Numerical investigation of Rayleigh–Bénard convection in a cylinder of unit aspect ratio

Abstract

Thermal convection in a vertical cylindrical cavity with a heated bottom, cooled top and insulated sidewall is investigated numerically. The radius to height ratio (Γ = height/radius) is fixed to unity and the Prandtl number is varied from 0.04 to 1. Rayleigh numbers up to 16 000 are considered in this study. Ten different kinds of flow regime have been identified, including both steady and unsteady patterns. The transition from steady to oscillatory flow occurs at a much lower Rayleigh number for small Prandtl number flow than for large Prandtl number flow. A bifurcation analysis shows the coexistence of two flow patterns in a certain parameter regime. The effect of flow structure on heat transfer is studied for a Prandtl number of unity.