Non-modal growth analysis of high-speed flows over an inclined cone

Abstract

Spatial optimal responses to both inlet disturbances and harmonic external forcing for hypersonic flows over a blunt cone at nonzero angles of attack are obtained by efficiently solving the direct-adjoint equations with a parabolic approach. In either case, the most amplified disturbances initially take the form of localized streamwise vortices on the windward side and will undergo a two-stage evolution process when propagating downstream: they first experience a substantial algebraic growth by exploiting the Orr and lift-up mechanisms, and then smoothly transition to a quasi exponential-growth stage driven by the crossflow-instability mechanism, accompanied by an azimuthal advection of the disturbance structure towards the leeward side. The algebraic-growth phase is most receptive to the external forcing, whereas the exponential-growth stage relies on the disturbance frequency and can be significantly strengthened by increasing the angle of attack. The wavemaker delineating the structural sensitivity region for the optimal gain is shown to lie on the windward side immediately downstream of the inlet, implying a potent control strategy. Additionally, considerable non-modal growth is also observed for broadband high-frequency disturbances residing in the entropy layer.