Heat Transfer in Turbulent Rayleigh-Benard Convection below the Ultimate Regime

A Rayleigh-B'enard cell has been designed to explore the Prandtl (Pr) dependence of turbulent convection in the cross-over range $0.7<Pr<21$ and for the full range of soft and hard turbulences, up to Rayleigh number $Ra\simeq 10^{11}$. The set-up benefits from the favourable characteristics of cryogenic helium-4 in fluid mechanics, in-situ fluid property measurements, and special care on thermometry and calorimetric instrumentation. The cell is cylindrical with $diameter\mathrm{/}height=0.5$. The effective heat transfer $Nu(Ra,Pr)$ has been measured with unprecedented accuracy for cryogenic turbulent convection experiments in this range of Rayleigh numbers. Spin-off of this study include improved fits of helium thermodynamics and viscosity properties. Three main results were found. First the $Nu(Ra)$ dependence exhibits a bimodality of the flow with $4-7$ difference in $Nu$ for given $Ra$ and $Pr$. Second, a systematic study of the side-wall influence reveals a measurable effect on the heat transfer. Third, the $Nu(Pr)$ dependence is very small or null : the absolute value of the average logarithmic slope $(dlnNu\mathrm{/}dlnPr{)}_{Ra}$ is smaller than 0.03 in our range of $Pr$, which allows to disciminate between contradictory experiments [Ashkenazi $\mathit{\text{et}}\mathit{\text{al.}}$, Phys. Rev.Lett. 83:3641 (1999)][Ahlers $\mathit{\text{et}}\mathit{\text{al.}}$, Phys.Rev.Lett. 86:3320 (2001)].