A compressible magneto hydrodynamic (MHD) model composed of MHD Navier-Stokes (N-S) equations and magnetic induction equations is proposed in the present study for analyzing the magneto hydrodynamic characteristics in the MHD generator and MHD accelerator channels of the Magneto-Plasma-Chemical propulsion system. Baldwin-Lomax turbulence model is utilized. A splitting algorithm based on an alternative iteration is also developed for solving the two sets of equations. 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.

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