The wake structure evolution and the drag force decay of an impulsively stopped sphere with a transverse magnetic field

The evolution of the flow structure around an impulsively stopped sphere is investigated in an incompressible viscous fluid under a transverse magnetic field. The study focuses on the wake structure and drag force over the range of Reynolds numbers 60⩽ReD ⩽300 and ReD =1000, with the interaction parameters 0⩽ N ⩽10, where N characterises the strength of the magnetic field. The wake is fully developed before the impulsive stop, after which it moves downstream and interacts with the sphere under the influence of a transverse magnetic field. The complex flow structures are characterised by skin friction lines on the downstream side of the sphere and categorised into five regimes in the {N,ReD} phase diagram based on nearly 200 cases. The drag force generally decays over time following the impulsive stop. A drag decomposition model based on the vorticity diffusion scale is proposed, attributing the drag decay to three components: the original Stokes contribution, an inertia correction at high Reynolds numbers and a magnetohydrodynamic (MHD) correction, where the inertia and MHD effects both contribute a temporal power-law decay with an exponent of −1/6. Temporal scaling laws of the drag decay are derived by coupling these three different effects, considering flow structures at short and long time scales, as well as the dependence on ReD and N.The prediction results are consistent with present simulations. Furthermore, the proposed drag decomposition model is successfully extended to complex vortex flow past a sphere at ReD =1000, to an anisotropic ellipsoidal particle and to different magnetic field orientations.