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Thermally driven flow in a gas centrifuge with an insulated side wall

Published online by Cambridge University Press:  29 March 2006

Takuya Matsuda ,
Kiyoshi Hashimoto  and
Hidenori Takeda
Takuya Matsuda
Affiliation:
Department of Aeronautical Engineering, Faculty of Engineering, Kyoto University, Kyoto, Japan
Kiyoshi Hashimoto
Affiliation:
Department of Aeronautical Engineering, Faculty of Engineering, Kyoto University, Kyoto, Japan
Hidenori Takeda
Affiliation:
Department of Aeronautical Engineering, Faculty of Engineering, Kyoto University, Kyoto, Japan
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Abstract

A thermally driven steady axisymmetric flow of gas of small diffusivity in a vertical circular cylinder rotating rapidly about its axis of symmetry is studied. The side wall is a thermal insulator and the horizontal end plates are perfect conductors. The temperature of the top end plate is kept slightly higher than that of the bottom one.

The boundary-layer method is applied to solve the linearized basic equations and the following results are obtained.

  1. The axial velocity in the inner core is fully controlled by the Ekman suction on the horizontal plates and is the same as that in the case of a perfectly conducting side wall.

  2. The closed circulation in the side-wall Stewartson E½ layer is strongly suppressed compared with the case of a perfectly conducting side wall.

This situation is reflected in the inner temperature field, which deviates from that in the case of a perfectly conducting side wall. The critical parameter governing the solution is found to be (γ − 1) PrG0E−1/3/4γ, where Pr is the Prandtl number, γ the ratio of specific heats, E the Ekman number and G0 the square of the Mach number based on the peripheral speed of the cylinder.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 2 , 27 January 1976 , pp. 389 - 399
Copyright
© 1976 Cambridge University Press

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References

Abajian, V. V. & Fishman, A. M. 1973 Supplying enriched uranium. Phys. Today, August, pp. 23–29.Google Scholar
Barcilon, V. & Pedlosky, J. 1967 On the steady motions produced by a stable stratification in a rapidly rotating fluid J. Fluid Mech. 29, 673–690.Google Scholar
Cohen, K. P. 1951 The Theory of Isotope Separation as Applied to the Large Scale Production of U-235. McGraw-Hill.
Hashimoto, K. 1975 A source-sink flow in an incompressible rotating fluid J. Phys. Soc. Japan, 38, 1508–1515.Google Scholar
Homsy, G. M. & Hudson, J. L. 1969 Centrifugally driven thermal convection in a rotating cylinder J. Fluid Mech. 35, 33–52.Google Scholar
Kanagawa, K. & Oyama, Y. 1961 On the isotope separation by counter-current gas centrifuge J. Atomic Energy Soc. Japan, 3, 868–922. (See also 3, 918-922 (in Japanese).)Google Scholar
Matsuda, T. 1975 Isotope separation by thermally driven countercurrent gas centrifuge J. Nucl. Sci. Tech. 12, 512–518.Google Scholar
Matsuda, T., Sakurai, T. & Takeda, H. 1975 Source-sink flow in a gas centrifuge J. Fluid Mech. 69, 197–208.Google Scholar
Nakayama, W. & Usui, S. 1974 Flow in rotating cylinder of gas centrifuge J. Nucl. Sci. Tech. 11, 242–262.Google Scholar
Olander, D. R. 1972 Technical basis of the gas centrifuge. In Advances in Nuclear Science and Technology, vol. 6, pp. 105–174. Academic.
Sakurai, T. & Matsuda, T. 1974 Gasdynamics of a centrifugal machine J. Fluid Mech. 62, 727–736.Google Scholar
Williams, W. E. 1973 Fourier Series and Boundary Value Problems. London: George Allen & Unwin.