Modeling the dynamics of magnetic semilevitation melting
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I. INTRODUCTION
THE melting techniques for high purity and reactive metal alloys, like titanium aluminides, require avoiding contact with a refractory material crucible. Magnetic levitation melting[1,2,3] is a well-known method for this purpose, yet suffers from disadvantages in terrestrial conditions of the limit in the amount of levitated mass (typically 50 to 100 g) and stability problems.[1,4] However, the pure magnetic levitation method for casting applications could be very successful in microgravity conditions.[3,5,6] The cold crucible technique[7,8] is actually used for this type of melting in industry, offering all the advantages of electromagnetic liquid metal processing and avoiding the crucible wall contact with the liquid metal. Several kilograms of metal are melted and levitated in the cold crucible experiment.[8] However, the water-cooled crucible sections make the process inherently inefficient. A compromise between the levitation and cold crucible methods is known as magnetic semilevitation or suspension melting,[9] which uses a water-cooled annular chill block support at the base of the metal charge to be melted. Initially, a solid cylindrical billet is placed on the chill block and a coaxial a.c. coil is gradually lowered as the metal is simultaneously melted, confined, and stirred by the induced electric current and the magnetic field. Finally, the melting front reaches the bottom and the liquid metal pours through the central hole in the chill block to fill the mold. In principle, there is no limit on the mass that can be treated using the semilevitation melting technique. Induction melting was theoretically and numerically studied for many years using different quasimagnetostatic and boundary layer approximations,[2–7,9–13] where the free surface shape is determined by the “magnetic pressure” at the external boundary. In the case of pure levitation melting, relatively high frequencies are typically used (105 to 106 Hz), which justifies the use of the electromagnetic skinlayer based theories.[12,13] However, a typical frequency used in the semilevitation melting process (103 to 104 Hz) is two orders of magnitude lower and the magnetic field penetration is significant (approximately 10 pct of the charge radius in V. BOJAREVICS, Senior Research Fellow, K. PERICLEOUS, Professor, and M. CROSS, Professor and Director of Research, are with the School of Mathematics, University of Greenwich, London SE109LS, United Kingdom. Manuscript submitted July 28, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS B
the computed example case, Figure 1). Moreover, often, the top turn(s) of the source coil are carrying an oppositely directed “stabilizing” current, that leads to a zero tangential magnetic field at a neutral point on the free surface of liquid metal (top part of Figure 2). This neutral point can be a new source of hydrodynamic instability for some coil designs, because no magnetic holding force is exerted there. The magnetic field lines of the current induced in the metal are closing within the interna
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