Liquid-metal flows in sliding electrical contacts with arbitrary magnetic-field orientations

In certain situations, liquid-metal sliding electrical contacts for high-current and low-voltage electrical machines may prove a viable alternative to solid metal brushes. Before it can be ascertained whether such an option is feasible, the problems inherent in a liquid-metal flow through a narrow gap between a fixed and a moving surface with free surfaces beyond each gap end must be explored. The flow occurs in the presence of an arbitrarily, oriented magnetic field. By assuming that the secondary flow is negligible, the problem reduces to a fully developed magnetohydrodynamic (MHD) duct flow problem. In the parameter range presented here, the liquid-metal flow can be laminar or turbulent, requiring that both regimes be analyzed. The numerical results from the mathematical model presented herein for laminar flow with arbitrary Hartmann number M and with arbitrary magnetic-field orientation indicate that, even with an O(1) Hartmann number, the flow is already beginning to evolve into the distinct regions predicted by the asymptotic solution for M»1 derived from singular perturbation theory. However, the actual velocity and electric potential distributions only agree approximately with those predicted by the large M asymptotic solutions. The numerical results presented in this work for the turbulent MHD flow are profoundly different from then corresponding laminar counterparts. Velocity magnitudes are significantly reduced in the turbulent MHD flows, and as a consequence, the magnitude of the current density increases. Thus, according to the mathematical model presented in this paper, liquid-metal sliding electrical contacts in external magnetic fields appear to transport current more efficiently in the turbulent regime than the laminar regime under the conditions of the calculations.