Free-stream receptivity of a hypersonic blunt cone using input–output analysis and a shock-kinematic boundary condition

Traditional stability tools have done much in the last few decades to demonstrate the significance of modal instabilities as a pathway for laminar to turbulent transition in hypersonic flows, but are less effective at predicting transition in flows with significant streamwise variation and strong shock waves. Because of this, most stability analyses over blunt cones tend to focus on the growth of instabilities in regions of the flow away from the blunt tip and downstream of any strong shock waves. We develop a new shock-kinematic boundary condition which is compatible with both the finite-volume method and input–output analysis. This boundary condition enables analysis of the receptivity of blunt cones to disturbances in the free stream by careful treatment of linear interactions of small disturbances with the shock. In particular, a Mach 5.8 flow over a 7^∘ half-angle cone with a 0.15" nose radius is analyzed, showing significant amplification of disturbances along the cone frustum in a 5–15 kHz bandwidth due to the destabilization of a slow acoustic boundary layer mode, and significant amplification of entropy layer instabilities between 100 and 180 kHz due to rotation/deceleration of entropy/vorticity waves. These mechanisms are receptive to free-stream disturbances in very localized positions upstream of the bow shock.