Geometrical Structure of Small Scales and Wall-bounded Turbulence
Geometrical Structure of Small Scales and Wall-bounded Turbulence
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小尺度和壁面湍流的几何结构
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发表时间：
2012
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通讯作者：
Fettah Aldudak
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作者：
Fettah Aldudak
在大多数涉及流体运动的技术和自然环境中都可以观察到湍流。然而，背后的理论仍未完全被理解。由于湍流具有不规则、复杂的特征，因此通常无法采用确定性方法，因此需要对其进行统计处理。湍流中的空间结构（称为涡流）对于描述湍流至关重要。本文采用Wang & Peters (2006)提出的一种新方法来完全分解湍流标量场
并独特地分成小的空间子单元。该方法称为耗散元法。标量场中的梯度轨迹在上升和下降方向上追踪，它们不可避免地分别达到最小值和最大值点。所有的轨迹通向
同一对极值点定义耗散元素 (DE)。
在目前的工作中，DE 分析被扩展到规范壁界湍流通道流。将特别关注墙边界对 DE 大小及其分布的影响
沿着通道的壁法线方向。为了获得分析数据，在不同的雷诺数下进行了直接数值模拟 (DNS)，如第 2 章中第 1 节中简要介绍所示。湍流通道流量统计在第 3 节中讨论，稍后将解释 DE 分析的结果。在第四章中，提出了用经典方法获得的三维湍流结构，称为涡流。
在第 6 章应用 DE 方法之前，第 5 章对泊肃叶流中的经典湍流长度尺度进行了分析。DE 的平均长度及其随距壁面距离的变化将得到广泛讨论。
讨论了雷诺数的影响和标量变量的选择。极值点之间的欧氏距离和标量差的边际概率密度、联合概率密度和条件概率密度 (pdf) 为
调查了。利用李对称分析，获得了 pdf 的不变解。此外，导出了 pdf 的对数正态模型。
除了经典的泊肃叶流之外，还通过 DE 方法研究了三种不同的通道流，即具有壁法线和流向旋转的通道流以及壁蒸腾作用。
最后，第 7 章检查了流线段的长度和端点之间的速度差。与 DE 的情况一样，边际和条件 pdf 以及
讨论了壁距和雷诺数。
Turbulence is observed in most technical and natural environments involving fluid motion. However, the theory behind is still not fully understood. Due to the irregular, complex character of turbulence, it is treated statistically since a deterministic approach is usually not possible. Spatial structures in turbulence, known as eddies, are essential to describe the turbulent flow. In this thesis, a new method proposed by Wang & Peters (2006) is employed to decompose turbulent scalar fields completely
and uniquely into small spatial sub-units. The approach is called Dissipation Element method. Gradient trajectories in the scalar field are traced in ascending and descending directions where they inevitably reach a minimum and a maximum point, respectively. All trajectories leading to the
same pair of extremal points define a dissipation element (DE).
In the present work, DE analysis is extended to the canonical wall-bounded turbulent channel flow. Special focus will be given to the effect of the wall boundaries with respect to the size of the DEs and their distribution
along the wall-normal direction of the channel. To obtain data for analysis, Direct Numerical Simulations (DNS) have been conducted at different Reynolds numbers as presented in chapter 2 following a brief introduction in §1. Turbulent channel flow statistics are discussed in §3 which are later addressed to interpret results from DE analysis. In chapter 4, three-dimensional turbulent structures, called vortices, are presented which are obtained with classical methods.
Classical turbulent length scales in Poiseuille flow are analyzed in §5 before the DE method is applied in chapter 6. Mean length of DEs and its variation with the distance from the wall will be addressed extensively.
The influence of the Reynolds number and the choice of the scalar variable is discussed. Marginal, joint and conditional probability densities (pdf) of the Euclidean distance and scalar difference between extremal points are
investigated. Employing Lie symmetry analysis, invariant solutions of the pdf are obtained. Further, a log-normal model for the pdf is derived.
In addition to the classical Poiseuille flow, three different channel flows are investigated by means of the DE method, namely channel flows with wall-normal and streamwise rotations and wall transpiration.
Finally, streamline segments are examined in chapter 7 with respect to the length and the velocity difference between their ending points. As in the case of DEs, marginal and conditional pdfs, as well as the influence of the
wall distance and Reynolds number are discussed.