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The purpose of this paper is to present a method for the ultrasonic characterization of air-saturated porous media, by solving the inverse problem using only the reflected waves from the first interface to infer the porosity, the tortuosity, and the viscous and thermal characteristic lengths. The solution of the inverse problem relies on the use of different reflected pressure signals obtained under multiple obliquely incident waves, in the time domain. In this paper, the authors propose to solve the inverse problem numerically with a first level Bayesian inference method, summarizing the authors' knowledge on the inferred parameters in the form of posterior probability densities, exploring these densities using a Markov-Chain Monte-Carlo approach. Despite their low sensitivity to the reflection coefficient, it is still possible to extract the knowledge of the viscous and thermal characteristic lengths, allowing the simultaneous determination of all the physical parameters involved in the expression of the reflection operator. To further constrain the problem and guide the inference, the knowledge of a particular incident angle is used at one's advantage in order to more precisely define the thermal length, by effectively yielding a statistical relationship between tortuosity and characteristic length ratio.

This paper presents a statistical inference method for impedance eduction in a flow-duct facility. The acoustic impedance is recast into a random variable, and Bayes's theorem is used to obtain the posterior probability density function of both its real and imaginary parts, thus expressing the knowledge/uncertainty one has on the impedance value, given a certain experimental data uncertainty. An evolutionary Markov chain Monte Carlo technique is selected to explore the probability space, and a surrogate model based on the method of snapshots is employed to speed up the calculations. The linearized Euler equations are solved using a two-dimensional discontinuous Galerkin scheme, accounting for the presence of a grazing flow. The inference process is first validated on published NASA Grazing Incidence Tube results, in which acoustic-pressure measurements on the wall opposite the liner are used as inputs. Then, the same procedure is applied to educe the impedance of a conventional single degree-of-freedom liner in the ONERA-The French Aerospace Lab B2A acoustic bench, in which a laser Doppler velocimetry (LDV) technique is used to measure the two components of the acoustic-velocity fields above the liner. The primary conclusion of the study is that the Bayesian inference method allows for consistent impedance eductions, as compared to a classical deterministic eduction approach, for both microphone and LDV measurements. Furthermore, it yields the credibility intervals of the identified impedance, which represent the uncertainty on the identified impedance values, given an uncertain measurement. The identified parameters are less correlated using an LDV-based inference than a microphone-based inference, which might be due to the more limited number of data.

This paper investigates the combined effects of high sound pressure level and grazing flow on impedance eduction for classical liners. Experiments are conducted in the grazing flow duct at ONERA (B2A). The impedance is then educed with an inverse method adapted to a shear flow. To take into account the effects of incident sound pressure level, a new strategy for impedance eduction is developed, using a space-dependent variable term. The new strategy is applied to different experimental cases and the results are compared to those obtained with the classical method.

In this paper, a modeling extension for the description of wave propagation in rigid porous media at high frequencies is used. To better characterize the visco-inertial and thermal interactions between the fluid and the structure in this regime, two additional characteristic viscous and thermal surfaces Σ and Σ are taken into account, as initially introduced in [J. Kergomardet al., Acta Acust united Ac 99 (4) (2013) 557-571]. This extends the modeling order of the dynamic tortuosity and compressibility. A sensitivity analysis is performed on the additional parameters, showing that only the viscous surface Σ has an influence on transmitted waves in the high frequency regime, for materials having a low viscous characteristic length. A general Bayesian inference is then conducted to infer simultaneously the posterior probability densities of the parameters associated with the visco-inertial effects, i.e., the porosity, tortuosity, the viscous characteristic length, and the viscous characteristic surface. The proposed method is based on the measurement of waves transmitted by a slab of rigid porous material in the time domain. Bayesian inference results obtained on three different porous materials are presented.

In this paper, a modeling extension for the description of wave propagation in porous media at low-mid frequencies is introduced. To better characterize the viscous and inertial interactions between the fluid and the structure in this regime, two additional terms described by two parameters α1 and α2 are taken into account in the representation of the dynamic tortuosity in a Laurent-series on frequency. The model limitations are discussed. A sensitivity analysis is performed, showing that the influence of α1 and α2 on the acoustic response of porous media is significant. A general Bayesian inference is then conducted to infer simultaneously the posterior probability densities of the model parameters. The proposed method is based on the measurement of waves transmitted by a slab of rigid porous material, using a temporal model for the direct and inverse transmission problem. Bayesian inference results obtained on three different porous materials are presented, which suggest that the two additional parameters are accessible and help reducing systematic errors in the identification of other parameters: porosity, static viscous permeability, static viscous tortuosity, static thermal permeability and static thermal tortuosity.

The present study provides theoretical details and experimental validation results to the approach proposed by Minotti et al. (2008) for measuring amplitudes and phases of acoustic velocity components (AVC), that are waveform parameters of each component of velocity induced by an acoustic wave, in fully turbulent duct flows carrying multitone acoustic waves. Theoretical results support that the turbulence rejection method proposed, based on the estimation of cross-power spectra between velocity measurements and a reference signal such as a wall-pressure measurement, provides asymptotically efficient estimators with respect to the number of samples. Furthermore, it is shown that the estimator uncertainties can be simply estimated, accounting for the characteristics of the measured flow turbulence spectra. Two laser-based measurement campaigns were conducted in order to validate the acoustic velocity estimation approach and the uncertainty estimates derived. While in previous studies estimates were obtained using Laser Doppler Velocimetry (LDV), it is demonstrated that high-repetition-rate Particle Image Velocimetry (PIV) can also be successfully employed. The two measurement techniques provide very similar acoustic velocity amplitude and phase estimates for the cases investigated, that are of practical interest for acoustic liner studies. In a broader sense, this approach may be beneficial for non-intrusive sound emission studies in windtunnel testings.

As part of a cooperation between ONERA and NASA, the liner impedance eduction methods developed by the two research centers are compared. The NASA technique relies on an objective function built on acoustic pressure measurements located on the wall opposite the test liner, and the propagation code solves the convected Helmholtz equation in uniform flow using a finite element method that implements a continuous Galerkin discretization. The ONERA method uses an objective function based either on wall acoustic pressure or on acoustic velocity acquired above the liner by Laser Doppler Anemometry, and the propagation code solves the linearized Euler equations by a discontinuous Galerkin discretization. Two acoustic liners are tested in both ONERA and NASA flow ducts and the measured data are treated with the corresponding impedance eduction method. The first liner is a wire mesh facesheet mounted onto a honeycomb core, designed to be linear with respect to incident sound pressure level and to grazing flow velocity. The second one is a conventional, nonlinear, perforate-over-honeycomb single layer liner. Configurations without and with flow are considered. For the nonlinear liner, the comparison of liner impedance educed by NASA and ONERA shows a sensitivity to the experimental conditions, namely to the nature of the source and to the sample width.