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A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

Published online by Cambridge University Press:  26 April 2006

R. J. Bodonyi ,
W. J. C. Welch ,
P. W. Duck  and
M. Tadjfar
R. J. Bodonyi
Affiliation:
Department of Aeronautical & Astronautical Engineering, The Ohio State University, 2036 Neil Ave. Mall, Columbus, OH 43210, USA
W. J. C. Welch
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
P. W. Duck
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
M. Tadjfar
Affiliation:
Department of Aeronautical & Astronautical Engineering, The Ohio State University, 2036 Neil Ave. Mall, Columbus, OH 43210, USA
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Abstract

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989 , pp. 285 - 308
Copyright
© 1989 Cambridge University Press

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