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A method for integrating the boundary-layer equations through a region of reverse flow

Published online by Cambridge University Press:  29 March 2006

J. B. Klemp  and
Andreas Acrivos
J. B. Klemp
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California Present Address: National Center for Atmospheric Research, Boulder, Colorado.
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California
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Abstract

If a region of reverse flow remains confined within a boundary layer the conventional boundary-layer equations should continue to apply downstream of the point of detachment of the surface streamline (ω = 0). Nevertheless, standard numerical techniques fail in the presence of backflow since these methods become highly unstable and, in addition, neglect the upstream flow of information. A procedure for numerically integrating the boundary-layer equations through a region of reverse flow which takes downstream influence into account is therefore presented. This method is then applied to the problem of uniform flow past a parallel flat plate of finite length whose surface has a constant velocity directed opposite to that of the main stream. Although singularities occur at both the point of detachment (xs) and reattachment (xr) of the ω = 0 streamline, this integration technique provides a solution which ceases to apply only in the close proximity of these singular points. From this solution it is evident that, throughout a large portion of the separated region, the flow is strongly affected by conditions near xr, thereby demonstrating the importance of allowing information to be transmitted upstream in a region of backflow. Near (xs), however, it is found that, in spite of the presence of reverse flow, the solution has a self-similar form in this particular example.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 53 , Issue 1 , 9 May 1972 , pp. 177 - 191
Copyright
© 1972 Cambridge University Press

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