Reynolds number dependence of mean flow structure in square duct turbulence
Reynolds number dependence of mean flow structure in square duct turbulence
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DOI：
10.1017/s0022112009992242
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发表时间：
2010-02-10
影响因子：
3.7
通讯作者：
Kawahara, Genta
中科院分区：
文献类型：
--
作者：
Pinelli, Alfredo;Uhlmann, Markus;Kawahara, Genta
我们对方形管道中的湍流进行了直接数值模拟，考虑了从边缘状态到低雷诺数下完全发展的湍流状态的一系列雷诺数。主要动机源于对基本物理机制的了解相对较少，这些机制导致了此类湍流最突出的特征之一：第二类普朗特二次运动。特别是，重点是增加雷诺数时流动结构在其生成和表征中的作用。我们提出了一个双重场景。一方面，缓冲层结构决定了平均流向涡度的分布。另一方面，通过平均横流函数定义的平均二次流的形状和定量特征受到更大尺度上发生的运动的影响。结果表明，高速条纹优先位于角落区域（例如，距侧壁不到 50 个墙单位），两侧是低速条纹。这些位置是通过具有与上述速度条纹位置一致的优先旋转符号的准流向涡流的定位来确定的。经典缓冲层结构的这种优先排列决定了随着雷诺数的增加而接近拐角的平均流向涡度的模式。另一方面，平均二次流的中心，定义为平均跨流函数的极值位置（使用平均流向涡度计算），对于较大的雷诺数，保持在偏离平均流向涡度场的恒定位置，即它以外部单位缩放。本文还对数值技术进行了详细验证，包括将数值结果与配套实验获得的数据进行比较。
We have performed direct numerical Simulations of turbulent flows in a square duct considering a range of Reynolds numbers spanning from a marginal state up to fully developed turbulent states at low Reynolds numbers. The main motivation stems from the relatively poor knowledge about the basic physical mechanisms that are responsible for one of the most outstanding features of this class of turbulent flows: Prandtl's secondary motion of the second kind. In particular, the focus is upon the role of flow structures in its generation and characterization when increasing the Reynolds number. We present a two-fold scenario. On the one hand, buffer layer structures determine the distribution of mean streamwise vorticity. On the other hand, the shape and the quantitative character of the mean secondary flow, defined through the mean cross-stream function, are influenced by motions taking place at larger scales. It is shown that high velocity streaks are preferentially located in the corner region (e.g. less than 50 wall units apart from a sidewall), flanked by low velocity ones. These locations are determined by the positioning of quasi-streamwise vortices with a preferential sign of rotation in agreement with the above described velocity streaks' positions. This preferential arrangement of the classical buffer layer structures determines the pattern of the mean streamwise vorticity that approaches the corners with increasing Reynolds number. On the other hand, the centre of the mean secondary flow, defined as the position of the extrema of the mean cross-stream function (Computed using the mean streamwise vorticity), remains at a constant location departing from the mean streamwise vorticity field for larger Reynolds numbers, i.e. it scales in outer units. This paper also presents a detailed validation of the numerical technique including a comparison of the numerical results with data obtained from a companion experiment.