Impedance Eduction Method Research Articles

An uncertainty investigation for liner impedance eduction methods

Impedance eduction methods have been developed for decades to meet the increasing need for high-quality impedance data in the design and optimization of acoustic liners. To this end, it is important to fully investigate the uncertainty problem, to which only limited attention has been devoted so far. This paper considers the possibility of acoustically-induced structural vibration as a nonnegligible uncertainty or error source in impedance eduction experiments. As the frequency moves away from the resonant frequency, with the increase in the value of cavity reactance, the acoustic particle velocity inside liner orifices possibly decreases to the extent comparable to the vibration velocity of liner facing sheet. Thus, the acoustically-induced vibration, although generally being weak except at the inherent structural frequencies, may considerably affect the impedance eduction results near the anti-resonant frequency where the liner has poor absorption. To demonstrate the effect of structural vibration, the vibration velocity of liner facing sheet is estimated from the experimentally educed admittance of the liner samples whose orifices are sealed with tape. Further, a three-dimensional numerical model is set up, in which normal particle velocity is introduced over the solid portion of liner facing sheet to imitate structural vibration, rather than directly solving the acoustic-structural coupling problem. As shown by the results, the vibration of liner facing sheet, whose velocity is as small as estimated by the experiment, can result in anomalous deviation of the educed impedance from the impedance model near the anti-resonant frequency. The trend that the anomalous deviation varies with frequency is numerically captured.

Study On the Effect of Operating Conditions on Acoustic Three-Port Measurements of Perforates in presence of Grazing Flow

Different impedance eduction methods have been previously used to study the acoustic properties of perforated plates in the presence of grazing flow, giving varying results. The work presented here is to contribute to the ongoing experimental research on the acoustic behaviour of perforates under different acoustic excitations and flow conditions. Here, a three-port technique is used to study the aero-acoustic properties of perforates, which allows to observe the acoustic field on both sides of the perforate. Experimentally determined characteristics of the perforate are dependent on the operating conditions like grazing flow speed, microphone distances, standing wave pattern, and temperature. This study aims to provide the experimental analysis on the effect these factors have on the calculated perforate properties, namely the transfer impedance and the scattering matrix. Global sensitivity analysis is performed to study the individual effect of these factors in the post-processing, as well as the overall effect of error in the determination of these operating conditions.

Experimental Investigation of Mean Flow Profile Effects on Impedance Eduction

The results of experimental and computational studies of the three-dimensional mean flow velocity profile influence on the impedance eduction are presented. In order to measure the three-dimensional velocity profile, the TsAGIâ€(tm)s “Interferometer with flow†facility was upgraded so that additional holes were made in one cross section of the rectangular duct. As a result, it became possible to measure the longitudinal flow velocity in this cross section along 6 lines using a Pitot tube or a hot wire anemometer. The full three-dimensional velocity profile is determined by interpolating the values measured.Experimental results of the velocity profile for various experiment conditions are presented. Based on the numerical solution of the three-dimensional Pridmore-Brown equation by means of Finite Element Method and the gradient descent method, the problem of impedance eduction are investigated. The influence of the flow velocity profile and the form of functional on the obtained impedance values are discussed. The impedance values educted by means of this approach are compared with the impedance values obtained using two-dimensional impedance eduction methods, which didnâ€(tm)t taking into account the three-dimensional non homogeneity of the flow velocity field.

Investigation of Extended-Tube Liners for Control of Low-Frequency Duct Noise

Existing models of extended-tube liners are mainly applicable to the normal-incidence case, and the influence of the grazing-flow effect is often ignored. In the current paper, an impedance model is developed based on the transfer matrix method, and the grazing-flow effect on the surface impedance is taken into account in terms of the end corrections. The validity of the model is examined on a flow-duct facility, and the liner impedances are obtained from an impedance eduction method. The proposed model shows a reasonable agreement with the educed data, and better accuracy is found in terms of the transmission loss. Geometric parameters including the length of the extended tube and the grazing-flow speed are then investigated. It is found that the frequency for maximum attenuation is shifted to lower frequencies for a longer extended tube, but it is less sensitive to the grazing-flow speed. The effects of the sound pressure level and nonlinearities are also investigated.

