Flow states and heat transport in liquid metal convection

We present an experimental study of Rayleigh-Bénard convection using liquid metal alloy gallium-indium-tin as the working fluid with a Prandtl number of Pr = 0.029. The flow state and the heat transport were measured in a Rayleigh number range of 1.2 × 10⁴ ≤ Ra ≤ 1.3 × 10⁷. The temperature fluctuation at the cell centre is used as a proxy for the flow state. It is found that, as Ra increases from the lower end of the parameter range, the flow evolves from a convection state to an oscillation state, a chaotic state and finally a turbulent state for Ra > 10⁵. The study suggests that the large-scale circulation in the turbulent state is a residual of the cell structure near the onset of convection, which is in contrast with the case of Pr ∼ 1, where the cell structure is transiently replaced by high order flow modes before the emergence of the large-scale circulation in the turbulent state. The evolution of the flow state is also reflected by the heat transport characterised by the Nusselt number Nu and the probability density function (p.d.f.) of the temperature fluctuation at the cell centre. It is found that the effective local heat transport scaling exponent γ, i.e. Nu ∼ Ra^γ, changes continuously from γ = 0.49 at Ra ∼ 10⁴ to γ = 0.25 for Ra > 10⁶. Meanwhile, the p.d.f. at the cell centre gradually evolves from a Gaussian-like shape before the transition to turbulence to an exponential-like shape in the turbulent state. For Ra > 10⁶, the flow shows self-similar behaviour, which is revealed by the universal shape of the p.d.f. of the temperature fluctuation at the cell centre and a Nu = 0.19Ra^0.25 scaling for the heat transport.