Numerical analysis on magnetic levitation of liquid metals, using a spectral finite difference scheme

A spectral finite difference method is applied to analysis on magnetic levitation as a major unsteady-state problem in magnetohydrodynamics. Vorticity-stream function formulation is introduced in conjunction with Maxwell's equations, and the non-linear term of Ohm's law for a liquid metal is included. For the purpose of analysis treated is a liquid metal occupying a volume such that no shear stresses and no normal velocity components on the free surface are used as dynamic boundary conditions. Externally applied electromagnetic fields consist of no electromagnetic field at infinity and fields produced by circular coils placed horizontally near the liquid metal. Presented are lift force, magnetic fields and flow fields for several parameters. Numerical data for high viscosity on dimensionless force with the dimensionless vertical coil position are qualitatively in good agreement with experimental data for a solid metal [J. Appl. Phys. 23 (1952) 545]. The effects of the Reynolds number, the Strouhal number and the number of the external coil(s) on levitation force, the magnetic field and the flow field are clarified.