Biglobal instabilities of compressible open-cavity flows

摘要

The stability characteristics of compressible spanwise-periodic open-cavityflows are investigated with direct numerical simulation and biglobal stabilityanalysis for rectangular cavities with aspect ratios of $L/D=2$ and 6. Thisstudy examines the behavior of instabilities with respect to stable/unstablesteady states in the laminar regimes for subsonic and transonic conditionswhere compressibility plays an important role. It is observed that an increasein Mach number destabilizes the flow in the subsonic regime and stabilizes theflow in the transonic regime. Biglobal stability analysis is conducted toextract 2D and 3D eigenmodes for prescribed spanwise wavelengths about the 2Dsteady state. The properties of 2D eigenmodes agree well with those observed inthe 2D nonlinear simulations. In the analysis of 3D eigenmodes, it is foundthat an increase of Mach number stabilizes dominant 3D eigenmodes. For a shortcavity with $L/D=2$, the 3D eigenmodes primarily stem from centrifugalinstabilities. For a long cavity with $L/D=6$, other types of eigenmodes appearwhose structures extend from the aft-region to the mid-region of the cavity. Aselected number of 3D DNS are performed at $M_\infty=0.6$. For $L/D=2$, theproperties of 3D structures present in the 3D nonlinear flow correspond closelyto those obtained from linear stability analysis. However, for $L/D=6$, the 3Deigenmodes cannot be clearly observed in the 3D DNS, due to the strongnonlinearity that develops over the length of the cavity. In addition, it isnoted that three-dimensionality in the flow helps alleviate violentoscillations for the long cavity. The analysis performed in this paper canprovide valuable insights for designing effective flow control strategies tosuppress undesirable aerodynamic and pressure fluctuations in compressibleopen-cavity flows.