Global input-output analysis of flow instabilities in high-speed compressible flows

Abstract

We present a global framework for quantifying the amplification of small perturbations in high-speed compressible boundary layer flows over complex geometries in the presence of exogenous disturbances. Our global input-output approach generalizes the hydrodynamic stability analysis by accounting for energy amplification due to time-periodic inputs as well as initial conditions over a finite-time horizon. Our analysis of hypersonic flows over curved geometries demonstrates how the dominant response's spatial structure can be used to investigate the physical mechanisms for perturbation growth in realistic flow configurations. To demonstrate the usefulness of this approach, we utilize it to investigate the origin of three-dimensional streaks observed in various experiments of two-dimensional laminar shock-wave boundary layer interaction. These streaks are associated with heat flux striations at the wall near flow reattachment, and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favorably with observations from multiple hypersonic shock-wave boundary layer interaction experiments. Further investigations into the dominant structures obtained from this analysis, both with and without external disturbances, demonstrate that physical effects unique to compressible separated flows result in the emergence of experimental three-dimensionality.