标题： 可压缩开腔流动的全局不稳定性 显示英文标题

标题： Biglobal instabilities of compressible open-cavity flows

摘要： 可压缩横向周期性开腔流的稳定性特性通过直接数值模拟和全局稳定性分析进行研究，针对长宽比为$L/D=2$和 6 的矩形腔体。本研究考察了在亚音速和跨音速条件下层流区域中不稳定性的行为，此时可压缩性起着重要作用。观察到马赫数的增加会破坏亚音速区域的流动并稳定跨音速区域的流动。进行全局稳定性分析以提取关于二维稳态的指定横向波长的二维和三维特征模态。二维特征模态的特性与二维非线性模拟中观察到的结果非常一致。在三维特征模态的分析中发现，马赫数的增加会稳定主要的三维特征模态。对于短腔体$L/D=2$，三维特征模态主要源自离心不稳定性。对于长腔体$L/D=6$，出现其他类型的特征模态，其结构从腔体后部延伸到中部。在$M_\infty=0.6$进行了若干三维DNS。对于$L/D=2$，三维非线性流动中存在的三维结构特性与线性稳定性分析得到的结果非常接近。然而，对于$L/D=6$，由于在腔体长度上发展出强烈的非线性，无法在三维DNS中清晰观察到三维特征模态。此外，注意到流动中的三维性有助于缓解长腔体的剧烈振荡。本文进行的分析可以为设计有效的流动控制策略提供有价值的见解，以抑制可压缩开腔流中不利的气动和压力波动。 显示英文摘要

摘要： The stability characteristics of compressible spanwise-periodic open-cavity flows are investigated with direct numerical simulation and biglobal stability analysis for rectangular cavities with aspect ratios of $L/D=2$ and 6. This study examines the behavior of instabilities with respect to stable/unstable steady states in the laminar regimes for subsonic and transonic conditions where compressibility plays an important role. It is observed that an increase in Mach number destabilizes the flow in the subsonic regime and stabilizes the flow in the transonic regime. Biglobal stability analysis is conducted to extract 2D and 3D eigenmodes for prescribed spanwise wavelengths about the 2D steady state. The properties of 2D eigenmodes agree well with those observed in the 2D nonlinear simulations. In the analysis of 3D eigenmodes, it is found that an increase of Mach number stabilizes dominant 3D eigenmodes. For a short cavity with $L/D=2$, the 3D eigenmodes primarily stem from centrifugal instabilities. For a long cavity with $L/D=6$, other types of eigenmodes appear whose structures extend from the aft-region to the mid-region of the cavity. A selected number of 3D DNS are performed at $M_\infty=0.6$. For $L/D=2$, the properties of 3D structures present in the 3D nonlinear flow correspond closely to those obtained from linear stability analysis. However, for $L/D=6$, the 3D eigenmodes cannot be clearly observed in the 3D DNS, due to the strong nonlinearity that develops over the length of the cavity. In addition, it is noted that three-dimensionality in the flow helps alleviate violent oscillations for the long cavity. The analysis performed in this paper can provide valuable insights for designing effective flow control strategies to suppress undesirable aerodynamic and pressure fluctuations in compressible open-cavity flows.