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On the severe non-symmetric constriction, curving or cornering of channel flows

Published online by Cambridge University Press:  19 April 2006

F. T. Smith  and
P. W. Duck
F. T. Smith
Affiliation:
Applied Mathematics Department, University of Western Ontario, London, Ontario, Canada
Permanent address: Mathematics Department, Imperial College, London SW7, U.K.
P. W. Duck
Affiliation:
Department of Aeronautical and Astronautical Engineering, Ohio State University, Columbus, Ohio 43210, U.S.A.
Permanent address: Mathematics Department, The University, Manchester, U.K.
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Abstract

Considered below is the plane, high-Reynolds-number (Re), flow of an incompressible fluid through a channel suffering a severe non-symmetric constriction, ‘severe’ meaning ‘of typical dimensions comparable with the channel width a*’. The (mainly inviscid) flow description is governed by free streamline theory, to be consistent with the viscous incompressible separation from the constriction surface and with a relatively slow eddy motion beyond. Separation also occurs far ahead of the constriction, at a distance $O(Re^{\frac{1}{7}} a^{*})$ upstream. Attention is given primarily to the flow features for a particular class of slowly varying severe constrictions, from which however the features for the probably more useful classes of slender (i.e. of large length but O(a*) height) and moderately severe (i.e. of O(a*) length but small height) constriction follow, as do those for curved or cornered channel flows. In all these cases a long-scale flow response is induced upstream and downstream and in many cases remarkably simple universal formulae for the separation and reattachment positions result. The corresponding O(a*) corrections to the upstream separation distance above are also derived.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 4 , 26 June 1980 , pp. 727 - 753
Copyright
© 1980 Cambridge University Press

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