Heat and fluid flow phenomena in a levitation melted sphere under zero gravity conditions
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Heat and Fluid Flow Phenomena in a Levitation Melted Sphere under Zero Gravity Conditions
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N. EL-KADDAH and J. SZEKELY In a previous paper we presented a formulation and computed results describing the electromagnetic force field, the velocity field, and the temperature field in a levitated metal droplet.~The theoretical predictions were found to be in reasonable agreement with experimental measurements regarding the lift force, the mean temperature; furthermore, the predicted velocities were comparable to those estimated on the basis of visual observations. The purpose o f this communication is to report on the extension o f these calculations to the consideration o f systems under zero gravity. While the formulation and the computational procedure employed were the same as described in the previous paper the significant differences in the computed results, as caused by the zero gravity environment, are thought to warrant their publication. In the presentation of the computed results emphasis will be placed on the application o f theseto the interpretation o f previous experimental measurements, notably the SPAR 1 series and on their use in the design o f the Space Shuttle experiments, which involve scale-up. In the SPAR 1 experiments 2 zero gravity (actually 10--~ g) conditions were produced for brief time periods, say 5 to 7 minutes, by using a rocket. In the studies beryllium spheres, 9 mm in diameter were levitated, using a spherical coil, sketched in Figure 1. The coil was made of copper tubing, 2.5 mm in diameter. The coil consisted o ftwo turns, each hemisphere wound on a 16 mm diameter sphere. The azimuthal angles formed by the two turns of the coil were 46 deg and 74 deg, respectively. The power supply was a 107 kHz radio frequency generator, which drew 1.2 kW, DC from a battery. The coil current was 300 A and it was estimated that a power absorption rate of about 46 watts produced a mean sample temperature o f 1400 °C. Figure 2 shows the computed electromagnetic force field and the heat generation pattern, while Figure 3 shows the computed velocity and temperature fields. It is of interest t o compare these predictions with the previously published velocity and temperature fields, computed for earthbound conditions, for a 6 mm diameter steel sphere, given in Figure 4. It is seen that vigorous circulation exists in both cases, but for the zero gravity case we have four, rather than two recirculating loops in each half sphere. This significant difference between the two flow patterns is not due to the absence of gravity, but rather attributable to the difference in coil configuration and the actual position o f the sphere N. EL-KADDAH is Associate Professor in the Department of Mining, Petroleum, and Metallurgy, Cairo University, and is currently on sabbatical leave at MIT. J. SZEKELY, Professor, Materials Engineering, is with Massachusetts Institute of Technology, Cambridge, MA 02139. Manuscript submittedJanuary 18, 1983.
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