Analysis and Finite Element Simulation of MHD Flows, with an Application to Liquid Metal Processing

"We present a novel approach to the mathematical analysis and computational simulation of fully three-dimensional, nonlinear, viscous, incompressible MHD flow in complex configurations involving several liquid and solid conductors. Such configurations arise in numerous metallurgical processes. Employing the current density rather than the magnetic field as the primary electromagnetic variable, it is possible to avoid artificial or highly idealized boundary conditions for electric and magnetic fields and to account exactly for the electromagnetic interaction of the flow region with the surrounding space. In addition, the approach lends itself naturally to finite-element based discretization techniques. As an application, we simulate the stationary flow of an electrically conducting fluid around a solid spherical particle of arbitrary conductivity, in the presence of crossed uniform electric and magnetic fields, and compute the Lorentz, pressure, and viscous forces exerted on the particle. This problem arises in connection with the electromagnetic filtration (purification) of molten metals before the casting stage.IntroductionNumerous metallurgical processes are governed by MHD effects resulting from the macroscopic interaction of liquid metals with applied or induced currents, electric and magnetic fields. Frequently these effects are technologically exploited in order to drive or to control the flow of metallic melts. Typical examples include the electromagnetic stirring of molten metals before the casting stage [1]; electromagnetic turbulence control in induction furnaces [2]; electromagnetic damping of buoyancy-driven flow during solidification [3]; and the electromagnetic shaping of ingots in continuous casting [4]."