Abstract
We numerically investigate turbulent Rayleigh–Bénard convection through two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number $\mbox {Nu}$) in two-layer systems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number $\mbox {Ra}=10^8$, Prandtl number $\mbox {Pr}=4.38$ and Weber number $\mbox {We}=5$. We vary the relative thickness of the upper layer between $0.01 \le \alpha \le 0.99$ and the thermal conductivity coefficient ratio of the two liquids between $0.1 \le \lambda _k \le 10$. Two flow regimes are observed. In the first regime at $0.04\le \alpha \le 0.96$, convective flows appear in both layers and $\mbox {Nu}$ is not sensitive to $\alpha$. In the second regime at $\alpha \le 0.02$ or $\alpha \ge 0.98$, convective flow only exists in the thicker layer, while the thinner one is dominated by pure conduction. In this regime, $\mbox {Nu}$ is sensitive to $\alpha$. To predict $\mbox {Nu}$ in the system in which the two layers are separated by a unique interface, we apply the Grossmann–Lohse theory for both individual layers and impose heat flux conservation at the interface. Without introducing any free parameter, the predictions for $\mbox {Nu}$ and for the temperature at the interface agree well with our numerical results and previous experimental data.
Funder
Partnership for Advanced Computing in Europe AISBL
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
11 articles.
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