关键词: 密度倒置, 穿透Rayleigh-Bénard对流, 旋转系统, 数值模拟

Abstract: The rotating penetrative convection in the fields of Earth science and engineering has attracted extensive attention. Due to the density inversion property of water near 4℃, cold water is used as the working fluid in the present paper to study the rotating penetrative Rayleigh-Bénard convection in a vertical annulus. Direct numerical simulation is performed to analyze the convective heat transfer of cold water under various parameter conditions, with the density inversion parameter θ_m=0.0,0.5, the inverse Rossby number 1/Ro and the Rayleigh number Ra changing in the ranges 0≤1/Ro≤10 and 10⁴≤Ra≤10⁸. The present results show that in the non-rotating cases (i.e. 1/Ro=0), the penetrative convection of cold water with θ_m=0.5 exhibits significant up-down asymmetry, with the top thermal boundary layer thickness δ_top^θ greater than the bottom one δ_bottom^θ. The scaling exponents of the Nusselt number Nu and δ^θ versus Ra are approximately ±0.3. In the rotating cases (i.e. 1/Ro>0), the flow changes with increasing the rotation rate (i.e. 1/Ro), leading to the transition of flow regime from thermal plumes to vortex columns at moderate 1/Ro. Particularly noteworthy is that for θ_m=0.0 both the cold and hot plumes are strong enough to form vortex columns in a certain range of 1/Ro, while the density inversion property at θ_m=0.5 renders the cold plumes weak so that only hot plumes can be converted into vortex columns. As a result, the augmentation of heat transfer, induced by the formation of vortex columns, for θ_m=0.5 is not as significant as that for θ_m=0.0. For the rotating penetrative convection of cold water with θ_m=0.5, at moderate to high 1/Ro, the thermal boundary layer thickness δ^θ exhibits a scaling law δ^θ~1/Ro^1/2, while the velocity boundary layer thickness δ^u still follows δ^u~1/Ro^-1/2.

Key words: density inversion, penetrative Rayleigh-Bénard convection, rotating system, numerical simulation