本论文源于欧洲-中国有关减阻研究的项目--DRAGY,该项目旨在研究湍流控制策略以减少流动阻力。本文重点研究了湍流近壁结构动力学以制定有效的流动控制策略,因此本文,分析了湍流近壁结构的减阻情况。通过建立了基于POD方法的尺度分离,以得出POD方法在分离不同尺度流动结构的方面的能力。文章针对槽道湍流的涡量和速度分量进行了正交分解。因为POD能谱取决于可用快照的数量,文章强调需要使用与模式信息内容相关的标准来进行尺度分离。同时,因为POD模态的组合显示出比单一模式更小的NRMS,所以应该使用这些模态组合来进行流动尺度分离。文章提出了基于卷积计算的模态和瞬时流场的相似性度量来对流动中的尺度进行分离。从相似性度量的图谱中得到一个明显的趋势:高能量模态显示高相似值,相反的,低能量模态显示出低相似值。基于两个假设之上,我们定义了一个尺度分离的方法:首先,假设一模态的组合可以重建流动结构,其次,在任意时间具有大相似度的POD模态包含有大尺度流动结构,反之亦然。我们把这种方法用于流场中的涡量和速度分量来进行尺度分离。为了验证这些假设,文章计算了每个模态组合在垂直壁面方向上的相似性。结果显示两个假设是错误的,且POD技术最大化模式信息内容的方法混淆了模式中的尺度。结论表明正交分解并不适用于分离流量。
This thesis fits into the European Chinese research project DRAGY, which deals with drag reduction. The DRAGY project aims to investigate the ability of different flow control strategies to reduce drag. To do so, the researchers’ efforts are mainly focused on the understanding of the turbulent near-wall structure dynamics in order to set efficient control strategies. In that context, the study investigates the turbulent near-wall structures for drag reduction analysis. Specifically, the study concludes on the ability of the Proper Orthogonal Decomposition to separate the flow scales by implementing a POD-based scale separation. The decomposition of a turbulent channel flow is computed for all the vorticity and velocity components. Because the POD energy spectra depends on the number of snapshots available, we highlight the need to use a criterion related to the mode information content for separating scales. We also highlight that sets of POD modes show a smaller NRMS than isolated modes and, thus, that sets of modes should be used to separate the flow scales. We propose to use the likeness of the POD modes to the flow as a criterion for the scale separation. The mode likeness is computed by a convolution-based measure. It emerges from the likeness map that high energy modes show high likeness values, and conversely. Two assumptions are made regarding the POD ability to reconstruct the flow and the likeness trend. It is firstly assumed that sets of modes can reconstruct flow structures. Secondly, it is also assumed that POD modes having large likeness value along time contain large scale flow structures, and vice versa. We define a scale-separation method relying on those two assumptions and apply it to all the vorticity and velocity components. In order to check the assumptions, the likeness of each mode set is computed along the wall normal direction. Doing so show, on the one hand, that the two assumptions are wrong and, on the other hand, that the POD technique mixes the scales in the modes by maximizing the mode information content. The Proper Orthogonal Decomposition is then not suitable for separating flow scales.