Computing the Dynamic Interaction of Magnetic Fields and Turbulent Conducting Fluids in Metals Processing

"Magnetic fields have many actual applications in the metals processing industry. Externally applied magnetic fields give rise to electromagnetic (Lorentz) forces formed by the cross product JxB, between the induced current density J and the magnetic field density B. When the metal is in liquid form, the Lorentz force generates motion in the fluid which in applications of practical interest becomes turbulent. In modelling terms, the Lorentz force appears as a source in the momentum equations. In addition, the induced current generates heat (Joule heating) in the metal that is in proportion to J2, with a corresponding source of heat in the energy equation. Whether as heat or as a force, these effects represent action at a distance - a most useful attribute when dealing with hot metal. The Lorentz force is used to stir solidifying alloys, pump liquid metal in conduits, dampen the flow in the meniscus of a continuous caster, levitate metal drops, induce artificial gravity conditions in suspensions or contain liquid metal. Elsewhere, the Lorentz force may be a by-product of some other operation, so leading to wave excitation in aluminium electrolysis cells, or altering the shape of the weld pool in arc welding. Joule heating is most commonly used with applied AC fields, to melt metal in induction furnaces.The author and his colleagues have been involved in the modelling of most of these processes in the past decade. Modelling is not however straightforward, since most of the examples mentioned represent genuine multi-physics challenges. There is a strong coupling between the flow field and electromagnetic field. The addition of a dynamically varying metal free surface and the moving solidus front means the flow, heat and electromagnetic fields need to be computed simultaneously. In situations involving metal containment, the metal free surface position is governed by the interplay of gravity, Lorentz force, surface tension and fluid inertia. Since all the interesting effects often happen in thin boundary layers at the surface due to the skin effect, mesh generation and mesh control during the computation become non trivial problems that need to be addressed. This paper presents a review of numerical methods used to model droplet levitation, semi-levitation melting and cold crucible induction melting of metals. The first method is based on spectral collocation techniques and the second is the traditional FV approach. Steps taken to validate the computations and typical transient results are also given."