In this work, a multi-pressure equivalent fluid (MPEF) approach is applied to model non-conventional acoustic materials that combine different, separate pore networks with contrasting tortuosities. A technique for the informed design of such multi-tortuous materials is proposed. It is based on the observation that broadband performance of such a material can be achieved by tuning the quarter-wavelength resonances corresponding to each network. The material design consists therefore in adding and tailoring the separate pore networks to obtain contrasting tortuosities that evenly distribute these resonances over the desired frequency range. Additional improvement is achieved by independent isotropic scaling of the separate networks. The proposed technique is accurate and also very efficient because it is based on semi-analytical calculations. All this is demonstrated on several examples of multi-tortuous materials which, for simplicity, have an essentially two-dimensional structure. The results obtained in the material design process are verified by Navier-Stokes direct numerical simulations as well as by the MPEF numerical model. Final validation was also carried out experimentally on an additively manufactured sample of one of the multi-tortuous materials designed for this study. The multi-resonance phenomenon observed in sound absorption as well as the experimentally demonstrated anomalous behaviour of the multi-tortuous material backed by an air gap are very well predicted by the modelling and explained in detail on physical grounds.

Prediction of the acoustic performance of 3D printed materials is investigated at normal and grazing incidence. A direct numerical (microscopic) simulation that solves the full set of Navier-Stokes equations is used as a reference. It is compared with a macroscopic approach in which the material is represented by an equivalent fluid. The materials have a periodic microstructure, consisting either of a single network of spherical or cubic cavities connected by cylindrical channels or of a double-nested network. The samples are printed using the stereolithography technique and are tested using an impedance tube and a duct test bench. For single network geometries, the results of sound absorption at normal and grazing incidence predicted using the equivalent fluid approach are in good agreement with those obtained by the microscopic approach. Comparisons with impedance tube measurements confirm that both approaches can accurately predict the absorption coefficient of the samples. For the in-duct liner configuration, the transmission loss measurements and predictions show similar evolution with frequency change, despite the discrepancy in amplitude. For the double network geometry, the equivalent fluid approach cannot exactly reproduce the results obtained with the direct numerical simulation. Finally, while the predictions with the microscopic approach provide a good match with the impedance tube measurements, only a poor agreement is obtained using the duct testing bench.

The impact of leakage on sound properties of open porosity 3D printed samples with a periodic microstructure is investigated at normal and grazing incidence. For that, direct numerical simulations (DNS) accounting for leakage are performed. In addition, an extension of the model proposed by Cummings [(1991). J. Sound Vib. 151, 63-75] is developed to predict the surface impedance of a sample surrounded by an air space at normal impedance accounting for dissipation in the leak. Experiments in a Kundt tube are performed for three series of 3D printed samples with different external diameter. Overall, leakage is responsible for a shift of the absorption peak toward higher frequencies and to an increase in its amplitude. Comparison of the measurements with the DNS and the extended Cummings model shows that both approaches predict satisfactorily the impact of leakage on the absorption coefficient. In addition, a duct wall configuration is studied for three geometries of 3D printed samples. DNS results reveal that the impact of leakage on transmission loss varies significantly depending on the 3D printed sample unit cell. Finally, discrepancies between the measured and predicted transmission loss are shown to be attributable to leakage for two of the three geometries.

The low frequency peaks in the absorption spectra of layers of conventional porous materials correspond to quarter wavelength resonances and the peak frequencies are determined essentially by layer thickness.If the layer cannot be made thicker, the frequency of the peak can be lowered by increasing the tortuosity of the material.Modern additive manufacturing technologies enable exploration of pore network designs that have high tortuosity.This paper reports analytical models for pore structures consisting of geometrically complex labyrinthine networks of narrow slits resembling Greek meander patterns.These networks offer extremely high tortuosity in a non-porous solid skeleton.However, additional enhancement of the low frequency performance results from exploiting the dual porosity pressure diffusion effect by making the skeleton microporous with a significantly lower permeability than the tortuous network of slits.Analytical pre-

