Heat transport by turbulent Rayleigh-B\'enard convection for $\Pra\ \simeq 0.8$ and $3\times 10^{12} \alt \Ra\ \alt 10^{15}$: Aspect ratio $\Gamma = 0.50$

TL;DR

This study experimentally investigates heat transport in turbulent Rayleigh-Bénard convection at high Rayleigh numbers and a specific aspect ratio, revealing a transition from laminar to turbulent boundary layers and supporting the ultimate state theory.

Contribution

First detailed experimental measurements of Nusselt number in turbulent convection at high Rayleigh numbers for aspect ratio 0.50, identifying boundary layer transition points.

Findings

Nu scales with Ra as Ra^0.312 below Ra*_1

Nu scaling increases to Ra^0.37 between Ra*_1 and Ra*_2

Evidence supports transition to the ultimate turbulent boundary layer state

Abstract

We report experimental results for heat-transport measurements, in the form of the Nusselt number \Nu, by turbulent Rayleigh-B\'enard convection in a cylindrical sample of aspect ratio $\Gamma \equiv D/L = 0.50$ ($D = 1.12$ m is the diameter and $L = 2.24$ m the height). The measurements were made using sulfur hexafluoride at pressures up to 19 bars as the fluid. They are for the Rayleigh-number range $3\times 10^{12} \alt \Ra \alt 10^{15}$ and for Prandtl numbers \Pra\ between 0.79 and 0.86. For $\Ra < \Ra^*_1 \simeq 1.4\times 10^{13}$ we find $\Nu = N_0 \Ra^{\gamma_{eff}}$ with $\gamma_{eff} = 0.312 \pm 0.002$, consistent with classical turbulent Rayleigh-B\'enard convection in a system with laminar boundary layers below the top and above the bottom plate. For $\Ra^*_1 < \Ra < \Ra^*_2$ (with $\Ra^*_2 \simeq 5\times 10^{14}$) $\gamma_{eff}$ gradually increases up to $0.37\pm 0.01$. We argue that above $\Ra^*_2$ the system is in the ultimate state of convection where the boundary layers, both thermal and kinetic, are also turbulent. Several previous measurements for $\Gamma = 0.50$ are re-examined and compared with the present results.