Direct Numerical Simulations of Hypersonic Boundary-Layer Transition for a Flared Cone

Abstract

Direct Numerical Simulations (DNS) were carried out to investigate the laminar-turbulent transition for a flared cone at Mach 6 and zero angle of attack. The flared cone geometry of the experiments in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University was chosen for the simulations. This study explored the linear and secondary instability regimes as well as the nonlinear breakdown to turbulence using a controlled disturbance input (“controlled” breakdown) and “natural” transition models. Low amplitude, axisymmetric, short-duration pulse calculations were performed in order to map out the linear stability regime for the flow conditions of the BAM6QT facility. A parametric study of the secondary instability regime was carried out in order to identify the azimuthal wavenumber that led to the strongest fundamental and subharmonic resonance. For the BAM6QT conditions, the fundamental resonance was found to be much stronger compared to the subharmonic resonance and was therefore considered to be the relevant breakdown scenario. For the case which led to the strongest fundamental resonance onset, detailed investigations were carried out using high-resolution DNS. The simulation results exhibit streamwise streaks of very high skin friction and of high heat transfer at the cone surface. Streamwise “hot” streaks on the flared cone surface were also observed in the experiments carried out at the BAM6QT facility using temperature sensitive paint (TSP). Two different “natural” transition models were employed to assess the differences between “controlled” and “natural” breakdown. Both “natural” transition models resulted in a streak pattern similar to that obtained with the “controlled” break- down DNS and in the experiments. A detailed flow analysis revealed that the streamwise streaks are generated by steady longitudinal modes that are nonlinearly generated by the primary and secondary disturbance waves. The presented findings provide strong evidence that the fundamental breakdown is the most likely nonlinear transition mechanism in the BAM6QT flared cone experiments.