Mathematical modeling of electromagnetic field, free surface, heat transfer, and fluid flow phenomena in electromagnetic confinement systems

The use of electromagnetic fields in materials processing has evolved over the years from mere simple utilization of the electric energy to more sophisticated use of electromagnetic forces. Electromagnetic confinement of molten metal is one such application and is finding wide use in melting and casting processes such as electromagnetic casting (EMC) and magnetic suspension melting (MSM). These systems are characterized by four coupled phenomena-electromagnetic field, free boundary, heat transfer, and fluid flow. Development of a fundamental understanding of these phenomena is of scientific and practical importance. This dissertation attempts to provide insight into these phenomena in melting and casting processes through mathematical modeling.; A methodology has been developed for solving the coupled electromagnetic field, free surface dynamic, heat transfer, and fluid flow equations in arbitrary two dimensional irregular shapes without regridding the solution domain during the search for the equilibrium meniscus shape. This methodology is based upon the solution of the governing equations in a fixed computational domain using a variable non-orthogonal coordinate transformation. Within this framework, a general computer algorithm is developed for simulating electromagnetic confinement systems. The technique of mutual inductance is used for computing the electromagnetic field, while control volume technique is used for calculating the temperature and velocity fields in the metal. The equilibrium shape is determined from the balance of normal stresses on the free surface using an efficient computer algorithm. The developed computer program was critically tested by comparing numerical predictions against laboratory measurements, regarding meniscus shape, fluid velocity, turbulent properties, and temperature distribution in the metal.; Analysis of electromagnetic casting of aluminum using the model showed that confinement and solidification of the molten pool depend on the inductor current and casting speed. Analysis of the MSM showed that the shape of the molten pool depends on the extent of melting, and that the flow in the molten pool is turbulent. Melt shape was found to depend on the coil current, and to be independent of coil frequency and electrical conductivity of the metal. The latter parameter had a more pronounced effect on electrical energy dissipation in the metal, and, hence, melting time.