DMD和POD对超燃冲压发动机凹腔流动的稳定性分析

开式凹腔作为超燃冲压发动机中增加掺混和稳焰的装置, 其流动稳定性的研究对深入理解凹腔增加掺混和稳焰机理以及凹腔的设计有着重要的学术意义和工程应用价值.基于大涡模拟方法对超燃冲压发动机开式凹腔流动进行数值模拟, 分别采用动力学模态分解(dynamic mode decomposition, DMD)和本征正交分解方法(proper orthogonal decomposition, POD)对自激振荡流动进行稳定性分析. DMD方法可准确提取凹腔的振荡频率, 与Rossiter模型以及压力脉动FFT分析得到的频率吻合较好, 且DMD中对应Rossiter前3阶频率的模态在流动中的主导作用顺序也与FFT分析结果一致, 自激振荡中RossiterⅢ模态占据主导作用, 同时DMD方法对Rossiter 3阶以上模态频率的预测能力明显强于FFT分析方法.在对低频的提取方面, DMD方法比Rossiter模型更具有优势.与前6阶Rossiter模态对应DMD模态均缓慢收敛, 主要表现为剪切层中的分离涡结构和中部及下游区域中的涡结构.前3阶不稳定模态中的分离涡结构主要集中在中部剪切层以及后缘附近区域. POD方法中较少的模态包含流场绝大部分的能量.但是, 通过POD方法提取的模态频率在分辨率上效果不佳, 提取到最低频率为Rossiter 3阶模态对应的频率, 且模态中均存在次频, 次频与主频之间的耦合导致模态的形态相差较大.另外, 与DMD方法相比POD方法无法判断所提取的模态的稳定性. 

Stability Analysis of Scramjet Open Cavity Flow Base on POD and DMD Method

Study on stability analysis of open cavity which is a device of scramjet for mixing enhancement and flame holding has significant value to academic and engineering application. Large eddy simulation method was used to simulate the scramjet open cavity flow. And the dynamic mode decomposition method (DMD) and the proper orthogonal decomposition(POD) were carried out on the stability analysis for self-sustained oscillation flow. The DMD method can accurately extract the oscillation frequency. And the results are in good agreement with Rossiter model and FFT analysis of pressure fluctuation. The order of leading role of the DMD modes which is corresponding the first three Rossiter modes in the flow is also consistent with the FFT analysis results. The Rossiter Ⅲ mode occupies the most leading role in the self-sustained oscillation flow. At the same time, the predictive ability of the DMD method for over third order Rossiter mode frequencies is better than that of FFT analysis method. As for the extracting low frequencies, DMD method has more advantages over Rossiter model. The DMD modes corresponding to the first six Rossiter modes converge slowly and show as the shear layer separated vortex and the vortex in middle region and downstream region. The separated vortex structure of the first three order unstable modes mainly focuses on the shear layer and the region near the trailing edge. For the POD method, a small number of modes contain most of the energy in the flow field. However, the resolution ratio of the mode frequency extracted by POD is not high enough. The lowest frequency extracted is corresponding with Rossiter three-order mode. Second frequencies exist in the mode, and the coupling between the main and the second frequencies results in a large difference of the mode form. In addition, the stability of the mode could not be decided by POD method compared with DMD method.