Liner Impedance Research Articles

Experimental and calculation investigation on perforated Liners’ acoustic impedance

Abstract Acoustic impedance models are the most common method for representing the properties of engine nacelle liners. Although various models have been developed, it is difficult to validate the accuracy due to the limitation of impedance eduction techniques. For obtaining accurate impedance results, a series of perforated liners are manufactured and the impedance of all is measured by using both the microphone array method and in-situ method. The results of the test demonstrate that acoustic resistances are not sensitive to percent open areas, hole diameter, and the face sheet’s thickness, but the Mach number of the grazing flow in the duct can have a considerable effect on resistance. Furthermore, excellent agreement between predictions and measured data gives confidence that the Goodrich perforated liner impedance model is suitable for the design of engine nacelle liner.

Statistical Metamodel of Liner Acoustic Impedance Based on Neural Network and Probabilistic Learning for Small Datasets

The main novelty of this paper consists of presenting a statistical artificial neural network (ANN)-based model for a robust prediction of the frequency-dependent aeroacoustic liner impedance using an aeroacoustic computational model (ACM) dataset of small size. The model, focusing on percentage of open area (POA) and sound pressure level (SPL) at a zero Mach number, takes into account uncertainties using a probabilistic formulation. The main difficulty in training an ANN-based model is the small size of the ACM dataset. The probabilistic learning carried out using the probabilistic learning on manifolds (PLoM) algorithm addresses this difficulty as it allows constructing a very large training dataset from learning the probabilistic model from a small dataset. A prior conditional probability model is presented for the PCA-based statistical reduced representation of the frequency-sampled vector of the log-resistance and reactance. It induces some statistical constraints that are not straightforwardly taken into account when training such an ANN-based model by classical optimizations methods under constraints. A second novelty of this paper consists of presenting an alternate solution that involves using conditional statistics estimated with learned realizations from PLoM. A numerical example is presented.

Mirror-based multimodal straightforward method for impedance eduction using a zigzag array

The Mirror-based Multimodal StraightForward Method (MM-SFM) is proposed herein to realize accurate and reliable liner impedance eduction covering the wide frequency range of aeroengine fan noises. It adopts a novel zigzag array in the flow duct, and unfolds them by a coordinate transformation into a mapping diagonal array in an extended duct, which can increase the array transverse spacing Δz considerably. Then, it invokes the M-SFM incorporating the trust-region and extended Prony's algorithms, to decompose the three-dimensional multimodal aeroacoustic field and educe the impedance. A parametric study based on the Monte-Carlo uncertainty analysis is conducted through finite-element numerical experiments on a 51 × 51 mm2 flow duct, to survey the method performance under random perturbations. It indicates that, the educing accuracy and reliability are promoted by increasing Δz or the axial spacing Δx properly, and the decomposed-mode number M×N=10 is appropriate herein. In our studied cases, using the recommended array of Δz=25.5mm and Δx=22mm locating at the nodes of transverse mode m = 2, the MM-SFM generally produces accurate averaged educed impedances in a considerably extended frequency range from 100 Hz up to nearly 10 kHz, and has small educing uncertainties at most absorptive frequencies and thus a good reliability.

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.

Aeroacoustic Liner Impedance Metamodel from Simulation and Experimental Data Using Probabilistic Learning

To be able to calculate a parameterized aeroacoustic liner impedance, a robust statistical metamodel is constructed as a function of the frequency and of the control parameters that are the percentage of open area and the sound pressure level. This construction is based on the use of simulated data generated with a computationally expensive aeroacoustic model, which translates to a very small training dataset. This means that the learning process has to be used and the probabilistic learning on manifolds algorithm is chosen. Although the aeroacoustic simulation is conducted on a large aeroacoustic computational model, some approximations are introduced, generating model errors that are taken into account by a probability model in the constructed training dataset. This probability model is calibrated using dimensionless experiments available from the open literature. Despite the fact that only a small amount of data is available, a novel statistical metamodel is successfully developed for which the predictions are consistent. This statistical framework allows for exhibiting a confidence region of the parameterized aeroacoustic liner impedance, which gives an information about the level of uncertainties as a function of the frequency and the control parameters.

Evaluation of the Impedance Variability Effect of Acoustic Liner on Aircraft Engine Fan Noise in Calculation of Far Field Sound Modes Propagation

The influence of the impedance variability of the acoustic liner of an air intake on aircraft engine fan noise in the far field has been studied. The calculations were carried out in an axisymmetric statement for single modes based on the finite element solution to the Blokhintsev equation for the acoustic potential. The acoustic liner impedance was determined from a well-developed semiempirical model that takes into account the influence of a high sound pressure level (SPL) and grazing flow. A procedure has been developed for calculating the propagation of single sound modes through the air intake of an aircraft engine with a variable liner impedance depending on the flow velocity and SPL at a local point. The calculation procedure has been validated. Calculations were made for single mode propagation into the forward hemisphere for an air intake on the wall of which the following conditions were set: rigid wall, constant impedance (the impedance does not change along the liner) and variable impedance (the impedance changes along the liner depending on the changes in the velocity of the grazing flow and SPL). According to the calculation results, it was found that constant and variable impedances yield different SPL values in the far field; as well, taking into account the impedance variability changes not only the SPL values in the far field, but also the direction of the maximum mode radiation.

