Numerical investigation of the linear and nonlinear transition stages for 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^◦ opening half-angle and a “sharp” nose tip at Mach 10 and zero angle of attack. The cone geometry and flow conditions of the experiments in the Arnold Engineering Development Complex (AEDC) Hypervelocity Wind Tunnel No. 9 (Tunnel 9) is used for the numerical investigations. Two unit Reynolds numbers, corresponding to the “sharp” cone experiments carried out at the T9 facility, are considered. Primary instability calculations using Linear Stability Theory (LST) confirmed that the linear amplification rates and the corresponding N-factors increase with increasing unit Reynolds numbers as expected. For all investigated cases the axisymmetric second mode disturbances are the dominant primary (linear) instability. Subsequent 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. Subsequent 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. The numerical investigations showed that larger unit Reynolds numbers do not only result in increased growth rates for the linear (primary) instability but also in a stronger secondary instability.