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Turbulent boundary-layer interaction with a shock wave at a compression corner

Published online by Cambridge University Press:  20 April 2006

S. Agrawal  and
A. F. Messiter
S. Agrawal
Affiliation:
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, Michigan 48109
A. F. Messiter
Affiliation:
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, Michigan 48109
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Abstract

The local interaction of an oblique shock wave with an unseparated turbulent boundary layer at a shallow two-dimensional compression corner is described by asymptotic expansions for small values of the non-dimensional friction velocity and the flow turning angle. It is assumed that the velocity-defect law and the law of the wall, adapted for compressible flow, provide an asymptotic representation of the mean velocity profile in the undisturbed boundary layer. Analytical solutions for the local mean-velocity and pressure distributions are derived in supersonic, hypersonic and transonic small-disturbance limits, with additional intermediate limits required at distances from the corner that are small in comparison with the boundary-layer thickness. The solutions describe small perturbations in an inviscid rotational flow, and show good agreement with available experimental data in most cases where effects of separation can be neglected. Calculation of the wall shear stress requires solution of the boundary-layer momentum equation in a sublayer which plays the role of a new thinner boundary layer but which is still much thicker than the wall layer. An analytical solution is derived with a mixing-length approximation, and is in qualitative agreement with one set of measured values.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 143 , June 1984 , pp. 23 - 46
Copyright
© 1984 Cambridge University Press

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