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Receptivity of a supersonic two-dimensional jet due to acoustic excitations near the nozzle lip

Published online by Cambridge University Press:  20 March 2025

Binhong Li Open the ORCID record for Binhong Li [Opens in a new window] ,
Sicheng Zhang  and
Benshuai Lyu Open the ORCID record for Benshuai Lyu [Opens in a new window]
Binhong Li
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, 5 Yiheyuan Road, Haidian District, Beijing 100871, PR China
Sicheng Zhang
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, 5 Yiheyuan Road, Haidian District, Beijing 100871, PR China
Benshuai Lyu*
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, 5 Yiheyuan Road, Haidian District, Beijing 100871, PR China Laoshan Laboratory, Qingdao 266100, PR China
*
Corresponding author: Benshuai Lyu, [email protected]
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Abstract

In this paper, we develop an analytical model to investigate the generation of instability waves triggered by the upstream acoustic forcing near the nozzle lip of a supersonic jet. This represents an important stage, i.e. the jet receptivity, of the screech feedback loop. The upstream acoustic forcing, resulting from the shock-instability interaction (SII), reaches the nozzle lip and excites new shear-layer instability waves. To obtain the newly excited instability wave, we first determine the scattered sound field due to the upstream forcing using the Wiener–Hopf technique, with the kernel function factored using asymptotic expansions and overlapping approximations. Subsequently, the unsteady Kutta condition is imposed at the nozzle lip, enabling the derivation of the dispersion relation for the newly excited instability wave. A linear transfer function between the upstream forcing and the newly excited instability wave is obtained. We calculate the amplitude and phase delay in this receptivity process and examine their variations against the frequency. The analytically obtained phase delay enables us to evaluate the phase condition for jet screech and predict the screech frequency accordingly. The results show improved agreement with the experimental data compared with classical models. It is hoped that this model may help in developing a full screech model.

JFM classification

Acoustics: Jet noise Acoustics: Aeroacoustics Instability: Shear-flow instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1007 , 25 March 2025 , A80
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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