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Flow states and heat transport in liquid metal convection
Published online by Cambridge University Press: 28 October 2022
Abstract
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 
$1.2\times 10^{4} \le Ra \le 1.3\times 10^{7}$. 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 
$Ra>10^5$. 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 
$Pr\sim 1$, 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 
$\gamma$, i.e. 
$Nu\sim Ra^{\gamma }$, changes continuously from 
$\gamma =0.49$ at 
$Ra\sim 10^4$ to 
$\gamma =0.25$ for 
$Ra>10^6$. 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 
$Ra>10^6$, 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.
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