Instabilities and transition in cooled-wall hypersonic boundary layers

TL;DR

This study investigates how wall cooling influences instabilities and transition in hypersonic boundary layers at Mach 6, revealing that cooling accelerates transition and increases skin friction and heat transfer due to wavepacket elongation and turbulence.

Contribution

It provides a comprehensive analysis combining linear stability theory and DNS to show how wall cooling affects instability mechanisms and transition in hypersonic boundary layers, highlighting new behaviors of wavepackets.

Findings

Wall cooling destabilizes second-mode instabilities and accelerates transition.

Cooled-wall boundary layers exhibit wavepacket elongation and turbulence spurts.

Highly-cooled walls lead to increased skin friction and heat transfer.

Abstract

Wall cooling has substantial effects on the development of instabilities and transition processes in hypersonic boundary layers (HBLs). A sequence of linear stability theory, two-dimensional and non-linear three-dimensional DNSs is used to analyze Mach~6 boundary layers, with wall temperatures ranging from near-adiabatic to highly cooled conditions, where the second-mode instability radiates energy. Fluid-thermodynamic analysis shows that this radiation comprises both acoustic as well as vortical waves. 2D simulations show that the conventional "trapped" nature of second-mode instability is ruptured. Although the energy efflux of both acoustic and vortical components increases with wall-cooling, the destabilization effect is much stronger and no significant abatement of pressure perturbations is realized. In the near-adiabatic HBL, the wavepacket remains trapped within the boundary layer and attenuates outside the region of linear instability. However, wavepackets in the cooled-wall HBLs amplify and display nonlinear distortion, and transition more rapidly. The structure of the wavepacket displays different behavior; moderately-cooled walls show bifurcation into a leading turbulent head region and a trailing harmonic region, while highly-cooled wall cases display lower convection speeds and significant wavepacket elongation, with intermittent spurts of turbulence in the wake of the head region. This elongation effect is associated with a weakening of the lateral jet mechanism due to the breakdown of spanwise coherent structures. In moderately cooled-walls, the spatially-localized wall loading is due to coherent structures in the leading turbulent head region. In highly-cooled walls, the elongated near-wall streaks in the wake region of the wavepacket result in more than twice as large levels of skin friction and heat transfer over a sustained period of time.