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Streaming flow induced by an oscillating cascade of circular cylinders

Published online by Cambridge University Press:  26 April 2006

B. Yan ,
D. B. Ingham  and
B. R. Morton
B. Yan
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds, LS2 9JT, UK
D. B. Ingham
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds, LS2 9JT, UK
B. R. Morton
Affiliation:
Department of Mathematics, Monash University, Clayton 3168, Victoria, Australia
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Abstract

The fluid flow induced by a cascade of circular cylinders which oscillates harmonically in an unbounded, incompressible, viscous fluid which is otherwise at rest is investigated both numerically and experimentally. Attention in this paper is mainly concentrated on the induced steady streaming flow which occurs when the ratio of the amplitude of the oscillation of the cascade to the size of the cylinder, ε, is very small. The leading-order flow is then governed by the steady Navier-Stokes equations. In order to solve these equations numerically we first generate numerically a grid system using the boundary element method and then use a finite-difference scheme on the newly generated rectangular grid system. Numerical results show that for small values of the streaming Reynolds number Rs there are four recirculating flows of equal strength around each circular cylinder of the cascade. At large values of Rs symmetry breaks down and numerical solutions are found for asymmetrical flows. Numerically, a critical value of Rs, Rso say, is identified such that the flow is symmetrical when Rs < Rso and asymmetrical when Rs > Rso and these results are in reasonable agreement with experimental results, which are also presented in this paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 252 , July 1993 , pp. 147 - 171
Copyright
© 1993 Cambridge University Press

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