Abstract
The development of a mathematical model for the electromagnetic casting of steel is described. The model is three dimensional and computes the evolution of the electromagnetic field, the turbulent liquid metal flow and the free surface of the metal pool with time. This is achieved by simultaneous solution of the MHD form of Maxwell's equations, Ohm's law, the Navier–Stokes and continuity equations (by large eddy simulation) and an equation for the free surface. Solution is by a combination of finite element (field and flow equations) and finite difference (surface equation) methods on an Eulerian-Lagrangian grid. The model was first tested against measurements, by others, of magnetic fields and induced currents in an apparatus akin to an electromagnetic caster, and then against computations, performed using finite difference methods by other investigators, of laminar flow within a 2D rectangular cavity. The model was also tested against classical equations for the oscillations of a free surface in a rectangular trough and then against measurements, at Nippon Steel Corporation, of the surface oscillations of a mercury pool surrounded by an inductor carrying alternating current. Use of the model to predict the behavior of a steel caster is to be described in a subsequent paper.
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