Implicit time-marching solution of partially ionized flows in self-field MPD thruster

Self-filed magneto-plasma dynamic (MPD) viscous flows are numerically investigated. The axisymmetric compressible Navier-Stokes equations with the Lorentz force and Joule heating, the equation of magnetic induction derived from Maxwell's equations with Ohm's law, and the continuity equation of electrons are simultaneously solved with the use of an implicit time-marching method based on the LU-SGS scheme. Partially ionized flows in the experimental MPD thruster are simulated and compared with the experimental results. The calculated current stream lines and the pressure of the cathode tip are found to agree well with the experiments. The values of the pressure of the cathode tip and the thrust are also numerically predicted by changing the distance from the cathode tip to the anode.