Numerical study of liquid metal flow in a rectangular duct under the influence of a heterogenous magnetic field

We simulated numerically the laminar flow in the geometry and the magnetic field of the experimental channel used in [Andreev, Kolesnikov, and Thess (2006)]. This provides detailed information about the electric potential distribution for the laminar regime (numerical simulation) and in the turbulent regime as well (experiment). As follows from comparison of simulated and experimental results, the flow under the magnet is determined by the interaction parameter N = Ha2/Re representing the ratio between magnetic force, determined by the Hartmann number Ha, and inertial force, determined by the Reynolds number Re. We compared two variants: (i) (Re,N)=(2000,18.6) (experiment), (400,20.25) (simulation), and (ii) (Re,N) =(4000,9.3) (experiment), (400,9) (simulation) and found an excellent agreement for the numerical and experimental distributions of the electric potential. This is true despite of the fact that the experimental inflow is turbulent while that in the simulation is laminar. As a special feature of the electric potential distribution local extrema under the magnets are observed, as well experimentally as numerically. They are shown to vanish, if the interaction parameter falls below a critical value. Another interesting new detail found in our numerical calculations is the appearance of helical paths of the electric current. Using a simplified magnetic field without span-wise dependence, we show that important physical features of the considered problem are sensitive to small variations in the spatial structure of the magnetic field: the local extrema of the electric potential and also the helical current paths disappear when the simplified magnetic field is used. The structure of the three dimensional velocity field is also investigated, in particular, a swirling flow is found in the corners of the duct caused by Hartmann layer destruction behind the magnets. keyword: 3D Numerical simulation, laminar liquid 1 Institut für Physik, Technische Universität Ilmenau, PF 100565, 98684 Ilmenau, Germany metal flow in a rectangular duct, localized heterogenous magnetic field