Heat transfer in turbulent Rayleigh–Bénard convection through two immiscible fluid layers. (10th May 2022) - Liu, Hao-Ran; Chong, Kai Leong; Yang, Rui; Verzicco, Roberto; Lohse, Detlef
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 $Nu$ ) in two-layer systems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number $Ra=10^8$, Prandtl number $Pr=4.38$ and Weber number $We=5$ . We vary the relative thickness of the upper layer between $0.01 \le α \le 0.99$ and the thermal conductivity coefficient ratio of the two liquids between $0.1 \le λ _k \le 10$ . Two flow regimes are observed. In the first regime at $0.04\le α \le 0.96$, convective flows appear in both layers and $Nu$ is not sensitive to $α$ . In the second regime at $α \le 0.02$ or $α \ge 0.98$, convective flow only exists in the thicker layer, while the thinner one is dominated by pure conduction. In this regime, $Nu$ is sensitive to $α$ . To predict $Nu$ 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 $Nu$ and for the temperature at the interface agree well with our numerical results and previous experimental data.