Experimental Confirmation of an Analytical Model of the Sound Propagation in a Rectangular Duct in the Presence of Impedance Transitions and Development of an Impedance Eduction Method Based on it

The authors have carried out a systematic study of the accuracy in the impedance eduction of liners in “interferometer with flow” rigs in the absence of grazing flow. A method is proposed for determining the confidence interval of sound pressure measurements for such a rig. The analytical model of sound propagation in a rectangular duct in the presence of impedance transitions, previously proposed by the authors and described with the Wiener–Hopf method, is experimentally confirmed. A method is developed and implemented for impedance eduction of liners in the absence of flow, based on an analytical method that takes into account the passage of sound modes through the impedance transition.

A three-dimensional straightforward method for liner impedance eduction in uniform grazing flow

There are increasing demands for a more efficient acoustic liner design in measuring liner impedance over a broad frequency range in a large-sized duct. But few impedance eduction methods can be applied when the sound pressure field in the flow duct is three-dimensional as frequency or duct size increases. To solve this issue, a 3-D straightforward method has been developed by combining the traditional mode decomposition method with the original 2-D straightforward method. The unknown impedance is straightforwardly determined by using the measured pressure data at the measuring microphones which are flush mounted on the rigid wall opposite to the test liner in the form of an evenly spaced rectangular array. By conducting the numerical simulation experiments and Monte-Carlo-method-based uncertainty analysis, the efficiency and feasibility of the present 3-D method are validated in a wide Helmholtz number range through comparing the educed and imposed impedances for both flow-off and flow-on cases. It is found that this method performs quite well even with measured data polluted by random perturbations. A solution selection process is proposed to completely solve the multi-solution problem existing in all straightforward methods. The optimized layout of the measuring microphone array has been investigated and greater sound pressure difference between adjacent measuring points results in a narrower uncertainty range. The present method is found to have several obvious advantages such as practicability in real experiments and significantly saving the measurement time and consumption.

ON IMPROVEMENT OF THE IMPEDANCE EDUCATION ACCURACE BY ACCOUNT OF IMPEDANCE VARIABILITY ALONG THE ACOUSTIC LINER

An impedance eduction method considering impedance variability along the acoustic liner is proposed. Impedance eduction is based on minimization of the residual functional, which is the discrepancy between the experimental and computed values of acoustic pressure at the interferometer microphones. The computed values are obtained by solving the Helmholtz equation, convected Helmholtz equation and linearized Navier-Stokes equations for a two-dimensional duct with an impedance wall and flow based on finite-element method. The cases of constant and variable impedance along the liner sample are considered. It is established that when taking into account the variable impedance, the residual functional decreases more than twofold against the case of constant impedance.

Investigation of straightforward impedance eduction method on single-degree-of-freedom acoustic liners

In order to address the current aircraft noise problem, the knowledge of impedance of acoustic liners subjected to high-intensity sound and grazing flow is of crucial importance to the design of high-efficiency acoustic nacelles. To this end, the present study is twofold. Firstly, the StraightForward impedance eduction Method (SFM) is evaluated by the strategy that the impedance of a liner specimen is firstly experimentally educed on a flow duct using the SFM, and then its accuracy is checked by comparing the numerical prediction with the measured wall sound pressure of the flow duct. Secondly, the effects of grazing flow and high-intensity sound on the impedance behavior of two single-layer liners are investigated based on comparisons between educed impedance and predictions by three impedance models. The performance of the SFM is validated by showing that the educed impedance leads to excellent agreement between the simulation and the measured wall sound pressure for different grazing flow Mach numbers and Sound Pressure Levels (SPLs) and over a frequency range from 3000 Hz down to 500 Hz. The grazing flow effect generally has the tendency that the acoustic resistance exhibits a slight decrease before it increases linearly with an increase in Mach, predicted successfully by the sound-vortex interaction theoretical model and the Kooi semi-empirical impedance model. However, the Goodrich semi-empirical impedance model gives only a simple linear relation of acoustic resistance starting from Mach zero. Additionally, when the SPL increases from 110 to 140 dB in the present investigation, the acoustic resistance exhibits a significant increase at all frequencies in the absence of flow; however, the resistance decreases slightly under a grazing flow of Mach 0.117. It indicates that the SPL effect can be greatly inhibited when flow is present, and the grazing flow effect can be reduced partly as well at a relatively high SPL.

