Evaluation of turbulence models in MHD channel and square duct flows

In this paper, several low and high Reynolds number versions of k-ε and Reynolds stress turbulence models have been evaluated in a channel and a square duct flow with and without a magnetic field by comparing the predictions with direct numerical simulations data. The simulations are performed using FLUENT solver. The additional source terms for magnetic field effects on turbulence have been included through user-defined functions. A systematic assessment of the predicted mean flow, turbulence quantities, frictional losses and computational costs of the various turbulence models is presented. All the models predict mean axial velocity reasonably well, but the predictions of turbulence parameters are less accurate. Velocity predictions are worse for the square duct flow due to secondary flows generated by the turbulence. The implementation of the MHD sources generally improves predictions in MHD flows, especially for low-Re k-ε models. The high-Re models using the wall treatments show little improvement, perhaps due to the lack of MHD effects in the wall formulations. Finally, at low Reynolds numbers, the LamBremhorst (LB) low-Re k-ε model was found to give better predictions than other models for both hydrodynamic and magnetic field influenced turbulent flows.