Numerical Characterization of a Liquid Metal Magnetohydrodynamic Alternate Generator in the Laminar-Regime under Inductionless Approximation

The performance characterization of a liquid metal magnetohydrodynamic alternate generator is numerically investigated via its electric isotropic efficiency. The model consists of a harmonically driven liquid metal oscillatory flow confined to a thin-walled closed rectangular duct interacting with a uniform magnetic field transverse to its motion and attached to a load resistance. Spectral collocation method is used to solve the properly boundary-conditioned Navier-Stokes equation under inductionless approximation for the magnetic field with implementation of gradient formulation for the electric field. Flow is considered fully developed in the direction perpendicular to the applied uniform magnetic field (i.e., motion direction), incompressible, viscous, and laminar in regime. Currently, there are neither purely analytical or experimental results on this problem, but ours were cross-referenced with those from a one-dimensional analytical model as close as possible to it, finding reasonable correspondence. Dimensional estimates on the power production of prospective mesoscale devices having in mind household application are provided for different liquid metals as well.