Transition of natural convection of liquid metal in an annular enclosure under a magnetic field

Abstract

Natural convection of a low-Prandtl-number conductive fluid driven by a horizontal temperature gradient in an annular enclosure with a square cross section was investigated. The surface temperatures of the inner and outer cylinders were differentially maintained. A static magnetic field was applied in the azimuthal direction. A three-dimensional (3D) numerical simulation was performed for a part of an annulus divided into 20 or 28 equal parts. The natural convection found changes on the order of a two-dimensional (2D) steady, a 3D steady, a 3D non-half-symmetric simply periodic oscillatory, a 3D indefinite oscillatory, a 3D half-symmetric simply periodic oscillatory, and a 3D aperiodic oscillatory flow as the Hartmann number decreases. This transition pattern is identical to that as the Rayleigh number increases in the same system without a magnetic field. In high Rayleigh numbers, the transition is accompanied by an axisymmetric oscillation. A disturbance causing the transition consists of three modes as a 3D steady, a 3D half-symmetric oscillatory, and a 2D axisymmetric oscillatory mode. The Nusselt numbers in most 3D flows are smaller at low Rayleigh numbers and larger at high Rayleigh numbers than that in 2D flows at a same condition, while the kinetic energy of a 3D flow is necessarily smaller than that of a 2D flow.