scholar
Maksimov V. P.1979 Genesis of Tollmien—Schlichting waves in oscillating boundary layers (in Russian). In Development of Perturbations in Boundary Layers (ed. V. Ya. Levchenko), pp. 68–75. Inst. Theor. & Applied Mech., Siberian Div. Akad. Nauk USSR. Novosibirsk.
Morkovin M. V.1978 Instability, transition to turbulence and predictability. AGARDograph 236.Google Scholar
Morkovin, M. V. & Paranjape S. V.1971 On acoustic excitation of shear layers. Zeit. Flugwiss. 19, 328–335.Google Scholar
Morse, P. M. & Ingard K. U.1968 Theoretical Acoustics. McGraw-Hill.
Mungur C. J.1977 On the sensitivity of shear layers to sound. AIAA Paper No. 77–1369.Google Scholar
Murdock, J. W. 1980 The generation of Tollmien—Schlichting wave by a sound wave Proc. R. Soc. Lond. A 372, 1517.Google Scholar
Polyakov N. F.1979 Laminar boundary layer in “natural” transition to turbulence. In Development of Perturbations in Boundary Layers (ed. V. Ya. Levchenko). pp. 23–67. Inst. Theor. & Applied Mech., Siberian Div. Akad. Nauk USSR, Novosibirsk (in Russian).
Polyakov N. F., Domaratskii, A. N. & Skurlatov A. I.1976 On the interaction of acoustic fields with incompressible laminar boundary layers. Izv. Sib. Otd. Akad. Nauk. USSR Seria Tekhn. Nauk, Novosibirsk 13, 19–27 (in Russian).Google Scholar
Reshotko E.1976 Boundary stability and transition. Ann. Rev. Fluid Mech. 8, 311–350.Google Scholar
Reshotko E.1984 Environment and receptivity. In Special Course on Stability and Transition of Laminar Flow (ed. R. Michel), section 4. AGARD Rep. 709.
Salwen, H. & Grosch Ch. E.1981 The continuous spectrum of the Orr—Sommerfeld equation. Part 2. Eigenfunction expansions. J. Fluid Mech. 104, 445–465.Google Scholar
Schubauer, G. B. & Skramstad H. K.1948 Laminary boundary-layer oscillations and transition on a flat plate. NACA Tech. Rep. 909.Google Scholar
Shapiro P. J.1977 The influence of sound upon laminar boundary layer instability. MIT Acoustics and Vibration Lab. Rep. 83458–83560–1.Google Scholar
Spangler, I. G. & Wells C. S.1968 Effects of free-stream disturbances on boundary-layer transition. AIAA J. 6, 543–545.Google Scholar
Tam Ch. K. W.1981 The excitation of Tollmien—Schlichting waves in low subsonic boundary layers by free-stream sound waves. J. Fluid Mech. 109, 483–501.Google Scholar
Thomas A. S. W.1984 Control of boundary-layer transition using a wave-superposition principle. J. Fluid Mech. 137, 233–250.Google Scholar
Vlasov E. V., Ginevskii, A. S. & Karavosov R. K.1977 Reaction of an unstable laminar boundary layer to acoustic excitation. Turbulent Flows, pp. 90–96. Moscow: Nauka (in Russian).
Wazzan A. R., Okamura, T. T. & Smith A. M. O.1969 Stability characteristics of the Falkner—Skan profiles. Enclosure in A Portfolio of Stability Characteristics of Incompressible Boundary Layers (by H. J. Obremski, M. V. Morkovin & M. Landahl). AGARDograph no. 134.