Evolution of instability modes in Mach 10 frozen and chemically reacting boundary layers by means of non-linear parabolized stability equations

Abstract

The physical mechanisms and laminar-to-turbulent transition scenarios characterizing hypersonic flows are not yet completely identified and well described as in low-supersonic and subsonic regimes. Particularly, there is a lack of knowledge about the role chemistry plays and the effects that high temperature has on the transition non-linear stages. In this study, transition in a Mach 10 adiabatic flat-plate boundary layer is investigated by means of non-linear parabolized stability equations, considering both frozen and chemical non-equilibrium (CNE) flow assumptions. A tendency to switch from a H- to a K-type transition scenario at the increment of the primary-mode initial amplitude is found, similar to what occurs in subsonic and low-supersonic regimes. Secondary-waves' initial amplitudes do not affect directly the occurring breakdown type, but they significantly influence the evolution of the higher harmonics, in particular the generation of streamwise steady vortices. Chemical reactions play an indirect role in transition through the determination of the laminar base flow and the linear stability characteristics of the primary instability. Excitation of secondary modes is weaker in CNE than in frozen conditions, but qualitatively similar. Contrary to previous studies, assuming frozen perturbations in a chemically reacting base flow is found to have a significant effect on the higher-harmonics amplitudes, in particular on the relative evolution of the secondary modes.