Hostname: page-component-7dd5485656-zlgnt Total loading time: 0 Render date: 2025-10-28T21:19:59.793Z Has data issue: false hasContentIssue false
  • English
  • Français

Matched-asymptotic analysis of low-Reynolds-number flow past two equal circular cylinders

Published online by Cambridge University Press:  20 April 2006

Akira Umemura
Akira Umemura
Affiliation:
Department of Mechanical Engineering, Faculty of Engineering, Yamagata University, 4–3–16 Jonan, Yonezawa, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

Jeffery's solution in bi-polar co-ordinates of the two-dimensional Stokes equations cannot be applied to the low-Reynolds-number flow past two parallel circular cylinders because of severe mathematical difficulties. These difficulties can be overcome by considering the flow field far from the cylinders and then modifying the solution near the cylinders so that it becomes the inner expansion for an application of the method of matched asymptotic expansions. After the calculation of the drag, lift and moment coefficients of two adjacent equal circular cylinders to O(1) in the Reynolds number R, the analysis is extended to incorporate partially the effects of fluid inertia of order R. The results show fairly good agreement with Taneda's experimental data.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 345 - 363
Copyright
© 1982 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Davis, A. M. J., O'Neill, M. E., Dorrepaal, J. M. & Ranger, K. B.1976 J. Fluid Mech. 77, 625.
Dean, W. R. & Montagnon, P. E. 1949 Proc. Camb. Phil. Soc. 45, 389.
Dorrepaal, J. M. & O'Neill, M. E.1979 Quart. J. Mech. Appl. Math. 32, 95.
Fujikawa, H. 1956 J. Phys. Soc. Japan 11, 690.
Fujikawa, H. 1957 J. Phys. Soc. Japan 12, 423.
Jeffery, G. B. 1922 Proc. R. Soc. A 101, 169.
Jeffery, D. J. & Sherwood, J. D. 1980 J. Fluid Mech. 96, 315.
Jeffrey, D. J. & Onishi, Y. 1981 Quart. J. Mech. Appl. Math. 34, 129.
Kaplun, S. 1957 J. Math. Mech. 6, 595.
Kuwabara, S. 1957 J. Phys. Soc. Japan 12, 291.
Moffatt, H. K. 1964 J. Fluid Mech. 27, 1.
Moffatt, H. K. & Duffy, B. R. 1980 J. Fluid Mech. 96, 299.
O'Neill, M. E.1964 Mathematika 11, 67.
Proudman, I. & Pearson, J. R. A. 1957 J. Fluid Mech. 2, 237.
Raasch, J. K. 1961 D. Eng. thesis, Karlsruhe Technical University, Karlsruhe, Germany.
Stimson, M. & Jeffery, G. B. 1926 Proc. R. Soc. 111, 110.
Taneda, S. 1957 J. Phys. Soc. Japan 12, 419.
Tomotika, S. & Aoi, T. 1950 Quart. J. Mech. Appl. Math. 3, 140.
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.
Wakiya, S. 1975 J. Phys. Soc. Japan 39, 1603.
Yano, H. & Kieda, A. 1980 J. Fluid Mech. 97, 157.