Mathematical modeling of flows in large tundish systems in steelmaking
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I.
INTRODUCTION
A tundish is an intermediate vessel used in the manufacture of steel by the continuous casting process. It plays a role both as a distributor of liquid metal from the ladle to mold and. as a removal tank for nonmetallic inclusions. Since the time for inclusions entrained within the melt to be removed is limited, a detailed hydrodynamic description is of primary importance in the optimal design of a tundish. Little information has been published in the open literature on tundish hydrodynamics. Full-scale hydrodynamic experiments in liquid metals are difficult owing to the hostile environment, the opacity of melts, and the very high temperatures involved. Using the approach of water modeling, Kemeny et al. ~ and Heaslip and McLean 2 have studied fluid motion and residence times for various tundish configurations. While good insight can be obtained by such modeling, there are considerable limitations, the most important being related to similitude criteria. Dynamic similitude requires equality of Froude as well as Reynolds numbers between models and prototypes. This is difficult to satisfy for other than full-scale models which can be expensive and somewhat cumbersome. The heat transfer modeling further complicates the problem as it implies satisfying further similitude parameters. Wong 3 developed a mathematical model to study fluid flows associated with heat transfer in a "T" shaped tundish. However, resulting computations were not tested against experiments.
II.
PRESENT W O R K
The objective of the present work has been to develop a three-dimensional calculation procedure for tundish systems. By comparing its performance against experimental data from a water model, its value for predicting the typically complex turbulent flows encountered in actual steelmaking tundishes can be assessed. Thus, a 65 tonne capacity tundish for a twin slab caster arrangement was chosen for K. Y. M. LAI is Research Associate, Department of Mechanical Engineering, Princeton University. M. SALCUDEAN is Professor and Head, Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, Canada. S. TANAKA is Research Engineer, Nippon Steel Corporation, Japan. R.I.L. GUTHRIE is Macdonald Professor, Department of Metallurgical Engineering, McGill University, Montreal, PQ, Canada. Manuscript submitted June 10, 1985.
METALLURGICAL TRANSACTIONS B
study. This corresponds to recent large-scale equipment used in the industry (Nippon Steel, Oita Works), the basic industrial configuration being shown in Figure l(a). Characteristic internal dimensions for the prototype tundish, as well as for the rectangular 1/6 scale model, are provided in Table I. Scaling procedures were carried out based on Froude criterion. Thus, for a flow of molten steel of 11.75 tonnes/ min, the corresponding water flow-rate in a one-sixth scale model was 19 liters/min. Further comments on the validity of Froude modeling are reserved until later, following a discussion of computations for the full-scale system.
III.
EXPERIMENTAL PRO
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