The objective of this study is to model and characterize the behaviour of different materials made with 3D printing when they are placed in the wall of a duct.The considered materials present a periodic structure of a volume linked to the volumes of other cells by small channels.Cubic and spherical volumes are used.Two model of the materials are studied.The first is based on a macroscopic description using an equivalent fluid by its dynamic characteristic functions.The semi-phenomenological parameters of the JCALP model are obtained using a hybrid multi-scale approach.The second model consists in describing the material as a whole at the microscopic scale and solving the Linearized Navier-Stokes equations in the material.The results of the two models are compared in normal incidence and in a duct wall.The behavior of the various materials is also investigated experimentally.Measurements at normal incidence are conducted in a circular Kundt Tube.The measurements in the wall of a duct are performed in the MATISSE experimental bench.The experimental and model results show a correct agreement.Finally, the potential differences between the model and the experiment are discussed.

An assembly of additively-manufactured modules to form two-dimensional networks of labyrinthine slits results in a sound absorber with extremely high tortuosity and thereby a relatively low-frequency quarter wavelength resonance. Fully analytical modelling is developed for the generic design of such composite acoustic panels, allowing rapid exploration of various specific designs. In addition to labyrinthine channels in a non-porous solid skeleton, a case is also considered where the skeleton has microporosity such that its permeability is very much lower than that due to the labyrinthine channels alone. The analytical modelling is verified by numerical calculations as well as sound absorption measurements performed on several 3D printed samples of modular composite panels. The experimental validation required overcoming the non-trivial difficulties related to additive manufacturing and testing samples of extreme tortuosity. However, due to the two-dimensionality and modularity of the proposed design, such absorbers can possibly be produced without 3D printing by assembling simple, identical modules produced separately. The experimental results fully confirmed the theoretical predictions that significant sound absorption, almost perfect at the peak, can be achieved at relatively low frequencies using very thin panels, especially those with double porosity.

Perforated plates experience a nonlinear response at high excitation levels.They are largely used in duct applications, such as aircraft engine nacelles, for which broadband noise and the presence of flow must be considered.Time-domain methods are well-suited to predict sound propagation under such conditions.Recently, a timedomain admittance boundary condition (TDABC) was proposed by Diab et al. (J.Sound.Vib., 528, 2022) [1] to account for the nonlinear response of perforated plates and was implemented in a finite difference time-domain solver of the linearized Euler equations.A numerical study on sound propagation in a lined duct was performed in the absence of flow.This paper extends the TDABC to a lined duct with flow.First, the time-domain model is experimentally validated with a perforated plate placed in an impedance tube at normal incidence.Second, a flow duct lined with the perforated plate is considered.Numerical simulations are performed to evaluate noise reduction due to the liner for several incident sound pressure levels.Subsequently, experiments are carried out in the Caïman wind-tunnel of Ecole Centrale de Lyon and the experimental and numerical results are compared.

The behavior of perforated plates at high excitation level is generally modeled by a surface impedance that depends on the rms velocity in the perforations. A time-domain admittance boundary condition (TDABC) is developed to account for this variation using a multipole model. Two formulations are considered, based on the interpolation either of the admittance or of the multipole coefficients from a data set of reference values. These TDABC are implemented in a finite-difference time-domain solver of the linearized Euler equations and are validated by comparison with experimental results on an impedance tube. Application to a two-dimensional lined duct corresponding to the reference geometry of the NASA Grazing Incidence Tube is then performed. The spatial variation of the perforated plate liner impedance is highlighted and it is shown that assuming a uniform impedance can lead to an unacceptable prediction of the liner attenuation. These results are confirmed both for a harmonic or broadband excitation.

