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Axisymmetric rotating flow past a circular disk

Published online by Cambridge University Press:  11 April 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, La Jolla
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Abstract

The steady, inviscid, axisymmetric, rotating flow past a circular disk in an unbounded liquid is determined on the hypothesis that all streamlines originate in a uniform flow far upstream of the body. The characteristic parameter for the flow is k = 2ωa/U, where ω and U are the angular and axial velocities of the basic flow and α is the radius of the disk. Forward separation is found to occur for k > k = 1.9, in agreement with observation (Orloff & Bossel 1971). The length of the upstream separation bubble is determined on the hypothesis that the previous solution remains valid for k > k, despite the existence of closed streamlines within the upstream separation bubble (which may, but do not necessarily, inva,lidate the solution). This length increases rapidly for k > 3, in qualitative agreement with observation. The hypothesis of unseparated flow implies a singularity at the rim of the disk, just as in potential flow. The strength of this singularity departs only slightly from its potential-flow value for 0 ≤ k ≤ 2, but increases rapidly with k for k > 3, which suggests that (quite apart from the difficulties implied by the existence of closed streamlines) the solution cannot remain valid for sufficiently large k.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 53 , Issue 4 , 27 June 1972 , pp. 689 - 700
Copyright
© 1972 Cambridge University Press

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