Laminar and turbulent Rayleigh–Bénard convection in a perfectly conducting cubical cavity

Abstract

This paper discusses flow structures and heat transfer rates generated by Rayleigh–Bénard convective motions of a Boussinesq fluid with a Prandtl number of 0.7 in a perfectly conducting cubical cavity. Complete numerical simulations of laminar flows were conducted in the range of Rayleigh numbers 7×10 3⩽ Ra⩽10 5. The large-eddy simulation (LES) technique was used for the simulations at two high Rayleigh numbers ( Ra=10 6 and 10 8). LES were carried out using a second-order accurate finite volume code with a dynamic localized one-equation subgrid-scale (SGS) model with constant SGS Prandtl number. In the laminar regime, two single roll structures and a four-roll structure in which the axis of each roll is perpendicular to one sidewall were found to be stable. LES of Rayleigh–Bénard convection in an infinite fluid layer were initially carried out and results were seen to be in agreement with direct numerical simulations (DNS) reported in the literature. At Ra=10 6 and 10 8, the instantaneous velocity and temperature fields present strong fluctuations with respect to the time-averaged flow field. The confining effect of the conductive lateral walls of the cavity generates, in the unsteady flows at Ra=10 6 and 10 8, persistent vertical currents near these walls. The recirculation of these ascending and descending flows towards the central region of the cavity produces large-scale organized rolling motions, which imprint the topology of the time-averaged flow field in form of two vortex ring structures located near the horizontal walls.