Global receptivity analysis of the flow over a hypersonic cone*

In high-speed flight, increased viscous heating past the onset of transition to turbulence is a critical limiting factor in the design of hypersonic vehicles. Acoustic exponential instabilities, which are ineffective at low Mach numbers, become active and open up additional avenues for breakdown to turbulence in the compressible boundary layer. The seeding of the instabilities is generated during the receptivity stage which governs the initiation of a disturbance field inside the shear, for instance by external disturbances. The present study rigorously analyses the receptivity process of the high-speed flow over a cone geometry by leveraging the structural sensitivity information provided by the adjoint linearized governing equations. As such, the approach enables the direct identification of the free-stream conditions which are most effective at triggering perturbation growth in the boundary layer. The study is facilitated via a curvilinear formulation of the governing equations which allows the incorporation of the effects of the cone geometry as well as shock waves.