Computation of unstable liquid metal convection in a vertical closed cylinder heated from the side and cooled from above

Abstract

Three-dimensional unsteady numerical computation was carried out to investigate buoyancy-driven unstable convection processes in a side-wad-heated and top-wad-cooled vertical closed cylinder containing liquid metal. The time-dependent basic flow equations were directly solved by the implicit Marker-and-Cell (MAC) scheme with the power law approximation to treat the convection-diffusion couplings. Results were obtained for liquid metal (Pr = 0.02) in a cylinder of finite aspect ratio (Gamma = 2) for various Rayleigh numbers. The predicted results indicate that the flow is relatively unstable except at low buoyancy. Specifically, of Ra = 2000 the flow evolves to a steady state but is highly asymmetric. As Ra = 3000 and 4000, the flow Becomes time periodic after the transient has died out with increasing asymmetry. At a still higher buoyancy the oscillation amplitude and flow asymmetry get larger, and a second fundamental frequency appears. The flow is quasi-periodic. Qualitatively, the flow structure is characterized by a main recirculation ill the major portion of the cylinder along with two uprising smaller cells near the side wall in the bottom half of the cylinder and another two counter rotating cells in the top half of the cylinder Finally, the critical Rayleigh number for the transition from a steady to a time periodic state was evaluated.