Transverse Velocity Effect on Hunt’s Flow

Benchmark solutions for the validation of magnetohydrodynamic (MHD) codes are of great importance in the development of MHD solver. Hunt's case II is recommended as a benchmark case to validate MHD codes related to fusion applications. Hunt's analytical solution is based on 2-D fully developed laminar flow assumption, which means that the velocity vector has only the flow direction component. In this paper, Hunt's case II has been numerical simulated to investigate the transverse velocity effect using a 3-D MHD solver developed in OpenFOAM environment. A wide range of Hartmann numbers, Reynolds numbers, and wall conductance ratios is tested. Our results show that the 2-D assumption becomes invalid when the transverse velocity is over the order of 10
^-3
. Therefore, the analytical solution is not suitable for the validation of MHD duct flow at high Reynolds numbers.