Reconstruction of 3D MHD liquid metal velocity from measurements of electric potential on the external surface of a thick-walled pipe

Abstract Liquid metal magnetohydrodynamic pipe flow experiments have been performed in a non-uniform strong magnetic field in order to get further insight into the physics of this type of three-dimensional MHD flow and to enlarge the database for validation of numerical tools. In these experiments, in addition to measurements of the axial pressure distribution, the electric potential has been recorded at a large number of axial and circumferential positions by probes distributed around the periphery of the pipe. Since the wall of the pipe is relatively thick, the electric potential varies across the wall thickness, and surface potentials differ from those at the fluid-wall interface. However, the dense population of potential sensors on the pipe surface allows for a reconstruction of data on the fluid-wall interface, from which we can determine components of potential gradient in the fluid in a plane perpendicular to the magnetic field. The latter ones are closely related to the velocity field, because the electric potential may serve as approximate streamfunction of the flow.