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°C, 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 ${{\theta }_{m}}=0.0,0.5$, the inverse Rossby number $1/Ro$ and the Rayleigh number $Ra$ changing in the ranges $0\le 1/Ro\le 10$ and ${{10}^{4}}\le Ra\le {{10}^{8}}$. The present results show that in the non-rotating cases (i.e. $1/Ro=0$), the penetrative convection of cold water with ${{\theta }_{m}}=0.5$ exhibits significant up-down asymmetry, with the top thermal boundary layer thickness $\delta _{\text{top}}^{\theta }$ greater than the bottom one $\delta _{\text{bottom}}^{\theta }$. The scaling exponents of the Nusselt number $Nu$ and ${{\delta }^{\theta }}$ versus $Ra$ are approximately $\pm 0.3$. 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 ${{\theta }_{m}}=0.0$ 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 ${{\theta }_{m}}=0.5$ 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 ${{\theta }_{m}}=0.5$ is not as significant as that for ${{\theta }_{m}}=0.0$. For the rotating penetrative convection of cold water with ${{\theta }_{m}}=0.5$, at moderate to high $1/Ro$, the thermal boundary layer thickness ${{\delta }^{\theta }}$ exhibits a scaling law ${{\delta }^{\theta }}\tilde{\ }1/R{{o}^{1/2}}$, while the velocity boundary layer thickness ${{\delta }^{u}}$ still follows ${{\delta }^{u}}\tilde{\ }1/R{{o}^{-1/2}}$.

Key words: Density inversion, Penetrative Rayleigh-Bénard convection, Rotating system, Numerical simulation