Numerical simulation of turbulent magnetohydrodynamic flows

The development of a computational tool for the solution of turbulent magnetohydrodynamic (MHD) flows is presented. For the MHD solver, option is given to solve the full MHD equations or consider the low magnetic Reynolds number formulation. For turbulence, the Reynolds Averaged approach is considered for its low requirement in terms of computational resources. Six turbulence models, ranging from simple algebraic model to more sophisticated two-equation models are considered to evaluate the eddy viscosity. Since the turbulence models were originally designed for non-magnetic flows, they require some modifications to account for the presence of a magnetic field. The governing equations are numerically solved by a modified Runge-Kutta scheme augmented with a Total Variation Diminishing scheme for accurate shock capturing. The numerical solutions are compared with available experimental data and existing analytical solutions. The calibration of the modified turbulence models is performed based on the turbulent MHD Hartmann flow, for which a relaminarization process has been experimentally observed. Original models do not accurately predict the relaminarization process, whereas modified models show good agreement with experiments. Application of the original and modified turbulence models to a supersonic flow over a flat plate leads to a reduction in the skin friction by about 20% to 30% when the fluid has a low conductivity. A complete relaminarization is observed for high conductivity fluids. The heat transfer could also be substantially reduced for the hypersonic flow over a cone, as a result of a relaminarization of the flow.