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Low Reynolds number shear flow past a rotating circular cylinder. Part 1. Momentum transfer

Published online by Cambridge University Press:  29 March 2006

C. R. Robertson  and
A. Acrivos
C. R. Robertson
Affiliation:
Department of Chemical Engineering, Stanford University Present address: Marathon Oil Company, Littleton, Colorado.
A. Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University
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Abstract

The two-dimensional flow of an incompressible viscous fluid past a circular cylinder, symmetrically placed in a uniform shear field, is considered both theoretically and experimentally for small values of the shear Reynolds number. A series of angular rotational speeds is covered, each giving rise to a fundamentally different flow pattern. It is shown first that the Stokes solution to this problem is not entirely consistent everywhere with the linear shear boundary condition which presumably exists far from the body. Using the method of inner and outer expansions, this solution is then improved by properly taking into account the first-order effects of the inertia terms, but, surprisingly, the streamline structure in the outer region is still found to depart from that of the uniform shear sufficiently far away from the object.

In spite of the somewhat bizarre nature of the theoretical solution far from the cylinder, experimental studies clearly show, however, that it accurately represents the actual flow within the inner region over a wide range of cylinder rotation rates.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 40 , Issue 4 , 9 March 1970 , pp. 685 - 703
Copyright
© 1970 Cambridge University Press

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