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Stokes flow in a half-filled annulus between rotating coaxial cylinders

Gaskell, P.H., Savage, M.D. and Wilson, M. (1997) Stokes flow in a half-filled annulus between rotating coaxial cylinders. Journal of Fluid Mechanics, 337. pp. 263-282. ISSN 1469-7645

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Abstract

A model is presented for viscous flow in a cylindrical cavity (a half-filled annulus lying between horizontal, infinitely long concentric cylinders of radii R-i,R-0 rotating with peripheral speeds U-i,U-0). Stokes' approximation is used to formulate a boundary value problem which is solved for the streamfunction, phi, as a function of radius ratio (R) over bar = R-i/R-0 and speed ratio S = U-i/U-0.

Results show that for S > 0 (S < 0) the flow domain consists of two (one) large eddies (eddy), each having a stagnation point on the centreline and a potentially rich substructure with separatrices and sub-eddies. The behaviour of the streamfunction solution in the neighbourhood of stagnation points on the centreline is investigated by means of a truncated Taylor expansion. As (R) over bar and S are varied it is shown that a bifurcation in the flow structure arises in which a centre becomes a saddle stagnation point and vice versa. As (R) over bar --> 1, a sequence of 'flow bifurcations' leads to a flow structure consisting of a set of nested separatrices, and provides the means by which the two-dimensional cavity flow approaches quasi-unidirectional flow in the small gap limit. Control-space diagrams reveal that speed ratio has little effect on the flow structure when S < 0 and also when S > 0 and aspect ratios are small (except near S = 1). For S > 0 and moderate to large aspect ratios the bifurcation characteristics of the two large eddies are quite different and depend on both (R) over bar and S.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 1997 Cambridge University Press.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds)
The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
The University of Leeds > Faculty of Engineering (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds)
Depositing User: Repository Officer
Date Deposited: 15 May 2006
Last Modified: 07 Jun 2014 08:23
Published Version: http://journals.cambridge.org/action/displayIssue?...
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
URI: http://eprints.whiterose.ac.uk/id/eprint/1198

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