Numerical Investigation of Laminar-Turbulent Transition in a Cone Boundary Layer at Mach 6

Abstract

Direct Numerical Simulations (DNS) are performed to investigate laminar-turbulent transition in a boundary layer on a sharp cone at Mach 6. The main objective of this dissertation research is to explore which nonlinear breakdown mechanisms may be dominant in a broad--band "natural" disturbance environment and then use this knowledge to perform controlled transition simulations to investigate these mechanisms in great detail. Towards this end, a "natural" transition scenario was modeled and investigated by generating wave packet disturbances. The evolution of a three-dimensional wave packet in a boundary layer has typically been used as an idealized model for "natural" transition to turbulence, since it represents the impulse response of the boundary layer and, thus, includes the interactions between all frequencies and wave numbers. These wave packet simulations provided strong evidence for a possible presence of fundamental and subharmonic resonance mechanisms in the nonlinear transition regime. However, the fundamental resonance was much stronger than the subharmonic. In addition to these two resonance mechanisms, the wave packet simulations also indicated the possible presence of oblique breakdown mechanism. To gain more insight into the nonlinear mechanisms, controlled transition simulations were performed of these mechanisms. Several small and medium scale simulations were performed to scan the parameter space for fundamental and subharmonic resonance. These simulations confirmed the findings of the wave packet simulations, namely that, fundamental resonance is much stronger compared to the subharmonic resonance. Subsequently a set of highly resolved fundamental and oblique breakdown simulations were performed. In these DNS, remarkable streamwise arranged "hot'' streaks were observed for both fundamental and oblique breakdown. The streaks were a consequence of the large amplitude steady longitudinal vortex modes in the nonlinear régime. These simulations demonstrated that both second--mode fundamental breakdown and oblique breakdown may indeed be viable paths to complete breakdown to turbulence in hypersonic boundary layers at Mach 6.