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The proximity of obstacles in a ventilation network can result in a significant increase of the noise production. In this paper, a tandem diaphragm inserted in a rigid duct with rectangular cross section is investigated and compared to a single diaphragm obstruction. The disturbed flow which reaches the second obstacle causes an amplification of the radiated noise which goes beyond a simple doubling of the power. Experimental results, carried with various spacing between the two diaphragms and bulk velocity, allows identifying other aeroacoustic source mechanisms which does not appear with a single diaphragm. Depending on the configuration, the broadband level can increase by more than 10 dB and feedback phenomena can appear at low frequency. Explanations and illustrations of those phenomena are given thanks to compressible-fluid simulations.

Duct acoustic network modeling is commonly carried out using the transfer matrix formalism which is limited to the low frequency range. The aim of this work is to extend it to higher frequencies by taking into account the multi-mode acoustic propagation. The first step is to compute, via Finite Element Method (FEM), the multi-port multi-modal scattering matrix of each element. The second step is to transform it into a scattering matrix for the acoustic power, relying on assumptions which are often used for the study of medium-to-high frequency broadband noise. The method is applied to typical elements such as expansion chamber mufflers and air conditioning veins. In all cases, the power-flow model is compared to the FEM solution in terms of Transmission Losses. It is concluded that this simplified model is a reliable tool for the analysis of complex networks encountered in Heat and Ventilation Air Conditioning (HVAC) duct networks.

The Partition of Unity Finite Element Method (PUFEM) is now a well established and efficient method used in computational acoustics to tackle short-wave problems. This method is an extension of the classical finite element method whereby enrichment functions are used in the approximation basis in order to enhance the convergence of the method whilst maintaining a relatively low number of degrees of freedom. For exterior problems, the computational domain must be artificially truncated and special treatments must be followed in order to avoid or reduce spurious reflections. In recent papers, different Non-Reflecting Boundary Conditions (NRBCs) have been used in conjunction with the PUFEM. An alternative is to use the Perfectly Match Layer (PML) concept which consists in adding a computational sponge layer which prevents reflections from the boundary. In contrast with other NRBCs, the PML is not case specific and can be applied to a variety of configurations. The aim of this work is to show the applicability of PML combined with PUFEM for solving the propagation of acoustic waves in unbounded media. Performances of the PUFEM-PML are shown for different configurations ranging from guided waves in ducts, radiation in free space and half-space problems. In all cases, the method is shown to provide acceptable results for most applications, similar to that of local approximation of NRBCs.

Noise generation by low Mach number air flows through circular orifices in rectangular ducts is investigated. In particular, the influence of the number and position of the orifices maintaining a constant flow area is addressed. A review of the available theories suggests a certain importance of such parameters in the excitation of higher-order acoustic duct modes. A qualitative coefficient is proposed for a first characterization of the ability to enhance or lessen a given higher-order acoustic mode by the plate geometry. An experimental campaign is performed to measure the total emitted acoustic power by different plate geometries as well as its modal composition. It is found that the orifices' numbers and positions greatly influence the acoustic emissions while the flow pressure drop caused by the obstacles is similar. The proposed qualitative coefficient shows good agreement with the experimental results. A particle image velocimetry measurement campaign is performed to visualize the near-field average flow behavior upstream and downstream of the orifice plates. An increase in the turbulent velocity fluctuations in the vicinity of the orifices is observed on both sides, further validating previous studies on the subject.

Due to the manufacturing process, some fibrous materials like glasswool may be transversely isotropic (TI): fibers are mostly parallel to a plane of isotropy within which material properties are identical in all directions whereas properties are different along the transverse direction. The behavior of TI fibrous material is well described by the TI Biot's model, but it requires one to measure several mechanical parameters and to solve the TI Biot's equations. This paper presents an equivalent fluid model that can be suitable for TI materials under certain assumptions. It takes the form of a classical wave equation for the pressure involving an effective density tensor combining both limp and rigid frame behaviors of the material. This scalar wave equation is easily amenable to analytical and numerical treatments with a finite element method. Numerical results, based on the proposed model, are compared with experimental results obtained for two configurations with a fibrous material. The first concerns the absorption of an incident plane wave impinging on a fibrous slab and the second corresponds to the transmission loss of a splitter-type silencer in a duct. Both configurations highlight the effect of the sample orientation and give an illustration of the unusual TI behavior for fluids.

