The effect of a uniform magnetic field on vortex breakdown in a cylinder with rotating upper lid

Abstract

The effects of an axial uniform magnetic field on vortex breakdown in the swirling flow, which is steady, axisymmetric and generated by the rotation of upper lid of an enclosed cylinder, are investigated. A collocation spectral solver is developed. After validating by dynamic and magnetohydrodynamic (MHD) problems, it is applied for the solution of the swirling flow in an enclosed cylinder with aspect ratio (height/radius) of 1.5⩽γ⩽2. In the presence of an axial uniform magnetic field, the effects of magnetic field on the dimensionless lengths of vortex along the z-axis and the central positions of vortex on the z-axis are analyzed. The conductivities of the upper lid, lower base and side wall are considered. The results show that, for different electrical boundary conditions, the behaviors of vortex are significantly different and even converse. In particular, when the upper rotating lid is the only perfectly conducting, the magnetic effects are the strongest.