Numerical investigation of MPD thrusters using a density-based method with semi-discrete central-upwind schemes for MHD equations

Abstract

The magnetohydrodynamic (MHD) equations which combines the Navier-Stokes equations with the Maxwell equations are essential for the investigations of many research areas as earth's core modelling, metal casting, fusion devices and electrical and aerospace devices. In the present work, the central-upwind schemes proposed by Kurganov, Noelle and Petrova for hydrodynamics are extended and combined with the divergence cleaning method of Dedner in order to investigate the performance of the self-field and applied magneto-plasma dynamic thrusters which still involving some outstanding problems. This new algorithm is developed for the single temperature, ideal and resistive MHD equations in a finite volume discretization framework with Gaussian integration. The electrical conductivity is predicted according to the Spitzer-Härm formulation and the real gas ratio of specific heats proposed by Sankaran is implemented for higher discharge current. To improve the quality of the solution, the limiter function of first and second order interpolation scheme is used. The accuracy and the robustness of the obtained solver are demonstrated through numerical simulations of ideal MHD benchmark problems. first, the ability of the developed code to handle shocks, rarefactions and contact discontinuities is tested with the Brio-Wu shock-tube problem. The Minmod and the Van Albada limiter functions has been found to perform better than the other limiter used and the obtained results agree well with both the analytic and the simulations results of previous work. Secondly, the complex and multiple shock interactions and the transition from smooth to turbulent flow involved in the Orszag-Tang vortex problem is well described by the present code and the comparison with the WENO-5 scheme of Shen shows good agreement. Lastly, The ability to described the interaction of an denser cloud with a MHD shock is tested by simulating the 2D cloud-shock interaction problem. The main phases of the interaction are well captured by the solver and the temporal progression of the density contour is in accordance with those obtained by Xisto. The ability of the developed resistive solver to deal with plasma flow acceleration is tested by simulating the well experimental investigated thrusters: The full scale benchmark thruster and the extended anode thruster of Princeton. The results show good agreement with the experimental and simulations results of previous work for discharge current less than the critical current just before the beginning of the onset phenomenon. Simulations are also conducted on the Villani-H thruster to determine the effect of geometric changes over the thruster performance and a first designing attempts is proposed according to the stability analysis. Confident with the results obtained with ideal and resistive MHD problems, the present code is extended to applied-field MPD thrusters. The purpose is to achieve a high thrust level required for space missions with less input power than with self-field MPD thrusters and thus avoid the onset instabilities. For the verification of the code, the NASA Lewis Research Center's (NASALeRC) MPD thruster is chosen because of its wide range of experimental data bank. The method presented reproduce the theory of thrust production and plasma acceleration. Some difficulties as the limitation of the maximum rotational speed and the depletion of the plasma density on the anode surface have been captured. Moreover, the present density-based method compares very well with experimental data of Myers and simulations of Mikellides.