A three-dimensional mathematical model of electromagnetic casting and testing against a physical model: Part II. Results
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I.
INTRODUCTION
P A R T I of this two-part series described a three-dimensional (3-D) mathematical model for electromagnetic casting of metals as is currently widely practiced for aluminum. The model exploited the horizontal nature of induced currents in the metal to arrive at a fast algorithm for computing the electromagnetic fields and forces. The latter shape the molten metal surface (meniscus) as well as cause melt flow at the periphery of the metal pool. Consequently, the electromagnetic field calculations are iterative ones, where the meniscus is adjusted followed by recomputation of the field. After convergence, the electromagnetic forces can be used to compute the turbulent recirculating flow o f the metal using a k-e model for turbulence. In the present article, a physical model, designed to test the mathematical modeI, is described. Probes were used to measure electromagnetic fields, meniscus shapes, and melt flow in the model. II.
THE PHYSICAL M O D E L
The physical model was intended to provide measurements for a comparison with the predictions of the mathematical model described in part I. The mathematical model predicts electromagnetic fields, melt surface shape, and electromagnetically driven flow and does not include heat transport and solidification. Consequently, the physical model excludes heat transport/solidification but is otherwise intended to mimic, with safe, readily available materials, the electromagnetic phenomena of a real caster (Table I). Figure 1 is a schematic diagram of the apparatus. A more detailed picture of the "caster" part appears in Figure 2, and the dimensions are shown in Figure 3. The solidified aluminum was represented by a block of aluminum bronze
D.P. COOK, Mathematical Modeler, is with the Reynolds Metals Co., Richmond, VA 23261. S. NISHIOKA, Engineer, is with the Materials and Processing Research Center, NKK Corporation, Kawasaki 210, Japan. J.W. EVANS, Professor of Metallurgy, is with the Department of Materials Science and Mineral Engineering, University of California, Berkeley, CA 94720. Manuscript submitted April 4, 1994, METALLURGICAL AND MATERIALSTRANSACTIONSB
(176-ram square in section, as seen from above). Into the top surface of this block an inverted pyramid was machined (to a depth of 80 mm) in order to simulate the solidification front. A collar, fabricated from phenolic resin, was positioned at the top of the aluminum-bronze block. The collar contained a pool of molten Wood's metal alloy (50 wt pct bismuth, 25 wt pct lead, 12.5 wt pct tin, and 12.5 wt pct cadmium, melting point 353 K). Surrounding the top of the block was a horizontal inductor connected via a transformer to a 3-kHz power supply. Current in the inductor was measured by a current transformer. In most experiments, a screen was positioned between the inductor and the Wood's metal. The vertical positions of the inductor and screen were independently adjustable. The inductor, screen, and aluminum-bronze block were water-cooled. The experimental measurements were carried out using various p
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