Gaskell, P.H., Savage, M.D. and Wilson, M. (1997) Stokes flow in a halffilled annulus between rotating coaxial cylinders. Journal of Fluid Mechanics, 337. pp. 263282. ISSN 14697645

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Abstract
A model is presented for viscous flow in a cylindrical cavity (a halffilled annulus lying between horizontal, infinitely long concentric cylinders of radii Ri,R0 rotating with peripheral speeds Ui,U0). 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 = Ri/R0 and speed ratio S = Ui/U0.
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 subeddies. 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 twodimensional cavity flow approaches quasiunidirectional flow in the small gap limit. Controlspace 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 