Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection

TL;DR

This study investigates how the aspect ratio influences heat transfer and large-scale flow structures in turbulent Rayleigh-Bénard convection through detailed numerical simulations, revealing aspect ratio-dependent behaviors and transitions in flow patterns.

Contribution

It provides a comprehensive analysis of the aspect ratio effects on heat transfer and flow configurations, including the transition points and the independence of heat transfer at large aspect ratios.

Findings

Heat transfer coefficients depend on aspect ratio for small and moderate values.

Transition from single-roll to double-roll flow occurs at a specific aspect ratio.

Heat transfer becomes independent of aspect ratio for large values (Γ ≥ 8).

Abstract

The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh-B\'{e}nard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio $\Gamma$ of a closed cylindrical cell and the Rayleigh number $Ra$. For small and moderate aspect ratios, the global heat transfer law $Nu=A\times Ra^{\beta}$ shows a power law dependence of both fit coefficients $A$ and $\beta$ on the aspect ratio. A minimum Nusselt number coincides with the point where the LSC undergoes a transition from a single-roll to a double-roll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations. The aspect ratio dependence of the turbulent heat transfer for small and moderate $\Gamma$ is in line with a varying amount of energy contained in the LSC, as quantified by the Proper Orthogonal Decomposition analysis. For $\Gamma\gtrsim 8$ the heat transfer becomes independent of the aspect ratio.