Straightforward impedance eduction method for non-grazing incidence wave with multiple modes

The control of modern aeroengine noise poses great challenge to the design of acoustic liners, due to the existence of multiple higher-order modes over a very wide frequency range in acoustic nacelles. In order to meet the pressing demand, the straightforward impedance eduction method is further developed such that it can be applied to more general acoustic environment where there are both plane mode and higher-order modes incident upon a test liner. A novelty of the present method is using a diagonally mounted microphone array on the opposite wall of the test liner in a flow duct, thus the measured wall sound pressure simultaneously contains the information of the modes in both the axial and transverse directions. Then, the employment of Prony's method enables the realization of the full modal decomposition to the acoustic field in the flow duct. Numerical experiments simulating acoustic fields with a finite element model are conducted to investigate and validate the feasibility of the present method for both a small-scale and a large-scale flow ducts. Two ceramic tubular liners and a perforated liner are tested as specimens, whose impedance values to be educed are known a priori by means of existing impedance models. Random perturbation is added into the acoustic field data to simulate realistic noisy acoustic environments. The results show that the present method can educe the imposed impedance with a good accuracy when the liner specimens are subjected to the sound field composing of multiple incident modes including several transverse modes in both ducts. The frequency scope of the impedance eduction is considerably extended when compared with the methods restricted by the assumption of plane incident mode, with the upper frequency reaching up to 6.0 kHz and 5.0 kHz for the ducts, respectively. A parametric study indicates that the accuracy of impedance eduction can be promoted by increasing the signal-to-noise ratio and the number of microphones.

Efficient Impedance Eductions for Liner Tests in Grazing Flow Incidence Tube

This paper presents an efficient impedance eduction method for grazing flow incidence tube by using a surrogating model along with the Wiener–Hopf method, which enables rapid acoustic predictions and effective impedance eductions over a range of parametric values and working conditions. The proposed method is demonstrated by comparing to the theoretical results, numerical predictions, and experimental measurements, respectively. All the demonstrations clearly suggest the capability and the potential of the proposed solver for parametric studies and optimizations of the lining methods.

Broadband liner impedance eduction for multimodal acoustic propagation in the presence of a mean flow

A new broadband impedance eduction method is introduced to identify the surface impedance of acoustic liners from in situ measurements on a test rig. Multimodal acoustic propagation is taken into account in order to reproduce realistic conditions. The present approach is based on the resolution of the linearized 3D Euler equations in the time domain. The broadband impedance time domain boundary condition is prescribed from a multipole impedance model, and is formulated as a differential form well-suited for high-order numerical methods. Numerical values of the model coefficients are determined by minimizing the difference between measured and simulated acoustic quantities, namely the insertion loss and wall pressure fluctuations at a few locations inside the duct. The minimization is performed through a multi-objective optimization thanks to the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The present eduction method is validated with benchmark data provided by NASA for plane wave propagation, and by synthesized numerical data for multimodal propagation.

Effects of Mean Flow Assumption and Harmonic Distortion on Impedance Eduction Methods

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 DLR, German Aerospace Center and tested in the NASA Langley Grazing Flow Impedance Tube. Two key assumptions are explored in this investigation. First, a comparison of results achieved with uniform-flow and shear-flow impedance eduction methods is considered. Second, an approach based on the Prony method is used to extend these methods from single-mode to multimode implementations. In addition, a detailed study 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.

Investigation of straightforward impedance eduction in the presence of shear flow

