Modelling the unsteady melt flow under a pulsed magnetic field

A numerical model for the unsteady flow under a pulsed magnetic field of a solenoid is developed, in which magneto-hydrodynamic flow equations decouple into a transient magnetic diffusion equation and unsteady Navier-Stokes equations in conjunction with two equations of the kappa-epsilon turbulent model. A Fourier series method is used to implement the boundary condition of magnetic flux density under multiple periods of a pulsed magnetic field (PMF). The numerical results are compared with the theoretical or experimental results to validate the model under a time-harmonic magnetic field; it is found that the toroidal vortex pair is the dominating structure within the melt flow under a PMF. The velocity field of a molten melt is in a quasi-steady state after several periods; changing the direction of the electromagnetic force causes the vibration of the melt surface under a PMF.