基于POD和DMD方法的跨声速抖振模态分析

跨声速抖振现象是由于非定常跨声速流动中激波的自激振荡而引起的结构强迫振荡，这种现象在跨声速飞行器中普遍存在，对飞机的结构强度和疲劳寿命有不利影响。基于模态分解的分析方法是进一步发展抖振控制手段的有效工具。本文通过两类典型模态分析方法（本征正交分解（POD）和动态模态分解（DMD））对OAT15A翼型的跨声速抖振现象进行分析，通过对模态频率、翼面压力分布、流场重构误差等方面的研究，将两种模态分解方法进行对比。发现基于频率特征的DMD方法能够准确捕捉抖振的临界稳定特征和抖振主频的典型模态，同时能够更准确反映流场变量在激波间断附近随时间的变化过程；而POD方法尽管在流场重构时具有较小的总体误差，但对激波附近压强随时间的变化历程拟合较差。

Modal analysis of transonic buffet based on POD and DMD method

Transonic buffet is due to the self-sustained oscillations of shock wave in the unsteady transonic flow, which induces the forced periodically motion of the structure. For aircraft in transonic flow, this phenomenon exists commonly, leading to negative effects on the structural strength and fatigue life. Analysis based on mode decomposition is an effective tool for developing buffet control design. In this paper, two typical mode analysis methods, i.e., proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are utilized for analyzing the transonic buffet of the OAT15A airfoil. Two techniques are compared by studying the frequency of dominant modes, pressure distributions on the surface and the errors of flow construction. Results indicate that because of the consideration of frequency characteristics in DMD, the critical stable characteristics and dominant frequency of transonic buffet are well captured. Besides, DMD method accurately mimic the time evolutions of flow variables near the shock wave. Although POD method provides relatively small errors for flow reconstruction, it performs worse than DMD near the shock wave region, because of the poorer approximation of pressure evolution in time.