Significance of Prandtl Number on the Heat Transport and Flow Structure in Rotating Rayleigh–Bénard Convection

Abstract

A direct numerical simulation of rotating Rayleigh–Bénard convection (RBC) for different fluids (Pr=0.015,0.7,1,7,20, and 100) in a cylindrical cell of aspect ratio Γ=0.5 is carried out in this work. The effect of rotation on the heat transfer rate, flow structures, their associated dynamics, and influence on the boundary layers are investigated. The Rayleigh number is fixed to Ra=106 and the rotation rates are varied for a wide range, starting from no rotation (Ro→∞) to high rotation rates (Ro≈0.01). For all the Prandtl numbers (Pr=0.015–100), a reduction in heat transfer with increase in rotation is observed. However, for Pr=7 and 20, a marginal increase of the Nusselt number for low rotation rates is obtained, which is attributed to the change in the flow structure from quadrupolar to dipolar state. The change in flow structure is associated with the statistical behavior of the boundary layers. As the flow makes a transition from quadrupolar to dipolar state, a reduction in the thermal boundary layer thickness is observed. At higher rotation rates, the thermal boundary layer thickness shows a power law variation with the rotation rate. The power law exponent is close to unity for moderate Pr, while it reduces for both lower and higher Pr. At extremely high rotation rates, the flow makes a transition to the conduction state. The critical rotation rate (1/Roc) for which transition to the conduction state is observed depends on the Prandtl number according to 1/Roc∝Pr0.5.