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The flow between two finite rotating disks enclosed by a cylinder

Published online by Cambridge University Press:  20 April 2006

D. Dijkstra  and
G. J. F. Van Heijst
D. Dijkstra
Affiliation:
Department of Applied Mathematics, Twente University of Technology, Enschede, The Netherlands
G. J. F. Van Heijst
Affiliation:
Department of Applied Mathematics, Twente University of Technology, Enschede, The Netherlands
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Abstract

The flow between two finite rotating disks enclosed by a cylinder is investigated both numerically and experimentally. For this finite geometry the full stationary Navier–Stokes equations are solved numerically without similarity assumptions. Experimental results are obtained by means of stereophotography of small tracer particles. The results are in good agreement with the numerical solution. Owing to the presence of the cylinder sidewall, the solution is found to be unique for all values of the parameters considered. When the disks rotate in opposite senses with counter-rotation above 15%, a stagnation point appears at the slower-rotating disk. This stagnation point is associated with a two-cell structure in the meridional plane and is experimentally observed as a ring of particles at the slower-rotating disk. Near the axis of rotation the solution is found to satisfy similarity demands; for weak counter-rotation the solution is of Batchelor type near the axis of rotation, but for strong counter-rotation a Stewartson profile is found to be more adequate for the description of the tangential velocity near the axis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 128 , March 1983 , pp. 123 - 154
Copyright
© 1983 Cambridge University Press

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