Two dimensional MHD duct flow: Numerical analysis and measurements

The problem dealt with is that of the turbulent compressible flow between the insulator walls of an MHD duct, for which a set of equations is derived, accounting for turbulent transport phenomena, nonequilibrium ionization, and ambipolar diffusion. The equations are solved with a finite difference method of second order accuracy in both directions. A transformation of the coordinate perpendicular to the wall accounts for the large gradients close to the wall. Still, special attention had to be given to higher order derivates in the wall region to get around singular behavior problems. The streamwise pressure gradient dp/dx is found as a part of the solution of the gasdynamic quantities. The electromagnetic quantities are not actually found from a full solution of the electronic equations but from the experimental values and empirical relations worked out by Brederlow which, together with two-dimensional current-potential calculations, give information on the Hall-component of the current density in Ohm's law. The numerical calculations show good agreement with a series of measurements made by Merck at the 200 kW plasma jet MHD test rig of the Max Planck Institute for Plasmaphysics in Garching.