Axisymmetric expansion of an ionized propellant gas under the effect of magnetic fields in advanced rocket nozzle

An iterative finite-difference mathematical model is formulated to predict the effect of magnetic fields applied to an ionized propellant gas expanding through a converging-diverging rocket nozzle. The numerical model solves the fluid mechanical equations of motion combined with energy and electromagnetic equations. A multi-step pressure correction procedure with an implicit density treatment is used to establish the pressure and velocity fields. The algorithm is valid for the flow regimes encountered in a rocket nozzle, from subsonic to supersonic flow.; The possibility of reducing heat transfer at the nozzle's throat by means of an applied magnetic field is considered. This is the first known model that addresses the effect of magnetic fields on the flow of an ionized propellant gas, as it expands through a rocket nozzle of the type proposed for high power electrothermal thrusters. The computational model developed produces results that demonstrate critical physical processes occurring in connection with the coupling of magnetic and flow fields. It is found that the magnetic field affects the flow field not only in relation to the magnitude of its field strength, but most importantly the magnetic effect is driven by the relative magnitude of its gradients as it relates to the inherent flow gradients in the nozzle. Further, when the gas pressure is less than one percent of the magnetic pressure, a reduction in heat losses to the wall of the nozzle is possible. At the conditions of the test cases investigated, local heat transfer rates are reduced up to 30%. It is concluded that, at the flow conditions envisioned for high-power electrothermal thrusters, modest magnetic insulation is possible with a properly aligned magnetic field.