动力学模态分解和本征正交分解对圆柱绕流稳定性的分析
Anslysis Circular Cylinder Flow Using Dynamic Mode and Proper Orthogonal Decomposition

对雷诺数Re=100下的圆柱绕流非定常流场进行数值模拟，分别采用DMD方法和POD方法对圆柱绕流卡门涡街发展过程中的不稳定平衡阶段、过渡阶段以及稳定极限环阶段进行稳定性分析。分析结果表明：DMD方法准确地提取了不稳定平衡阶段和过渡阶段中的不稳定模态以及频率，在稳定极限环阶段准确提取了脱落涡模态及其高阶谐波模态和频率。DMD方法不仅可以高效提取主要流场结构模态和频率，且可分析相应模态的稳定性，从而得到动力学系统在时间和空间上的主要特征。POD方法中较少的模态包含流场绝大部分的能量，通过对模态系数进行FFT分析，可得到模态频率，但有时会存在多个频率耦合的模态，且POD方法无法判断所提取模态的稳定性，因此，POD方法主要得到的是动力学系统在空间上的主要特征。另外，DMD方法对流动类型范围的适用性更广。因此，在对复杂动力学系统进行稳定性分析时，DMD方法更具有优势。
The unsteady flow field of circular cylinder flow at Re =100 is numerically simulated. The stability of unstable equilibrium regime, transient regime and stable limit cycle regime which are in the process of Karman vortex street flow around a cylinder is analyzed by using DMD and POD methods respectively. The results show that: DMD method can accurately extract unstable mode and frequency in the unstable equilibrium regime and the transition regime, and extract shedding vortex modal, the high order harmonic mode and frequency in the stable limit cycle regime. DMD method not only can efficiently extract the main flow field structure mode and frequency, but also analyze the stability of the corresponding mode. Thus, it can get main characteristic of the dynamic system on the level of time and space. For POD method, a small number of modes contain most of the energy in the flow field. Based on FFT analysis mode amplitude, mode frequency can be obtained. However, sometimes there are modes whose multiple frequencies are coupled. POD method is unable to determine the stability of the mode extracted. So POD method gets the main space characteristic of dynamic system. In additional, DMD method has a broader applicability for flow type. Therefore, DMD method is more advantageous when stability of complex dynamics system need to be analyzed