Analytical studies of the limiting flow regimes in MHD channels

This paper presents the analytical study results for a steady single-phase quasi-one-dimensional flow in a gas-dynamic path of the magnetohydrodynamic (MHD) generator of the Hall-type plasma. It is shown that, depending on generator working conditions, two different regimes of transition are possible: with and without shock wave formation. The parametric studies are carried out in a regime with compression shock waves. The calculated results are highly dependent on the heat capacity ratio, $k$. For $k = 1.1$, with an increase in the dimensionless interaction parameter $A$, the shock wave position shifts from the origin of the electrode zone to a diffuser. For $k = 1.2$, at the same value of $A$, either shock-wave-free recompression or shock-wave recompression can occur. For $k = 1.3$, two different shock-wave recompressions are possible.
Since the solution to a steady-state problem may be non-unique, the false transient method is generally considered as an appropriate numerical method for solving the problems of the flow in MHD channels. This method allows one to simulate unstable physical processes accounting for initial conditions of the problem and also to calculate the flows with shock waves when conservative difference schemes are used.