Stabilities and transition of a hypersonic boundary layer with three-dimensional distributed roughnesses

Roughness surfaces likely present on high-speed flight vehicles due to ablation can greatly impact the laminar-turbulent transition process. In this work, effects of a randomly distributed roughness patch with roughness Reynolds number Rekk=474 on the stability and transition in a Mach 6.5 boundary-layer flow over a flat plate have been investigated via stability analyses and direct numerical simulation (DNS). The roughness patch induces several streamwise streaks downstream. The streaks slightly stabilize the Mack mode instability, yet sustain strongly unstable shear-layer modes, achieving a significantly larger integrated growth rate than the smooth case. The most amplified shear-layer mode extracts energy primarily through the spanwise velocity gradient and develops nonlinearly into hairpin vortices residing on the strongest low-speed streak. The hairpin vortices eventually contaminate the whole flowfield, leading to a fully turbulent state. We further assess the influences of wall-temperature ratio and the roughness geometry on the flowfield and the pertaining instability characteristics. The results reveal that the high wall-temperature ratio weakens the streak amplitudes and shear-layer instabilities; while randomly distributed roughness tends to induce larger-amplitude streaks than the regular counterpart with the same Rekk, the flowfield of the former one can even be more stable than the latter. We find that the spanwise gradient of streamwise velocity should also be considered along with the streak amplitude in determining the strength of shear-layer instabilities.