An analytical model based on a homogenization process is used to predict and understand the behavior of finite length splitter/baffle-type silencers inserted axially into a rigid rectangular duct. Such silencers consist of a succession of parallel baffles made of porous material and airways inserted axially into a rigid duct. The pore network of the porous material in the baffle and the larger pores due to the airway can be considered as a double porosity (DP) medium with well-separated pore sizes. This scale separation leads by homogenization to the DP model, widely used in the porous material community. This alternative approach based on a homogenization process sheds physical insight into the attenuation mechanisms taking place in the silencer. Numerical comparisons with a reference method are used to show that the theory provides good results as long as the pressure wave in the silencer airways propagates as a plane wave parallel to the duct axis. The explicit expression of the axial wavenumber in the DP medium is used to derive an explicit expression for the optimal resistivity value of the porous material, ensuring the best dissipation for a given silencer geometry.

Recently Chazot et al. [J. Sound Vib. 332, 1918-1929 (2013)] applied the Partition of Unity Finite Element Method for the analysis of interior sound fields with absorbing materials. The method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard Finite Element Method. The work is however restricted to a certain class of absorbing materials that react like an equivalent fluid. This paper presents an extension of the method to the numerical simulation of Biot's waves in poroelastic materials. The technique relies mainly on expanding the elastic displacement as well as the fluid phase pressure using sets of plane waves which are solutions to the governing partial differential equations. To show the interest of the method for tackling problems of practical interests, poroelastic-acoustic coupling conditions as well as fixed or sliding edge conditions are presented and numerically tested. It is shown that the technique is a good candidate for solving noise control problems at medium and high frequency.

In the present work, the propagation of sound in a lined duct containing sheared mean flow is studied. Walls of the duct are acoustically treated with absorbent poroelastic foams. The propagation of elasto-acoustic waves in the liner is described by Biot's model. In the fluid domain, the propagation of sound in a sheared mean flow is governed by the Galbrun's equation. The problem is solved using a mixed displacement-pressure finite element formulation in both domains. A 3D implementation of the model has been performed and is illustrated on axisymmetric examples. Convergence and accuracy of the numerical model are shown for the particular case of the modal propagation in a infinite duct containing a uniform flow. Practical examples concerning the sound attenuation through dissipative silencers are discussed. In particular, effects of the refraction effects in the shear layer as well as the mounting conditions of the foam on the transmission loss are shown. The presence of a perforate screen at the air-porous interface is also considered and included in the model., (© 2011 Acoustical Society of America)

A mode matching method for predicting the transmission loss of a cylindrical shaped dissipative silencer partially filled with a poroelastic foam is developed. The model takes into account the solid phase elasticity of the sound-absorbing material, the mounting conditions of the foam, and the presence of a uniform mean flow in the central airway. The novelty of the proposed approach lies in the fact that guided modes of the silencer have a composite nature containing both compressional and shear waves as opposed to classical mode matching methods in which only acoustic pressure waves are present. Results presented demonstrate good agreement with finite element calculations provided a sufficient number of modes are retained. In practice, it is found that the time for computing the transmission loss over a large frequency range takes a few minutes on a personal computer. This makes the present method a reliable tool for tackling dissipative silencers lined with poroelastic materials.

Classical finite-element and boundary-element formulations for the Helmholtz equation are presented, and their limitations with respect to the number of variables needed to model a wavelength are explained. A new type of approximation for the potential is described in which the usual finite-element and boundary-element shape functions are modified by the inclusion of a set of plane waves, propagating in a range of directions evenly distributed on the unit sphere. Compared with standard piecewise polynomial approximation, the plane-wave basis is shown to give considerable reduction in computational complexity. In practical terms, it is concluded that the frequency for which accurate results can be obtained, using these new techniques, can be up to 60 times higher than that of the conventional finite-element method, and 10 to 15 times higher than that of the conventional boundary-element method.