Interaction of inertia and magnetic force in the liquid metal flow past a magnetic obstacle

In this paper, we present a numerical study of the three-dimensional behavior of a liquid metal flow in an insulating rectangular duct of narrow cross section past a localized magnetic field (i.e., a magnetic obstacle) produced by two parallel square magnets arranged externally on the walls of the duct. A series of simulations are conducted focused mainly on describing the interplay between inertial and magnetic forces in a wide range of interaction parameters (1.8<N<48) by varying the Reynolds number while the Hartmann number is kept fixed (Ha = 75). The analyzed configuration coincides with that studied experimentally by Domínguez et al. [“Experimental and theoretical study of the dynamics of wakes generated by magnetic obstacles,” Magnetohydrodynamics 51(2), 215–224 (2015)] and, as a first step, experimental data from local variables (streamwise velocity component) and global parameters (oscillation frequency and kinetic energy of the wake) are consistently replicated by the numerical model. Furthermore, to complement the flow phenomenology, the transition to different flow structures as the interaction parameter varies is explored. It is found that when the magnetic forces predominate over inertia, stationary vortex patterns with two, four, and six vortices appear while, unlike the hydrodynamic flow past a bluff body, the increase in inertial effects leads to a reduction in the number of vortices and eventually to their disappearance, reaching a state in which the magnetic obstacle becomes imperceptible to the flow. The existence of a critical value of the interaction parameter that maximizes the kinetic energy of the wake is confirmed numerically and corroborated from the experimental data.