Finite element simulation of noise radiation through shear layers

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 in full in 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

Numerical Investigation on the Spectral Broadening of Acoustic Waves by a Turbulent Layer

International audienceWhen acoustic waves are propagating through turbulence, a scattering phenomenon occurs leading to a broadening of the acoustic spectrum. This phenomenon has been observed experimentally for a harmonic source radiating through the shear layer of a cold jet at low speed. The observed spectra are displaying a characteristic shape consisting in a more or less reduced peak amplitude at the source frequency, surrounded by sidebands (also called haystacks). The levels and width of these sidebands appear to be evolving with the source and flow parameters. This spectral broadening is studied in this paper for a simplified configuration consisting in a monopole radiation propagating through a turbulent layer with a constant thickness and convected by a uniform mean flow. The numerical method used relies on a finite difference code solving the linearized Euler equations in the time domain. The turbulence is synthesized using a stochastic method based on the filtering of white noise to impose prescribed statistical properties to the turbulent velocity field. These turbulent fluctuations are then added to the steady mean flow to form an unsteady base flow around which the Euler equations are linearized. This new set of equations contains terms involving products between the turbulent and acoustic fluctuations, which are responsible for the scattering. In this paper, the trends deduced from this numerical study can be compared to analytical models and experimental data obtained for a jet shear layer. They can also be related to the trends observed in a previous study on the scattering of sound by a single convected vortex

An integral formulation for wave propagation on weakly non-uniform potential flows

An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels for wave propagation on non-uniform flow. The integral solution is formulated using a Green's function obtained by combining the Taylor and Lorentz transformations. Although most conventional approaches based on either transform solve the Helmholtz problem in a transformed domain, the current Green's function and associated integral equation are derived in the physical space. A dimensional error analysis is developed to identify the limitations of the current formulation. Numerical applications are performed to assess the accuracy of the integral solution. It is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field, and as a means of solving scattering problems by rigid surfaces in non-uniform flows. The results show that the error associated with the physical model deteriorates with increasing frequency and mean flow Mach number. However, the error is generated only in the domain where mean flow non-uniformities are significant and is constant in regions where the flow is uniform

Analysis of high-order finite elements for convected wave propagation

In this paper, we examine the performance of high-order finite element methods (FEM) for aeroacoustic propagation, based on the convected Helmholtz equation. A methodology is presented to measure the dispersion and amplitude errors of the p-FEM, including non-interpolating shape functions, such as ‘bubble’ shape functions. A series of simple test cases are also presented to support the results of the dispersion analysis. The main conclusion is that the properties of p-FEM that make its strength for standard acoustics (e.g., exponential p-convergence, low dispersion error) remain present for flow acoustics as well. However, the flow has a noticeable effect on the accuracy of the numerical solution, even when the change in wavelength due to the mean flow is accounted for, and an approximation of the dispersion error is proposed to describe the influence of the mean flow. Also discussed is the so-called aliasing effect, which can reduce the accuracy of the solution in the case of downstream propagation. This can be avoided by an appropriate choice of mesh resolution

Compact resonant systems for perfect and broadband sound absorption in wide waveguides in transmission problems

[EN] This work deals with wave absorption in reciprocal asymmetric scattering problem by addressing the acoustic problem of compact absorbers for perfect unidirectional absorption, flush mounted to the walls of wide ducts. These absorbers are composed of several side-by-side resonators that are usually of different geometry and thus detuned to yield an asymmetric acoustic response. A simple lumped-element model analysis is performed to link the dependence of the optimal resonators surface impedance, resonance frequency, and losses to the duct cross-sectional area and resonator spacing. This analysis unifies those of several specific configurations into a unique problem. In addition, the impact of the potential evanescent coupling between the resonators, which is usually neglected, is carefully studied. This coupling can have a strong impact especially on the behavior of compact absorbers lining wide ducts. To reduce the evanescent coupling, the resonators should be relatively small and therefore their resonances should be damped, and not arranged by order of increasing or decreasing resonant frequency. Finally, such an absorber is designed and optimized for perfect unidirectional absorption to prove the relevance of the analysis. The absorber is 30 cm long and 5 cm thick and covers a single side of a 14.8 x 15 cm(2) rectangular duct. A mean absorption coefficient of 99% is obtained experimentally between 700 and 800 Hz.The authors acknowledge the financial support from the ANR industrial chair MACIA (ANR-16-CHIN-0002). They also acknowledge the Safran group for supporting and funding this research.Boulvert, J.; Gabard, G.; Romero-García, V.; Groby, J. (2022). Compact resonant systems for perfect and broadband sound absorption in wide waveguides in transmission problems. Scientific Reports. 12(1):1-13. https://doi.org/10.1038/s41598-022-13944-111312

