Behavior of Supersonic Flow under Energy Exchange and Lorentz Force

The behavior of supersonic flow under the energy exchange and the Lorentz force was studied analytically. The shock relations (MHD Rankine-Hugoniot relations) including the energy exchange and the Lorentz force were derived for the first time. The relations indicate that the shock wave strength can be weakened by the energy addition or the negative Lorentz force acting upstream and that the weakening of shock wave is always accompanied by total pressure loss. The relation between the isentropic efficiency and the enthalpy extraction of the MHD generator was derived using the MHD Rankine-Hugoniot relations, the interaction parameter and the electrical efficiency. The derived relation suggests that shock wave tends to appear at lower isentropic efficiency and this agrees with experimental results qualitatively. Effects of the energy exchange and the Lorentz force on velocity of propagation shock wave were also studied by one-dimensional numerical simulation. The results show that the reflected shock wave and the secondary shock wave appear under a certain condition. Furthermore, it is shown that the velocity of the propagation shock wave can be controlled by the energy exchange and the Lorentz force.