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Optimal growth in hypersonic flows over an inclined cone

Published online by Cambridge University Press:  10 April 2025

Xi Chen Open the ORCID record for Xi Chen [Opens in a new window] ,
Bingbing Wan ,
Guohua Tu ,
Maochang Duan ,
Xiaohu Li  and
Jianqiang Chen Open the ORCID record for Jianqiang Chen [Opens in a new window]
Xi Chen
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang, Sichuan 621000, PR China
Bingbing Wan*
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang, Sichuan 621000, PR China
Guohua Tu
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang, Sichuan 621000, PR China
Maochang Duan
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang, Sichuan 621000, PR China
Xiaohu Li
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang, Sichuan 621000, PR China
Jianqiang Chen*
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang, Sichuan 621000, PR China
*
Corresponding authors: Bingbing Wan, [email protected]; Jianqiang Chen, [email protected]
Corresponding authors: Bingbing Wan, [email protected]; Jianqiang Chen, [email protected]
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Abstract

Spatial optimal responses to both inlet disturbances and harmonic external forcing for hypersonic flows over a blunt cone at non-zero 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 localised 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.

JFM classification

Boundary Layers: Boundary layer stability Compressible Flows: Hypersonic Flow Instability: Shear-flow instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1008 , 10 April 2025 , A51
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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