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Steady flows in rectangular cavities

Published online by Cambridge University Press:  28 March 2006

Frank Pan  and
Andreas Acrivos
Frank Pan
Affiliation:
Department of Chemical Engineering, Stanford University
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University
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Abstract

This paper deals with the steady flow in a rectangular cavity where the motion is driven by the uniform translation of the top wall. Creeping flow solutions for cavities having aspect ratios from ¼ to 5 were obtained numerically by a relaxation technique and were shown to compare favourably with Dean & Montagnon's (1949) similarity solution, as extended by Moffatt (1964), in the region near the bottom corners of a square cavity as well as throughout the major portion of a cavity with aspect ratio equal to 5. In addition, for a Reynolds number range from 20 to 4000, flow patterns were determined experimentally by means of a photographic technique for finite cavities, as well as for cavities of effectively infinite depth. These experimental results suggest that, within finite cavities, the high Reynolds number steady flow should consist essentially of a single inviscid core of uniform vorticity with viscous effects being confined to thin shear layers near the boundaries, while, for cavities of infinite depth, the viscous and inertia forces should remain of comparable magnitude throughout the whole domain even in the limit of very large Reynolds number R.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 4 , 22 June 1967 , pp. 643 - 655
Copyright
© 1967 Cambridge University Press

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References

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