Physical modeling of liquid/liquid mass transfer in gas stirred ladles
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INTRODUCTION
D U E to the need for cleaner steels and higher productivity, secondary refining or ladle metallurgy has grown dramatically in the past few years. The ladle metallurgical processes can vary from simple addition of a synthetic slag into the ladle followed by argon bubbling to highly sophisticated arc heated ladle systems equipped with vacuum, powder injection, argon bubbling, and in some cases induction stirring for inclusion removal, desulfurization, dephosphorization, and alloying. The advantages of ladle refining by gas stirring are that its capital cost is low, it enhances inclusion flotation, and it gives good refining efficiency by leading to a faster approach to equilibrium because of a better mass transfer rate between slag and metal. In a gas stirred ladle, bubbles rising through the liquid induce a recirculatory flow of fluid because of the reduced density in a gas/liquid plume. Bubbles may also cause the ejection of small droplets of one phase into the other. Much of the previous work ~-~~on physical and mathematical modeling of gas stirred ladles was concerned with fluid flow and mixing times in the metal. However, the rate-controlling process for most metallurgical reactions such as desulfurization is two phase mass transfer between slag and metal, not one phase mixing as represented by mixing times. The mixing of liquids in metallurgical vessels has been studied to relate the mixing time (~'m) with mixing power density (e). 11-~5'27The mixing time was defined as the time corresponding to the arbitrary level of approach to the final SEON-HYO KIM, formerly Graduate Student in the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, is Assistant Professor with the Department of Metallurgy and Materials Science, Pohang Institute of Science and Technology, Pohang, Kyungbuk, Korea. R. J. FRUEHAN, Professor, is with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213. Manuscript submitted May 12, 1986. METALLURGICALTRANSACTIONS B
steady state concentration. Empirical relationships of the type z,, ~ e" have been proposed, and various values of n have been reported. Asai et al. " and Mazumdar ~3have analyzed theoretically and experimentally these relationships and confirmed their theoretical results by carrying out water model experiments. In separate studies, they agreed that "Cm is proportional to e -~/3 and is dependent on the vessel size in a flow regime predominated by turbulent viscous force. Mazumdar further related the mixing times in the model ladle (~-. . . . de1) to those in full scale systems ('Tm,f.s.) through the geometrical scaling factor for axisymmetrically gas agitated systems using the relationship: "/'re,model ~ 'Tm,f.s. ~ /~ 3/4
The effect of the presence of a slag layer in gas stirred ladles on the mixing time was investigated by Haida et al. 14 and Ying et al. 15In these respective works, they showed that mixing time increases with the presence of s
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