Understanding effects of nose-cone bluntness on hypersonic boundary layer transition using input-output analysis

This paper presents a new numerical method for investigating the relationship between cone nosetip bluntness on boundary layer transition in hypersonic flows. For years, Linear Stability Theory (LST) and the Parabolized Stability Equations (PSE) have provided the tools for analysis and prediction of laminar to turbulent transition for plates, sharp cones, and geometries for which the parallel or slowly-varying boundary layer assumptions are valid. Experiments on blunt cones have demonstrated that small nose bluntness radii delay transition, but when the bluntness reaches some critical value, the trend sharply reverses. It is difficult for LST and PSE to represent complex physics near blunt cone tips, including a curved bow shock that generates an entropy layer and strong streamwise flow acceleratation away from the stabgnation point. We apply input-output analysis based on numerical Jacobians to directly capture the effect of these physics upon instabilities leading to transition. The numerical Jacobian method extracts a global linear operator from the non-linear hypersonic flow solver US3D and does not make the assumptions of either the LST or PSE approaches, providing a more powerful tool for transition analysis. In this paper, the numerical Jacobian method along with input-output analysis is applied to 7^o half-angle sharp and blunt cones at Mach 6. Our method is able to accurately predict growth and transition of both the second mode instability and the entropy layer instability for blunt cones of various radii, and provides new insight into the phenomenon of transition reversal.