A new method for three-dimensional numerical simulation of electromagnetic and fluid-flow phenomena in electromagnetic separation of inclusions from liquid metal

The magnetohydrodynamic (MHD) flow around a suspended particle in a liquid metal subjected to electric and magnetic fields can affect the force exerted by the applied electromagnetic field on the particle. In this article, a novel approach to the computational simulation of three-dimensional nonlinear MHD flow in two-phase systems is proposed. The electromagnetic field in the conducting fluid, including the particle, is represented using the current vector potential (T) and reduced magnetic scalar potential ( Psi ) to avoid the discontinuity of the electric field at the fluid-particle interface. To avoid the solution of the electromagnetic field in free space and to account exactly for the electromagnetic field interactions with the fluid and the particle, the electric and magnetic fields are specified at the boundary of the fluid-flow domain using Ampere's law. This formulation permits the numerical solution of the coupled electromagnetic and fluid-flow equations on a common mesh. The discretized equations are derived using a finite-element formulation, and an iterative procedure is described for the efficient solution of these equations. This method is used to investigate the electromagnetic and fluid flow phenomena in electromagnetic separation of a nonconducting spherical particle in crossed uniform electric and magnetic fields at intermediate Hartmann numbers. The computed results show that the magnetic field has no effect on either the velocity field or the net force on the particle when the Hartmann number is less than 1. Beyond this threshold value of the Hartmann number, the velocity decreases almost linearly with increasing magnetic-field strength. The damping of the flow by the magnetic field manifests itself in a reduction of the separation force, even though it is relatively small for this system.