Numerical Simulation of 2D Supersonic Magnetohydrodynamic Channel and Study on Hall Effect

In this research effort, numerical simulation of two-dimensional magnetohydrodynamic (MHD) channel is performed and Hall effect is studied. The computational model consists of the Navier-Stokes (N-S) equations coupled with electrical-magnetic source terms, Maxwell equations and the generalized Ohmʹs law. Boundary conditions for the electrical potential equation considering Hall effect are derived. To start with, the MHD channel with single-pair electrodes is studied and flow of the electric current is in accordance with physical principle. Then the MHD channel with five-pair electrodes is numerically simulated. The results show that the electrical current concentrates on the downstream of the anode and the upstream of the cathode due to Hall effect, and the flow field becomes asymmetrical. At the current value of the magnetic interaction parameter, the electrical-magnetic force affects the flow remarkably, decreasing the outlet Mach number and increasing the outlet pressure; whatʹs more, the flow structure in the channel becomes extremely complex. Performances of MHD channels with continual electrodes and segmented electrodes are compared. The results show that performance of the MHD channel with segmented electrodes is better than that with continual electrodes with the increase of Hall parameter.