Numerical Investigation of the Nonlinear Transition Stages of Hypersonic Boundary Layers

Abstract

High-order accurate Direct Numerical Simulations (DNS) conducted for a straight cone at Mach 6 is presented and compared to an quivalent flared cone (Hader & Fasel, 2019) 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. Parameter studies were conducted for the primary and secondary instability regimes to identify the frequency-wavenumber pair for the fundamental resonance model. The flared cone was found to be more unstable with respect to both primary and secondary instabilities. For both cases, so-called "controlled" breakdown simulations presented in this thesis showed a similar patterns 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 thesis 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 than the straight cone, leading to larger growth rates of the secondary disturbance waves 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. However, qualitative similarities of the nonlinear behavior between the flared and straight cone suggest that for the BAM6QT quiet conditions the fundamental resonance would likely be the relevant nonlinear breakdown mechanism for the straight cone as well.