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Analysis of a rapidly rotating gas in a pie-shaped cylinder

Published online by Cambridge University Press:  26 April 2006

Houston G. Wood  and
Richard Babarsky
Houston G. Wood
Affiliation:
Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22901, USA
Richard Babarsky
Affiliation:
Mathematics and Computer Science, James Madison University, Harrisonburg, VA 22801, USA
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Abstract

By using asymptotic analysis, an eigensolution technique has been developed for predicting the flow of gas contained in a pie-shaped cylinder of finite length rotating rapidly about its vertex. This problem has application to a conventional cylindrical gas centrifuge with radial walls. Three different types of boundary layers exist in the flow: Ekman layers on the top and bottom, buoyancy layers on the radial walls, and a cylindrical ‘pancake’ layer on the outer wall of the cylinder. A single sixth-order partial differential equation is obtained for the axial velocity in the cylindrical layer, and the other layers provide matching conditions. The problem is formulated for no-slip and prescribed temperature conditions on the solid surfaces and for adiabatic no shear stress with zero pressure at the inner free surface. Eigenvalues are computed for this problem and compared with those for the open cylinder, and solutions are presented for flows induced by mass throughput and by differential temperature conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 239 , June 1992 , pp. 249 - 271
Copyright
© 1992 Cambridge University Press

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References

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