A mathematical model for the dynamic behavior of melts subjected to electromagnetic forces: Part II. Measurement of surf
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I. INTRODUCTION
THE development of a mathematical model for the dynamic behavior of a cylindrical pool of molten metal within an axisymmetric electromagnetic field was described in Part I[12] of this two-part series of articles. The model entailed first the solution of the field equations (Maxwell’s equations and Ohm’s law) to obtain the magnetic field, electric field, induced currents, and electromagnetic body forces. The field equations were solved using a “modified hybrid method” and finite differences. The forces were then used in the fluid flow equations to compute the flow of metal and the behavior of the free surface of the melt. The continuity and Navier–Stokes equations were solved in their instantaneous (rather than the more usual time averaged) form by making an assumption concerning the anisotropy of the turbulence. These fluid flow equations were solved using an explicit finite difference method. At each time-step, the position of the free surface was recomputed, as was the electromagnetic field. In Part I, the model was tested against the experimental measurements of Vive`s and Ricou,[1] Taberlet and Fautrelle,[2] and Fukumoto et al.,[3] with satisfactory results. However, those measurements are quasistatic measurements, rather than dynamic ones, and Part II describes an experimental apparatus that was used to measure the dynamic behavior of a mercury pool, in particular, free surface motion, subjected to an electromagnetic force. II. EXPERIMENTAL APPARATUS AND PROCEDURE Figure 1 is a diagram of the experimental apparatus used in this investigation. It consists of a mercury pool in a thinwalled stainless steel vessel surrounded by a multiturn coil R. KAGEYAMA is with Nippon Steel Corporation, Bangkok 10330, Thailand. J.W. EVANS, Chancellor’s Professor, is with the Department of Materials Science and Mineral Engineering, University of California, Berkeley, CA 94720. Manuscript submitted May 7, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS B
connected to a 3 kHz power supply. Coil current was measured using a current transformer based device (Tektronix A621), and the maximum current achievable was approximately 600 A (rms). At that current, the computed maximum magnetic flux density (absolute value of !Br2 1 Bz2) at the surface of the mercury pool was 0.074 tesla. The vessel was closed by a glass lid and constantly purged with argon to minimize oxidation of the mercury. It was contained within an outer plastic vessel with a flow of cooling water between the two. The position of any point on the surface could be measured by means of a Polytec laser vibrometer (OFV/ OFD). This device measured the Doppler shift of a laser beam reflected from the melt surface. A lens focused the reflected beam onto the sensing element of the laser vibrometer so as to minimize sensitivity to surface orientation. The electronic circuitry of this instrument interpreted the Doppler shift as a surface velocity and integrated the velocity to obtain displacement. The analog displacement signal was then digitized using a Tektron
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