Computational study of the spectral broadening of an acoustic tone by turbulence

International audienceSpectral broadening results from the unsteady scattering of acoustic waves propagating across a region of turbulence. This phenomenon has been observed previously for an harmonic source radiating through the shear layer of a cold jet at low speed. The resulting spectra displayed a reduced tone peak surrounded by lateral bands, with changes in these bands levels and width depending on the source and flow parameters. In this paper, spectral broadening is studied numerically for a simple configuration, consisting of a monopole radiation scattered by a turbulent layer with a constant thickness and convected by a uniform mean velocity. The numerical method relies on a finite difference code solving the linearized Euler equations in the time domain. The turbulent layer is synthesized with a stochastic method based on the filtering of white noise to impose prescribed statistical properties to the turbulence. The turbulent fluctuations are then added to the steady mean flow to form an unsteady base flow around which the Euler equations are linearized. This introduces terms involving products between the turbulent and acoustic fluctuations which are responsible for the scattering. Such a numerical methodology allows to vary the properties of the turbulence generated for the chosen configuration such as the turbulent kinetic energy and the integral length scale. In this paper, the effects of several parameters such as the convection velocity and source frequency on the spectral broadening are studied. The trends deduced from the results can be compared to previous models and experimental data for a jet shear layer, and they can also be related to the trends observed in a previous study of the scattering of sound by a single convected vortex

Coupling of Finite-Element and Plane Waves Discontinuous Galerkin methods for time-harmonic problems

A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation problems. While wave-based methods can significantly reduce the computational cost, especially at high frequencies, their efficiency is hindered by the need to use small elements to resolve complex geometric features. This can be alleviated by using a standard Finite-Element Model close to the surfaces to model geometric details and create large, simply-shaped areas to model with a wave-based method. This strategy is formulated and validated in this paper for the wave-based discontinuous Galerkin method together with the standard finite element method. The coupling is formulated without using Lagrange multipliers and results demonstrate that the coupling is optimal in that the convergence rates of the individual methods are maintained

General method to retrieve all effective acoustic properties of fully-anisotropic fluid materials in three dimensional space

Anisotropic fluid materials are of growing interest with the development of metamaterials and transformation acoustics. In the general three-dimensional case, such materials are characterized by a bulk modulus and a full symmetric matrix of density. Here, a method is presented to retrieve the bulk modulus and all six components of the density matrix from a selected set of six incident plane waves impinging on a layer of the material. From the six components of the density tensor, the three principal directions and the three principal densities of the material are recovered. The approach relies on the analytical expression of the reflection and transmission coefficients derived from a state vector analysis. It results in simple, closed-form, and easily-implementable inverse relations for the material parameters. As an illustration, the case of sound propagation through an orthorhombic lattice of overlapping air-filled ellipsoids is considered, the effective complex and frequency-dependent bulk modulus and density matrix of which are derived from homogenization cell problems and account for viscothermal losses. The retrieval method is then applied to the homogenized layer and results bear testament to its robustness to extract accurately all seven material parameters. This makes possible the characterization and design of anisotropic fluid materials in three dimensions

Couplage entre la MEF et la DGM avec ondes planes pour l'acoustique

L’objectif de ce travail est de coupler pour des problèmes acoustiques simples la Méthode des Eléments Finis (MEF) et la Discontinuous Galerkin Method (DGM) avec ondes planes. Le travail consiste principalement à réécrire les opérateurs de surface de la MEF en les décomposant sur les caractéristiques entrantes et sortantes de l’interface. Cela est effectué à l’aide des techniques classique en DGM de décomposition des flux et qui doivent dans le cas présent être discrétisés à l’aide des fonctions de forme du problème éléments-finis. Il sera montré que cela entrainera, en raison de la dérivation des fonctions de forme, la perte d’un ordre convergence si une interpolation de Lagrange est utilisées et par une conservation de l’ordre de convergence pour une interpolation de type Hermite. Plusieurs problèmes acoustiques simples académiques avec et sans matériaux poreux seront présentés

Vers un couplage plus naturel des méthodes de Galerkin Discontinue avec ondes planes et Élements Finis pour l'acoustique

