Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T11:05:04.905Z Has data issue: false hasContentIssue false

Onsager's pancake approximation for the fluid dynamics of a gas centrifuge

Published online by Cambridge University Press:  19 April 2006

Houston G. Wood
Affiliation:
Union Carbide Corporation, Nuclear Division, Oak Ridge, Tennesse
J. B. Morton
Affiliation:
University of Virginia, Charlottesville, Virginia

Abstract

A previously unpublished theory for describing the internal flow in a gas centrifuge is presented. The theory is based on boundary-layer-type arguments on the side walls of the centrifuge with the additional approximation of neglecting radial diffusion of radial momentum. The effects of the top and bottom end caps are incorporated through Ekman-layer solutions. The results are presented in a form amenable to numerical calculations.

Some sample calculations are presented for the special case of a centrifuge with a linear temperature profile on the wall and the top and bottom of the centrifuge at the same temperature as the corresponding end of the side wall.

Type
Research Article
Copyright
© 1980 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

Avery, D. G. & Davies, E. 1973 Uranium Enrichment by Gas Centrifuge. London: Mills and Boon.
Bark, F. H. & Bark, T. H. 1976 On vertical boundary layers in a rapidly rotating gas. J. Fluid Mech. 78, 749761.Google Scholar
Brouwers, J. J. H. 1976 On the motion of a compressible fluid in a rotating cylinder. Ph.D. thesis, Twente University of Technology, Enschede, The Netherlands.
Carrier, G. F. 1964 Phenomena in rotating fluids. Proc. 11th Int. Cong. Appl. Mech., Munich, Germany.
Carrier, G. F. & Maslen, S. H. 1962 Flow phenomena in rapidly rotating systems. USAEC Rep. TID-18065.Google Scholar
Courant, G. & Hilbert, D. 1953 Methods of Mathematical Physics, vol. I. Wiley-Interscience.
Durivault, J. & Louvet, P. 1976 Etude théorique de l’écoulement dans une centrifugeuse à contre-courant thermique. Centre d'Etudes Nucl. de Saclay, Rapport CEA-R-4714.Google Scholar
Ekman, V. W. 1905 On the influence of the earth's rotation on ocean currents. Arkin. Mat. Astron. och Fysik 2, no. 11.Google Scholar
Erdélyi, A. 1953 Higher Transcendental Functions, vol. I. McGraw-Hill.
Hoglund, R. L., Shacter, J. & Von Halle, E. 1979 Diffusion separation methods. In Encyclopedia of Chemical Technology, vol. 7, 3rd edn (ed. R. E. Kirk & D. F. Othmer). Wiley.
Lotz, M. 1973 Die rein axiale Strömung in einer Gegenstrom-Gasultrazentrifuge. Atomkernenergie 22, 4145.Google Scholar
Matsuda, T. & Hashimoto, K. 1976 Thermally, mechanically or externally driven flows in a gas centrifuge with insulated horizontal end plates. J. Fluid Mech. 78, 337354.Google Scholar
May, W. G. 1977 Separation parameters of gas centrifuges. A.I.Ch.E. Symp. Series, no. 169, vol. 73.
Olander, D. R. 1972 Technical basis of the gas centrifuge. Advances in Nuclear Science and Technology, vol. 6. Academic.
Soubbaramayer 1979 Centrifugation. In Uranium Enrichment. Topics in Applied Physics, vol. 35 (ed. S. Villani). Springer.
Stewartson, K. 1957 On almost rigid rotations. J. Fluid Mech. 3, 1726.Google Scholar
Villani, S. 1976 Isotope Separation. American Nuclear Society.
Von Halle, E. 1977 The countercurrent gas centrifuge for the enrichment of U-235. Proc. 70th Ann. Meeting A.I.Ch.E., New York (to appear). (Also Union Carbide Corporation, Nuclear Division, Oak Ridge, Tennessee, Rep. K/OA-4058.)