A Numerical Study of Magnetohydrodynamic Flows with Respect to the Hall Effect

Abstract

With a view to the utilization of magnetic fields in hypersonic flow control an extension of the Navier-Stokes equations by magnetohydrodynamic source terms is described. The DLR TAU Code is employed as numerical tool and enhanced to simulate magnetohydrodynamic effects. As axisymmetric numerical setup a hemisphere-cylinder in a Mach 9 flow in air with an onboard 3-D dipole is chosen. The wall of the blunt body is assumed to be electrically conducting. The induced electric current density is determined by the generalized Ohm's Law. Different simulations with application of the magnetic field and with respectively without Hall effect are presented. The results are compared to a reference simulation without magnetic field. The impact of the magnetohydrodynamic source terms results in an increment of the shock distance compared to simulations without magnetic field. Thereby the effect depends on the treatment of the Hall parameter. In particular it turns out that the enhancement is reduced significantly if the Hall parameter is calculated as a local variable.