Numerical simulation of 3D magnetohydrodynamic liquid metal flow in a spatially varying solenoidal magnetic field

•Liquid metal flow in non-uniform magnetic field shows 3D magnetohydrodynamic effects.•Consistent and conservative formulation for spatially varying magnetic field.•Incoming turbulent flow transforms into magnetohydrodynamic laminar steady-state.•Thick pipe walls are numerically resolved for computation of electric potential. Motivated by experiments currently under investigation in the MEKKA laboratory at KIT, numerical simulations have been performed for a liquid metal pipe flow entering a strong magnetic field. Magnetohydrodynamic (MHD) flows in non-uniform magnetic fields are relevant in blanket engineering, in regions where the liquid breeder PbLi enters or exits the magnetic field confining the fusion plasma. Simulations provide insight into 3D phenomena near the non-uniform region of the magnetic field in particular velocity distribution and electric current pattern that cannot be directly observed in the experiments. Moreover, simulations describe the transition from a highly turbulent hydrodynamic entrance flow to a fully established laminar MHD flow. The present work addresses in particular a conservative formulation of the magnetic field, generation and decay of inlet turbulence by means of direct numerical simulation, as well as fluid–wall interaction by electric currents that are exchanged between the liquid metal and the thick electrically conducting pipe wall.