Optimum performance of electron beam driven magnetohydrodynamic generators for scramjet inlet control

This paper is devoted to the analysis and optimization of magnetohydrodynamic control of forebody flow compression and shock incidence in scramjet-powered vehicles that would fly at Mach 5-8. The short (about 30 cm long) magnetohydrodynamic region is created by placing a magnetic coil with B-field strength of several Tesla inside the forebody and ionizing the cold air flow by high-energy electron beams propagating along the magnetic field lines. The Faraday current flowing in the spanwise direction is presumed to be collected with electrodes that are mounted on sidewalls. The purpose of the magnetohydrodynamic device is to restore a shock-on-lip condition at Mach 8 for a vehicle geometry designed for Mach 5, while operating in self-powered mode (the magnetohydrodynamic generated electricity is enough to power the ionizing beams). Location and spatial dimensions of the magnetohydrodynamic region, beam-generated ionization profiles, magnetic field strength, and the magnet size are varied to maximize performance and reduce the magnet size. Two-dimensional inviscid steady-state flow equations are solved jointly with equations describing electron beam-induced ionization profiles, plasma kinetics, vibrational relaxation, and magnetohydrodynamic effects. The model predicts an interesting phenomenon of electric current reversal due to the nonuniformity of velocity, magnetic field, and conductivity in the magnetohydrodynamic region. Vibrational nonequilibrium effects are found to be substantial. Overall, the modeling shows that a considerable reduction in magnet size is possible with the optimum choice of parameters.