A Non-Overlapping Schwarz Domain Decomposition Method with High-Order Finite Elements for Flow Acoustics

International audienceA non-overlapping domain decomposition method is proposed to solve large-scale finite element models for the propagation of sound with a background mean flow. An additive Schwarz algorithm is used to split the computational domain into a collection of sub-domains, and an iterative solution procedure is formulated in terms of unknowns defined on the interfaces between sub-domains. This approach allows to solve large-scale problems in parallel with only a fraction of the memory requirements compared to the standard approach which is to use a direct solver for the complete problem. While domain decomposition techniques have been used extensively for Helmholtz problems, this is the first application to aero-acoustics. The optimized Schwarz formulation is extended to the linearized potential theory for sound waves propagating in a potential base flow. A high-order finite element method is used to solve the governing equations in each sub-domain, and well-designed interface conditions based on local approximations of the Dirichlet-to-Neumann map are used to accelerate the convergence of the iterative procedure. The method is assessed on an academic test case and its benefit demonstrated on a realistic turbofan engine intake configuration

Acoustic wave propagation in effective graded fully anisotropic fluid layers

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Optimally graded porous material for broadband perfect absorption of sound

International audienceThis article presents a numerical optimization procedure of continuous gradient porous layer properties to achieve perfect absorption under normal incidence. This design tool is applied on a graded porous medium composed of a periodic arrangement of ordered unit cells allowing to link the effective acoustic properties to its geometry. The best micro-geometry continuous gradient providing the optimal acoustic reflection and/or transmission is designed via a nonlinear conjugate gradient algorithm. The acoustic performances of the so-designed continuous graded material are discussed with respect to the optimized homogeneous, i.e. non-graded, and monotonically graded material. The numerical results show a shifting of the perfect absorption peak to lower frequencies or a widening of the perfect absorption frequency range for graded materials when compared to uniform ones. The results are validated experimentally on 3D-printed samples therefore confirming the relevance of such gradient along with the efficiency of the control of the entire design process. a) [email protected]

Boundary layer effects on liners for aircraft engines

The performance of acoustic treatments installed on aircraft engines is strongly influenced by the boundary layer of the grazing flow on the surface of the liner. The parametric study presented in this paper illustrates the extent of this effect and identifies when it is significant. The acoustic modes of a circular duct with flow are calculated using a finite difference method. The parameters are representative of the flow conditions, liners and sound fields found in current turbofan engines. Both the intake and bypass ducts are considered. Results show that there is a complex interplay between the boundary layer thickness, the direction of propagation and the liner impedance and that the boundary layer can have a strong impact on liner performance for typical configurations (including changes of the order of 30dB on the attenuation of modes associated with tonal fan noise). A modified impedance condition including the effect of a small but finite boundary layer thickness is considered and compared to the standard Myers condition based on an infinitely thin boundary layer. We show how this impedance condition can be implemented in a mode calculation method by introducing auxiliary variables. This condition is able to capture the trends associated with the boundary layer effects and in most cases provides improved predictions of liner performance

Méthodes numériques et modèles de sources aéroacoustiques fondés sur l’équation de Galbrun

Propagation and generation of sound in fluid flows represent an important problem for several industrial applications, particularly for transports. The main characteristic of this thesis is the use of an original model, Galbrun’s equation, to describe acoustic wave propagation in flows. Concerning numerical methods, a dispersion analysis is carried out for several finite element models for aeroacoustic propagation. Furthermore, several non-reflecting boundary conditions for Galbrun’s equation in the frequency domain are derived. Two aerodynamic noise source models based on Galbrun’s equation are proposed. The first one stems from the source term for the linearized Euler equations proposed by Bailly while the second is obtained with the E.I.F. approach originally proposed by Hardin and Pope.La propagation et la production de bruit dans les écoulements de fluides représentent un problème crucial pour de nombreuses applications industrielles en particulier les transports. Cette thèse a pour originalité d’utiliser un modèle peu employé, l’équation de Galbrun, pour modéliser la propagation acoustique dans les écoulements. Concernant les méthodes numériques, on présente une analyse de dispersion de plusieurs méthodes d’éléments finis pour la propagation aéroacoustique. D’autre part, plusieurs conditions de non-réflexion pour l’équation de Galbrun dans le domaine fréquentiel sont obtenues. On propose deux modèles de sources aéroacoustiques formulés à l’aide de l’équation de Galbrun. Le premier modèle est issu du modèle de source proposé pour les équations d’Euler linéarisées par Bailly et le second modèle est obtenu par la méthode des développements autour d’un écoulement incompressible initialement développée par Hardin et Pope