Numerical study of compressible viscous MHD equations with a bi-temperature model for supersonic blunt body flows

Abstract

In recent years, the possibility of supersonic drag reduction by imposing a magnetic field on a slightly ionized plasma has received a great deal of attention. Some of the results reported in the Russian literature indicate that the shock structure in a slightly ionized gas (plasma) is significantly weaker than that in nonionized gases at the same temperature. For example, the shock standoff distance of a sphere moving at supersonic speed in a slightly ionized air heated to plasma temperature is considerably larger than in a nonionized air heated to the same temperature. Furthermore, the shock front is highly diffused, sometimes to the point of being scarcely visible besides lacking sharp boundary normally observed in photographs obtained under such conditions in nonionized gases. These concepts and others for shock wave modification/dissipation in supersonic flow are currently being investigated by the U.S. Air Force under the AJAX program. One of the concepts of interest is the effect of large magnetic field (approximately 2 Tesla or more) on supersonic tlowfield about blunt bodies to evaluate the possibility of shock wave dissipation/elimination. This paper evaluates this concept by numerical simulation. In this paper, the effect of magnetic field on the weakly ionized flow is studied for a blunt body moving at hypersonic speeds using the compressible viscous MHD equations with a bi-temperature model. Two-dimensional MHD equations in generalized coordinates with and without a bi-temperature model are solved using a modified Runge-Kutta time integration scheme with second-order accurate spatial discretization. A symmetric Davis-Yee Total Variation Diminishing (TVD) flux limiter is employed to damp the oscillations in the shock regions. Numerical results indicate the feasibility of