Computational modelling of an electromagnetic system for separation of solid inclusions from molten aluminum

Mathematical models and numerical solution methods for the computer simulation of solid particle trajectories in flows of molten aluminum subjected to steady, uniform, electric and magnetic fields are presented in this thesis. The underlying subject is electromagnetic (EM) filtration of molten metals.Attention is focused on steady, laminar, fully developed flows of molten aluminum inside a straight separation chamber of uniform rectangular cross-section. The walls of this chamber are assumed to be electrically non-conducting. The investigation is limited to solid inclusions (particles) that are electrically non-conducting and have an effective diameter in the range 5 mum to 100 mum. Steady, uniform, electric and magnetic fields are prescribed, and the induced currents are assumed to be negligible.Mathematical models of three-dimensional parabolic (developing) and fully developed flows of molten aluminum in the separation chamber are provided, nondimensionalized, and discussed. A rudimentary model of the magnetohydrodynamic (MHD) flow is proposed, in which Maxwell's equations are decoupled from the Navier-Stokes equations. The particle momentum equation is presented, nondimensionalized, and discussed in detail.The fluid flow problem is solved using a control-volume finite element method (CVFEM). The particle momentum equation is solved using a fourth-order Runge-Kutta (RK) method. An efficient method is proposed for locating the particle in the finite element mesh during the RK integration of the particle momentum equation.The proposed methods are applied to four test problems, and the results are compared to those obtained using analytical and numerical solutions available in the literature. Finally, the scope of the proposed methods and some of the possibilities they offer are explored by applying them to a simple electromagnetic system for the separation of solid inclusions from molten aluminum