Numerical investigation of boundary-layer transition initiated by a wave packet for a cone at Mach 6

Direct Numerical Simulations are performed to investigate transition initiated by a wave packet in a sharp cone boundary layer at Mach 6. In order to understand the natural transition process in hypersonic cone boundary layers, the flow was pulsed through a hole on the cone surface to generate a wave packet which consisted of a wide range of disturbance frequencies and wave numbers. The flow parameters for the simulations are based on the experimental conditions of the Boeing/AFOSR Mach 6 quiet-flow Ludwieg Tube at Purdue University. ¹ First, the linear development of the wave packet was studied by forcing the flow with a low amplitude pulse (0.001% of the freestream velocity). The dominant waves within the resulting wave packet were identified as the second mode two-dimensional disturbance waves. In addition, weaker first mode oblique waves were also observed on the lateral sides of the wave packet. In order to investigate the weakly nonlinear transition regime, medium amplitude pulse disturbances (0.5% of the freestream velocity) were introduced. The response of the flow to the medium amplitude pulse disturbances indicated the presence of a fundamental resonance mechanism. Lower secondary peaks in the disturbance wave spectrum were identified at approximately half the frequency of the high amplitude frequency band for azimuthal mode numbers k _c±55, which would be an indication of a sub-harmonic resonance mechanism. Finally, in order to identify more clearly which of these mechanisms ultimately leads to turbulent breakdown, a simulation with a higher forcing amplitude (5% of the freestream velocity) was performed. The developing strongly nonlinear wave packet eventually leads to localized patches of turbulent flow (turbulent spots). In these nascent turbulent spots various known properties of mature turbulent spots could be identified.