A method is presented to characterize general sound-absorbing materials through a pole-based identification of the equivalent fluid. This is accomplished by 1) determining the extended equivalent fluid of the material sample through the transfer function method (TFM), 2) identification of the acoustic response of the material through the poles of the extended effective density and compressibility, and 3) build the effective density and compressibility from the poles associated to the local acoustic response. Real pole pairs describe a dissipative medium (or equivalently an over-damped resonating medium), which is the natural behavior of rigid-frame porous materials, while complex-conjugate pole pairs describe a locally-resonant medium typical of metamaterials. Complex-conjugate poles associated to elastic resonances of the sample are discarded. We test the method for several non-conventional porous materials. In general, a better fit to the measured surface impedance is obtained than with an acoustics-based identification to the Johnson-Champoux-Allard-Pride-Lafarge model (JCAPL), and the method appears also to be robust to errors of the TFM. (C) 2020 The Authors. Published by Elsevier Ltd.

A general methodology to simulate acoustic propagation in ducts with extended-reacting liners in the time domain is presented, including a generic perforated sheet on the air-material interface. The Linearized Euler Equations (LEE) with a mean flow profile are solved in the duct and the linearized equations on an equivalent fluid are solved in the liner material. The auxiliary differential equation method (ADE) is used to prevent the computation of convolution integrals, and leads to a formulation compatible with high-order numerical schemes. The methodology is illustrated for the case of liners consisting of rigid-frame porous materials and a prototype of locally-resonant acoustic metamaterials. A one-dimensional (1D) test case is first used to validate the algorithm and assess the numerical error. The numerical order of the algorithm is the expected one, independently of the interface, as long as the number of poles retained in the partial fraction expansions involved in the formulation is high enough. The algorithm is then applied to a realistic two-dimensional (2D) configuration in a duct with flow, and is used to illustrate the restrained validity of the locally-reacting approximation. Finally, the impact of the flow Mach number on the acoustic performance of porous and metamaterial extended-reacting liners is briefly assessed.

The gradient term suppression (GTS) method for removing the hydrodynamic instability appearing in the time-domain solutions of the linearized Euler equations (LEE) along a lined flow duct is assessed. For this, the characterization of a convective instability in the time domain, with the aid of a complementary modal analysis, is first presented. The effect of the mesh size and spatial filtering on the instability is investigated. In particular, a convergence of the instability in the time domain is achieved for a small enough grid size. The consequence of suppressing the mean flow gradient term on the modes is then investigated. It is shown that the unstable modes are indeed removed, but also that acoustic modes are significantly modified, especially for low Helmholtz numbers. The GTS method is finally applied to the NASA grazing impedance tube benchmark. It is found that tuning the weight of the mean flow gradient term within the LEE can be effective for suppressing the instability while conserving a reasonable accuracy of the acoustic component.

A partial gradient term suppression (GTS) method aiming at removing hydrodynamic instabilities generated during acoustic propagation along a lined flow duct is presented. Time-domain simulations are conducted to assess impacts of the partial GTS method based on the NASA Grazing Incidence Tube (GIT) benchmark experiment. The effectiveness of the partial GTS method for removing hydrodynamic instabilities is shown. However the sound pressure is underestimated by several dBs for certain frequencies especially in the low Helmholtz number range. It is found that a relatively accurate prediction of acoustic propagation can be obtained with partially suppressing the mean flow gradient term, in particular for high Helmholtz number.

A finite-difference time-domain (FDTD) approach is proposed to model extended-reacting liners under a grazing mean flow. It is based on an equivalent fluid model of the material together with the auxiliary differential equation method (ADE). The methodology is applicable to any liner material amenable to an equivalent fluid description, such as rigid-frame porous materials and metamaterials. It has been validated against a semi-analytical solution in a 1D test case and against experimental measurements in a duct.

The purpose of this work is to check if additive manufacturing technologies are suitable for reproducing porous samples designed for sound absorption. The work is an inter-laboratory test, in which the production of samples and their acoustic measurements are carried out independently by different laboratories, sharing only the same geometry codes describing agreed periodic cellular designs. Different additive manufacturing technologies and equipment are used to make samples. Although most of the results obtained from measurements performed on samples with the same cellular design are very close, it is shown that some discrepancies are due to shape and surface imperfections, or microporosity, induced by the manufacturing process. The proposed periodic cellular designs can be easily reproduced and are suitable for further benchmarking of additive manufacturing techniques for rapid prototyping of acoustic materials and metamaterials.