Numerical Simulation of Supersonic MHD Channel Flows

A compressible magnetohydrodynamic (MHD) model composed of MHD Navier-Stokes (N-S) equations and magnetic induction equations is proposed in the present study for analyzing the magnetohydrodynamic characteristics in MHD generator and MHD accelerator channels of Magneto-Plasma-Chemical propulsion system [10, 11, 12] . A splitting algorithm based on an alternative iteration is also developed for solving the two sets of equations [9] . As a test case, a supersonic MHD flow in a square duct was simulated. The numerical results are compared with the results computed by solving the classical N-S equations for the perfect gas flow, together with the results computed utilizing the degenerate MHD N-S equations for the same channel flow with constant applied magnetic field. The thermo-electro-magnetic performances of the test cases with constant and variable applied fields are then discussed Nomenclature B = Magnetic field strength M = Mach number µ = Viscosity m µ = Magnetic viscosity p = Pressure ρ = Density e R = Renauld number σ R = Magnetic Renauld number b R = Magnetic force number T = Temperature t = time U = Velocity u = X component of velocity v = Y component of velocity w = Z component of velocity