Boundary layer structure in turbulent Rayleigh-Benard convection
Boundary layer structure in turbulent Rayleigh-Benard convection
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DOI：
10.1017/jfm.2012.207
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发表时间：
2012-09-10
影响因子：
3.7
通讯作者：
Schumacher, Joerg
中科院分区：
文献类型：
--
作者：
Shi, Nan;Emran, Mohammad S.;Schumacher, Joerg
通过三维直接数值模拟研究了湍流瑞利-贝纳德对流的边界层结构。我们考虑在固定普朗特数 Pr = 0.7 下，瑞利数为 R a D 3 x 109 和 3 x 1010 时，圆柱电池中纵横比为 1 的对流。与相同装置和相同普朗特数下的实验结果类似，速度场和温度场的层流边界层结构与普朗特-布拉修斯-波尔豪森理论的预测存在偏差。当对具有瞬时定义的边界层厚度的数据进行动态重新缩放并且分析平面与闭合单元中大尺度环流的瞬时方向对齐时，偏差会减少。我们的数值结果表明，现有经典的强制对流和自然对流层流边界层理论的重要假设被违反，例如动力学的严格二维性或流体运动的稳定性。边界层动力学由两个重要的局部动力学构建块组成：羽流分离和羽流后阶段。前者与速度和温度边界层的瞬时厚度的较大变化以及全三维局部流动相关。后羽流动力学与从上方穿透边界区域的细胞内的大规模循环有关。还将在每个动态相的边界层局部部分中获取的平均湍流剖面与强制或自然对流向混合对流的边界层方程的扰动展开的解进行比较。我们对两个边界层的分析表明，近壁动力学结合了强制 Blasius 型和自然对流的元素。
The structure of the boundary layers in turbulent Rayleigh-Benard convection is studied by means of three-dimensional direct numerical simulations. We consider convection in a cylindrical cell at aspect ratio one for Rayleigh numbers of R a D 3 x 109 and 3 x 1010 at fixed Prandtl number Pr = 0.7. Similar to the experimental results in the same setup and for the same Prandtl number, the structure of the laminar boundary layers of the velocity and temperature fields is found to deviate from the prediction of Prandtl-Blasius-Pohlhausen theory. Deviations decrease when a dynamical rescaling of the data with an instantaneously defined boundary layer thickness is performed and the analysis plane is aligned with the instantaneous direction of the large-scale circulation in the closed cell. Our numerical results demonstrate that important assumptions of existing classical laminar boundary layer theories for forced and natural convection are violated, such as the strict two-dimensionality of the dynamics or the steadiness of the fluid motion. The boundary layer dynamics consists of two essential local dynamical building blocks, a plume detachment and a post-plume phase. The former is associated with larger variations of the instantaneous thickness of velocity and temperature boundary layer and a fully three-dimensional local flow. The post-plume dynamics is connected with the large-scale circulation in the cell that penetrates the boundary region from above. The mean turbulence profiles taken in localized sections of the boundary layer for each dynamical phase are also compared with solutions of perturbation expansions of the boundary layer equations of forced or natural convection towards mixed convection. Our analysis of both boundary layers shows that the near-wall dynamics combines elements of forced Blasius-type and natural convection.