Heat transfer in turbulent Rayleigh–Bénard convection through two immiscible fluid layers. (10th May 2022)

• Record Type: Journal Article
• Authors: Liu, Hao-Ran; Chong, Kai Leong; Yang, Rui; Verzicco, Roberto; Lohse, Detlef
• Is Part Of: Journal of fluid mechanics. Volume 938(2022)
• Publication Date: 2022-05-10
• Subjects: Bénard convection -- multiphase flow -- turbulence simulation; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2022.181
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: 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.