Instabilities and transition in cooled wall hypersonic boundary layers

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Abstract
Wall cooling has substantial qualitative and quantitative effects on the development of instabilities and subsequent transition processes in hypersonic boundary layers (HBLs). A sequence of linear stability theory, nonlinear two-dimensional and three-dimensional direct numerical simulations is used to analyse Mach 6 boundary layers, with wall temperatures ranging from near-adiabatic to highly cooled conditions, where the second-mode instability is accompanied by radiation of energy. Decomposition of linear stability modes into their fluid-thermodynamic (acoustic, vortical and thermal) components shows that this radiation comprises both acoustic as well as vortical waves. Furthermore, in these cases, two-dimensional simulations show that the conventional ‘trapped’ nature of second-mode instability is ruptured. A quantitative analysis indicates that 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. The direct impact of these mechanisms on the transition process itself is examined with high-fidelity simulations of three-dimensional second-mode wavepacket propagation. 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 also displays different behaviour; 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. These features have a direct impact on wall loading, including skin friction and heat transfer. In moderately cooled walls, the spatially localized wall loading is similar to those in near-adiabatic walls, with dominant impact 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.

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