Hypersonic boundary-layer transition: Comparison of the fundamental resonance breakdown for a flared and straight cone at mach 6

A side-by-side comparison of high-order accurate Direct Numerical Simulations (DNS) conducted for a straight and flared cone at Mach 6 is presented in order to investigate the effects of geometry on the linear and nonlinear stages of laminar-turbulent transition. The cone geometries and the flow conditions of the simulations are chosen to closely match those of the experiments conducted at the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. Linear stability regime calculations using low amplitude short-duration pulse simulations indicate, as expected, that the cone flare shifts the dominant second mode frequencies to higher values and significantly increases the spatial growth rates. Secondary instability investigations revealed that for both geometries the fundamental resonance would be most likely the relevant mechanism leading to transition for the Purdue quiet tunnel conditions. However, the azimuthal wave number leading to the strongest resonance (largest N-factor for secondary instability) has shifted to lower values for the flared cone compared with the straight cone. For both cases, so-called “controlled” breakdown simulations presented in this paper showed a similar pattern of “hot streaks” that appear, disappear, and reappear further downstream which was also observed in the Purdue experiments (for the flared cone only) using temperature sensitive paint (TSP). A detailed flow field analysis of the DNS data confirmed that these streaks are generated by a streamwise vortical mode. Both geometries showed good agreement of the streamwise development of the secondary streak pattern and subsequent breakdown to smaller structures in the final breakdown. The results presented in this paper confirm the destabilizing effect of the cone flare with regard to the primary instability. In addition, the flared cone is also more unstable with respect to the secondary instability, leading to larger growth rates of the secondary disturbance wave after resonance onset. As a result, the cone flare accelerates the transition process leading to the breakdown to turbulence further upstream compared to the straight cone. Hoewever, the qualitative similarities of the nonlinear behavior between the flared and straight cone suggest that for the BAM6QT quiet conditions the fundamental resonance is likely the relevant nonlinear breakdown mechanism for the straight cone as well.