© 1993 by Oxford University Press
ON THE HIGH-REYNOLDS-NUMBER FLOW BETWEEN NON-COAXIAL ROTATING CYLINDERS
( Department of Mathematics, University of Manchester Manchester M13 9PL )
The high-Reynolds-number flow between two rotating eccontric circular cylinders is studied. The flow model comprises an invisicid core, involving closed streamlines, and hence (by Batchelor (J. Fluid Mech. 1 (1956) 177) this must be a region of constant vorticity, with a viscous boundary layer on each cylinder.
The problem involves two fundamental constants, which are unknown a priori, namely the core vorticity, and the mass flux circulating between the two cylinders. These constants are both determined by the simultaneous/consistent solution of all three regions.
The model fails with the formation of a stagnation point inside one of the boundary layers. Results for a variety of ratios of rotation rates of the cylinders, over a range of eccentricities, are presented for the cases of the inner-outer radius ratios of one-third and one-fifth. We also consider the case of small ecentricities, which yields analytic estimates for the key unknown constants.
Asymptotic solutions for very large and very small rotation rates of the outer cylinder are also presented, and are found in both cases to reduce to the problem of a solitary rotating cylinder, immersed in an infinite uniform flow, a problem which has been quite extensively investigated in the past and is also computed for comparison, using our numerical techniques.