The Calculation of Transport Phenomena in Electromagnetically Levitated Metal Droplets
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MATERIALSPROCESSING IN THE REDUCED GRAVITY ENVIRONMENTOF SPATE Guy E.
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THE CALCULATION OF TRANSPORT PHENOMENA IN ELECTROMAGNETICALLY LEVITATED METAL DROPLETS
N. El-Kaddah and J. Szekely Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 USA
ABSTRACT
A mathematical representation has been developed for the electromagnetic force field, the fluid flow field, the temperature field (and for transport controlled kinetics) in a levitation melted metal droplet. The technique of mutual inductances was employed for the calculation of the electromagnetic force field, while the turbulent Naviet-Stokes equations and the turbulent convective transport equations were used to represent the fluid flow field, the temperature field and the concentration field. The governing differential equations, written in spherical coordinates, were solved numerically. The computed results were found to be in good agreement with measurements reported in the literature, regarding the lifting force and the average temperature of the specimen.
1.
INTRODUCTION
The purpose of this paper is the development of quantitative representation of the electromagnetic force field, fluid flow field, temperature field and of diffusive transport phenomena in levitated metal droplets. The principal motivation for this work is threefold. One of these is the widespread use electromagnetic positioning of metal samples in space processing experiments, thus the real need for information concerning transport phenomena both for the rational design of experiments and for the interpretation of measured data. Additional interest in such work is provided by the extensive use of levitation melting in ordinary, ground based experiments, particularly for kinetic studies, where knowledge of the velocity and the temperature fields in the melt should of course be very helpful in the interpretation of rate data. Finally, levitation melted systems represent a very interesting class of systems from the fundamental standpoint, involving, turbulent electromagnetically driven transport phenomena in a spherical coordinate system, which have received very little attention up to the present. Previous work in the area of levitation melting may be divided into two categories, namely experimental studies concerned with physico-chemical measurements at high temperatures, which did not Consider transport phenomena in the melt on the one hand, [1] and purely electrodynamic work, concerned with the calculation of the lifting force on the other [2]. The principal purpose of the present paper is to develop the theoretical framework for combining the electrodynamic and the transport aspects of this problem. 2.
FORMATION
Let us consider a metal droplet levitated between two opposing coils, through which a current is being passed, as sketched in Fig. 1, which also shows the coordinate system employed. The passage of the current through the coils will generate an electromagnetic force field which will hav
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