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A numerical method for treating time-periodic boundary layers

Published online by Cambridge University Press:  26 April 2006

P. W. Duck
P. W. Duck
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
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Abstract

The development of an incompressible, laminar, pulsatile boundary layer over a semi-infinite flat plate is studied. Although the undisturbed free stream flow is taken to be non-reversing (following previous studies), sufficiently far downstream, the flow in part of the boundary layer must ultimately reverse direction during part of the cycle.

A novel numerical (finite-difference) scheme is described, which builds in the time periodicity of the flow, and also takes into account the direction of the flow in deciding the form of the differencing in the streamwise direction. The effect of variations in numerical grid is investigated, and comparison is made with asymptotic formulae applicable close to and far from the leading edge of the plate, together with linearized (small oscillation) results obtained using the analysis of Ackerberg & Phillips (1972), which is shown to yield remarkably accurate results when compared with the solution for the full problem, even for quite large oscillation amplitudes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989 , pp. 549 - 561
Copyright
© 1989 Cambridge University Press

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