Numerical Simulation of Secondary Flow in a Weakly Ionized Supersonic Flow with Applied Electromagnetic Field

Abstract

This paper investigates, by numerical simulation of Navier Stokes equations, Magnetohydrodynamic (MHD) effects of an imposed electromagnetic field on secondary flow in a plasma wind tunnel with a weakly ionized supersonic flow in the range of Mach number 2.6 to 3.0. The imposed magnetic field is generated by a magnet flush- mounted in the tunnel side wall. Flow is pre-ionized by an R-F discharge and DC electric field is generated in the flow by 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 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 upwind numerical scheme. A series of cases with different imposed magnetic fields, electric fields and electrical conductivities, for two different stagnation pressures at the nozzle entrance, were investigated. A strong secondary flow was observed in the cold flow, i.e. flow with magnetic field and electric field switched off. However when a strong electric field is applied at constant electrical conductivity, the Mach number in the inviscid core is seen to drop. Also, the boundary layer thickness increases. More importantly, the strong cross flow is reduced downstream of the zone of electric field imposition. The negative magnetic field, acting in conjunction with the strong electric field further retards the flow and generates stronger secondary flow. To account for the scenario when time lag is large between application of electromagnetic field and Joule heating of flow, calculations were carried out by neglecting Joule heating terms in energy equation. Actual solutions are expected to be in between those obtained with and without considering Joule heating effects. In absence of Joule heating, constant acceleration (retardation) of flow was observed with accelerating (retarding) electromagnetic field although the changes in flow properties were minor as compared to the Joule heated flow with same electromagnetic fields. Under the assumption of no Joule heating, accelerating magnetic fields reduce the secondary flow while retarding flow makes the secondary flow stronger. Flow with a lower Reynolds number is expected to be more stable because of viscous effects. On the contrary, secondary flow near side wall is observed to be stronger for cold flows of lower Reynolds number. Also, Lower Reynolds number flow is observed to be affected more strongly by applied electromagnetic forces. In general, an accelerating magnetic field applied with electric field was observed to produce much lower secondary flow than the retarding magnetic field in same situation for almost all of the cases considered in the study.