Direct numerical simulation of Rayleigh-Bénard convection in a cylindrical container of aspect ratio 1 for moderate Prandtl number fluid

摘要

A series of three-dimensional numerical simulations were conducted for the Rayleigh-Bénard convection in a cylindrical container with the aspect ratio γ = 1. The Prandtl number of the fluid is 7 and the Rayleigh number varies from 10 ~3 to 10 ~5. Results show that the aspect ratio of the cylinder has an important influence on the multiplicity of the steady flow state. The sidewall of the cylinder at γ = 1 restricts the increase of the number of rolls in the fluid layer. Therefore, only two-roll and single-roll flow patterns are observed at the whole simulation range of the Rayleigh number. During the transition of the Rayleigh-Bénard convection to the unsteady flow, it is found that the unsteady flow pattern and the bifurcation sequence of the oscillation flow are very sensitive to the initial condition.