Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-07-05T17:59:13.854Z Has data issue: false hasContentIssue false
  • English
  • Français

The effects of curvature on the flow field in rapidly rotating gas centrifuges

Published online by Cambridge University Press:  20 April 2006

Houston G. Wood ,
Jo Ann Jordan  and
Max D. Gunzburger
Houston G. Wood
Affiliation:
University of Virginia, Charlottesville, Virginia
Jo Ann Jordan
Affiliation:
Union Carbide Corporation, Nuclear Division, Oak Ridge, Tennessee
Max D. Gunzburger
Affiliation:
Carnegie-Mellon University, Pittsburgh, Pennsylvania
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of curvature on the fluid dynamics of rapidly rotating gas centrifuges are studied. A governing system of a linear partial differential equation and boundary conditions is derived based on a linearization of the equations for viscous compressible flow. This system reduces to the Onsager pancake model if the effects of curvature are neglected. Approximations to the solutions of the governing equations with and without curvature terms are obtained via a finite-element method. Two examples are considered: first where the flow is driven by a thermal gradient at the wall of the centrifuge, and then for the flow being driven by the introduction and removal of mass through the ends of the centrifuge. Comparisons of the results obtained show that, especially for the second example, the inclusion of the terms due to curvature in the model can have an appreciable effect on the solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 140 , March 1984 , pp. 373 - 395
Copyright
© 1984 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

Babarsky, R. & Wood, H. G. 1982 An analysis from first principles of the source/sink terms in the pancake equation. Univ. Virginia, Charlottesville, Rep. UVA-ER-795-82.Google Scholar
Durivault, J. & Louvet, P. 1976 Etude théorique de l'écoulement dans une centrifugeuse-contre-courant thermique. Centre d'Etudes Nucléaires de Saclay, Rep. CEA-R-4714.Google Scholar
Eastham, J. F. 1981 The finite element method in anisotropic Sobolev spaces. Ph.D. thesis, University of Tennessee, Knoxville, Tennessee.
Gunzburger, M. D. & Wood, H. G. 1982 A finite element method for the Onsager pancake equation. Comp. Meth. Appl. Mech. Engng 31, 43–59.Google Scholar
Gunzburger, M. D., Wood, H. G. & Jordan, J. A. 1984 A finite element method for gas centrifuge problems. SIAM J. Sci. Stat. Comp. 5.Google Scholar
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 and D. F. Othmer). Wiley.
Jordan, J. A. 1983 A numerical study of the effects of curvature on the fluid dynamics of gas centrifuges. M.S. thesis, University of Tennessee, Knoxville.
Jung, E. 1983 An analytic solution of the linearized flow equations using the method of eigenvalues. In Proc. of the 5th Workshop on Gases in Strong Rotation (ed. H. G. Wood). University of Virginia, Charlottesville.
Maslen, S. H. 1979 The basic steady-state flow models for computing countercurrent motions. Univ. Virginia, Charlottesville, Rep. UVA-ER-540-80.Google Scholar
May, W. G. 1977 Separation Parameters of Gas Centrifuges. AIChE Symp. Series, no. 169, vol. 73.Google Scholar
Soubbaramayer, 1979 Centrifugation. In Uranium Enrichment (ed. S. Villani). Springer.
Strang, G. & Fix, G. 1972 An Analysis of the Finite Element Method. Prentice-Hall.
Viecelli, J. A. 1983 Exponential difference operator approximation for the sixth order Onsager equation. J. Comp. Phys. 50, 162–170.Google Scholar
Von Halle, E. 1977 The countercurrent gas centrifuge for the enrichment of U-235. In Proc. 70th Ann. Meeting AIChE, New York.
Wood, H. G. & Morton, J. B. 1980 Onsager's pancake approximation for the fluid dynamics of a gas centrifuge. J. Fluid Mech. 101, 1–31.Google Scholar