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.

The near-orifice aerodynamic response of a single degree of freedom acoustic liner to tonal and multi-tonal excitation with grazing flow was experimentally studied. A high-magnification PIV setup was designed in order to provide dense 2D velocity field measurements above a millimeter-sized orifice of the liner. The resonator near-orifice velocity dynamics near and far from resonance were shown to be significantly different, with dynamic velocity scales well captured by a lumped-element model that was also satisfactorily applied to multi-tonal forcing cases. The effects of varying the forcing acoustic sound pressure level and the tangential flow velocity scale (the friction velocity) were investigated. It was observed that a "rough-wall" analogy was not suited to account for the induced aerodynamic effects, but that, under certain conditions, a "transpiration wall" analogy may be adequate.

This study investigates the temperature effect on the impedance of conventional singledegree-of-freedom liners, both without and with grazing flow. Experiments are performed in a controlled environment, with a detailed monitoring of the temperature all along the liner sample. The liner impedance is either derived from the reflection coefficient measured in a normal impedance tube, or is educed with an inverse method from acoustic velocity or wall pressure fields measured in the ONERA grazing flow duct. The influence of the acoustic source level on the temperature of the sample is also addressed, which enlights strong multiphysics coupling between acoustics, flow and thermal phenomena.

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While intrinsic by definition, the impedance measured by impedance eduction has been shown to depend on the direction of the incident waves relative to the mean flow. The purpose of the present work is to evaluate whether part of the observed differences could stem from a biased wavenumber definition made during the impedance eduction process.Comparisons are made between the results of impedance eductions with uniform flow and the Ingard-Myers boundary condition, with the 1D linearized Euler equations and with the 2D linearized Euler equations, i.e., in the cross section. Both numerical synthetic data and experimental data are used for the eduction of two sample liners, with bulk Mach numbers ranging from 0 to 0.3, and at frequencies ranging from 400 to 3000 Hz.Results show that for a rectangular cross-section duct, the knowledge of the 2D flow profile in the cross section is valuable for impedance eduction. Using only 1D flow profiles bias the educed impedance estimation.