Numerical Study of Hypersonic Boundary-Layer Receptivity and Stability with Freestream Hotspot Perturbations

This dissertation presents a numerical simulation study of linear hypersonic boundary-layer receptivity and stability over blunt compression cones with freestream hotspot perturbations. This study is conducted for freestream disturbances with broad, continuous frequency spectra over cones that have nose radii of 1, 0.5 and 0.1 mm under freestream conditions of Mach 6, 10 and 15. The simulations are carried out using the high-order shock-fitting finite-difference scheme developed by Zhong (1998), the results of which are shown to agree well with linear stability theory (LST) and experiments. The general receptivity mechanism is then studied by the simulation-LST comparisons under two parametric effects: nose bluntness and freestream Mach number. Among the new findings of the current study, the mechanisms of the receptivity process are found to be mainly caused by the fast acoustic waves that are generated behind the bow shock from the hotspot/shock interaction in the nose region. It is these fast acoustic waves that substantially enter the boundary layer and generate mode F through the synchronization of fast acoustic waves and mode F in the upstream part of the cone. Subsequently, the synchronization of modes F and S generates mode S, or the second mode, which eventually grows into a dominant level at the downstream part of the cone. Additionally, we have obtained the receptivity coefficients of mode S along the Branch-I neutral stability curve using a method that combines LST predicted N-factors and simulated disturbance amplitudes. These receptivity coefficients agree well with those obtained from the theoretical modal decomposition method.;In addition to obtaining the general receptivity mechanism and receptivity coefficients, we have also studied the parametric effects of nose bluntness and freestream Mach number on boundary-layer receptivity and stability over cones. Specifically, our results have shown that nose bluntness reduces the boundary-layer receptivity to freestream entropy perturbations and stabilizes the perturbed boundary layer over a cone. The boundary layer is more receptive to freestream entropy perturbations at higher freestream Mach numbers, while the perturbed boundary layer is stabilized at higher freestream Mach numbers.;The current receptivity and stability study has not only shed new light on the receptivity mechanism to freestream entropy spots over blunt cones, but also advanced the understanding of nose bluntness and freestream Mach number effects on the receptivity and stability over blunt cones. Furthermore, the currently-obtained broad, continuous spectra of unstable-second-mode receptivity coefficients could potentially provide the initial amplitudes for future amplitude-based transition predicting methods.