Magnetohydronamic and thermal behavior of electroslag remelting slags
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electroslag remelting (ESR) operation. The model assumes axisymmetrical geometry and steady state. Maxwell equations are first solved to determine the electromagnetic forces and Joule heating. Next, coupled fluid flow and heat transfer equations are written for the two liquids (slag and liquid metal). The k-e model is used to represent turbulence. The system of coupled partial differential equations is then solved, using a control volume method. Using the operating parameters as inputs, the model calculates the current density, velocity, and temperature throughout the fluids. This paper is concerned with fluid flow and heat transfer in the slag phase. After being validated by comparing its results with experimental observation, the model is used to evaluate the influence of operating variables, such as the fill ratio, and the thermophysical properties of the slag. I.
INTRODUCTION
DURING the last 30 years, the important development of consumable electrode remelting processes has lead to numerous mathematical modeling studies. The work presented here follows along this path and is aimed at allowing numerical simulation of the electroslag remelting (ESR) operation. A schematic diagram showing the principle of the ESR process is given in Figure 1. A consumable electrode is remelted through a slag into an ingot mold. The passage of an electric current melts the end of the immersed electrode by resistance heating in the slag. The remelted alloy cools and solidifies on contact with the mold walls. The metallurgical properties of the remelted ingot are directly related to the solidification process, which strongly depends on hydrodynamic and thermal conditions in the liquid pool and the mushy zone. On the other hand, fluid flow and heat transfer in the slag phase influence the electrode melting process and, thus, the energy efficiency of the operation. Mathematical modeling often offers an efficient approach for analyzing this kind of process, in which several coupled physical phenomena (electromagnetic effects, fluid flow, heat transfer, phase changes, etc.) occur. The work performed at Ecole des Mines in Nancy, in collaboration with Imphy S.A., is composed of two complementary steps: (1) The development of a transient-state thermal model of the ingot enables determination of the local solidification conditions, m This model, similar to that of Ballantyne and Mitchell, tEl can predict the liquid pool depth and also the cooling rate at any place in the ingot. Unfortunately, such models require the introduction of adjustable parameters, such as the temperature profile at
A. JARDY, Research Associate, Centre National de la Recherche Scientifique (CNRS), and D. ABLITZER, Professor, are with the Laboratoire de Science et G6nie des Mat6riaux M6talliques (URA 159 CNRS), Ecole des Mines, 54042 Nancy Cedex, France. J.F. WADIER, formerly with Imphy S.A., is Head of the Ugine Research Centre, Compagnie Europ6enne du Zirconium CEZUS, 73400 Ugine, France. Manuscript submitted June 13, 1988. METALLURGICAL TRANSACTIONS B
the slag/li
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