Numerical Investigation of the Hypersonic Boundary Layer Transition Over a Blunt Cone Using High-Order Discontinuous Galerkin Methods and Stability Theories

This study investigates the hypersonic boundary layer transition over a blunt cone using
high-order Discontinuous Galerkin methods and stability theories. The receptivity of the
boundary layer to freestream acoustic disturbances is modeled through a two-dimensional axisymmetric Direct Numerical Simulation performed with the ArgoDG solver. A combination of fast and slow acoustic waves at a single frequency is considered. The imposed disturbances induce the growth of second mode instability, which is the most dominant instability leading to transition to turbulence for the geometry and the flow conditions considered in this work. The onset of nonlinear interactions, which manifest as the characteristics rope-like structures and the generation of higher harmonics, as well as characteristic wall pressure fluctuations are also observed. The perturbations remain consistent with the predictions of Linear Stability Theory as long as nonlinear effects are weak. Once nonlinearities become significant, the two-dimensional axisymmetric Direct Numerical Simulation results alignwith those obtained from the Nonlinear Parabolized Stability Equations. Comparisons with the numerical results show consistent behavior in both the receptivity region and the phase of harmonics generation in thenonlinear region.