Transition of natural convection of liquid metal in an annular enclosure

Abstract

Natural convection of a low-Prandtl-number fluid in an annular enclosure with a square cross section and radius ratio of the annulus of 0.5 is numerically studied using a finite-difference method in the cylindrical coordinate system. The fluid in the annular enclosure is heated from an inner vertical wall and cooled from an opposing vertical outer wall, both isothermally, whereas the two horizontal walls are adiabatic. Characteristics of the present natural convection are investigated in detail, with one of the annular computational domains divided into several equal parts. Three-dimensional (3D) regular oscillatory flow appears for a range of Rayleigh numbers when the computational domain angle is set to 90° or less. It is revealed that both the average Nusselt number and kinetic energy obtained from 3D flow are smaller than those obtained from a two-dimensional (2D) computation for the same Rayleigh number. When considered for an annular domain divided into 20 equal parts, flow transition of natural convection occurs gradually on the order of 2D steady, 3D regular steady, 3D regular oscillatory, and 3D irregular oscillatory flows, as the Rayleigh number increases. Most of the 3D regular oscillatory flows exhibit half-period symmetry in time and space. Both steady and oscillatory disturbance components coexist during the growing process from an initial state. In a fully developed stage of the 3D steady flow, only the steady disturbance component survives, whereas in that of the 3D regular half-symmetric oscillatory flow, only the oscillatory disturbance component survives.