Numerical Investigation of Boundary-Layer Transition on a Sharp Cone at Mach 10

Numerical investigations were carried out to explore the linear and nonlinear stability regimes for boundary layers on a straight (right) cone with a 7 degree opening half-angle and a ``sharp'' nose tip at Mach 10 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) is used for the numerical investigations. Primary instability calculations using Linear Stability Theory (LST) exhibit unstable first, second, and third mode waves. For the investigated flow conditions and geometry the axisymmetric second mode disturbances are the dominant primary (linear) instability. Primary wave saturation calculations including transition onset were carried out in order to investigate the possibility to align transition onset in the simulations with that observed in the experiments. By varying the forcing amplitude of the axisymmetric second mode waves a range of frequencies was identified for which transition onset obtained in simulations and observed in experiments can be aligned. Secondary instability investigations, focusing on the so-called fundamental resonance, were carried out for the primary wave frequencies identified in the transition onset simulations. The results showed that the fundamental resonance is indeed a viable nonlinear mechanism that may be responsible for transition in the AEDC T9 experiments. Based on the primary and secondary instability calculations high-resolution ``controlled'' transition simulations were carried out and demonstrate that fundamental breakdown can lead to sustained turbulent flow. The Stanton number development observed in experiments shows slight differences compared to that obtained in the controlled transition simulations.