A Comparison of three mathematical modeling procedures for simulating fluid flow phenomena in bubble-stirred ladles
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The authors would like to thank Drs. I. limbo and Alok Sharan (Carnegie Mellon University) for their help in this project.
REFERENCES 1. J. Peace and D. Engledow: lronmaking and Steelmaking, 1987, vol. 14 (5), pp. 248-52. 2. R J . Schmidt: in Recycling of Metals and Engineered Materials, TMS, Warrendale, PA, 1990, pp. 315-32. 3. M. Iwase and K. Tokinori: Steel Res., 1991, No. 6, pp. 235-239. 4. I. limbo, M.S. Sulsky, and R.J. Fruehan: lron Steelmaker, 1988, vol. 15 (8), pp. 20-23. 5. A,W. Cramb and R.J. Fruehan: Iron Steelmaker, 1991, pp. 61-68. 6. J.F. Jordan: U.S. Patent 2,512,578, 1950. 7. T. Imai and N. Sano: Trans. Iron Steellnst. Jpn., 1988, vol. 28, pp. 999-1006. 8. C. Wang, T. Nagasaka, M. Hino, and S. Ban-ya: ISU Int., 1991, vol. 31, pp. 1300-08.
OUt(1-121 in order to simulate, numerically, the hydrodynamics and relevant transport processes associated with ladle refining operations. To date, three different computational procedures have been investigated for the type of problem posed and illustrated in Figure 1. There, a porous plug is shown to release a rising plume of bubbles and entrained liquid, which act to intermix the contents of the vessel, promoting chemical and thermal homogeneity (for steelmaking) and inclusion agglomeration and float-out. From a conceptual stand point, these models can be broadly divided into three categories: (1) a quasi single-phase calculation procedure, l~-4l in which the rising gas-liquid mixture is assumed to be a homogeneous liquid of reduced density. In general, the gas volume fraction within the plume together with the latter's geometry (determined empirically) are specified a priori in the numerical solution scheme. These data constitute the important input parameters for the mathematical model; (2) a Lagrangian two-phase calculation procedure, 17'8l in which the liquid-phase continuity and momentum balance equations are solved simultaneously with an appropriate bubble trajectory equation. The procedure, in contrast to the quasi single-phase models provides estimates of gas voidages as well as the shape/geometry of the bubble plume; and (3) a Eulerian two-phase calculation procedure, popularly known as the two-fluid model, 19-~2] in which the continuity and the momentum conservation equations are solved for a gas as well as the liquid-phase continuum. The two-fluid model provides estimates of gas voidages,
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A Comparison of Three Mathematical Modeling Procedures for Simulating Fluid Flow Phenomena in Bubble-Stirred Ladles DIPAK MAZUMDAR and RODERICK I.L. GUTHRIE Over the last two decades, extensive mathematical modeling of gas-stirred ladle systems has been carried RODERICK I.L. GUTHRIE, MacDonald Professor of Metallurgy, is with the Department of Mining and Metallurgical Engineering, McGill Metals Processing Centre, McGill University, Montreal, Canada. H3A2A7. DIPAK MAZUMDAR, Visiting Professor, on leave from the Department of Materials and Metallurgical Engineering, Indian Institute of Technology, K
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