Detection of Energetic Low Dimensional Subspaces in Spatio-Temporal Space in Turbulent Pipe Flow

IF 2 3区 工程技术 Q3 MECHANICS
Amir Shahirpour, Christoph Egbers, Jörn Sesterhenn
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Abstract

Low dimensional subspaces are extracted out of highly complex turbulent pipe flow at \(Re_{\tau }=181\) using a Characteristic Dynamic Mode Decomposition (CDMD). Having lower degrees of freedom, the subspaces provide a more clear basis to detect events which meet our understanding of large-scale coherent structures. To this end, a temporal sequence of state vectors from direct numerical simulations are rotated in space-time such that persistent dynamical modes on a hyper-surface are found travelling along its normal in space-time, which serves as the new time-like coordinate. The main flow features are captured with a minimal number of modes on a moving frame of reference whose velocity matches that of the most energetic scale. Reconstruction of the candidate modes in physical space gives the low rank model of the flow. The structures living in this subspace have long lifetimes, posses wide range of length-scales and travel at group velocities close to that of the moving frame of reference. The modes within this subspace are highly aligned, but are separated from the remaining modes by larger angles. We are able to capture the essential features of the flow like the spectral energy distribution and Reynolds stresses with a subspace consisting of about 10 modes. The remaining modes are collected in two further subspaces, which distinguish themselves by their axial length scale and degree of isotropy.

湍流管流时空中能量低维子空间的检测
利用特征动态模态分解(CDMD)从\(Re_{\tau }=181\)高度复杂的湍流管道流动中提取低维子空间。由于自由度较低,子空间为检测符合我们对大规模相干结构的理解的事件提供了更清晰的基础。为此,在时空中旋转直接数值模拟的状态向量时间序列,使得超表面上的持续动力模式沿其时空法线行进,作为新的类时坐标。在一个速度与最高能量尺度相匹配的运动参照系上,用最少数量的模态捕获了主要的流特征。在物理空间中对候选模态进行重构,得到流的低阶模型。生活在这个子空间中的结构具有很长的寿命,具有很宽的长度尺度范围,并且以接近运动参照系的群速度运动。该子空间内的模态高度对齐,但与其他模态以较大的角度分开。我们能够用大约10个模态组成的子空间捕捉到流的基本特征,如频谱能量分布和雷诺应力。其余模态收集在两个进一步的子空间中,它们通过轴向长度尺度和各向同性程度来区分自己。
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来源期刊
Flow, Turbulence and Combustion
Flow, Turbulence and Combustion 工程技术-力学
CiteScore
5.70
自引率
8.30%
发文量
72
审稿时长
2 months
期刊介绍: Flow, Turbulence and Combustion provides a global forum for the publication of original and innovative research results that contribute to the solution of fundamental and applied problems encountered in single-phase, multi-phase and reacting flows, in both idealized and real systems. The scope of coverage encompasses topics in fluid dynamics, scalar transport, multi-physics interactions and flow control. From time to time the journal publishes Special or Theme Issues featuring invited articles. Contributions may report research that falls within the broad spectrum of analytical, computational and experimental methods. This includes research conducted in academia, industry and a variety of environmental and geophysical sectors. Turbulence, transition and associated phenomena are expected to play a significant role in the majority of studies reported, although non-turbulent flows, typical of those in micro-devices, would be regarded as falling within the scope covered. The emphasis is on originality, timeliness, quality and thematic fit, as exemplified by the title of the journal and the qualifications described above. Relevance to real-world problems and industrial applications are regarded as strengths.
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