Numerical investigation of nonlinear wave packets in a hypersonic high-enthalpy boundary layer on a 5° sharp cone

Stability and transition of a boundary-layer is numerically investigated for a 5° sharp cone in high-enthalpy ow using weakly nonlinear and strongly nonlinear wave packet simulations. Towards this end, a short-duration pulse through a small hole in the surface of the cone is utilized to excite a broad spectrum of frequencies and streamwise/azimuthal wave numbers. The ow conditions chosen for the simulations are those from the high- enthalpy experiments by Jewell et al.^1,2 in the T5 tunnel at Caltech. The experimental measurements indicate the presence of turbulent spots. In these experiments, the free- stream temperature is much higher than the wall temperature due to the high-enthalpy conditions. The wall temperature of the cone remains at room temperature (isothermal wall) due to the short-duration of the experiments. Salemi and Fasel³ have investigated the linear regime for this ow utilizing low-amplitude wave packets. However, to date no nonlinear wave packet numerical simulation data are available for comparison with the hot ow/cold wall experimental data of Jewell et al.^1,2 The stability investigations discussed in the present paper represent another step towards understanding the physical mechanisms that are maybe responsible for generating the turbulent spots. Our present results indicate that a nonlinear resonance mechanism is present in such experiments and may be a fundamental resonance of the second mode waves. For the strongly nonlinear regime, a significant 2-D higher harmonic arises, which may be Mack's third mode, and becomes increasingly important downstream. According to our previous DNS results,³ the wave packet in the linear regime changes its character as amplified wave components synchronize their phase speeds with the vorticity/entropy, and slow acoustic modes. The current weakly nonlinear and strongly nonlinear results also exhibit a similar phase speed synchronization. However, the packet envelope spatial modulation changed considerably compared to the linear packet. The packet envelope change during synchronization is not observed in axisymmetric pulse simulations.