Numerical simulation of thin-film MHD flow for nonuniform conductivity walls

Liquid metals offer unique properties and their use in a nuclear fusion reactor, both as confined flows and free surface flow, is widely studied in the fusion community. The interaction between this conductive fluid and the tokamak magnetic fields leads to Magnetohydrodynamic (MHD) phenomena that influence the flow features. To properly design components that employ liquid metals, it is necessary to accurately predict these features and, although the efforts made in development, a mature code specifically customized to simulate MHD flows is still unavailable. In this work, the general purpose computational fluid dynamics code ANSYS CFX 18.2 is validated for MHD free surface thin film flow with insulated walls, up to Ha=1000 and for several values of the characteristic width/thickness ratio, comparing the results with the theoretical relation available in the literature. For all the cases considered, the maximum integral error is found below 10 %. Successively, the validated code is used to investigate the MHD flow in a chute with a characteristic film ratio equal to 0.1 and for Ha=300. Uniform and non-uniform wall electrical conductivity cases are considered with the latter modeled by placing on the side walls and on the back wall localized regions with different conductivity. The electrical conductivity of the back wall is found to have a negligible effect on the global flow when the lateral wall in insulated, similarly to what is observed for the analogous bounded flow. Contrariwise, an electrically conductive lateral wall is found to enhance the free surface jet and to modify the Hartmann layer structure.