FLOW FIELD AND FORCE FOR FLOW PAST A NEAR-WALL SPHERE UNDER A MAGNETIC FIELD

The three-dimensional flow of an insulating sphere near a wall in an incompressible electrically conducting fluid under the influence of a magnetic field is investigated by direct numerical simulation method. The evolution of wake structure and force on sphere is analyzed under the influence of a magnetic field within a sphere-wall gap 0.5 < \alpha \leqslant 1.0 with respect to the Reynolds number 1 \leqslant Re \leqslant 100and the interaction number 0 \leqslant N \leqslant 10, where N and \alpha represent the magnetic field strength and the dimensionless distance between the sphere center and the wall, respectively. The study reveals that reducing the sphere-wall distance leads to the emergence of a new wake mode characterized by dual stagnation points. It is shown that within the current parameter range, three basic flow modes exist in the absence of a magnet field: unseparated flow at low Reynolds numbers with small spacing, separated flow with double stagnation points, and separated flow with a single stagnation point after the spacing is increased. As the magnetic field intensifies, the unseparated flow exhibits streamlines straightened along the magnetic field direction due to magnetic damping, while the flow perpendicular to the magnetic field is suppressed. For the wake mode with dual stagnation points, the Lorentz force acts at different positions on the trailing vortices, initially suppressing and reducing the separation vortices before elongating them along the magnetic field. Under a strong magnetic field, both the drag and lift force on the sphere vary linearly with N^1/2. Based on this, expressions for the drag and lift force on the sphere under a magnetic field are constructed. These expressions consist of three parts: the low-Reynolds-number solution, the inertial correction term, and the magnetic contribution. Numerical simulations validate the accuracy of the drag and lift expressions, showing good agreement between theoretical predictions and computational data, with maximum errors of 6.5% for drag and 17.9% for lift.