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Low-Reynolds-number flow past an elliptic cylinder

Published online by Cambridge University Press:  20 April 2006

Kazuhito Shintani
Affiliation:
Department of Mechanical Engineering, University of Electro-Communications, Chofu, Tokyo, Japan
Akira Umemura
Affiliation:
Department of Mechanical Engineering, Yamagata University, Yonezawa, Yamagata, Japan
Akira Takano
Affiliation:
Department of Aeronautics, University of Tokyo, Bunkyo-ku, Tokyo, Japan

Abstract

The primary objective of this paper is to obtain the detailed description of the flow field near an elliptic cylinder that is placed perpendicularly in a uniform stream at low Reynolds number. Attention is paid to the shape effects due to the flattening of the cylinder and to the inertial effects of the fluid. The analysis resorts to the method of matched asymptotic expansions. The main part of the inner expansion describes the near flow field as a Stokes flow, which is characterized by the singularities arranged at the two foci of the ellipse. The first three terms $O({\mathbb R}) ({\mathbb R}$ = Reynolds number) in the inner expansion are developed, and the flow aspects under the influence of the fluid inertia are investigated. The streamline patterns with one or two vortices round a finite flat plate of zero thickness, which is a special case of the elliptic cylinder, are presented.

Type
Research Article
Copyright
© 1983 Cambridge University Press

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References

Bentwich, M. & Miloh, T. 1978 The unsteady matched Stokes-Oseen solution for the flow past a sphere J. Fluid Mech. 88, 1732.Google Scholar
Bretherton, F. P. 1962 Slow viscous motion round a cylinder in a simple shear J. Fluid Mech. 12, 591613.Google Scholar
Chester, W. & Breach, D. R. 1969 On the flow past a sphere at low Reynolds number J. Fluid Mech. 37, 751760.Google Scholar
Hasimoto, H. 1953 On the flow of a viscous fluid past an inclined elliptic cylinder at small Reynolds numbers J. Phys. Soc. Japan 8, 653661.Google Scholar
Imai, I. 1954 A new method of solving Oseen's equations and its application to the flow past an inclined elliptic cylinder. Proc. R. Soc. Lond A 224, 141160.Google Scholar
Kaplun, S. 1957 Low Reynolds number flow past a circular cylinder J. Math. Mech. 6, 595603.Google Scholar
Lamb, H. 1911 On the uniform motion of a sphere through a viscous fluid. Phil. Mag. (6) 21, 112810.
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder J. Fluid Mech. 2, 237262.Google Scholar
Sano, T. 1981 Unsteady flow past a sphere at low Reynolds number J. Fluid Mech. 112, 433441.Google Scholar
Skinner, L. A. 1975 Generalized expansions for slow flow past a cylinder Q. J. Mech. Appl. Maths 28, 333340.Google Scholar
Taneda, S. 1968 Standing twin-vortices behind a thin flat plate normal to the flow Rep. Res. Inst. Appl. Mech. Kyushu Univ. 16, 155163.Google Scholar
Tomotika, S. & Aoi, T. 1950 The steady flow of viscous fluid past a sphere and circular cylinder at small Reynolds number Q. J. Mech. Appl. Maths 3, 140161.Google Scholar
Tomotika, S. & Aoi, T. 1953 The steady flow of a viscous fluid past an elliptic cylinder and a flat plate at small Reynolds numbers Q. J. Mech. Appl. Maths 6, 290312.Google Scholar
Umemura, A. 1982 Matched-asymptotic analysis of low-Reynolds-number flow past two equal circular cylinders J. Fluid Mech. 121, 345363.Google Scholar
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.
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