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The structure of the Stewartson layers in a gas centrifuge. Part 2. Insulated side wall

Published online by Cambridge University Press:  12 April 2006

Takuya Matsuda  and
Hidenori Takeda
Takuya Matsuda
Affiliation:
Department of Aeronautical Engineering, Kyoto University, Kyoto, Japan Temporary Address: Department of Applied Mathematics and Astronomy, University College, Cardiff, Wales.
Hidenori Takeda
Affiliation:
Department of Aeronautical Engineering, Kyoto University, Kyoto, Japan
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Abstract

The Stewartson E½- and E¼-layers in a rapidly rotating compressible fluid are considered within the framework of linearized equations and the boundary-layer method. The fluid is contained in a cylinder made of a thermally insulated side wall and conducting top and bottom end plates. The end plates and the side wall rotate with slightly different angular velocities. The case of an incompressible fluid was discussed by Stewartson, who found that the flow is restricted to the side-wall boundary layers. In the case of a compressible fluid, however, the solutions are strongly dependent upon the thermal boundary conditions assumed on the side wall. In particular, if the wall is insulated the fluid in the inner core is dragged along too since it is coupled strongly to the flow in the side-wall Stewartson layers. The critical parameter governing the solutions is found to be $(\gamma -1) PrG_0 E^{-\frac{1}{3}}/4\gamma$, where γ is the ratio of specific heats, Pr the Prandtl number, G0 the square of the rotational Mach number and E the Ekman number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 85 , Issue 3 , 13 April 1978 , pp. 443 - 457
Copyright
© 1978 Cambridge University Press

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