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On the uniqueness of steady flow past a rotating cylinder with suction

Buldakov, E.V., Chernyshenko, S.I. and Ruban, A.I. (2000) On the uniqueness of steady flow past a rotating cylinder with suction Journal of Fluid Mechanics, 411, pp. 213-232. (doi:10.1017/S0022112099008162).

Record type: Article

Abstract

The subject of this study is a steady two-dimensional incompressible flow past a rapidly rotating cylinder with suction. The rotation velocity is assumed to be large enough compared with the cross-flow velocity at infinity to ensure that there is no separation. High-Reynolds-number asymptotic analysis of incompressible Navier–Stokes equations is performed.
Prandtl's classical approach of subdividing the flow field into two regions, the outer inviscid region and the boundary layer, was used earlier by Glauert (1957) for analysis of a similar flow without suction. Glauert found that the periodicity of the boundary layer allows the velocity circulation around the cylinder to be found uniquely. In the present study it is shown that the periodicity condition does not give a unique solution for suction velocity much greater than 1/Re. It is found that these non-unique solutions correspond to different exponentially small upstream vorticity levels, which cannot be distinguished from zero when considering terms of only a few powers in a large Reynolds number asymptotic expansion. Unique solutions are constructed for suction of order unity, 1/Re, and 1/[surd radical]Re. In the last case an explicit analysis of the distribution of exponentially small vorticity outside the boundary layer was carried out.

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Published date: 2000

Identifiers

Local EPrints ID: 21324
URI: http://eprints.soton.ac.uk/id/eprint/21324
ISSN: 0022-1120
PURE UUID: e2f5cfe1-a0fd-4904-86da-e2dc0eba932e

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Date deposited: 19 Jul 2006
Last modified: 17 Jul 2017 16:26

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Contributors

Author: E.V. Buldakov
Author: S.I. Chernyshenko
Author: A.I. Ruban

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