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On the finite Dean problem: linear theory

Published online by Cambridge University Press:  17 February 2009

B. J. Kachoyan  and
P. J. Blennerhassett
B. J. Kachoyan
Affiliation:
Department of Applied Mathematics, University of Sydney, Sydney, N.S.W. 2006, Australia.
P. J. Blennerhassett
Affiliation:
School of Mathematics, University of New South Wales, P. O. Box 1, Kensington, N.S.W., 2033, Australia.
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Abstract

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The Dean problem of pressure-driven flow between finite-length concentric cylinders is considered. The outer cylinder is at rest and the small-gap approximation is used. In a similar procedure to that of Blennerhassett and Hall [8] in the context of Taylor vortices, special end conditions are imposed in which the ends of the cylinder move with the mean flow, allowing the use of a perturbation analysis from a known basic flow. Difficulties specific to Dean flow (and more generally to non-Taylor-vortex flow) require the use of a parameter α which measures the relative strengths of the velocities due to rotation and the pressure gradient, to trace the solution from Taylor to Dean flow. Asymptotic expansions are derived for axial wavenumbers at a given Taylor number. The calculation of critical Taylor number for a given cylinder height is then carried out. Corresponding stream-function contours clearly show features not evident in infinite flow.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 2 , October 1988 , pp. 157 - 178
Copyright
Copyright © Australian Mathematical Society 1988

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