Turbulent heat transfer and large-scale flow in convection cells with aspect ratio Γ > 1

Abstract

One of the most comprehensively studied turbulent flow is the Rayleigh- Bénard convection, in which a complex three-dimension turbulent motion is initiated by heating the fluid from below and cooling from above. Detailed measurements of the turbulent heat transfer [1, 2], the statistics of the temperature fluctuations and its gradients [3, 4] and the analysis of coherent thermal plumes [5, 6] haven been conducted in the past. The variation of the global heat transfer with respect to two of the three dimensionless control parameters–the Rayleigh number Ra and the Prandtl number Pr – in thermal convection was the focus of most of the laboratory experiments and simulations [7]. The dependence of the third control parameter – the aspect ratio, Γ = D / H, with D the diameter and H the height of the cell – has been studied much less extensively. Only a few systematic analyses of high- Rayleigh number convection in flat cells with Γ > 1 have been conducted [7], although it is relevant in geophysics and astrophysics. Even more surprisingly, an explicit aspect ratio dependence of the heat transfer in turbulent convection is absent in the existing scaling theories. Within the framework of this study, we perform a systematic analysis of the aspect ratio dependence of convective turbulence in cylindrical cells by three-dimensional direct numerical simulation. Our parameter ranges are: Ra = 107 − 109, Γ = 0.5 − 12 for fixed Pr = 0.7. Our analysis is focused on the following questions: Does the turbulent heat transfer at fixed Ra depend on Γ? Which changes in the the global flow structures are associated with an aspect ratio variation and which fraction of the total kinetic energy and heat transfer is contained in the large-scale circulation (LSC)? It is found that the global heat transfer, as measured by the Nusselt number Nu, varies up to 10% for aspect ratio variation. It is also observed that the primary mode of the LSC is responsible for carrying almost 50% of the turbulent kinetic energy for Γ > 1.KeywordsHeat TransferAspect RatioNusselt NumberTurbulent Kinetic EnergyRayleigh NumberThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.