Numerical Simulation of Supersonic Boundary Layer Stability with Applied Electromagnetic Field in a Weakly Ionized Flow

Abstract

This paper investigates, by direct numerical simulation, the effect of an imposed electromagnetic field on a weakly ionized supersonic boundary layer in the range of 2.7 to 3.0 in a supersonic plasma wind tunnel, located at the non-equilibrium thermodynamics laboratory, under J. W. Rich and I. Adamovich, at the Ohio State University . The main emphasis of the study is on MHD effects on the supersonic boundary layer. The imposed magnetic field is generated by a magnet flush-mounted in the tunnel side wall and the electric field is generated in this supersonic flow, pre-ionized by the RF discharge, by applying a DC field using electrodes flush-mounted in the top and bottom walls, perpendicular both to the flow velocity and the magnetic field. The electrical conductivity of the flow varies between 0.1 and 0.5 mho/m. The magnetic Reynolds number of the flow is small so that the induced magnetic field is neglected. The governing equations of the MHD flow, which are the Navier-Stokes equations with the applied electromagnetic force terms, are computed by a third-order upwinded numerical scheme. A series of cases with different imposed magnetic fields, electric fields and electrical conductivity, for two different stagnation pressures at the nozzle entrance, have been investigated for the mean flow. Calculations on the second mode instability are planned. It is found that in the presence of electric fields and the absence of magnetic fields, i.e. joule heating, the flow at the centerline heats up strongly leading to retardation in the flow velocity. The boundary layer thickness also increases and the mean Mach number is brought down. In the presence of magnetic field only, it is observed that the boundary layer profile changes depending on the direction of the field and, also the effect on the boundary layer is less in magnitude compared to the effect of joule heating on the same. The magnetic field is limited in its ability to mitigate the effects of an imposed electric field on the flow field. Unsteady calculations are currently underway and comprehensive conclusions on effects of external electromagnetic fields are expected in future. We have also undertaken three dimensional calculations to understand the effects of the sidewall on the flow profile.