A history and progress of research on boundary-layer transition on a mach 6 flared cone

This paper summarizes the efforts to improve the understanding of boundary-layer transition caused by the second-mode instability on a 3-meter circular arc flared cone geometry by combining experimental and computational results. With a nominally smooth wall at unit Reynolds numbers from 7.3×10⁶/m to 12×10⁶/m, a hot-cold-hot heating pattern composed of streamwise streaks was measured under quiet flow at Mach 6. Simultaneous pressure-fluctuation measurements showed the non-linear growth and breakdown of the second-mode wave. A maximum second-mode magnitude of 30% of the mean surface pressure was measured prior to breakdown and transition to turbulence. Roughness elements that were small enough to interact with the second-mode wave without becoming boundary layer trips altered the pattern of heating, but pressure fluctuation data trends remained relatively unchanged. Stability analyses using the Parabolized Stability Equations implemented a Gaussian wave-packet formulation to study the physical processes that re-distribute energy as the second-mode instability amplifies. The general trends with this PSE formulation were similar to experimental results, but disturbance amplitudes were only 50% of what was measured experimentally. Direct Numerical Simulations were carried out using a “controlled” disturbance input. The forcing parameters were determined by mapping out the linear stability regime and carrying out a parameter study of the so-called fundamental resonance onset. The simulation results exhibit streamwise streaks of high skin friction and of high heat transfer at the cone surface, which were also observed in the experiments using temperature-sensitive paint.