Une des voies possibles vers la réduction des coûts de simulation passe par le développement de méthodes hybrides. Dans le but de construire une hybridation efficace, le choix des méthodes est primordial. Ce travail porte ainsi sur l'association de la Méthode des Éléments Finis (MEF) et la Méthode de Galerkin Discontinue avec Ondes Planes (PWDGM) avec la volonté de pouvoir tirer parti de leur spécificités. D'une part, la méthode des Éléments Finis (MEF), malgré sa versatilité, demande un maillage fin du domaine qui s'avère coûteux lorsque celui-ci devient grand. Ce fonctionnement, basé sur une discrétisation spatiale, permet toutefois à la méthode de s'adapter à des géométries complexes pouvant entre autres contenir diffracteurs et éléments résonnants. D'autre part, la méthode de Galerkin Discontinue avec ondes planes (PWDGM), approxime les champs en les décomposant sur une base d'ondes planes. Basée également sur un maillage, cette méthode ne requiert toutefois pas qu'il soit fin. En effet, elle fonctionne de manière optimale dans le cas de grands domaines. Une proposition de couplage entre ces méthodes a déjà été présenté. Ce couplage, s'appuyant sur la réécriture des champs MEF à l'interface dans le formalisme requis par la PWDGM, poussait à dériver les fonctions de forme et s'accompagnait de la perte d'un ordre de convergence. Ce travail vise à corriger cette faille de la technique de couplage en proposant une approche repose sur l'écriture de conditions de continuité entre les caractéristiques de la PWDGM et les champs de la MEF. Cette nouvelle proposition permet de conserver l'ordre de convergence et les résultats numériques ont montré un excellent accord entre la méthode hybride et des références. Dans le cadre de cette réécriture, la théorie a notamment été étendue à d'autres physiques. En particulier, les opérateurs pour des matériaux poroélastiques (théorie de Biot) sont introduits et mis en ?uvre dans les exemples. Cette méthode sera présentée d'abord sur des exemples académiques et ses propriétés seront discutées. Une attention particulière sera portée à l'impact que le couplage a sur les propriété de convergence et de dispersion, les résultats pour la méthode hybride seront mis en regard avec ceux pour le méthodes seules. Dans un second temps, des cas plus proches des cas d'utilisation réels seront présentés. Il sera montré notamment le cadre dans lequel le recours à la méthode hybride permet de réduire significativement la taille du système linéaire final tout en minimisant la perte de précision

Fundamental constraints on broadband passive acoustic treatments in unidimensional scattering problems

[EN] In a passive lossy acoustical system, sum rules derived from passivity explicitly relate the broadband response to the spatial dimension of the system, which provide important design criteria as well. In this work, the theory of Herglotz function is applied systematically to derive sum rules for unidimensional scattering problems relying on passive acoustic treatments which are generally made of rigid, motionless and subwavelength structures saturated by air. The rigid-boundary reflection, soft-boundary reflection and transmission problems are analysed. The derived sum rules are applied for guiding the designs of passive absorbers and mufflers: the required minimum space is directly predicted from the target (i.e. the desired absorption or transmission-loss spectra) without any specific design. Besides, it is possible to break this type of sum rules and fundamental constraints in particular cases. This property, if well used, could result in ultra-compact absorbers working at long wavelength up to infinity.This work is supported by Valeo company and the ANR-RGC METARoom project (grant nos. ANR-18-CE08-0021 and RGC A-HKUST601/18).Meng, Y.; Romero-García, V.; Gabard, G.; Groby, J.; Bricault, C.; Goudé, S.; Sheng, P. (2022). Fundamental constraints on broadband passive acoustic treatments in unidimensional scattering problems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Online). 478(2265):1-22. https://doi.org/10.1098/rspa.2022.0287122478226

Graded and anisotropic porous materials for broadband and angular maximal acoustic absorption

ABSTRACT: The design of graded and anisotropic materials has been of significant interest, especially for sound absorption purposes. Together with the rise of additive manufacturing techniques, new possibilities are emerging from engineered porous micro-structures. In this work, we present a theoretical and numerical study of graded and anisotropic porous materials, for optimal broadband and angular absorption. Through a parametric study, the effective acoustic and geometric parameters of homogenized anisotropic unit cells constitute a database in which the optimal anisotropic and graded material will be searched for. We develop an optimization technique based on the simplex method that is relying on this database. The concepts of average absorption and diffuse field absorption coefficients are introduced and used to maximize angular acoustic absorption. Numerical results present the optimized absorption of the designed anisotropic and graded porous materials for different acoustic targets. The designed materials have anisotropic and graded effective properties, which enhance its sound absorption capabilities. While the anisotropy largely enhances the diffuse field absorbing when optimized at a single frequency, graded properties appear to be crucial for optimal broadband diffuse field absorption

Generalised acoustic impedance for viscous fluids

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Spectral broadening of acoustic waves by convected vortices

The scattering of acoustic waves by a moving vortex is studied in two dimensions to bring further insight into the physical mechanisms responsible for the spectral broadening caused by a region of turbulence. When propagating through turbulence, a monochromatic sound wave will be scattered over a range of frequencies, resulting in typical spectra with broadband sidelobes on either side of the tone. This spectral broadening, also called 'haystacking', is of importance for noise radiation from jet exhausts and for acoustic measurements in open-jet wind tunnels. A semianalytical model is formulated for a plane wave scattered by a vortex, including the influence of the convection of the vortex. This allows us to perform a detailed parametric study of the properties and evolution of the scattered field. A time-domain numerical model for the linearised Euler equations is also used to consider more general sound fields, such as that radiated by a point source in a uniform flow. The spectral broadening stems from the combination of the spatial scattering of sound due to the refraction of waves propagating through the vortex, and two Doppler shifts induced by the motion of the vortex relative to the source and of the observer relative to the vortex. The fact that the spectrum exhibits sidebands is directly explained by the directivity of the scattered field which is composed of several beams radiating from the vortex. The evolution of the acoustic spectra with the parameters considered in this paper is compared with the trends observed in previous experimental work on acoustic scattering by a jet shear layer.</p