Direct Numerical Simulations of Magnetic Field Effects on Turbulent Duct Flows

Magnetic fields are crucial in controlling flow in various physical processes of significance. Magnetic fields are frequently used to pump, stir and stabilize liquid metal flows non-intrusively. One of these processes, which has significant application of a magnetic field, is continuous casting of steel, where different magnetic field configurations are used to control the turbulent steel flow in the mold to minimize defects in the cast steel. Recently, liquid metal MHD flows have been extensively studied for application to fusion reactor technology. This study has been undertaken to analyze the effect of magnetic field on mean velocities and turbulence parameters in the molten metal flows through a square duct. Direct Numerical Simulations without using a sub-grid scale (SGS) model have been used to characterize the three-dimensional transient flow. The coupled Navier-Stokes-MHD equations have been solved with a three-dimensional fractional-step numerical procedure. Convection as well as diffusion terms have been discretized using a central differencing scheme in space and the 2nd order Adams-Bashforth scheme for integration in time. Pressurevelocity coupling has been resolved using the fractional-step method and the pressure Poisson equation has been solved using a multigrid solver. Because liquid metals have low magnetic Reynolds number, the induced magnetic field has been neglected and the electric potential method for magnetic fieldflow coupling has been implemented. The equation for electric potential has been also been calculated using a multigrid solver. The known electric potential and velocities then provide the current density which is used in the expression for Lorentz force in the momentum equations. Initially, laminar simulations in a square duct have been performed and results generated were compared with previous series solutions. Next, simulations of a non-MHD flow in a square duct at low Reynolds number were performed and satisfactorily compared with results of a previous DNS study. Subsequently, different levels of a magnetic field were applied to study its effect on the turbulence until the flow completely laminarized. Time-dependent and time-averaged flows have been studied through mean velocities and fluctuations, and power spectrums of instantaneous velocities. INTRODUCTION Magnetic fields are effective in controlling flow in various physical processes of significance such as metal processing, MHD pumps, flow meters, plasma and fusion technology, to name a few (1). One such process is continuous casting of steel in which different magnetic field configurations are used to control the turbulent flow of steel in the mold to minimize defects in cast steel (2). When a magnetic field is applied to a flow field, the interaction of the current density with the magnetic field generates a Lorentz force, which then brakes the flow and alters the velocity field (3). In the case of turbulent flows, magnetic fields can relaminarize the flow and alter significantly the structure of the turbulent flow (4). Consequently the friction characteristics and mixing phenomena in turbulent flows subjected to magnetic fields can be significantly different from those without the magnetic field. Tailoring the magnetic field to alter the flow in the mold of the continuous caster of steel is a topic of significant practical interest (2). The common methodology used in many previous studies to simulate effects of magnetic field on turbulent flows has been the Reynolds-averaged approach (4-8). However, the