Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-12T14:52:01.648Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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.)

References

Bretherton, F. P. 1962 Slow viscous motion round a cylinder in a simple shear. J. Fluid Mech. 12, 591.Google Scholar
Cox, R. G., Zia, I. Y. Z. & Mason, S. G. 1968 Particle motions in sheared suspensions. XXV. Streamlines around cylinders and spheres. J. Colloid Interface Sci. 27, 7.Google Scholar
Darabaner, C. L., Raasch, J. K. & Mason, S. G. 1967 Particle motions in sheared suspensions. XX. Circular cylinders. Can. J. Chem. Engng 45, 3.Google Scholar
Deardorff, J. W. 1963 On the stability of viscous plane Couette flow. J. Fluid Mech. 15 623.Google Scholar
Frankel, N. A. & Acrivos, A. 1968 Heat and mass transfer from small spheres and cylinders freely suspended in shear flow. Phys. Fluids, 11, 1913.Google Scholar
Giesekus, H. 1962 Strömungen mit konstanten Geschwindigkeitsgradienten und die Bewegung von darin suspendierten Teilchen. Rheologica Acta, 2, 112.Google Scholar
Kohlman, D. L. & Mollo-Christensen, E. 1965 Measurement of drag of cylinders and spheres in a Couette-flow channel. Phys. Fluids, 8, 1013.Google Scholar
Kohlman, D. L. 1963 Experiments on cylinder drag, sphere drag, and stability in rectilinear Couette flow. Fluid Dynamics Report, 63–1, Massachusetts Institute of Technology.Google Scholar
Mason, S. G. & Trevelyan, B. J. 1951 Particle motions in sheared suspensions. Part I. Rotations. J. Colloid Sci. 6, 354.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics, Part II. New York: McGraw-Hill.
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, 237.Google Scholar