Numerical Investigation of Nonlinear Boundary-Layer Transition for Cones at Mach 6

Abstract

Direct numerical simulations were carried out for a straight and a flared cone at Mach 6 and zero angle of attack to investigate the effects of geometry on the linear and nonlinear stages of the laminar–turbulent transition process. 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. In the linear (primary) instability regime the flared cone resulted in larger integrated growth rates ( factors) and a higher dominant second mode frequency. Investigations of the secondary instability regime revealed that the flared cone also leads to a stronger fundamental resonance, characterized by larger integrated growth rates of the secondary instability waves after resonance onset. For both cases, the so-called controlled fundamental breakdown simulations were carried out, which showed the development of similar patterns of streamwise hot streaks on the surface of the cones. Streamwise streaks were also observed in the Purdue experiments (for the flared cone only) using temperature-sensitive paint. A detailed comparison of the results obtained for both geometries indicated that the streak development is caused by the same nonlinear mechanisms.