Assessment of Axial Wave Number and Mean Flow Uncertainty on Acoustic Liner Impedance Eduction

International audienceA key parameter in designing and assessing advanced broadband acoustic liners to achieve the current and future noise reduction goals is the acoustic impedance presented by the liner. This parameter, intrinsic to a specific liner configuration, is dependent on sound pressure level and grazing flow velocity. Current impedance eduction approaches have, in general, provided excellent results and continue to be employed throughout the acoustic liner community. However, some recent applications have indicated a possible dependence of the educed impedance on the direction of incident waves relative to the mean flow. The purpose of the current study is to investigate this unexpected behavior for various impedance eduction methods based on the Pridmore-Brown and convected Helmholtz equations. Specifically, the effects of flow profile and axial wavenumber uncertainties on educed impedances for upstream and downstream sources are investigated. The uniform flow results demonstrate the importance of setting a correct Mach number value in obtaining consistent educed impedances for upstream and downstream sources. In fact, the consistency of results over the two source locations was greatly improved by a slight modification of the uniform flow Mach number. In addition, uncertainty in educed axial wavenumber was also illustrated to correlate well with differences in the educed impedances, even with modified uniform flow Mach number. Finally, while less straightforward than in the uniform flow case, it appears that modification of the mean flow profile may also improve consistency of results for upstream and downstream results when shear flow is included

Evaluation of a Multizone Impedance Eduction Method

A computational study is used to evaluate the PyCHE impedance eduction method developed at the NASA Langley Research Center. This method combines an aeroacoustic duct propagation code based on numerical solution to the convected Helmholtz equation with a global optimizer that uses the Differential Evolution algorithm. The efficacy of this method is evaluated with acoustic pressure data simulated to represent that measured with one-zone, two-zone, and three-zone liners mounted in the NASA Langley Grazing Flow Impedance Tube. The PyCHE method has a normalized impedance error of approximately 0.2 for (uniform) one-zone liners with a length of at least 5, and produces quite reasonable results for liners as short as 2. Whereas the impedance of the liner has an effect on eduction accuracy, the amount of attenuation is shown to be the dominant parameter. Similar results are observed for two-zone liners, for which the impedance of each zone is unique. The two-zone results also indicate it is more difficult to accurately educe resistance than reactance, and a zone length of at least 6 (slightly longer than for uniform liners) is needed to limit the normalized error to 0.2. The PyCHE method is also demonstrated to successfully educe the impedances for each zone of a three-zone liner. These results are sufficiently encouraging to warrant the continued usage of the PyCHE impedance eduction method for single and multizone liners

Experimental validation of a two-dimensional shear-flow model for determining acoustic impedance

Tests were conducted to validate a two-dimensional shear-flow analytical model for determining the acoustic impedance of a liner test specimen in a grazing-incidence, grazing-flow environment. The tests were limited to a test specimen chosen to exhibit minimal effects of grazing flow so that the results obtained by using the shear-flow analytical model would be expected to match those obtained from normal-incidence impedance measurements. Impedances for both downstream and upstream sound propagation were generally consistent with those from normal-incidence measurements. However, sensitivity of the grazing-incidence impedance to small measurement or systematic errors in propagation constant varied dramatically over the range of test frequencies

On the Use of Experimental Methods to Improve Confidence in Educed Impedance

Results from impedance eduction methods developed by NASA Langley Research Center are used throughout the acoustic liner community. In spite of recent enhancements, occasional anomalies persist with these methods, generally at frequencies where the liner produces minimal attenuation. This investigation demonstrates an experimental approach to educe impedance with increased confidence over a desired frequency range, by combining results from successive tests with different cavity depths. A series of tests is conducted with three wire-mesh facesheets, for which the results should be weakly dependent on source sound pressure level and mean grazing flow speed. First, a raylometer is used to measure the DC flow resistance of each facesheet. These facesheets are then mounted onto a frame and a normal incidence tube is used to determine their respective acoustic impedance spectra. A comparison of the acoustic resistance component with the DC flow resistance for each facesheet is used to validate the measurement process. Next, each facesheet is successively mounted onto three frames with different cavity depths, and a grazing flow impedance tube is used to educe their respective acoustic impedance spectra with and without mean flow. The no-flow results are compared with those measured in the normal incidence tube to validate the impedance eduction method. Since the anti-resonance frequency varies with cavity depth, each sample provides robust results over a different frequency range. Hence, a combination of results can be used to determine the facesheet acoustic resistance. When combined with the acoustic reactance, observed to be weakly dependent on the source sound pressure level and grazing flow Mach number, the acoustic impedance can be educed with increased confidence. Representative results of these tests are discussed, and the complete database is available in electronic format upon request

Evaluation of Wall Boundary Conditions for Impedance Eduction Using a Dual-Source Method

