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Models for high-Reynolds-number flow down a step

Published online by Cambridge University Press:  26 April 2006

K. O'Malley ,
A. D. Fitt ,
T. V. Jones ,
J. R. Ockendon  and
P. Wilmott
K. O'Malley
Affiliation:
Department of Engineering Science, Parks Rd., Oxford, 0X1 3PJ, UK
A. D. Fitt
Affiliation:
Mathematics Department, University of Southampton, Hampshire, SO9 5NH, UK
T. V. Jones
Affiliation:
Department of Engineering Science, Parks Rd., Oxford, 0X1 3PJ, UK
J. R. Ockendon
Affiliation:
Mathematical Institute, 24–29 St. Giles, Oxford, 0X1 3LB, UK
P. Wilmott
Affiliation:
Department of Mathematics, Imperial College of Science & Technology, London, SW7 2BZ, UK
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Abstract

We consider inviscid, incompressible flow down a backward-facing step. Using thin-aerofoil theory, a model is proposed in which the separated region downstream of the back face of the step consists of a constant-pressure zone immediately behind the step, followed by a Prandtl–Batchelor constant-vorticity region. The motivation for this model is a series of experimental studies which showed the pressure just downstream of the step to be almost constant in some upstream portion of the separated region. Previous models have ignored this constant-pressure region and agreement with experiment has not been good. Agreement with experiment is clearly superior using the constant-pressure/constant-vorticity model, though it is possible that the comparison could be improved still further by consideration of the behaviour of the shear layer after reattachment. Some discussion of such models is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 139 - 155
Copyright
© 1991 Cambridge University Press

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