Effect of downstream wall on linear global instability of hypersonic flow over axi-symmetric open cavities

This study follows upon the experimental findings of (Das & Cohen - DOI: 10.2514/1.J055895), which demonstrated the attenuation of unsteadiness by modifying the downstream wall of an open cavity at transonic conditions. Qualitatively the effect was attributed to the disruption of the Rossiter resonance mechanism. Global stability analysis associated Rossiter modes with global modes of the steady subsonic (Bres & Colonius - DOI: 10.1017/s0022112007009925) and supersonic (Sun et al. - DOI: 10.1017/jfm.2017.416) 2D laminar baseflow. In this work, we extend the analysis to the hypersonic regime, employing a BiGlobal linear stability analysis of compressible open cavity flows. The impact of varying downstream wall geometry on the breakdown of self-sustaining oscillation mechanism is explored. A multi-domain matrix forming method, utilizing high-order accurate finite difference and spectral discretization in generalized coordinates, is used for LNSE-based stability analysis. A direct sparse parallel solver is employed, and the potential for matrix-free iterative schemes for eigendecomposition is examined. Future research will incorporate non-modal stability analysis and novel WENO schemes, further expanding the scope of this study.