Large eddy simulation of geometry sensitivity of magneotohydrodynamic turbulent flow in a rectangular duct

Velocity distributions and pressure drops in liquid metal magnetohydrodynamic (MHD) duct flows are closely associated with the shape of the duct cross-section. In order to investigate the effects of the cross-sectional shape on MHD turbulent flows, liquid metal flow in two kinds of rectangular duct with a uniform magnetic field applied transversely to the flow are simulated using large eddy simulation with the coherent structure model. One duct has a normal rectangular cross-section (N-duct), while the other rectangular duct has a triangular protrusion pointing into the flow domain at the middle of the walls parallel to the magnetic fields (P-duct). Both duct walls are electrically insulating, and the inlet and outlet of the computational domain are set to be periodic. The flow Reynolds number is kept constant in this study, while the Hartmann numbers vary from 10 to 42.4. The numerical results show that the protrusion at the parallel walls promotes flow turbulence and compensates the effect of turbulence suppression due to the magnetic field. As the Hartmann number increases, the turbulent MHD flow transits to a single-sided turbulent flow and finally to a laminar flow. The protrusion at the side wall promotes the turbulence and delays the MHD turbulent-laminar transition as the Hartmann number increases. However, the skin friction coefficient is higher in P-duct than that in N-duct when the flow is turbulent. The protrusion cannot reduce the pressure drop in rectangular duct with insulating walls.