The accuracy of the Ingard-Myers boundary condition and a recently proposed modified Ingard-Myers boundary condition is evaluated for use in impedance eduction under the assumption of uniform mean flow. The evaluation is performed at three centerline Mach numbers, using data acquired in a grazing flow impedance tube, using both upstream and downstream propagating sound sources, and on a database of test liners for which the expected behavior of the impedance spectra is known. The test liners are a hard-wall insert consisting of 12.6 mm thick aluminum, a linear liner without a facesheet consisting of a number of small diameter but long cylindrical channels embedded in a ceramic material, and two conventional nonlinear liners consisting of a perforated facesheet bonded to a honeycomb core. The study is restricted to a frequency range for which only plane waves are cut on in the hard-wall sections of the flow impedance tube. The metrics used to evaluate each boundary condition are 1) how well it educes the same impedance for upstream and downstream propagating sources, and 2) how well it predicts the expected behavior of the impedance spectra over the Mach number range. The primary conclusions of the study are that the same impedance is educed for upstream and downstream propagating sources except at the highest Mach number, that an effective impedance based on both the upstream and downstream measurements is more accurate than an impedance based on the upstream or downstream data alone, and that the Ingard-Myers boundary condition with an effective impedance produces results similar to that achieved with the modified Ingard-Myers boundary condition

Explanation of Anomalous Behavior Observed in Impedance Eduction Techniques Using Measured Data

Several enhancements that improve the accuracy and robustness of an impedance eduction technique that use an automatic optimizer are presented. These enhancements are then used to launch an intensive investigation into the cause of anomalous behavior that occurs for a small number of test conditions. This anomalous behavior is investigated for both a hardwall insert and a conventional liner. The primary conclusions of the study are that: (1) for the hard wall insert, the anomalies are due to narrow peaks in the objective function, (2) For the conventional liner, the anomalies are due to the presence of an extremely flat objective function, and (3) the anomalies appear to be triggered by inconsistencies between the duct propagation model and the measured data. At high frequencies, the duct propagation model may need to include the effects of higher-order duct modes, whereas at low frequencies, the effects of the mean boundary layer may have to be included

Impedance Eduction in Ducts with Higher-Order Modes and Flow

An impedance eduction technique, previously validated for ducts with plane waves at the source and duct termination planes, has been extended to support higher-order modes at these locations. Inputs for this method are the acoustic pressures along the source and duct termination planes, and along a microphone array located in a wall either adjacent or opposite to the test liner. A second impedance eduction technique is then presented that eliminates the need for the microphone array. The integrity of both methods is tested using three sound sources, six Mach numbers, and six selected frequencies. Results are presented for both a hardwall and a test liner (with known impedance) consisting of a perforated plate bonded to a honeycomb core. The primary conclusion of the study is that the second method performs well in the presence of higher-order modes and flow. However, the first method performs poorly when most of the microphones are located near acoustic pressure nulls. The negative effects of the acoustic pressure nulls can be mitigated by a judicious choice of the mode structure in the sound source. The paper closes by using the first impedance eduction method to design a rectangular array of 32 microphones for accurate impedance eduction in the NASA LaRC Curved Duct Test Rig in the presence of expected measurement uncertainties, higher order modes, and mean flow

Impedance Eduction in Large Ducts Containing Higher-Order Modes and Grazing Flow

Impedance eduction test data are acquired in ducts with small and large cross-sectional areas at the NASA Langley Research Center. An improved data acquisition system in the large duct has resulted in increased control of the acoustic energy in source modes and more accurate resolution of higher-order duct modes compared to previous tests. Two impedance eduction methods that take advantage of the improved data acquisition to educe the liner impedance in grazing flow are presented. One method measures the axial propagation constant of a dominant mode in the liner test section (by implementing the Kumarsean and Tufts algorithm) and educes the impedance from an exact analytical expression. The second method solves numerically the convected Helmholtz equation and minimizes an objective function to obtain the liner impedance. The two methods are tested first on data synthesized from an exact mode solution and then on measured data. Results show that when the methods are applied to data acquired in the larger duct with a dominant higher-order mode, the same impedance spectra are educed as that obtained in the small duct where only the plane wave mode propagates. This result holds for each higher-order mode in the large duct provided that the higher-order mode is sufficiently attenuated by the liner

Effects of Liner Length and Attenuation on NASA Langley Impedance Eduction

This study explores the effects of liner length and attenuation on the CHE (convected Helmholtz equation) impedance eduction method, in which the surface impedance of an acoustic liner is inferred through an iterative process based on repeated solutions to the convected Helmholtz equation. Wire mesh-over-honeycomb and perforate-over-honeycomb acoustic liners are tested in the NASA Langley Grazing Flow Impedance Tube, and the resultant data are processed using two impedance eduction methods. The first is the CHE method, and the second is a direct method (labeled the KT method) that uses the Kumaresan and Tufts algorithm to compute the impedance directly. The CHE method has been extensively used for acoustic liner evaluation, but experiences anomalous behavior under some test conditions. It is postulated that the anomalies are related to the liner length and/or attenuation. Since the KT method only employs data measured over the length of the liner, it is expected to be unaffected by liner length. A comparison of results achieved with the two impedance eduction methods is used to explore the interactive effects of liner length and attenuation on the CHE impedance eduction method