Heat transport by turbulent Rayleigh-Benard convection for Pr ≃ 0.8 and 3 x 1012 ≲ Ra ≲ 1015: aspect ratio Γ=0.50
Heat transport by turbulent Rayleigh-Benard convection for Pr ≃ 0.8 and 3 x 1012 ≲ Ra ≲ 1015: aspect ratio Γ=0.50
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DOI：
10.1088/1367-2630/14/10/103012
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发表时间：
2012-10-03
影响因子：
3.3
通讯作者：
Bodenschatz, Eberhard
中科院分区：
文献类型：
--
作者：
Ahlers, Guenter;He, Xiaozhou;Bodenschatz, Eberhard
本文报道了在长径比γ = 0.50（直径D = 1.12m，高度L = 2.24m）的圆柱形样品中，用湍流瑞利-贝纳德对流（RBC）测量热输运的实验结果。测量是在高达19巴的压力下使用六氟化硫作为流体进行的。它们对于小于或类似于10（15）的Ra的瑞利数范围3 X 10（12）和对于在0.79和0.86之间的普朗特数Pr。对于Ra < Ra-1* 类似于或等于1.4 × 10（13），我们发现Nu = N-0 Ra-γ eff，γ（eff）= 0.312 +/- 0.002，这与在顶板下方和底板上方具有层流边界层的系统中的经典湍流RBC一致。对于Ra-1* < Ra < Ra-2*（Ra-2* 类似或等于5 × 10（14）），γ（eff）逐渐增加到0.37 +/-0.01。我们认为，以上Ra-2* 的系统是在最终的对流状态的边界层，热和动力，也是湍流。伽马= 0.50的几个以前的测量重新检查，并与我们的结果进行比较。它们中的一些显示出到伽马（eff）在0.37至0.40范围内的状态的转变，尽管Ra值在9 × 10（10）至7 × 10（11）范围内，这远低于目前的Ra-1* 或Ra-2*。他们发现的过渡的性质是相对尖锐的，并没有揭示在这项工作中观察到的广泛的过渡范围。除了真正的Rayleigh-Benard系统的结果外，我们还对未完全密封的样品进行了测量;小开口允许由密度差和重力施加的外部电流通过样品。该系统不应再被视为真正的红细胞，因为外部施加的电流以主要方式修改了热传输。它显示了γ（eff）从0.308（Ra <Ra-t）（类似或等于4 × 10（13））突然降低到0.25（Ra较大）。一些可能的实验效果进行了检查，在一系列的附录中，没有发现这些效果有显着影响的测量。
We report on the experimental results for heat-transport measurements, in the form of the Nusselt number Nu, by turbulent Rayleigh-Benard convection (RBC) in a cylindrical sample of aspect ratio Gamma equivalent to D/L = 0.50 (D = 1.12m is the diameter and L = 2.24m the height). The measurements were made using sulfur hexafluoride at pressures up to 19 bar as the fluid. They are for the Rayleigh-number range 3 x 10(12) less than or similar to Ra less than or similar to 10(15) and for Prandtl numbers Pr between 0.79 and 0.86. For Ra < Ra-1* similar or equal to 1.4 x 10(13) we find Nu = N-0 Ra-gamma eff with gamma(eff) = 0.312 +/- 0.002, which is consistent with classical turbulent RBC in a system with laminar boundary layers below the top and above the bottom plate. For Ra-1* < Ra < Ra-2* (with Ra-2* similar or equal to 5 x 10(14)) gamma(eff) gradually increases up to 0.37 +/- 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 our results. Some of them show a transition to a state with gamma(eff) in the range from 0.37 to 0.40, albeit at values of Ra in the range from 9 x 10(10) to 7 x 10(11) which is much lower than the present Ra-1* or Ra-2*. The nature of the transition found by them is relatively sharp and does not reveal the wide transition range observed in this work. In addition to the results for the genuine Rayleigh-Benard system, we present measurements for a sample which was not completely sealed; the small openings permitted external currents, imposed by density differences and gravity, to pass through the sample. That system should no longer be regarded as genuine RBC because the externally imposed currents modified the heat transport in a major way. It showed a sudden decrease of gamma(eff) from 0.308 for Ra < Ra-t similar or equal to 4 x 10(13) to 0.25 for larger Ra. A number of possible experimental effects are examined in a sequence of appendices; none of these effects is found to have a significant influence on the measurements.