Convection in a closed cavity with a large body of neutral buoyancy

Abstract

Rayleigh-Benard convection in a square cell with a sufficiently large, heat-insulating body of neutral buoyancy is studied numerically for two moderate values of the Rayleigh number Ra=10⁵ and Ra=10⁶. The emphasis is placed on changes in the dynamics of bodies and convective flows observed at a significant increase in body size. In the absence of a body, stationary two-roll convection is formed in the cell at Ra=10⁵, and at Ra=10⁶ a periodic oscillatory regime occurs. The appearance of a freely floating circular body in a cell changes the flow behavior, which is qualitatively independent of the body size, but fundamentally different for two considered values of the Rayleigh number. Thus, at Ra=10⁵, in the presence of a body, a stable large-scale circulation is formed, occupying the entire cell.  The movement of the body is irregular, stopping at two diagonally located corners of the cell. At Ra=10⁶, the body movement scenario changes: a free-floating body performs quasi-stable oscillatory movements, moving back and forth along a trajectory representing the letter Pi rotated by 90 degrees. The introduction of a floating body leads to a decrease in the intensity of convective flow and convective heat transfer. It is shown that the values of the Reynolds and Nusselt numbers decrease significantly with increasing body size. The interaction between body and temperature boundary layers causes noticeable temporary fluctuations in heat fluxes, resulting in quasi-periodic fluctuations in the average temperature of the fluid. The most pronounced correlation between the temperature and the vertical coordinate of body position is observed in the case of large bodies and a higher value of the Rayleigh number.