A straightforward impedance eduction method is proposed which combines Prony׳s method with the Pridmore-Brown equation to obtain the impedance of acoustic liners in the presence of shear flow. Particular attention is paid to the reported inconsistency problems associated with the boundary layer effect in the development of impedance eduction techniques. A kind of flow-insensitive acoustic liner is considered which is placed in a rectangular flow duct containing predominant grazing incidence mode. Three slip or no-slip flow profiles are examined, which are the parabola, the one-seventh power law and the uniform core flow with linear boundary layer. A shear-flow FEM model is also set up to simulate the duct acoustic field. The present impedance eduction method has been tested and validated using both the simulated and the published measured data. It is shown that, despite of their distinct boundary layers, the selected flow profiles lead to essentially the same impedance results. And also, for the impedance eduction the strict consideration of no-slip shear flow is very consistent with the use of the Ingard–Myers׳ boundary condition with the uniform flow assumption over the test conditions. Although not susceptible to the exact shape of flow profile, the impedance eduction critically depends on the determination of the cross-sectional average Mach number. The usual practice of approximately representing the duct flow with the midspan profile results in a slight overestimation of the average Mach number in the two-dimensional acoustic models, and thus can considerably affect the accuracy of the impedance eduction. To solve this problem, the average flow profile is introduced to account for the actual three-dimensional flow non-uniformity in the rectangular duct. It is further found that the effective Mach number, corresponding to a slightly modified average flow profile, can be used to achieve a considerable collapse of the impedance spectra educed at different Mach numbers. Based on the new evaluation of the influence of boundary layer profile, the FEM simulation using the straightforwardly educed impedance as the boundary condition can achieve an excellent agreement with the benchmark data for the complex sound pressure in the flow duct.

Validation of an Improved Experimental Method for Use in Impedance Eduction

Results from impedance eduction methods developed by NASA Langley Research Center are used throughout the acoustic liner community. Occasional anomalies persist with these methods at frequencies where the liner produces minimal attenuation. An approach to educe impedance spectra with increased confidence is demonstrated, by combining results from successive tests with different cavity depths. First, a raylometer is used to measure the DC flow resistance of three wire-mesh facesheets. These facesheets are then mounted onto frames and a normal incidence tube is used to determine their respective acoustic impedance spectra. 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. Since the 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 (weakly dependent on the source sound pressure level and grazing flow Mach number), the acoustic impedance can be educed with increased confidence. Representative test results are discussed, and the complete database is available in electronic format upon request.

New Numerical Procedure for Impedance Eduction in Ducts Containing Mean Flow

A new impedance eduction method is presented and validated against a benchmark method, and the effects of measurement uncertainty errors on the impedances educedwith this newmethod are assessed.Unique features of the newmethod include the following: 1) the upstream and downstream boundary conditions contain higher-order duct modes, 2) the impedance spectra of unique nonuniform test liners on opposite walls may be educed simultaneously, and 3) the measured data for the impedance eduction are acquired only at the source and duct termination planes. The validation exercise is performedwith a rigid-wall insert and a conventional liner over a range of frequencies and flowMach numbers in the NASALangleyResearchCenter’s grazing flow impedance tube. The primary conclusions of the study are that the impedance spectra of the rigid-wall insert and the conventional liner that were educed from the newmethod are in very good agreement with those that were educed by using the benchmarkmethod. However, the effects of measurement uncertainty on the educed impedance are greater at the lower frequencies and the higher Mach numbers for the newmethod. All indications are that this occurs because the newmethod 1) uses significantly less data to perform the impedance eduction than the benchmark and 2) is currently based on a rather crude approximation to the measured pressure gradient, which is more sensitive to the refractive effects of the boundary layer than the measured lower-wall pressure that is required in the benchmark method.

Validation of an Impedance Eduction Method in Flow

Results are reported for validating a method for educing the normal incidence impedance of a locally reacting liner in a grazing incidence, nonprogressive acoustic wave environment with flow. The results demonstrate the ability of the method to reproduce the normal incidence admittance of a solid steel plate and normal incidence impedance of two soft test liners in a uniform flow. The selected test liners are known to be locally reacting and exhibit no amplitude-dependent impedance nonlinearities and only minimal flow effects. Baseline results for these liners are, therefore, established from measurements in a conventional normal incidence impedance tube. A key feature of the method is the expansion of the unknown impedance function as a piecewise continuous polynomial with undetermined coefficients. Stewart's adaptation (Stewart, G. W., III, A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives, Journal of ACM, Vol. 14, No. 1, 1967, pp. 72-83) of the Davidon-Fletcher-Powell optimization algorithm is used to educe the normal incidence impedance at each Mach number by optimizing an objective function. The method very Marly reproduces the normal incidence impedance spectrum for each of the test liners; thus, its usefulness for determining the normal incidence impedance of test liners for a broad range of source frequencies and flow Mach numbers is demonstrated.

Validation of an impedance eduction method in flow

Validation of an impedance eduction method in flow