Accurate Analysis of Turbulence Dynamics using Unstable Periodic Flow

使用不稳定周期流精确分析湍流动力学

基本信息

批准号：
17340118
负责人：
KIDA Shigeo
金额：
$ 10.29万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

项目摘要

Fluid mixing is one of the most prominent characteristics of turbulence. In order to understand the mixing dynamics and to develop a quantitative description of its statistical properties we performed the unstable-periodic-flow (UPF) analysis of the passive vectors advected in a Couette system. The unrepeatability of turbulence is one of the main causes which make the turbulence research difficult. In contrast the UPF discovered by Kawahara and Kida (2001), which has positive Lyapunof number, repeats exactly the same state for ever. Therefore, by using the UPF, we can calculate the statistics associated with flows as accurately as desired in proportion to the time devoted. We distribute many passive vectors in this UPF, and compare their stretching rate and orientation with the flow structures. It is found that those passive vectors which start at the same position but with different orientation, will align in direction in a finite time (of order of the period of UPF). This suggests th … More at the directional field of passive vectors may be uniquely defined as a function of the time and position of the UPF. We examine then how are those passive vectors that are distributed uniformly in space will rearrange as the time progresses. We divide the flow field into many small cubes, and calculate the statistics of the direction of passive vectors in each cube. The passive vectors are aligned in a line in most of the cubes. On the other hand, there are quite a few cubes in which the directions of passive vectors are aligned in a plane. We confirmed that such planes are parallel to the vorticity vector and that it is caused by the advection due to strong tubular vortices in the flow. The fluid mixing is enhanced around such places where the direction of passive vectors is diverse. The main organized structure in the Couette turbulence is the streamwise vortex, which creates the ejection and sweep regions near the wall boundary. The linear alignment of passive vectors is found in the interior of the streamwise vortices as well as in the ejection region. The planar distribution, on the other hand, is observed in the periphery of the streamwise vortices and in the sweep region. Such correspondence between the directional distribution of passive vectors and the flow structure depends on the near-past (between the present time and the past about a half of the period of UPF). The passive vectors lose their memory in the characteristic time of the turbulence. This is of essential importance in considering turbulence mixing and in developing turbulence model. Less

流体混合是湍流最突出的特征之一，为了了解混合动力学并对其统计特性进行定量描述，我们对库埃特系统中平流的被动矢量进行了不稳定周期流 (UPF) 分析。湍流的不可重复性是湍流研究困难的主要原因之一，而Kawahara和Kida（2001）发现的UPF具有正的Lyapunof。因此，通过使用 UPF，我们可以按照所需的时间比例准确地计算与流相关的统计数据，并比较它们的拉伸率。研究发现，那些从相同位置开始但方向不同的被动向量将在有限时间内（UPF 周期的数量级）对齐方向。无源矢量的方向场可以是唯一定义为 UPF 的时间和位置的函数，然后我们检查那些在空间中均匀分布的被动向量如何随着时间的推移重新排列。我们将流场划分为许多小立方体，并计算的统计量。每个立方体中的被动向量的方向在大多数立方体中都排列在一条线上，另一方面，有相当多的立方体的被动向量的方向在一个平面上对齐。这些平面平行于涡度矢量，它是由流动中强烈的管状涡流引起的平流引起的，在被动矢量方向不同的地方，流体混合得到增强，库埃特湍流中的主要组织结构是流向涡流。另一方面，在流向涡流的内部以及喷射区域中发现了被动矢量的线性排列。另一方面，在流向涡流的外围和扫掠区域中观察到被动矢量的方向分布和流动结构之间的这种对应关系取决于近过去（当前时间和过去大约一半的周期）。 UPF 的）。被动矢量在湍流的特征时间中失去记忆，这对于考虑湍流混合和开发 Less 湍流模型至关重要。