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The boundary-layer flow due to a vortex approaching a cylinder

Published online by Cambridge University Press:  26 April 2006

H. Affes ,
Z. Xiao  and
A. T. Conlisk
H. Affes
Affiliation:
Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210, USA
Z. Xiao
Affiliation:
Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210, USA
A. T. Conlisk
Affiliation:
Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210, USA
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Abstract

The three-dimensional unsteady boundary layer induced by a vortex filament moving outside a circular cylinder is considered. In the present paper, we focus attention on the situation where the inviscid flow is fully three-dimensional but is symmetric with respect to the top centreline of the cylinder. The motion of the vortex toward the cylinder leads to separation of the boundary layer; in the present work a large unsteady adverse pressure gradient develops as well. Results for the three-dimensional streamlines, the vorticity distribution, and the velocity component normal to the cylinder indicate the presence of a region of unsteady three-dimensional secondary flow structure of rather complex shape located deep within the boundary layer. Within this three-dimensional secondary flow the fluid is progressively squeezed into a narrow region under the main vortex and it is expected that a local three-dimensional jet will develop sending boundary-layer fluid out into the main stream. It is pointed out that such three-dimensional eruptive behaviour has been observed in experiments. The results indicate the development of a three-dimensional singularity in the boundary-layer equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 275 , 25 September 1994 , pp. 33 - 57
Copyright
© 1994 Cambridge University Press

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