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Steady flow in rapidly rotating variable-area rectangular ducts. Part 3. Inertial perturbations for small divergences

Published online by Cambridge University Press:  19 April 2006

J. S. Walker  and
A. M. El-Consul
J. S. Walker
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana
A. M. El-Consul
Affiliation:
Department of Mathematics, University of Al-Fateh, Tripoli, Libya
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Abstract

This paper is part of a series treating the flow in a variable-area, rectangular duct which is rotating about an axis that is perpendicular to the duct's centre-line and parallel to one pair of walls (sides). The speed of rotation is assumed to be sufficiently large that viscous effects are confined to boundary layers and free shear layers and that inertial effects are much smaller than viscous effects everywhere. Earlier papers present inertialess solutions for a prototype with parallel sides everywhere, parallel top and bottom upstream of a cross-section, and straight, symmetrically diverging top and bottom downstream of the same cross-section. The present paper presents inertial perturbations to the inertialess solutions for the prototype when the slope of the diverging top and bottom is small. This paper begins to bridge the gap between papers treating inertialess flows in ducts with arbitrary geometries and papers treating flows with significant inertial effects in ducts with restricted geometries.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 97 , Issue 3 , 15 April 1980 , pp. 417 - 434
Copyright
© 1980 Cambridge University Press

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