Proceedings of ASME 2013 International Mechanical Engineering Congress & Exposition IMECE 2013 November 15-21, 2013, San Diego, California, USA IMECE2013-63144 DRAFT:NUMERICAL MODELLING OF ELECTRODE GEOMETRY EFFECTS IN A 2D SELF-FIELD MPD THRUSTER Carlos M. Xisto ∗ Departamento de Engenharia Electromec ˆ anica Universidade da Beira Interior Covilh ˜ a 6201-001 Portugal Email: xisto@ubi.pt Jos´ e C. P ´ ascoa Paulo J. Oliveira Departamento de Engenharia Electromec ˆ anica Universidade da Beira Interior Covilh ˜ a 6201-001 Portugal pascoa@ubi.pt; pjpo@ubi.pt ABSTRACT A self-field MPD thruster in its most basic form consists in a central cathode surrounded by a concentric anode. With this coaxial geometric shape is very difficult to use experimental tech- niques to visualize the plasma parameters. In the following pa- per we intend to present some preliminary results for a 2D self- field MPD thruster obtained with a new algorithm developed for solving the resistive magnetohydrodynamics (MHD) equations. The numerical method is based on the well known PISO algo- rithm and make use of AUSM-MHD scheme for flux calculation. NOMENCLATURE B Magnetic field vector. B Magnitude of the magnetic field vector. E Electric field vector. e t Total energy. F Momentum Thrust. F ELM Electromagnetic component of Thrust. F Term Thermal component of Thrust. g 0 Acceleration of gravity. Ha Hartmann number. I spec Specific impulse. j Electric current density. k B Boltzmann constant. ˙ m Mass flow rate. ∗ Address all correspondence to this author. n Particle density. p Thermodynamic pressure. q Electron charge. Re Reynolds number. T Static temperature. t Time. U Velocity vector. V Voltage drop. x, y , z Cartesian components. ρ Density. ε 0 Permittivity of free space. η Electric resistivity. σ Electric conductivity. μ 0 Permeability of free space. ϑ eff Thruster efficiency. γ Adiabatic index. INTRODUCTION A self-field MPD thruster in its most basic form consists in a central cathode surrounded by a concentric anode [1]. With this coaxial geometric shape is very difficult to use experimen- tal techniques to visualize the plasma parameters. The use of measuring probes can also be problematic since they will dis- turb the plasma flow. To overcome such problems Toki et al. [2] developed a multichannel two-dimensional device. With their approach an almost uniform current distribution can be obtained 1 Copyright c  2013 by ASME