Three-dimensional MHD flows in rectangular ducts with internal obstacles

We present a numerical simulation of the magnetohydrodynamic (MHD) liquid metal flow around a square cylinder placed in a rectangular duct. In the hydrodynamic case, for a certain parameter range the well-known Karman vortex street with three-dimensional flow patterns is observed, similar to the flow around a circular cylinder. In this study a uniform magnetic field aligned with the cylinder is applied and its influence on the formation and downstream transport of vortices is investigated. The relevant key parameters for the MHD flow are the Hartmann number M, the interaction parameter N and the hydrodynamic Reynolds number, all based on the side length of the cylinder. The Hartmann number M was varied in the range 0≤ M ≤ 85 and the interaction parameter N in the range 0 < N ≤ 36. Results are presented for two fixed Reynolds numbers Re = 200 and Re = 250. The magnetic Reynolds number is assumed to be very small. The results of the numerical simulation are compared with known experimental and theoretical results. The hydrodynamic simulation shows characteristic intermittent pulsations of the drag and lift force on the cylinder. At Re = 200 a mix of secondary spanwise three-dimensional instabilities (A and B mode, rib vortices) could be observed