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.
Bibliographical noteFunding Information:
Support from ONR grant number N00014-19-1-2037 is gratefully acknowledged. The authors thank Prof. Graham Candler for helpful comments on an early version of this manuscript. We are also grateful to an anonymous reviewer for extensive, thoughtful comments that helped significantly improve this manuscript.
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
- Input–output analysis
- Non-modal growth
- Shock-perturbation interaction