Effect of an axial magnetic field on the first transition to unsteady thermal convective regime in a counter-rotating von Karman flow

摘要

This paper provides a DNS of a flow enclosed in a vertical cylindrical container of aspect ratio г = height/radius = 2, driven by the counter-rotation of the two lids at, Re = ΩR~2/υ = 300. The fluid models an electrically conductive liquid, with low Prandtl number, Pr = υ/α = 0.015 and in the limit of a small magnetic Reynolds number Re_m 1. The numerical computations of the fully nonlinear time dependent equations have been performed using a second-order finite-volume scheme. Numerical results show that the axial magnetic field reduces the transverse flow, the parallel flow becoming. Moreover, while the azimuthal symmetry is preserved, the flow pattern is strongly modified for non-zero Hartmann number, (Ha = B_0R{the square root of}σ/μ). The resulting electric potential field presents also substantial modifications under both the effect of a gradient of temperature and of an axial magnetic field. These structural changes may have important consequences in the subsequent induction mechanisms.