Abstract The present work is a comparative analysis of Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) computed on experimental turbulent velocity fields measured in a 20L-tank stirred by two Rushton impellers at two rotating speeds, N = 150 and 300 rpm. POD identifies flow structures that optimally capture the total kinetic energy of the flow, while DMD identifies structures that significantly contribute to the dynamics of the flow. The experimental data, i.e. the instantaneous velocity fields U r ( r , z , t ) and U z ( r , z , t ) , come from 2-D Particle Image Velocimetry (PIV). The flow motion is turbulent, and it occurs over a wide range of length and time scales, from equipment-dependent large-scale coherent structures to the smallest-scale eddies where energy dissipation takes place. It thus provides an interesting benchmark case for the comparison between POD and DMD, which are based on energy and dynamic analysis, respectively. POD analysis reveals that the most energetic structures are related to the inherent periodic unsteadiness due to the relative motion between the rotating impeller blades and the non-moving baffles. Apart from the mean field, the first most energetic group of modes is related to trailing vortices induced by the Rushton turbines and is associated to a frequency equivalent to the blade passage frequency and its overtones. The second most energetic group of modes is related to vortical structures in the impeller stream and is associated to a frequency equivalent to the rotating speed. DMD analysis identifies flow structures that are found similar to these most energetic modes, although differences appear due to the fact that DMD isolates structures associated to a single frequency and their corresponding growth/decay rate. As in POD, the relative importance of each DMD mode can be estimated using an appropriately defined energy criterion. Comparison of the results from both modal decomposition methods points out their complementarity and their potential for describing the spatial and time characteristics of the flow within a stirred tank.

中文翻译：

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使用模态分解技术、POD 和 DMD 分析 PIV 测量，以研究搅拌釜反应器内的流动结构及其动力学

摘要 目前的工作是对由两个 Rushton 叶轮以两种转速（N = 150 和 300 rpm）搅拌的 20 升罐中测量的实验湍流速度场计算的适当正交分解 (POD) 和动态模式分解 (DMD) 的比较分析. POD 识别最佳捕获流动总动能的流动结构，而 DMD 识别对流动动力学有显着贡献的结构。实验数据，即瞬时速度场U r ( r , z , t ) 和U z ( r , z , t ) 来自二维粒子图像测速(PIV)。流动是湍流的，它发生在很宽的长度和时间尺度范围内，从依赖于设备的大规模相干结构到发生能量耗散的最小尺度涡流。因此，它为分别基于能量和动态分析的 POD 和 DMD 之间的比较提供了一个有趣的基准案例。POD 分析表明，由于旋转叶轮叶片和非移动挡板之间的相对运动，能量最高的结构与固有的周期性不稳定有关。除了平均场之外，第一组能量最高的模式与拉什顿涡轮机引起的尾涡有关，并且与等效于叶片通过频率及其泛音的频率有关。第二组能量最高的模式与叶轮流中的涡旋结构有关，并与与转速等价的频率相关。DMD 分析确定了与这些能量最高的模式相似的流动结构，尽管由于 DMD 隔离了与单个频率相关的结构及其相应的增长/衰减率，因此出现了差异。在 POD 中，可以使用适当定义的能量标准来估计每个 DMD 模式的相对重要性。两种模态分解方法的结果比较指出了它们的互补性以及它们在描述搅拌罐内流动的空间和时间特征方面的潜力。