基于模态分解的液环泵喷射器内非定常流动分析

为分析液环泵喷射器内复杂高速射流流场的瞬态流动特性，揭示射流尾迹涡脱落及激波自激振荡频率特征，该研究基于大涡模拟（Large Eddy Simulation, LES）数值模拟采用动态模态分解（Dynamic Mode Decomposition, DMD）和谱本征正交分解（Spectral Proper Orthogonal Decomposition, SPOD）方法对射流拟序结构进行时空解耦，对比分析2种模态分解方法在射流流动特征提取的差异性。研究结果表明，喷射器射流剪切层在与激波的干涉作用下呈现周期性振荡现象，且随着射流的演化其尾缘逐渐形成周期性脱落的尾迹涡。DMD和谱本征正交分解SPOD方法均能实现高速射流流场的解耦，且能够获得时空单频相干特征结构。主导频率1 250 Hz时，密度场DMD和SPOD 1阶模态均能反映激波及其与射流剪切层相互干扰形成的激波串结构特征；频率18 000 Hz时，DMD和SPOD动态模态则表征了射流尾缘周期性脱落的尾迹涡特征。相较于DMD方法，SPOD方法精准获取时空单频动态模态的同时能够反映出湍流射流的演变特征，而且有效避免了DMD基模态筛选时存在的不足。该研究基于LES数值模拟结果采用特征分解方法对喷射器内非定常流场进行了特征分解，为深入探索液环泵喷射器内复杂多物理耦合场奠定基础。

Unsteady flow in liquid ring pump ejector using mode decomposition

A liquid-ring pump is one of the commonly-used rotating positive-displacement machines. This study aims to analyze the transient flow characteristics of complex high-speed jet flow field in the ejector of liquid ring pump, in order to reveal the frequency characteristics of jet wake vortex shedding and shock wave self-excited oscillation. Dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD) were used to decouple the jet coherent structure using large eddy simulation (LES). Two modes of decomposition were compared to extract the jet flow features. The results show that the vortex band was formed in the mixing chamber for the strong shear effect of the jet shear layer. The shape of shear vortex was changed to fall off at the trailing edge of jet, due to the influence of vortex zone. The periodic oscillation was found in the shear layer of the jet under the interaction with the shock waves. As such, the periodic shedding wake vortex was gradually formed at the trailing edge of the jet. The decoupling analysis of the high speed jet flow field was also achieved to obtain the spatiotemporal single frequency coherence structure using DMD and SPODs. The flow field at the target time was accurately predicted using the first five-order DMD density modes, where the root mean square error (RMSE) and absolute percentage error were 3.5% and 1.5%, respectively. The DMD mode with the frequency of 0 Hz presented the highest energy proportion, indicating the steady-state characteristics of unsteady flow. The first-order DMD mode with the frequency of 1250Hz was utilized to capture the shock wave and the shock string structure that formed by the interaction between the shock wave and the jet shear layer. The spatial structure shared the periodic evolution characteristics of jet shear vortexes in the second and third order DMD modes with the frequencies of 17 and 18, respectively. In addition, there was the similarity of spatial structure in the DMD modes in the high frequency band, indicating a multi-frequency coupling shedding of jet wake vortexes. The dominant mode of SPOD was better reflected by the frequency amplitude. The characteristic values of SPOD were arranged in the descending order at each frequency. In the frequency of 1 250 Hz, the first-order SPOD mode also reflected the shock wave structure similar to the first-order DMD mode. Meanwhile, there was the similar characteristic structure in the SPOD and DMD mode in the high frequency band. The characteristic scale of the second-order SPOD mode was smaller than that of the first-order mode. It infers that the coherent structure of turbulent jet was constantly evolved into the multi-scale flows during the process of development. The SPOD can be expected to accurately obtain the spatiotemporal single frequency dynamic modes for the evolution characteristics of turbulent jet, compared with the DMD. In addition, the SPOD can also effectively avoid the DMD in the selection of dominant mode. Therefore, the SPOD has more advantages than the DMD in the coherent structure decoupling analysis of turbulent jets.