多孔介质壁面剪切湍流速度时空关联的研究

作为一个基础统计量,时空关联函数在湍流问题的研究中有着广泛的应用,是研究湍流噪声、湍流中物质扩散和大涡模拟亚格子模型等问题的重要参考.本文通过建立三维多孔结构壁面剪切湍流模型,采用含Darcy-Brinkman-Forchheimer作用力项的格子Boltzmann方程对无穷大多孔介质平行板之间壁湍流进行了数值模拟,进而研究其速度脉动时空关联函数的统计特性.一方面,根据计算得到的流场数据,对比分析了常规槽道湍流与多孔介质壁面槽道湍流的时间关联函数.另一方面,计算并讨论了不同孔隙率和渗透率的多孔介质壁面对速度脉动时空关联性的影响.通过研究表明:多孔结构壁面剪切湍流的时空关联函数等值线与椭圆理论相符;在研究参数范围内,多孔介质壁面的速度时空关联系数随着孔隙率增大而增大,随着渗透率增大而减小.同时发现在槽道壁面的近壁区、过渡区、对数律区和中心区等不同位置处,速度时空关联呈现较大差异性:越远离壁面位置(对数律区和中心区),其时空关联函数所呈现的关联等值线椭圆越细长,高值相关等值线越集中.多孔介质主要改变速度时空关联椭圆图像的椭圆率,说明多孔介质壁面主要影响湍流横扫速度.

SPACE-TIME CORRELATIONS OF FLUCTUATING VELOCTUATING IN POROUS WALL-BOUNDED TURBULENT SHEAR FLOWS1)

The space-time correlations are fundamental to the turbulence theory and have a broad application. In this paper, the authors perform direct numerical simulations of turbulent channel shear flows through the lattice Boltzmann method, and then study the space-time correlations of the velocity field. What’s more, the authors investigate space-time correlations of fluctuating velocities in porous wall-bounded turbulence, basing on the lattice Boltzmann equation which containing the Darcy-Brinkman-Forhheimer acting force term. On the one hand, the two-time correlations of velocities in porous wall-bounded shear flows are calculated and discussed. On the other hand, the author analyzes the space-time correlations of velocities in different porosity numbers and Darcy numbers in detail to investigate porous wall-bounded turbulent shear flows. It is found that there are elliptic curves on the iso-correlation contours that have a uniform preference direction and share a constant aspect ratio. Also, there are obvious differences among the space-time correlations of velocities in different normal-wise positions, such as near-wall region, buffer layer, log-law region and outer layer. These findings suggest that the farther it is away from the wall, the more slender elliptic curves are in iso-correlation contours. The computed results suggest that the correlations are enhanced with the Darcy number decreasing and the porosity number increasing.