Magnetohydrodynamic flows in a channel-induction furnace
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I.
INTRODUCTION
Tr E channel-induction furnaces are employed for melting and holding a wide range of metals and alloys. From an electrical standpoint, these furnaces may be considered as 60 (or 50) Hz transformers and constitute a typical case of process founded on the induction laws. The action of an induction electromagnetic field inside a crucible is summarized in terms of thermal effects (melting, followed by holding at the liquid state) caused by the Joule dissipation and in terms of hydrodynamic phenomena (motion of the bath) generated by the rotational part of the Lorentz forces. The first theoretical works dealing with inductively stirred metallic melts were carried out by Evans and coworkers t1'2[ and Szekely and co-workers t3'4] on coreless induction furnaces. The approach to the problem was to solve the Maxwell's equations in order to obtain an expression for the electromagnetic body force throughout the melt. Then, detailed maps of both the velocity field and of the turbulence parameters were obtained by integration of the Navier-Stokes equations, including the electromagnetic force, and use of either the k-W or k-e codes. Although these pioneering investigations were performed for the case of relatively simple geometries, their impact on the widespread applications of induction stirring in ferrous and nonferrous processing was invaluable. As a matter of fact, these calculation techniques became more and more sophisticated, [5,61 resulting in a good understanding of the electromagnetic and fluidflow phenomena characterizing the inductively stirred melts. As a result, the performances of several major casting technologies, such as the electric arc furnace, electromagnetic casting, the casting refining electromagnetic process, and the like, were improved and optimized through an extension of these mathematical models. [7-12] The channel furnace consisted originally of a primary
CHARLES VIVI~S, Professor, and RENI~ RICOU, Assistant Professor, are with the Laboratoire de Magnrtohydrodynamique, Universit6 d'Avignon, 33, rue Louis Pasteur, 84000 Avignon, France. Manuscript submitted May 29, 1990. METALLURGICAL TRANSACTIONS B
induction coil wound around an iron core, while a shortcircuited secondary consisting of a single turn of molten metal formed a hydraulic loop which was called a channel. Later, another inductor was developed with two primary coils surrounding a common core, while the molten secondary consisted electrically of two single turns flowing together into a common central channel (Figure 1). Several detachable inductors may be connected to the lower portion of a larger vessel which contains the bulk of the melt. This design was developed to meet increasing melt-rate requirements. As an example, for the case of a unit composed of six inductors and with a rating of 9000 kW, the loading capacity can reach 50 or more tons of aluminum alloy, with a melting rate on the order of 15 tons/h. The overall electrical efficiency of this process (75 pct) is better than that of the coreless-induction furna
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