Nonlinear stability of straight cones with sharp and blunt noses at Mach 6

摘要

In this study, the nonlinear energy transfer between different frequency modes for a straight cone at Mach 6 is explored. Considered are 7 degree half-angle straight cones with nose bluntness radii of 0.15mm, 3.556mm, 5mm, 9.525mm, 12.7mm and 25.4mm at tunnel conditions relevant to the AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. Previously, a similar study was performed on these geometries, which was used to study the mechanism by which nose bluntness suppresses the second-mode instability (Sakakeeney et al. and Batista et al.~(12,13)). Now, a more targeted study is conducted to explore the nonlinear energy transfer between unstable second mode wave packets with adjacent frequencies. It is found that such energy transfer can result in a 100% increase in pressure disturbance amplitude compared to the traditionally considered discrete frequency (δ-function) formulation. This energy transfer is related to the standard practice of assuming constant frequency primary second-mode instabilities and the 'banana' shape of the stability diagram.