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Theory and computations for breakup of unsteady subsonic or supersonic separating flows

Published online by Cambridge University Press:  26 April 2006

I. P. Vickers  and
F. T. Smith
I. P. Vickers
Affiliation:
Mathematics Department, University College London, Gower Street, London WC1E 6BT, UK
F. T. Smith
Affiliation:
Mathematics Department, University College London, Gower Street, London WC1E 6BT, UK
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Abstract

This study of flow just beyond a breakaway-separation point presents a description of planar nonlinear unsteady effects over a fairly wide parameter range, for a subsonic or supersonic boundary layer at large Reynolds numbers. The inviscid model thus produced essentially contains a vortex sheet near the smooth solid surface, with local inner–outer interaction. The governing equations couple the eddy velocity and pressure with the thicknesses of the detached boundary layer and the eddy. The computational method presented here uses a new adaptive gridding technique intended to capture accurately the spiky solution behaviour that develops and to compare with theory. Analysis and computations point to a breakup in the solution, suggesting an explanation for the start of transition and possible turbulent reattachment as found experimentally. The influence of the detached boundary-layer thickness proves crucial. The type of finite-time breakup encountered is studied analytically and the criterion for its occurrence is highlighted. This is guided by a characteristic analysis for a special case. The finite-time breakup is similar in spirit to, although different in detail from, a nonlinear breakup proposed earlier by one of the authors for general unsteady interactive boundary layers and it suggests a wide application of that nonlinear breakup theory and its criterion. Comparisons between computations and theory are found to be supportive.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 268 , 10 June 1994 , pp. 147 - 173
Copyright
© 1994 Cambridge University Press

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