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Acoustic emission due to the interaction between shock and instability waves in two-dimensional supersonic jet flows

Published online by Cambridge University Press:  06 January 2023

B. Li Open the ORCID record for B. Li [Opens in a new window]  and
B. Lyu Open the ORCID record for B. Lyu [Opens in a new window]
B. Li
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, 5 Yiheyuan Road, Haidian District, Beijing 100871, PR China
B. Lyu*
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, 5 Yiheyuan Road, Haidian District, Beijing 100871, PR China
*
†Email address for correspondence: b.lyu@pku.edu.cn
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Abstract

An analytical model is developed to study the sound produced by the interaction between shock and instability waves in two-dimensional supersonic jet flows. The jet is considered to be of vortex-sheet type and two-dimensional Euler equations are linearized to determine the governing equations for shock and instability waves and their interaction. Pack's model is used to describe shock waves, while instability waves are calculated using spatial stability analysis. The interaction between shock and instability waves can be solved analytically by performing Fourier transform and subsequently using the method of steepest descent. Sound produced by the interaction between the instability wave and a single shock cell is studied first, after which that due to a number of cells follows. We find that the model developed in this study can correctly predict the frequencies of the fundamental screech tone and its first and second harmonics. We show that the predicted sound directivity, even from a single shock cell, is in good agreement with experimental data. In particular, this model shows the strongest noise emission close to the upstream direction but the emitted noise starts to rapidly decay as the observer angle approaches $180^\circ$, which is in accordance with experimental results; this suggests that the effective noise from a single shock cell is far from of the monopole type as assumed in the classical Powell's model. We find that the noise directivity is very sensitive to the local growth rate of the instability waves and the noise is generated primarily through the Mach wave mechanism.

JFM classification

Acoustics: Aeroacoustics Acoustics: Jet noise Instability: Shear-flow instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A35
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

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