Analysis of thermal dissipation rates in turbulent Rayleigh–Bénard convection
Analysis of thermal dissipation rates in turbulent Rayleigh–Bénard convection
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DOI：
10.1017/s0022112005007408
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发表时间：
2005-12
影响因子：
3.7
通讯作者：
O. Shishkina;C. Wagner
中科院分区：
文献类型：
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作者：
O. Shishkina;C. Wagner
本文首次对瑞利数$10^5$、$10^6$和$10^7$以及普朗特数$Pr\,{=}\,0.7$进行了具有外侧壁面的宽圆柱容器（长径比$\Gamma\,{=}\,10$）内的瑞利-巴<s:1>纳德对流湍流的直接数值模拟。利用生成的DNS数据对热耗散速率进行评价，强调了热羽的形成和发展及其相互作用。定义了两个新函数$\sigma$和$\tau$，以定量地确定湍流背景的作用。根据DNS数据对这些函数进行评估，表明湍流背景将热羽流向后推，其对体积平均热耗散率的贡献随着瑞利数的增加而增加。进一步，分析证明了面积平均（顶部或底部板）与体积平均散热率的比值大于或等于所有纵横比的努塞尔数，以及普朗特数和瑞利数。
Direct numerical simulations (DNS) of turbulent Rayleigh–Bénard convection in a wide cylindrical container (aspect ratio $\Gamma\,{=}\,10$) with a lateral wall have been performed for the first time for the Rayleigh numbers $10^5$, $10^6$ and $10^7$ and Prandtl number $Pr\,{=}\,0.7$. Evaluating the thermal dissipation rates from the generated DNS data, the formation and development of the thermal plumes and their interaction are highlighted. Two new functions $\sigma$ and $\tau$ are defined to determine quantitatively the role of the turbulent background. Evaluating these functions from the DNS data, it is shown that the turbulent background pushes the thermal plumes back and that its contribution to the volume-averaged thermal dissipation rate increases with the Rayleigh number. Further, it is proven analytically that the ratio of the area-averaged (over the top or the bottom plates) to the volume-averaged thermal dissipation rate is greater than or equal to the Nusselt number for all aspect ratios, and Prandtl and Rayleigh numbers.