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

Abstract

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 their 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.

A model for the turbulent Hartmann layer

“…The state of Hartmann layers are also of relevance to the liquid metal flows within sliding electric power contacts; see Ref. 6 where the Reynolds number ͑see Sec. II for the definition of R͒ ranges from about 0.18 to 1.4ϫ10 3 .…”

Theoretical study of anisotropic MHD turbulence with low magnetic Reynolds number

“…Flow of electrically conducting fluid under the influence of a permanent magnetic field continues to be an important subject of scientific research because such flows have important practical utilization in metallurgy (Davidson 2001), in development of cooling blankets for magneto-confinement fusion reactors (Branover et al 1986, Sukoriansky et al 1989, Smolentsev et al 2015, in homopolar motors and generators (Talmage et al 1991) and more. Anisotropization of turbulence characteristics and transport properties in such flows with a tendency to two-dimensionalization under increasing strength of magnetic induction is a well-established fact that is utilized in technology and numerical modeling (Hamid et al 2015).…”