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Fluid dynamical aspects of the levitation-melting process

Published online by Cambridge University Press:  20 April 2006

A. D. Sneyd  and
H. K. Moffatt
A. D. Sneyd
Affiliation:
University of Waikato, Hamilton, New Zealand
H. K. Moffatt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge
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Abstract

When a piece of metal is placed above a coil carrying a high frequency current, the induced surface currents in the metal can provide a Lorentz force which can support it against gravity; at the same time the heat produced by Joule dissipation can melt the metal. This is the process of ‘levitation melting’, which is a well-established technique in fundamental work in physical and chemical metallurgy. Most theoretical studies of magnetic levitation have dealt only with solid conductors and so have a voided the interesting questions of interaction between the free surface, the magnetic field and the internal flow. These fluid dynamical aspects of the process are studied in this paper.

A particular configuration that is studied in detail is a cylinder levitated by two equal parallel currents in phase; this is conceived as part of a toroidal configuration which avoids a difficulty of conventional configurations, viz the leakage of fluid through the ‘magnetic hole’ at a point on the metal surface where the surface tangential magnetic field vanishes. The equilibrium and stability of the solid circular cylinder is first considered; then the dynamics of the surface film when melting begins; then the equilibrium shape of the fully melted body (analysed by means of a general variational principle proved in § 5); and finally the dynamics of the interior flow, which, as argued in § 2, is likely to be turbulent when the levitated mass is of the order of a few grams or greater.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 117 , April 1982 , pp. 45 - 70
Copyright
© 1982 Cambridge University Press

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References

Block, F. R. & Theissen, A. 1971 Electromagnetic levitation melting — method of cruciblefree melting. Elektrowärme Int. 29, 349.Google Scholar
Brancher, J. P. & Sero Guillaume, O. 1981 Sur l’équilibre des ferrofluides avec interface libre. Rapport interne, LEMTA, Nancy, France.
Brisley, W. & Thornton, B. S. 1963 Electromagnetic levitation calculations for axially symmetric systems. Brit. J. Appl. Phys. 14, 682.Google Scholar
El-Kaddah, N. H. & Robertson, D. C. C. 1978 The kinetics of Gas-Liquid metal reactions involving levitated drops. Metall. Trans. 9B, 191.Google Scholar
Harris, M. R. & Stephan, S. Y. 1975 Support of liquid metal surface by alternating magnetic field. IEEE Trans. MAG-11, 1508.
Hatch, A. J. 1965 Potential-well description of electromagnetic levitation. J. Appl. Phys. 36, 44.Google Scholar
Hunt, J. C. R. & Maxey, M. R. 1980 Estimating velocities and shear stresses in turbulent flows of liquid metals driven by low frequency electromagnetic fields. In MHD Flows and Turbulence, (ed. H. Branover & A. Yakhot), Israel Universities Press, Jerusalem.
Lighthill, M. J. & Whitham, G. B. 1955 On kinematic waves. I. Flood movement in long rivers. Proc. Roy. Soc. A, 229, 281.
Mestel, J. 1982 Magnetic levitation of liquid metals. J. Fluid Mech. 117, 27.Google Scholar
Moreau, R. 1980 Applications métallurgiques de la magnétohydrodynamique. In Proc. XVth Int. Cong. Theor. Appl. Mech. (ed. F. P. J. Rimrott & B. Tabarrok), North Holland.
Muck, O. 1923 German Pat. No. 422004, Oct. 30 1923.
Okress, E. C., Wroughton, D. M., Comenetz, C., Brace, P. N. & Kelly, J. C. K. 1952 Electromagnetic levitation of solid and molten metals. J. Appl. Phys. 23, 83.Google Scholar
Peifer, W. A. 1965 Levitation melting, a survey of the state-of-the-art, J. Metals 17, 487.Google Scholar
Piggot, L. S. & Nix, G. F. 1966 Electromagnetic levitation of a conducting cylinder. Proc. I.E.E. 113, 1229.Google Scholar
Smithells, C. J. 1967 Metals Reference Book 4th. edn. vols. I and III, Butterworths, London.
Sneyd, A. D. 1979 Fluid flow induced by a rapidly alternating or rotating magnetic field. J. Fluid Mech. 92, 35.Google Scholar
Stephan, S. Y. 1975 Support of liquid metal surfaces by alternating magnetic fields — an experimental and theoretical study. Ph.D. thesis, University College, London.
Volkov, T. F. 1962 Stability of a heavy conducting fluid contained by a rapidly varying magnetic field. Soviet Phys. – Tech. Phys., 7, 22.Google Scholar
Zhezherin, T. F. 1959 Problems of magnetohydrodynamics and plasma dynamics. Izv. AN Latv. SSR. Riga. 279.Google Scholar