On one-dimensional flow of a conducting gas between electrodes – with application to MHD thrusters

Abstract

Inviscid, adiabatic, one-dimensional flow of a conducting gas in the presence of crossed electric and magnetic fields is investigated for the case where the magnetic field is generated by the current being supplied to the gas. The electrode geometry and the connections to the electrical power supply are such that the magnetic field falls to zero at the downstream end of the MHD duct. The analysis allows for magnetic Reynolds number rm to be anywhere in the range 0 to ∞ The main part of the investigation is restricted to consideration of ducts with constant spacing between electrodes.The way in which the density of the gas varies along the duct with the changing magnetic field is analysed generally and the results are then applied to the case where gas is fed to the MHD duct from high pressure in a plenum chamber and where the duct exhausts to a region of negligible pressure. If the flow is choked by the converging entry to the duct and the magnetic Reynolds number is moderate to high, the main electromagnetic effect is for the j × B forces to accelerate the gas to supersonic speeds. As rm is reduced, ohmic heating becomes more important, and it may cause the flow to be choked at exit from the duct, giving rise to a reduction in mass flow. For certain ranges of rm and ratio of initial magnetic pressure to plenum-chamber pressure the flow may choke at a sonic point within the duct itself, while accelerating from subsonic to supersonic through the point.Some illustrative examples of how properties vary with distance along the duct have been computed and the consequences of the analysis for MHD thrusters are explored. The magnetic forces will augment thrust per unit cross-sectional area, the essential measure of this being the drop in magnetic pressure along the duct, but there is an upper limit on the ratio of magnetic pressure to plenum-chamber pressure for flows to be possible. Flow at low magnetic Reynolds number is favoured if the object is to increase specific thrust by reducing mass flow through the duct.