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

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

Impedance Eduction in Sound Fields With Peripherally Varying Liners and Flow

A two-dimensional impedance eduction theory is extended to three-dimensional sound fields and peripherally varying duct liners. The approach is to first measure the acoustic pressure field at a series of flush-mounted wall microphones located around the periphery of the flow duct. The numerical solution for the acoustic pressure field at these microphones is also obtained by solving the three-dimensional convected Helmholtz equation using the finite element method. A quadratic objective function based on the difference between the measured and finite element solution is constructed and the unknown impedance function is obtained by minimizing this objective function. Impedance spectra educed for two uniform-structure liners (a wire-mesh and a conventional liner) and a hard-soft-hard peripherally varying liner (for which the soft segment is that of the conventional liner) are presented. Results are presented at three mean flow Mach numbers and fourteen sound source frequencies. The impedance spectra of the uniform-structure liners are also computed using a two-dimensional impedance eduction theory. The primary conclusions of the study are: 1) when measured data is used with the uniform-structure liners, the three-dimensional theory reproduces the same impedance spectra as the two-dimensional theory except for frequencies corresponding to very low or very high liner attenuation; and 2) good agreement between the educed impedance spectra of the uniform structure conventional liner and the soft segment of the peripherally varying liner is obtained

A Numerical Theory for Impedance Education in Three-Dimensional Normal Incidence Tubes

A method for educing the locally-reacting acoustic impedance of a test sample mounted in a 3-D normal incidence impedance tube is presented and validated. The unique feature of the method is that the excitation frequency (or duct geometry) may be such that high-order duct modes may exist. The method educes the impedance, iteratively, by minimizing an objective function consisting of the difference between the measured and numerically computed acoustic pressure at preselected measurement points in the duct. The method is validated on planar and high-order mode sources with data synthesized from exact mode theory. These data are then subjected to random jitter to simulate the effects of measurement uncertainties on the educed impedance spectrum. The primary conclusions of the study are 1) Without random jitter the method is in excellent agreement with that for known impedance samples, and 2) Random jitter that is compatible to that found in a typical experiment has minimal impact on the accuracy of the educed impedance

Impedance Eduction in a Duct Using the Linearized Euler Equations

An impedance eduction technique that is based upon a numerical solution to the linearized Euler equations coupled with the minimization of an objective function is presented. The linearized Euler equations are solved numerically using a cubic finite element method and the minimum of the objective function is obtained via a gradient based optimizer. The mean flow is allowed to have a gradient in two coordinate directions and the impedance of the liner may vary arbitrarily over the liner surface. A new regularized wall impedance boundary condition presented by Rienstra which contains the effects of the mean boundary layer thickness is implemented. Impedances are educed for a perforate over honeycomb liner using test data acquired in the Langley Grazing Flow Impedance Tube. The impedance of the liner is educed both with an upstream source and a downstream source. The method is validated by comparing the educed impedance to a benchmark method. The primary conclusion of the study is that the impedances educed for upstream and downstream sources are not well matched and that the primary effect of the boundary thickness is to reduce the resistance of the liner

A Comparative Study of Four Impedance Eduction Methodologies Using Several Test Liners

A comparative study of four commonly used impedance eduction methods is presented for a range of liner structures and test conditions. Two of the methods are restricted to uniform flow while the other two accommodate both uniform and boundary layer flows. Measurements on five liner structures (a rigid-wall insert, a ceramic tubular liner, a wire mesh liner, a low porosity conventional liner, and a high porosity conventional liner) are obtained using the NASA Langley Grazing Flow Impedance Tube. The educed impedance of each liner is presented for forty-two test conditions (three Mach numbers and fourteen frequencies). In addition, the effects of moving the acoustic source from upstream to downstream and the refractive effects of the mean boundary layer on the wire mesh liner are investigated. The primary conclusions of the study are that: (1) more accurate results are obtained for the upstream source, (2) the uniform flow methods produce nearly identical impedance spectra at and below Mach 0.3 but significant scatter in the educed impedance occurs at the higher Mach number, (3) there is better agreement in educed impedance among the methods for the conventional liners than for the rigid-wall insert, ceramic, or wire mesh liner, and (4) the refractive effects of the mean boundary layer on the educed impedance of the wire mesh liner are generally small except at Mach 0.5