Identification of transport-dominated large-scale structures in turbulent wall-bounded flows using a Characteristic DMD

使用特征 DMD 识别湍流壁面流动中以输运为主的大型结构

• 批准号: 429461620
• 负责人: Professor Dr. Jörn Lothar Sesterhenn
• 金额: --
• 依托单位: Lehrstuhl für Technische Mechanik und Strömungsmechanik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/429461620?language=en
• 关键词: Identification; transport; dominated; large; scale

Large Coherent structures are organized motions in turbulent flows. The organization – or coherence - refers to movements in space and time, which our brains easily spot when looking a turbulent flow. These structures contribute prominently to the turbulent kinetic energy and diffuse mass and momentum. Therefore, they come with large desirable or undesirable effects in the flow, like better mixture or more drag. Despite many studies in the last decade to understand their physical properties and the ease with which we spot them by the naked eye, there is still limited consensus in the scientific community on how to define these structures, what they physically look like, how long they live and how length scales depend on Reynolds numbers. We do not know what they feed on, how their regeneration mechanism works and how they interact with each other or with near wall turbulence.The main objective of this study is to extract low dimensional subspaces out of highly complex turbulent flow fields, which meet our intuitive understanding of large coherent structures. In particular the structures living in these subspaces shall have a long lifetime, live on large scales and travel with a certain group velocity. To this end, a temporal sequence of state vectors from DNS or time-resolved measurements, will be transformed such that we find a persistent dynamical mode on a hypersurface traveling along its normal in space and time on a moving frame of reference. Less technically speaking, we rotate the flow fields in space and time and carry out a Dynamic Mode Decomposition (DMD) on the transformed data, to capture the modes possessing small decay or growth rates. Reconstruction of the candidate modes along the normal to the hypersurface and transforming them back to physical space gives the low rank model of the flow. Next, we look at the flow in the same way for the next largest group with those modes projected out. This gives a hierarchy of structures. Again, in practical terms, we aim to separate large coherent structures, coherent structures, and an uncoherent remaining rest.The method will be applied to two canonical turbulent flows. The resulting structures will be tested against physical evidence, by verifying that the footprints of large-scale coherent structures in premultiplied energy spectra that can be reproduced by them. Each structure will be studied separately in terms of their lifetimes, spatiotemporal evolution, length scales and turbulent properties. Implementing each coherent structure or group of them as initial condition for a DNS, will provide the unique chance to observe evolution and self- sustainability of each set of structures, in absence of small-scale features and instabilities. We verify whether the large-scale motions survive in absence of small-scale structure or whether they feed on backscatter.

大相干结构是湍流中有组织的运动。组织性-或连贯性-指的是空间和时间的运动，当我们的大脑看到湍流时，很容易发现。这些结构对湍流动能、扩散质量和动量有显著贡献。因此，它们在流动中具有较大的期望或不期望的效果，如更好的混合或更大的阻力。尽管在过去的十年中有许多研究来了解它们的物理特性以及我们用肉眼发现它们的容易程度，但科学界对如何定义这些结构，它们的物理外观，它们的寿命以及长度尺度如何取决于雷诺数的共识仍然有限。 我们不知道它们以什么为食，它们的再生机制如何工作，它们如何相互作用或与近壁湍流相互作用，本研究的主要目标是从高度复杂的湍流流场中提取低维子空间，这符合我们对大相干结构的直观理解。特别是生活在这些子空间中的结构应具有长寿命，生活在大尺度上，并以一定的群速度传播。为此，从DNS或时间分辨测量的状态向量的时间序列将被转换，使得我们在超曲面上找到一个持久的动力学模式，该超曲面在移动的参考系上沿沿着其在空间和时间中的法线行进。 从技术上讲，我们在空间和时间上旋转流场，并对转换后的数据进行动态模式分解（DMD），以捕获具有小衰减或增长率的模式。沿着超曲面的法线沿着重构候选模式并将它们变换回物理空间给出了流动的低秩模型。接下来，我们以同样的方式查看下一个最大组的流，并将这些模式投影出来。 这给出了结构的层次结构。同样，在实际应用中，我们的目标是分离大的相干结构，相干结构，和一个非相干的剩余剩余。该方法将被应用到两个典型的湍流。由此产生的结构将被测试对物理证据，通过验证的足迹，大规模的相干结构的预乘能量谱，可以复制它们。每个结构将分别研究其寿命，时空演变，长度尺度和湍流特性。将每个相干结构或它们的组实施为DNS的初始条件，将提供在没有小尺度特征和不稳定性的情况下观察每组结构的演化和自维持性的独特机会。我们验证了大规模的运动是否在没有小规模结构的情况下生存，或者它们是否依赖于后向散射。