Direct Numerical Simulation of Second-Mode Oblique Breakdown in a Mach 6 Sharp Cone Boundary Layer

Direct Numerical Simulations (DNS) were carried out to investigate the laminar-turbulent boundary-layer transition process for a 7◦ half-angle cone with a circular cross-section and a sharp nose at Mach 6 and zero angle of attack. The cone geometry and the flow conditions of experiments in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University were used for the numerical investigations. Linear Stability Theory (LST) analysis revealed that while axisymmetric second-mode waves are the dominant primary instability, shallow second-mode waves also experience strong amplification. Consequently, the role of second-mode oblique breakdown was explored by introducing a pair of oblique second-mode waves at low amplitudes. The disturbance development in downstream direction and the laminar to turbulent transition process is investigated. It is shown how the disturbance wave spectrum is filled up due to nonlinear interactions and which flow structures arise and how these structures locally break down to small scales. The skin friction initially follows the laminar trend, then exhibits a slight rise, dips back toward laminar levels, and subsequently increases toward turbulent values. A significant difference between the second mode oblique breakdown and previously investigated fundamental breakdown is the much reduced “overshoot” of the turbulent values of skin-friction and Stanton number in the transitional region. The DNS data clearly demonstrate that second mode oblique breakdown can lead to laminar-turbulent transition and therefore may be arelevant mechanism for transition in hypersonic cone boundary layers at Mach 6.