Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-19T03:54:19.841Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermally, mechanically or externally driven flows in a gas centrifuge with insulated horizontal end plates

Published online by Cambridge University Press:  11 April 2006

Takuya Matsuda  and
Kiyoshi Hashimoto
Takuya Matsuda
Affiliation:
Department of Aeronautical Engineering, Kyoto University, Kyoto, Japan Temporary adress: Department of Applied Mathematics and Astronomy, University College, Cardiff, Wales.
Kiyoshi Hashimoto
Affiliation:
Department of Aeronautical Engineering, Kyoto University, Kyoto, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

The axisymmetric motion of a compressible fluid in a rapidly rotating cylinder is considered using a linear approach and boundary-layer techniques. The deviation of the fluid motion from rigid-body rotation is caused either by an applied temperature distribution on the side wall, a differential rotation of the top and bottom end plates or sources and sinks of fluid distributed on the end plates. The horizontal end plates are assumed to be thermally insulated, while the side wall is conducting. The critical parameter governing the problem is found to be E−½(γ − 1) PrG0/4γ, where E is the Ekman number, γ the ratio of specific heats, Pr the Prandtl number and G0 the square of a rotational Mach number. If this parameter is larger than unity, the coupled effect of the compressibility of the fluid and the thermal condition on the end plates suppresses the flow in the cylinder. The flow in the inner inviscid core is strongly coupled with the Ekman-layer flow through the boundary conditions on the end plates, something which does not occur if the fluid is Boussinesq nor if the fluid is compressible and the end plates are conducting.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 78 , Issue 2 , 23 November 1976 , pp. 337 - 354
Copyright
© 1976 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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.
Hunter, C. 1967 The axisymmetric flow in a rotating annulus due to a horizontally applied temperature gradient J. Fluid Mech. 27, 753–778.Google Scholar
Kanagawa, K. & Oyama, Y. 1961 On the isotope separation by counter-current gas centrifuge J. Atom. Energy Soc. Japan, 3, 868–922. (See also ibid. 3, 918–922; in Japanese.)Google Scholar
Matsuda, T., Sakurai, T. & Takeda, H. 1975 Source—sink flow in a gas centrifuge J. Fluid Mech. 67, 197–208.Google Scholar
Matsuda, T. 1975 Isotope separation by thermally driven countercurrent gas centrifuge J. Nucl. Sci. Tech. 12, 512–518.Google Scholar
Matsuda, T., Hashimoto, K. & Takeda, H. 1976 Thermally driven flow in a gas centrifuge with an insulated side wall J. Fluid Mech. 73, 389–399.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 Adv. Nucl. Sci. Tech. 6, 105–174.Google Scholar
Sakurai, T. & Matsuda, T. 1974 Gasdynamics of a centrifugal machine J. Fluid Mech. 62, 727–736.Google Scholar
Stewartson, K. 1957 On almost rigid rotations J. Fluid Mech. 3, 17–26.Google Scholar