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Steady flow in rapidly rotating variable-area rectangular ducts. Part 2. Small divergences

Published online by Cambridge University Press:  12 April 2006

A. Calderon and
J. S. Walker
A. Calderon
Affiliation:
Department of General Engineering, University of Puerto Rico, Mayaguez
J. S. Walker
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana
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Abstract

This paper treats the steady inertialess flow of an incompressible viscous fluid through an infinite rectangular duct rotating rapidly about an axis (the y axis) perpendicular to its centre-line (the x axis). The prototype considered has parallel sides at z = ± 1 for all x, parallel top and bottom at y = ± a for x < 0 and straight diverging top and bottom at y = ± (a + bx) for x > 0. An earlier paper (Walker 1975) presented solutions for b = ±(1), for which the flow in the diverging part (x > 0) is carried by a thin, highvelocity sheet jet adjacent to the side at z = 1, the flow elsewhere in this part being essentially stagnant. The present paper considers the evolution of the flow as the divergence decreases from O(1) to zero, the flow being fully developed for b = 0. This evolution involves four intermediate stages depending upon the relationship between b and E, the (small) Ekman number. In each successive stage, the flow-carrying side layer in the diverging part becomes thicker, until in the fourth stage, it spans the duct, so that none of the fluid is stagnant.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 2 , 24 June 1977, pp. 353 - 368
Copyright
© 1977 Cambridge University Press

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References

Calderon, A. 1976 Steady flow in rapidly rotating rectangular ducts with small divergences. Ph.D. thesis, University of Illinois at Urbana-Champaign.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
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