Numerical prediction of aft radiation of turbofan tones through exhaust jets

Özyörük, Yusuf

doi:10.1016/j.jsv.2009.03.012

Cited by 21 publications

(12 citation statements)

References 25 publications

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“…This equation models the transport of physical quantities along a 1D domain. We expect that this model adequately captures the behaviour of the oscillations of the vortex sheet in the problem of interest (17).…”

Section: Streamline Upwind Petrov-galerkinmentioning

confidence: 91%

Implementation of a Vortex Sheet in a Finite Element Model Based on Potential Theory for Exhaust Noise Predictions

Prinn

Gabard

Bériot

2012

18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)

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Predicting sound propagation through the jet exhaust of an aero-engine presents the specific difficulty of representing the refraction effect of the mean flow shear. This is described by the linearised Euler equations, but this model remains rather expensive to solve numerically. The other model commonly used in industry, the linearised potential theory, is faster to solve but needs to be modified to represent a shear layer. This paper presents a way to describe a vortex sheet in a finite element model based on the linearised potential theory. The key issues to address are the continuity of pressure and displacement that have to be enforced across the vortex sheet, as well as the implementation of the Kutta condition at the nozzle lip. Validation results are presented by comparison with analytical results. It is shown that the discretization of the continuity conditions is crucial to obtain a robust and accurate numerical model.

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Section: Streamline Upwind Petrov-galerkinmentioning

confidence: 91%

Implementation of a Vortex Sheet in a Finite Element Model Based on Potential Theory for Exhaust Noise Predictions

Prinn

Gabard

Bériot

2012

18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference)

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“…The PML can also be used to impose the incident wave. In practice, the PML equations are applied to the reflected field only [13,15]: q re = q − q in , where q in is the incident field and q re is the reflected field. The Linearised Euler Equations for incident wave injection in the PML are: 4.…”

Section: Perfectly Matched Layermentioning

confidence: 99%

A High-Order Finite Element Method for the Linearised Euler Equations

Hamiche¹,

Gabard²,

Bériot³

2016

Acta Acustica united with Acustica

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SummarySound propagation in complex non-uniform mean flows is an important feature of turbofan exhaust noise radiation. The Linearised Euler Equations are able to represent the strong shear layer refraction effects on the sound field, as well as multiple length scales. Frequency domain solvers are suitable for tonal noise and considered a way to avoid linear instabilities, which may occur with time domain solvers. However, the classical Finite Element Method suffers from dispersion error and high memory requirements. These shortcomings are particularly critical for high frequencies and for the Linearised Euler Equations, which involve up to five unknowns. In this paper, a high-order Finite Element Method is used to solve the Linearised Euler Equations in the frequency domain in order to overcome those issues. The model involves high-order polynomial shape functions, unstructured triangular meshes, numerical stabilisation and Perfectly Matched Layers. The acoustic radiation from a straight circular semi-infinite hard-wall duct with several mean flow configurations is computed. Comparisons with analytic solutions demonstrate the method accuracy. The acoustic and vorticity waves are well represented, as well as the refraction of the sound field across the jet shear layer. The high-order approach allows to use coarse meshes, while maintaining a sufficient accuracy. The benefits in terms of memory requirements are significant when compared to standard low-order Finite Element Method.

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“…Simple test cases therefore allow an exact comparison between the numerical simulation and an analytic solution, one of the simplest of which is that of an oblique plane wave reflecting from an impedance surface [29]; a number of common validations for 2D and 3D time-dependent numerical acoustics simulations with flow are described by Richter [19, chapter 7.1], and similar validations are also used in 2D and 3D frequency-domain simulations [e.g. 30]. However, while these situations are sufficiently simple to permit an exact closed-form analytical expression for the pressure field, all of these tests rely on accurately introducing an incoming acoustic wave at the boundary of the numerical domain, while many of them also do not test the correct simulation of surface waves, do not test the impedance surface at a range of axial wavelengths, nor test correct propagation to the far field.…”

Section: Introductionmentioning

confidence: 99%

Reflection of an acoustic line source by an impedance surface with uniform flow

Gabard

2014

Journal of Sound and Vibration

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An exact analytic solution is derived for the 2D acoustic pressure field generated by a time-harmonic line mass source located above an impedance surface with uniform grazing flow. Closed-form asymptotic solutions in the far-field are also provided. The analysis is valid for both locally-reacting and nonlocally-reacting impedances, as is demonstrated by analysing a nonlocally reacting effective impedance representing the presence of a thin boundary layer over the surface. The analytic solution may be written in a form suggesting a generalization of the method of images to account for the impedance surface. The line source is found to excite surface waves on the impedance surface, some of which may be leaky waves which contradict the assumption of decay away from the surface predicted in previous analyses of surface waves with flow. The surface waves may be treated either (correctly) as unstable waves or (artificially) as stable waves, enabling comparison with previous numerical or mathematical studies which make either of these assumptions.The computer code for evaluating the analytic solution and far-field asymptotics is provided in the supplementary material. It is hoped this work will provide a useful benchmark solution for validating 2D numerical acoustic codes.

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Numerical prediction of aft radiation of turbofan tones through exhaust jets

Cited by 21 publications

References 25 publications

Implementation of a Vortex Sheet in a Finite Element Model Based on Potential Theory for Exhaust Noise Predictions

Implementation of a Vortex Sheet in a Finite Element Model Based on Potential Theory for Exhaust Noise Predictions

A High-Order Finite Element Method for the Linearised Euler Equations

Reflection of an acoustic line source by an impedance surface with uniform flow

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