Collapse of Coherent Large Scale Flow in Strongly Turbulent Liquid Metal Convection

TL;DR

This study investigates how large-scale flow coherence in turbulent liquid metal convection breaks down at high Rayleigh numbers, affecting heat transfer scaling laws and Reynolds number, with detailed flow pattern measurements in different aspect ratios.

Contribution

It provides the first detailed experimental evidence of large-scale flow collapse in turbulent liquid metal convection and its impact on heat transfer scaling laws.

Findings

Large-scale flow coherence breaks down at high Rayleigh numbers for aspect ratio 0.5.

The heat transfer scaling exponent decreases from 0.221 to 0.124 after flow collapse.

Flow coherence loss correlates with a reduction in Reynolds number.

Abstract

The large-scale flow structure and the turbulent transfer of heat and momentum are directly measured in highly turbulent liquid metal convection experiments for Rayleigh numbers varied between $4 \times 10^5$ and $\leq 5 \times 10^9$ and Prandtl numbers of $0.025~\leq~Pr~\leq ~0.033$. Our measurements are performed in two cylindrical samples of aspect ratios $\Gamma =$ diameter/height $= 0.5$ and 1 filled with the eutectic alloy GaInSn. The reconstruction of the three-dimensional flow pattern by 17 ultrasound Doppler velocimetry sensors detecting the velocity profiles along their beamlines in different planes reveals a clear breakdown of coherence of the large-scale circulation for $\Gamma = 0.5$. As a consequence, the scaling laws for heat and momentum transfer inherit a dependence on the aspect ratio. We show that this breakdown of coherence is accompanied with a reduction of the Reynolds number $Re$. The scaling exponent $\beta$ of the power law $Nu\propto Ra^{\beta}$ crosses \FIN{eventually} over from $\beta=0.221$ to 0.124 when the liquid metal flow at $\Gamma=0.5$ reaches $Ra\gtrsim 2\times 10^8$ and the coherent large-scale flow is completely collapsed.