We combine reduced order modeling and system identification to reconstruct the temporal evolution of large-scale vortical structures behind the blades of a Rushton impeller. We performed direct numerical simulations at Reynolds number 600 and employed proper orthogonal decomposition (POD) to extract the dominant modes and their temporal coefficients. We then applied the identification algorithm, N4SID, to construct an estimator that captures the relation between the velocity signals at sensor points (input) and the POD coefficients (output). We show that the first pair of modes can be very well reconstructed using the velocity time signal from even a single sensor point. A larger number of points improves accuracy and robustness and also leads to better reconstruction for the second pair of POD modes. Application of the estimator derived at Re = 600 to the flows at Re = 500 and 700 shows that it is robust with respect to changes in operating conditions.

中文翻译：

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从有限的传感器数据重建搅拌罐中的大规模流动结构

我们结合降阶建模和系统识别来重建拉什顿叶轮叶片后面的大型涡流结构的时间演变。我们在雷诺数 600 处进行了直接数值模拟，并采用适当的正交分解 (POD) 来提取主要模式及其时间系数。然后，我们应用识别算法 N4SID 来构建一个估计器，该估计器捕获传感器点（输入）处的速度信号与 POD 系数（输出）之间的关系。我们表明，即使使用来自单个传感器点的速度时间信号，也可以很好地重建第一对模式。大量的点提高了准确性和鲁棒性，并且还为第二对 POD 模式带来了更好的重建。推导出的估计量的应用重 = 600向在流重 = 500所700表明，它是相对于在操作条件的变化的鲁棒性。