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The stability characteristics of compressible spanwise-periodic open-cavity flows are investigated with direct numerical simulation (DNS) 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 and unstable steady states in the laminar regimes for subsonic as well as 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 for spanwise-periodic flows over rectangular cavities with large aspect ratio is closely examined in this study due to its importance in aerodynamic applications. Moreover, biglobal stability analysis is conducted to extract 2D and 3D eigenmodes for prescribed spanwise wavelengths λ/D 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, in addition to the centrifugal instability mode located in the rear part of the cavity. A selected number of 3D DNS are performed at M ∞ = 0.6 for cavities with L/D = 2 and 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.

Designing effective control for complex three-dimensional flow fields proves to be nontrivial. Oftentimes, intuitive control strategies lead to suboptimal control. To navigate the control space, we utilize a linear parabolized stability analysis to guide the design of a control scheme for a trailing vortex flow field aft of a NACA0012 half-wing at an angle of attack α = 5 • and a chord-based Reynolds number Re = 1000. The stability results show that the unstable mode with the smallest growth rate (fifth wake mode) provides a pathway to excite a vortex instability, whereas the principal unstable mode remains in the wake of the wing. Inspired by this finding, we perform direct numerical simulations that excite each mode with body forces matching the shape function from the stability analysis. Relative to the baseline uncontrolled case, the principal wake mode reduces the vortex length, while the fifth wake mode further shortens the tip vortex. Analogously, the streamwise circulation of the trailing vortex is found to be significantly reduced. From these results, we conclude that a rudimentary linear stability analysis can provide key insight into the underlying physics and help engineers design more effective control.

The present work investigates sidewall effects on the characteristics of three-dimensional (3D) compressible flows over a rectangular cavity with aspect ratios of L/D = 6 and W/D = 2 at ReD = 10 4 using large eddy simulations (LES). For the spanwise-periodic cavity flow, large pressure fluctuations are present in the shear layer and on the cavity aft wall due to spanwise vortex roll-ups and flow impingement. For the finite-span cavity with sidewalls, pressure fluctuations are reduced due to interference to the vortex roll-ups from the sidewalls. Flow oscillations are also reduced by increasing the Mach number from 0.6 to 1.4. Furthermore, secondary flow inside the cavity enhances kinetic energy transport in the spanwise direction. Moreover, 3D slotted jets are placed along the cavity leading edge with the objective of reducing flow oscillations. Steady blowing into the boundary layer is considered with momentum coefficient Cµ = 0.0584 and 0.0194 for M∞ = 0.6 and 1.4 cases, respectively. The three-dimensionality introduced to the flow by the jets inhibits large coherent roll-ups of the spanwise vortices in the shear layer, yielding 9 − 40% reductions in rms pressure and rms velocity for both spanwise-periodic and finite-span cavities.

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 ∞ = 0.6 and depth-based Reynolds number of Re D = 502. In this study, we closely examine the influence of threedimensionality 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 β = 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 λ/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.