The influence of nonlinearities on jet noise modeling based on parabolized stability equation

Zhang, Peng-Jun-Yi

doi:10.1063/5.0060206

Cited by 4 publications

(1 citation statement)

References 49 publications

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“…The resulting inhomogeneous wave equations are solved to predict sound waves. For supersonic and subsonic jets respectively, Sinha et al (2014) and Zhang, Wan & Sun (2021) took linear instability modes and POD modes to represent CS in the near field, which are then propagated directly to the acoustic far field by using Kirchhoff method.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics and acoustic radiation of coherent structures consisting of multiple ring–helical modes in the near-nozzle region of a subsonic turbulent circular jet

Zhang,

2023

J. Fluid Mech.

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This paper investigates the nonlinear evolution and acoustic radiation of coherent structures (CS) in the near-nozzle region of a subsonic turbulent circular jet. A CS is taken to be a wavepacket consisting of multiple ring/helical modes, which are considered to be inviscid instability waves supported by the mean-flow profile. As the three-dimensionality of helical modes is weak in the near-nozzle region, the ring and helical modes with the same frequency have nearly the same growth rates and critical levels. They coexist and interact with each other in their common critical layer at high Reynolds numbers. The self and mutual quadratic interactions generate a mean-flow distortion and streaks, which act back on the fundamental components through the cubic interaction. The amplitude of the CS is governed by an integro-partial-differential equation, a significant feature of which is that differentiations with respect to the azimuthal coordinate appear in the history-dependent nonlinear terms. The non-parallelism of the mean flow as well as the impact of fine-scale turbulence on CS are taken into account and found to affect the nonlinear terms. By solving the amplitude equation, the development of the constituting modes, streamwise vortices and streaks are described. For CS consisting of frequency sideband, low-frequency components are excited nonlinearly and amplify to reach a considerable level. By analysing the large-distance asymptote of the perturbation, the low-frequency acoustic waves are found to be emitted by the temporally–spatially varying mean-flow distortion and streaks generated by the nonlinear interactions of the CS, and are thereby determined on the basis of first principles. Interestingly, the energetic part of the streaky structure that contributes to the nonlinear dynamics does not radiate directly, and instead the Reynolds stresses driving the subdominant radiating components represent the true physical sources.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics and acoustic radiation of coherent structures consisting of multiple ring–helical modes in the near-nozzle region of a subsonic turbulent circular jet

Zhang,

2023

J. Fluid Mech.

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Generation of sound waves by nonlinearly evolving ring-mode coherent structures on a turbulent subsonic circular jet: a comparative study of two mechanisms

Zhang

2022

Acta Mech. Sin.

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A unified theory for the envelope radiation of ring-mode coherent structures in the very-near-nozzle and developed regions of a circular jet

Zhang

2023

Physics of Fluids

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Large-scale coherent structures (CS) are present on a turbulent circular jet, and are known to constitute an important source of jet noise. These structures may be treated as wavepackets of instability modes supported by the time-averaged mean flow. The nonlinear evolution and acoustic radiation of such CS in the fully developed region of a jet have been described in our recent work, where the mechanism of envelope radiation, or low-frequency radiation, was identified. The present paper focuses on the distinguished very-near-nozzle region. The CS resides in the thin shear layer developing from the lip line. However, circularity causes a leading-order effect on the acoustic radiation. One of significant new features is the presence of an inner acoustic field in the potential core. The outer and inner acoustic fields interact with each other, and the equivalent sources of sound have to be determined along with the sound fields. The waves in the inner acoustic field propagate mainly upstream. It is shown that nonlinear interactions of CS in the thin shear layer excite via receptivity the so-called discrete `trapped acoustic modes' as well as low-frequency Kelvin--Helmholtz modes, which may evolve into preferred modes in the developed region. The envelope radiation provides a key mechanism coupling the dynamics in the thin shear layer with the dynamics in the jet column regions. It is demonstrated that the theory developed here for nonlinear dynamics and acoustic radiation is valid from the very-near-nozzle to the developed regions, and thus stands as a unified theory.

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The influence of nonlinearities on jet noise modeling based on parabolized stability equation

Cited by 4 publications

References 49 publications

Nonlinear dynamics and acoustic radiation of coherent structures consisting of multiple ring–helical modes in the near-nozzle region of a subsonic turbulent circular jet

Nonlinear dynamics and acoustic radiation of coherent structures consisting of multiple ring–helical modes in the near-nozzle region of a subsonic turbulent circular jet

Generation of sound waves by nonlinearly evolving ring-mode coherent structures on a turbulent subsonic circular jet: a comparative study of two mechanisms

A unified theory for the envelope radiation of ring-mode coherent structures in the very-near-nozzle and developed regions of a circular jet

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