A number of methods have been developed at NASA Langley Research Center for eduction of the acoustic impedance of sound-absorbing liners mounted in the wall of a flow duct. This investigation uses methods based on the Pridmore-Brown and convected Helmholtz equations to study the acoustic behavior of a single-layer, conventional liner fabricated by the German Aerospace Center and tested in the NASA Langley Grazing Flow Impedance Tube. Two key assumptions are explored in this portion of the investigation. First, a comparison of results achieved with uniform-flow and shear-flow impedance eduction methods is considered. Also, an approach based on the Prony method is used to extend these methods from single-mode to multi-mode implementations. Finally, a detailed investigation into the effects of harmonic distortion on the educed impedance is performed, and the results are used to develop guidelines regarding acceptable levels of harmonic distortion.

This paper presents the results of insertion loss measurements and numerical impedance eduction of three different liner samples. An overview of the test rig and methodology is given, and preprocessed results in terms of reflection and transmission coefficients as well as the energy dissipation are discussed. These coefficients are calculated for discrete frequencies within the investigated frequency range. Subsequently, a numerical postprocessing is performed in the time domain, and the educed impedance function for each sample and flow Mach number is presented. This postprocessing in the time domain uses an impedance model based on the extended Helmholtz resonator with five free parameters. The parameters of the model are fitted via an optimization, which determines the whole frequency response in one optimization process. The comparison of measured and numerically evaluated energy coefficients proves the reliability of the tools for impedance evaluation under flow conditions. Finally, the impedance results of the different samples are discussed, including a comparative study with Aermacchi data of the National Aerospace Laboratory (The Netherlands) flow tube and Aermacchi impedance tube experiments. NomenclatureA Facesheet = area of the liner facesheet A Hole = area of one hole c = speed of sound d = spacing between two holes e r = radial vector, pointing from the source to the boundary point f = frequency f R;H = Helmholtz resonance frequency f R;L = =4-resonance frequency F = objective function ImfZg = reactive part of the impedance l Cell = cell depth l Neck = thickness of the perforated facesheet/neck length l corr: Neck = neck length with correction M = mean Mach number in the duct m = facesheet reactance (extended Helmholtz resonator model) n Hole = number of holes in the liner facesheet p = pressure R = reflection (energy value) RefZg = resistive part of the impedance R f = facesheet resistance (extended Helmholtz resonator model) r = reflection (amplitude ratio)/radius r Hole = radius of one hole T = transmission (energy value) T l = time delay (extended Helmholtz resonator model) t = transmission (amplitude ratio)/time u = velocity field V Cell = volume of one cell behind a hole v g = group velocity = cavity reactance (extended Helmholtz resonator model) = ratio of specific heats = energy dissipation " = cavity resistance (extended Helmholtz resonator model) = wave length % = density of the fluid c = characteristic impedance of the fluid = open-area-ratio of the liner = porosity of the liner facesheet ! = angular frequency Superscripts = in downstream direction = in upstream direction 0 = perturbation 0 = mean value

A number of methods have been developed at NASA Langley Research Center for eduction of the acoustic impedance of sound-absorbing liners mounted in the wall of a flow duct. This investigation uses methods based on the Pridmore-Brown and convected Helmholtz equations to study the acoustic behavior of a single-layer, conventional liner fabricated by the German Aerospace Center and tested in the NASA Langley Grazing Flow Impedance Tube. Two key assumptions are explored in this portion of the investigation. First, a comparison of results achieved with uniform-flow and shear-flow impedance eduction methods is considered. Also, an approach based on the Prony method is used to extend these methods from single-mode to multi-mode implementations. Finally, a detailed investigation into the effects of harmonic distortion on the educed impedance is performed, and the results are used to develop guidelines regarding acceptable levels of harmonic distortion.

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