Magnetohydrodynamic flows around bodies in strong transverse magnetic fields

摘要

Unconfined magnetohydrodynamic flows around two-dimensional bodies of arbitrary cross-section in a strong magnetic field are considered. The direction of the free-stream velocity, the applied magnetic field, and the axis of the body are perpendicular to each other. The flow is supposed to be inertialess. A detailed asymptotic analysis of the flow at high values of the Hartmann number is presented. The results show that the local shape of the body cross-section in the vicinity of the front and rear stagnation points is very important for both the drag and the overall flow balance. For blunt-nosed bodies, the flow is severely disturbed in the vicinity of the magnetic field lines crossing these stagnation points. The asymptotics of the drag in this case strongly depends on the Hartmann number and the local shape of the cross-section, which means that any small, local deviation of the shape of the cylinder from being circular may significantly affect the drag. Also, previously suggested logarithmic asymptotics of the drag on the circular cylinder with the Hartmann number has been confirmed.