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On the stability of boundary-layer flow over a spring-mounted piston

Published online by Cambridge University Press:  20 April 2006

M. S. Howe
M. S. Howe
Affiliation:
University of Southampton, England
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Abstract

The stability of weakly compressible boundary-layer flow over a spring-mounted piston is examined theoretically by modelling the mean boundary layer at low Strouhal numbers by means of a step-function velocity profile. This constitutes a prototype problem for the treatment of the interaction of unsteady boundary-layer flow with a compliant surface, and the present discussion complements a recent analysis due to Ffowcs Williams and Purshouse by incorporating the influence of flow separation at the edges of the piston. This is effected analytically by application of the unsteady Kutta condition at both the leading and trailing edges of the piston. At high Reynolds numbers and in the case of light fluid loading i t is predicted that the separated flow can cause piston flutter. Stability criteria are derived for a rectangular piston of large aspect ratio.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 125 , December 1982 , pp. 59 - 73
Copyright
© 1982 Cambridge University Press

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References

Ashley, H. & Landahl, M. 1965 Aerodynamics of Wings and Bodies. Addison-Wesley.
Benjamin, T. B. 1960 Effects of a flexible boundary on hydrodynamic stability. J. Fluid Mech. 9, 513–532.Google Scholar
Benjamin, T. B. 1963 The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows. J. Fluid Mech. 16, 436–450.Google Scholar
Bisplinghoff, R. L. & Ashley, H. 1975 Principles of Aeroelasticity. Dover.
Curle, N. 1955 The influence of solid boundaries upon aerodynamic sound. Proc. R. Soc. Lond. A 231, 505–514.Google Scholar
Ffowcs Williams, J. E. & Lovely, D. J. 1975 Sound radiation into uniformly flowing fluid by compact surface vibration. J. Fluid Mech. 71, 689–700.Google Scholar
Ffowcs Williams, J. E. & Purshouse, M. 1981 A vortex sheet modelling of boundary-layer noise. J. Fluid Mech. 113, 187–220.Google Scholar
Frenkiel, F. N., Landahl, M. T. & Lumley, J. L. (eds) 1977 Proc. IUTAM Symp. on Structure of Turbulence and Drag Reduction, Washington, D.C., June 1976. Phys. Fluids Suppl. 20, S1-S297.
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Table of Integrals, Series and Products (corrected edn). Academic.
Howe, M. S. 1979 A note on the interaction of unsteady flow with an acoustic liner. J. Sound Vib. 63, 429–436.Google Scholar
Howe, M. S. 1981a The influence of mean shear on unsteady aperture flow, with application to acoustical diffraction and self-sustained cavity oscillations. J. Fluid Mech. 109, 125–146.Google Scholar
Howe, M. S. 1981b The role of displacement thickness fluctuations in hydroacoustics. Proc. R. Soc. Lond. A 374, 543–568.Google Scholar
Kramer, M. O. 1957 Boundary layer stabilisation by distributed damping. J. Aero. Sci. 24, 459–463.Google Scholar
Leppington, F. G. & Levine, H. 1979 The effect of flow on the piston problem of acoustics. J. Sound Vib. 62, 3–17.Google Scholar
Levine, H. 1980 A note on sound radiation into a uniformly flowing medium. J. Sound Vib. 71, 1–8.Google Scholar
Lighthill, M. J. 1958 Fourier Analysis and Generalised Functions. Cambridge University Press.
Titchmarsh, E. C. 1948 Theory of Fourier Integrals, 2nd edn. Oxford University Press.
Willmarth, W. W. 1975 Pressure fluctuations beneath turbulent boundary layers. Ann. Rev. Fluid Mech. 7, 13–38.Google Scholar