Heat transfer in turbulent Rayleigh-Benard convection through two immiscible fluid layers

We numerically investigate turbulent Rayleigh-Benard 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 <= alpha <= 0.99 and the thermal conductivity coefficient ratio of the two liquids between 0.1 <= lambda(k) <= 10. Two flow regimes are observed. In the first regime at 0.04 <= alpha <= 0.96, convective flows appear in both layers and Nu is not sensitive to alpha In the second regime at alpha <= 0.02 or alpha >= 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 alpha. 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.