Drag upon a sphere suspended in a low magnetic-Reynolds number MHD channel flow

A permanent magnetohydrodynamics (MHD) channel flow past a stationnary sphere is investigated, with a static magnetic field transversally applied and no-slip conditions taken into account. The sphere is subject to laminar flow conditions with the Reynolds number ranging from the Stokes regime up to values corresponding to the inertial regime (Re-p = 130 at most for the particle Reynolds number). The maximum value of the Hartmann number is Ha = 200. After a brief review of the existing literature of three-dimensional (3-D) MHD flows past an obstacle, a 3-D numerical approach is developed, which is systematically compared to asymptotic predictions (Ha = 0, Ha -> infinity). Atypical flow patterns are made evident, especially characterized by the gradual emergence of Hunt's wake for a sufficiently large particle Stuart number N-p. Some original correlations are put forward for the wake length and the drag coefficient. Finally, an original scaling law highlighting the significant influence of the outer magnetic field on the transition between different MHD flow regimes is drawn up.