Oblique transition in hypersonic double-wedge flow

Abstract

We utilize resolvent and weakly nonlinear analyses in combination with direct numerical simulations (DNS) to identify mechanisms for oblique transition in a Mach $5$ hypersonic flow over an adiabatic slender double wedge. Even though the laminar separated flow is globally stable, resolvent analysis demonstrates significant amplification of unsteady external disturbances to the linearized flow equations. These disturbances are introduced upstream of the separation zone and they lead to the appearance of oblique waves further downstream. We demonstrate that the large amplification of oblique waves arises from the growth of fluctuation shear stress due to streamline curvature of the laminar base flow in the separated shear layer. This is in contrast to the attached boundary layers, where no such mechanism exists. We also use a weakly nonlinear analysis to show that the resolvent operator associated with linearization around the laminar base flow governs the evolution of steady reattachment streaks that arise from quadratic interactions of unsteady oblique waves. These quadratic interactions generate vortical excitations in the reattaching shear layer which lead to the formation of streaks in the recirculation zone and their subsequent amplification, breakdown and transition to turbulence downstream. Our analysis of the energy budget shows that deceleration of the base flow near reattachment is primarily responsible for amplification of steady streaks. Finally, we employ DNS to examine latter stages of transition to turbulence and demonstrate the predictive power of a weakly nonlinear input–output framework in uncovering triggering mechanisms for oblique transition in separated high-speed boundary layer flows.

Stability of hypersonic flow over a curved compression ramp

“…(2021 b ) investigated numerically a transitional flow at Mach 5 over a hollow cylinder/flare, and found several possible transition paths, such as second mode, oblique mode and non-modal growth. Oblique transition in a hypersonic double-wedge flow was revealed by Dwivedi, Sidharth & Jovanović (2022).…”

Instability and transition onset downstream of a laminar separation bubble at Mach 6

“…Recent computational investigation of convective and global boundary-layer instabilities over a sharp cone-cylinder-flare model at Mach 6 by Paredes et al (2022) captured the distinct lobes within the disturbance amplification spectra measured with wall-pressure sensors at the BAM6QT with 10 • flare, and reported that the oblique Mack's first-mode waves that begin to amplify over the cone continue to grow along the separated shear layer. Weakly nonlinear input-output analysis and direct numerical simulations by Dwivedi, Sidharth & Jovanovic (2022) for a globally stable double wedge flow at Mach 5 discussed that shear stress fluctuation due to streamline curvature as the physical mechanism for the amplification of the oblique waves.…”

Stochastic receptivity of laminar compressible boundary layers: An input-output analysis

“…For instance, Dwidedi et al 29 quantified the amplification of streaks due to external harmonic excitation in supersonic laminar boundary layer and hypersonic compression ramp flows. Using the same framework, Dwidedi et al 30 investigated oblique transition in a Mach 5 hypersonic flow over an adiabatic slender double-wedge. For the turbulent regime, Bae et al 31 Although the above findings provide a good understanding of the amplification of first and second modes and streaks in supersonic boundary layers, it should be pointed out that the above mentioned models have some limitations.…”