Dissipation element analysis in turbulent channel flow
Dissipation element analysis in turbulent channel flow
复制标题
湍流通道流中的耗散元分析
DOI：
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发表时间：
2012
影响因子：
3.7
通讯作者：
M. Oberlack
中科院分区：
文献类型：
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作者：
Fettah Aldudak;M. Oberlack
摘要 为了分析湍流流型的几何结构及其对各种标量场的统计，我们采用耗散元（DE）方法，并通过纳维-斯托克斯方程的直接数值模拟（DNS）将其应用于湍流通道流。从标量场 $phi (x, y, z, t)$ 中的任意点开始，在标量梯度上升和下降的方向上的梯度轨迹总是会达到极值，即最小值或最大值点，其中 $oldsymbol{
abla} phi = 0$.属于同一对极值点的所有点和轨迹的集合定义了耗散元素。扩展以前仅适用于均匀湍流的 DE 方法，我们在此重点探讨实体壁对耗散单元分布的影响。利用群论方法和已知的纳维-斯托克斯方程对称性，我们观察到流动的核心区域，即缓冲层之外的区域，DE长度的概率分布函数（p.d.f.）表现出不变的函数形式，换句话说，相对于壁距离的自相似行为。平均 DE 长度尺度的缩放行为进一步增强了这一点，该缩放行为显示出与壁距离的线性缩放。平均 DE 长度和泰勒长度尺度的已知比例也被重新审视。利用几何类比，我们给出 DE 元素的数量作为壁距离的函数。此外，观察到 DE p.d.f.相当不敏感，即对于雷诺数和用于分析的实际标量 $phi $ 都是不变的。事实上，DE p.d.f 观察到了非常显着的各向同性程度。在高剪切区域。这与经典的柯尔莫哥洛夫标度定律形成鲜明对比，后者通常表现出对剪切力、各向异性和雷诺数等量的强烈依赖性。此外，在许多情况下，柯尔莫哥洛夫的缩放行为仅在非常大的雷诺数时可见。这与当前的 DE 方法相当不同，该方法也适用于低雷诺数。此外，我们表明 DE p.d.f.与对数正态分布非常吻合并导出对数正态 p.d.f.模型考虑了壁法线依赖性。最后，研究了 DE 极值点处湍流动能的条件平均标量差。我们提出了一个幂律，其标度指数为 $2/ 3$（根据科尔莫哥洛夫的通道中心假设可知）和靠近壁的对数定律。
Abstract In order to analyse the geometric structure of turbulent flow patterns and their statistics for various scalar fields we adopt the dissipation element (DE) approach and apply it to turbulent channel flow by employing direct numerical simulations (DNS) of the Navier–Stokes equations. Gradient trajectories starting from any point in a scalar field $phi (x, y, z, t)$ in the directions of ascending and descending scalar gradients will always reach an extremum, i.e. a minimum or a maximum point, where $oldsymbol{
abla} phi = 0$. The set of all points and trajectories belonging to the same pair of extremal points defines a dissipation element. Extending previous DE approaches, which were only applied to homogeneous turbulence, we here focus on exploring the influence of solid walls on the dissipation element distribution. Employing group-theoretical methods and known symmetries of Navier–Stokes equations, we observe for the core region of the flow, i.e. the region beyond the buffer layer, that the probability distribution function (p.d.f.) of the DE length exhibits an invariant functional form, in other words, self-similar behaviour with respect to the wall distance. This is further augmented by the scaling behaviour of the mean DE length scale which shows a linear scaling with the wall distance. The known proportionality of the mean DE length and the Taylor length scale is also revisited. Utilizing a geometric analogy we give the number of DE elements as a function of the wall distance. Further, it is observed that the DE p.d.f. is rather insensitive, i.e. invariant with respect both to the Reynolds number and the actual scalar $phi $ which has been employed for the analysis. In fact, a very remarkable degree of isotropy is observed for the DE p.d.f. in regions of high shear. This is in stark contrast to classical Kolmogorov scaling laws which usually exhibit a strong dependence on quantities such as shear, anisotropy and Reynolds number. In addition, Kolmogorov’s scaling behaviour is in many cases only visible for very large Reynolds numbers. This is rather different in the present DE approach which applies also for low Reynolds numbers. Moreover, we show that the DE p.d.f. agrees very well with the log-normal distribution and derive a log-normal p.d.f. model taking into account the wall-normal dependence. Finally, the conditional mean scalar differences of the turbulent kinetic energy at the extremal points of DE are examined. We present a power law with scaling exponent of $2/ 3$ known from Kolmogorov’s hypothesis for the centre of the channel and a logarithmic law near the wall.