ON THE HIGH-REYNOLDS-NUMBER FLOW BETWEEN NONCOAXIAL ROTATING CYLINDERS

The high-Reynolds-number flow between two rotating eccentric circular cylinders is studied. The flow model comprises an invisicid core, invo lving closed streamlines, and hence (by Batchelor (J. Fluid Mech. 1 (1 956) 177) this must be a region of constant vorticity, with a viscous boundary layer on each cylinder.The problem involves two fundamental c onstants, which are unknown a priori, namely the core vorticity, and t he mass flux circulating between the two cylinders. These constants ar e both determined by the simultaneous/consistent solution of all three regions. The model fails with the formation of a stagnation point ins ide one of the boundary layers. Results for a variety of ratios of rot ation rates of the cylinders, over a range of eccentricities, are pres ented for the cases of the inner-outer radius ratios of one-third and one-fifth. We also consider the case of small eccentricities, which yi elds analytic estimates for the key unknown constants. Asymptotic solu tions for very large and very small rotation rates of the outer cylind er are also presented, and are found in both cases to reduce to the pr oblem 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 techniqu es.