Heat transport in three-layer turbulent thermal convection

Abstract

We report an experimental study of heat transport in a three-layer turbulent Rayleigh-Bénard convection. The experiments were conducted in a cylindrical cell (with diameter $D$) filled with a FC77 layer with height $H=D$. A very thin layer of water and a very thin layer of mercury were introduced to the top and bottom of the FC77 layer to provide slippery boundary conditions. We performed high spatial resolution temperature measurements across the water-FC77 and FC77-mercury interfaces, determined the temperatures at the two interfaces, the Rayleigh number (Ra) and the Nusselt number (Nu) across the FC77 layer. The experiments were conducted in the Ra range of $2.81\times {10}^9$ to $1.24\times {10}^{11}$ for the FC77 layer. It is found that not only the amplitude but also the scaling exponent (with Ra) of Nu is greatly enhanced in this three-layer system compared to the canonical single-layer system, especially in the high Ra range. In particular, $\text{Nu}$ first scales as ${\text{Ra}}^{0.31}$ and then ${\text{Ra}}^{0.38}$ when Ra exceeds a transitional Rayleigh number ${\text{Ra}}_t=2.52\times {10}^{10}$, whereas in the canonical single-layer FC77 case, $\text{Nu}$ is found to scale as ${\text{Ra}}^{0.26}$. Temperature measurements show that the boundary condition above and below the FC77 layer is asymmetric especially when $\text{Ra}>{\text{Ra}}_t$: the temperature drop across the top half (in contact with the water layer) of the FC77 layer is smaller than that across the bottom half (in contact with the mercury layer), and the top thermal boundary layer (TBL) becomes thinner and follows a steeper scaling with $\text{Ra}$ compared to the bottom TBL. We consider a hypothetical experiment where the top and the bottom boundary conditions are symmetric, denoted as a “water-FC77-water” three-layer system, in which the temperature drop across the bottom boundary layer $\mathrm{\Delta }{T}_b$ would be the same as that across the top boundary layer $\mathrm{\Delta }{T}_t$. We found in this water-FC77-water three-layer system, with the increase of Ra, $\text{Nu}$ vs $\text{Ra}$ scaling transitions from $\text{Nu}\sim {\text{Ra}}^{0.31}$ to $\text{Nu}\sim {\text{Ra}}^{0.46}$ with the transitional Ra the same as ${\text{Ra}}_t$ identified before. A closer check of the evolution of Ra of the water layer, FC77 layer, and the mercury layer reveal that the transition of the $\text{Nu}$ vs $\text{Ra}$ scaling is due to the transition of the thin water layer from a conduction state to a convection state, whereas the mercury layer remains in a conduction state.