Simulation of three-dimensional nonideal MHD flow at low magnetic Reynolds number

Abstract

A numerical procedure based on a five-wave model associated with non-ideal, low magnetic Reynolds number magnetohydrodynamic (MHD) flows was developed. It is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential of flow field. To validate the developed procedure, two different test cases were used which included MHD Rayleigh problem and MHD Hartmann problem. The simulations were performed under the assumption of low magnetic Reynolds number. The simulated results were found to be in good agreement with the closed form analytical solutions deduced in the present study, showing that the present algorithm could simulate engineering MHD flow at low magnetic Reynolds number effectively. In the end, a flow field between a pair of segmented electrodes in a three dimensional MHD channel was simulated using the present algorithm with and without including Hall effects. Without the introduction of Hall effects, no distortion was observed in the current and potential lines. By taking the Hall effects into account, the potential lines distorted and clustered at the upstream and downstream edges of the cathode and anode, respectively.