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The linear stability of boundary-layer flow over compliant walls: effects of boundary-layer growth

Published online by Cambridge University Press:  26 April 2006

K. S. Yeo ,
B. C. Khoo  and
W. K. Chong
K. S. Yeo
Affiliation:
Department of Mechanical and Production Engineering, National University of Singapore, Kent Ridge, Singapore 0511, Republic of Singapore
B. C. Khoo
Affiliation:
Department of Mechanical and Production Engineering, National University of Singapore, Kent Ridge, Singapore 0511, Republic of Singapore
W. K. Chong
Affiliation:
Department of Mechanical and Production Engineering, National University of Singapore, Kent Ridge, Singapore 0511, Republic of Singapore
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Abstract

The linear stability of boundary-layer flow over compliant or flexible surfaces has been studied by Carpenter & Garrad (1985), Yeo (1988) and others on the assumption of local flow parallelism. This assumption is valid at large Reynolds numbers. Non-parallel effects due to growth of the boundary layer gain in significance and importance as one gets to lower Reynolds number. This is especially so for a compliant surface, which can sustain a variety of wall-related instabilities in addition to the Tollmien—Schlichting instabilities (TSI) that are found over rigid surfaces. The present paper investigates the influence of boundary-layer non-parallelism on the TSI and wall-related travelling-wave flutter (TWF) on compliant layers. Corrections to the growth rate of locally parallel theory for boundary-layer non-parallelism are obtained through a multiple-scale analysis. The results indicate that flow non-parallelism has an overall destabilizing influence on the TSI and TWF. Flow non-parallelism is also found to have a very strong destabilizing effect on the branch of TWF that stretches to low Reynolds number. The results obtained have important implications for the design and use of compliant layers at low Reynolds numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 280 , 10 December 1994 , pp. 199 - 225
Copyright
© 1994 Cambridge University Press

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