Title: Spanwise effects on instabilities of compressible flow over a long rectangular cavity Show Chinese title

Title: 可压缩流过长矩形腔体的不稳定性的展向效应

Abstract: The stability properties of two- (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of $L/D=6$ is analyzed at a free stream Mach number of $M_\infty=0.6$ and depth-based Reynolds number of $Re_D=502$. In this study, we closely examine the influence of three-dimensionality on the wake-mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the instability characteristics of the wake-mode. Using the bi-global stability analysis with the time-average flow as the base state, we capture the global stability properties of the wake-mode at a spanwise wavenumber of $\beta=0$. To uncover spanwise effects on the 2D wake-mode, 3D DNS are performed with cavity width-to-depth ratio of $W/D=1$ and $2$. We find that the 2D wake-mode is not present in the 3D cavity flow for a wider spanwise setting with $W/D=2$, in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of $\lambda/D=0.5-2.0$ to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake-mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities. Show Chinese abstract

Abstract: 二维（2D）和三维（3D）压缩流在长深比为$L/D=6$的矩形腔体上的稳定性特性在自由来流马赫数为$M_\infty=0.6$和基于深度的雷诺数为$Re_D=502$的情况下进行了分析。在本研究中，我们仔细考察了三维性对尾涡模式的影响，该尾涡模式已被报道会由于大尺度展向涡旋的形成和喷射而表现出高幅值波动。采用直接数值模拟（DNS）和双全局稳定性分析来研究尾涡模式的不稳定性特征。使用以时间平均流作为基本状态的双全局稳定性分析，我们在展向波数为$\beta=0$的情况下捕捉到了尾涡模式的全局稳定性特性。为了揭示展向效应对于二维尾涡模式的影响，进行了展宽比为$W/D=1$和$2$的三维DNS。我们发现，在展向更宽的设置下，即$W/D=2$，三维腔体流中不存在二维尾涡模式，在腔体后部区域观察到了展向结构。 这些三维不稳定性通过针对展向波长为$\lambda/D=0.5-2.0$的双全局稳定性分析进一步研究，以揭示三维本征模态的本征谱。 基于二维和三维全局稳定性分析的结果，我们得出结论，三维矩形腔流中缺乏尾迹模态是由于来自展向涡旋的动能释放到由展向不稳定性发展而来的流向涡旋结构。