Numerical investigation of the linear and nonlinear transition stages for a sharp cone at Mach 14

Numerical investigations were carried out to explore the linear and nonlinear stability regimes for boundary layers on a straight (right) cone with a 7◦ opening half-angle and a “sharp” nose tip at Mach 14 and zero angle of attack. The cone geometry of the experiments in the Arnold Engineering Development Complex (AEDC) Hypervelocity Wind Tunnel No. 9 (Tunnel 9) was used for the numerical investigations. The flow conditions corresponding to the “sharp” cone experiments carried out at the T9 facility were considered. The primary instability regime was explored using Linear Stability Theory (LST) and revealed unstable first, second and third mode waves. The axisymmetric second mode waves are the dominant primary instability. Primary wave saturation calculations were carried out for a range of frequencies that resulted in substantial N-factors near the transition onset location observed in the experiments. These investigations were used to adjust the forcing amplitudes of the primary waves such that transition onset in the simulations aligns approximately with that observed in the experiments. Based on the primary instability and primary wave saturation calculations, secondary instability calculations investigating the so-called fundamental resonance were carried out. These investigations confirmed that a strong fundamental resonance is present for the investigated flow conditions and geometry, therefore making this a viable mechanism that might lead to transition in the experiments. Based on the primary and secondary instability investigations, high-resolution “controlled” transition simulations have been set up and are currently underway.