Modified One-Equation Turbulence Models for Turbulent Magnetohydrodynamic Flows

摘要

The Baldwin-Barth and Spalart-Allmaras one-equation turbulence models are implemented to solve turbulent magnetohydrodynamic (MHD) flows. Because the original version of these turbulence models were not designed for MHD flows, some modifications are proposed to include the effect of the magnetic field on turbulence. In the case of the Baldwin-Barth model, an additional magnetic term is introduced into the turbulence model equation, whereas one of the closure coefficients is made dependent on the magnetic field for the Spalart-Allmaras model. The MHD equations are considered under the low magnetic Reynolds number approximation, that is, for low electrical conductivity fluids. The proposed modifications associated with the magnetic field are calibrated based on the turbulent Hartmann flow. The modified versions are able to predict accurately the experimentally observed relaminarization process at Ha/Re = 1/225. Investigation of the supersonic flow over a flat plate shows that a substantial reduction in the skin friction can be achieved; however, no relaminarization process was observed for the range of applied magnetic fields.