Surface-coupled modeling of magnetically confined liquid metal in three-dimensional geometry
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INTRODUCTION
AN alternating magnetic field imposed upon an electrically conducting liquid induces eddy currents within the metal that tend to shield the interior of the liquid from the field. These eddy currents generate heat and can be used to melt metals prior to casting. The interaction of these induced eddy currents with the imposed magnetic field creates a Lorentz force that can be used to confine and shape liquid metal.[1] Magnetic levitation is commonly used in many metallurgical experiments, including measuring surface tension, observing the nucleation and solidification process, and determining the existence of magnetic ordering.[2,3,4] The ability to process liquid metal while minimizing physical contact is of interest to the metallurgical industry, because physical contact introduces impurities and structural imperfections. This interest has led to research in the area of magnetic levitation casting and a patent for a method of melting, confining, and casting a metal using magnetic fields.[5,6] Recently, magnetic levitation has been applied to heated semiconducting material.[7] Further, it has been shown that the microstructure of a casting can be refined by using magnetically driven stirring during solidification.[8] Most of the engineering involved in the development of magnetic systems for material processing has been experimental. The large amounts of energy needed to magnetically process metals has prompted research into ways of more efficiently utilizing this electrical energy, creating a need for general purpose methods of modeling interactions between an applied magnetic field and liquid metal. When the frequency of the applied magnetic field is high enough to justify an assumption that the interior of the liquid metal is completely shielded from the magnetic field, a ‘‘surfacecoupled’’ model is appropriate. In this interaction, the magnetic field exerts a force that can deform the surface of molten metal, while the deformation of the metal affects the structure of the magnetic fields (Figure 1). Fugate and Hoburg[9,10] used a surface-coupled approach CHARLES H. WINSTEAD, Senior Automation Engineer, is with Intel Corporation, Hillsboro, OR 97124. PETER C. GAZZERRO, RF/Analog IC Engineer, is with Qualcomm, Inc., San Diego, CA 92121. JAMES F. HOBURG, Professor, is with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213. Manuscript submitted May 3, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS B
to predict the shape a free metal surface will assume given a configuration of source coils, and to determine the requisite source coil configuration that will produce a desired shape of liquid metal. Their free movement method has been experimentally verified to accurately predict the shape of levitated liquid metal as long as the frequency of the applied magnetic field is sufficiently high.[11,12] Prior to the work described here, the free movement method has only been implemented for two-dimensional configurations. In addition, free surface effec
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