An improved algorithm for liner impedance eduction in low signal-to-noise ratio flow duct

The impedance eduction technique is widely used by the aeroacoustics community to obtain liner property in a flow duct. However, the obtained impedance is often found to be discontinuous in the frequency domain which violates theoretical liner models. The low signal-to-noise ratio (SNR, in dB) is one factor leading to this unexpected result. To overcome this, a weighting coefficient, represented by an SNR dependent sigmoid function with two control parameters, is introduced to the cost function in the iteration process. The proposed algorithm is employed to measure the impedances of two liners and results show an improvement in the smoothness of the resultant impedance curves over those obtained from conventional cost function.

Nonlinear broadband time-domain admittance boundary condition for duct acoustics. Application to perforated plate liners

The behavior of perforated plates at high excitation level is generally modeled by a surface impedance that depends on the rms velocity in the perforations. A time-domain admittance boundary condition (TDABC) is developed to account for this variation using a multipole model. Two formulations are considered, based on the interpolation either of the admittance or of the multipole coefficients from a data set of reference values. These TDABC are implemented in a finite-difference time-domain solver of the linearized Euler equations and are validated by comparison with experimental results on an impedance tube. Application to a two-dimensional lined duct corresponding to the reference geometry of the NASA Grazing Incidence Tube is then performed. The spatial variation of the perforated plate liner impedance is highlighted and it is shown that assuming a uniform impedance can lead to an unacceptable prediction of the liner attenuation. These results are confirmed both for a harmonic or broadband excitation.

Acoustic characteristics of impingement cooling sheets; effect of bias-grazing flow interaction on the liner impedance in a thin annulus

This study investigates the acoustic characteristics of impingement sheets that are typically installed around can-combustors in stationary gas turbines for cooling purposes. From an acoustic point of view the impingement sheet is a perforated liner backed by the large compressor plenum of the gas turbine. The annular gap between the can and the liner is often only a few millimeters wide to allow for a strong jet impingement on the outer combustor wall. Due to the small cross sectional area of the annular gap, the grazing flow is strongly accelerated along the perforated liner. In this study, we present an acoustic model for impingement sheets, which accounts for bias-grazing flow effects. We experimentally investigate liners with four different porosities between 2% and 5%, in the frequency range between 60Hz and 700Hz. The bias flow Mach number is varied between 0.03 and 0.25, the axially varying grazing flow Mach number between 0 and 0.14 and setups with and without jet impingement on a solid center-body are investigated. Measured reflection coefficients agree well with predictions of the presented model. A significantly increased influence of grazing flow on aperture resistance, compared to existing studies without jet impingement, is noted. The acoustic damping potential of impingement sheets is elaborated and a condition of maximum damping in the low frequency limit is derived, which agrees well with the experimental observations. The results of this work provide the fundamentals for the acoustic analysis and acoustic design of impingement cooling sheets.

Spatially-varying impedance model for locally reacting acoustic liners at a high sound intensity

This paper is concerned with spatially-varying acoustic liner impedance in aeroacoustic ducts, in the presence of a high sound pressure level. It is shown that impedance discontinuity is a leading order parameter in the definition of the impedance variation. A large impedance discontinuity yields a high normal velocity variation, leading to significant nonlinear effects. An iterative numerical strategy is proposed to predict the spatially-varying acoustic impedance over a liner. A Bayesian inference process is coupled with a surrogate model to validate the model with measurements of the acoustic velocity fields above a liner at a high sound intensity, obtained using laser Doppler velocimetry.

Influence of Hole-to-Hole Interaction on the Acoustic Behavior of Multi-Orifice Perforated Plates

Abstract A key factor for developing low-emission combustion systems in modern gas turbines and aero-engines is the acoustic liner's optimized design. Several models are available in the literature for the acoustic impedance of perforated acoustic liners. Most of these impedance models neglect the interaction effect between the orifices. In practice, the orifices are generally closely distributed such that the interactions between acoustic radiation from neighboring orifices can affect their acoustical behavior. The hole-to-hole interaction effect may change the resonance frequency of the resonator due to the nonplanar wave propagation in the cavity, the orifices in the perforated plate, and the near-wall region in the combustor. Considering this effect may help to predict the resonance frequency of the resonator accurately. In this work, a three-dimensional (3D) analytical approach is developed to account for the nonplanar wave propagation in the cavity and orifices on the perforated plate. The present study employs the proposed 3D analytical method to determine the hole-to-hole interaction end correction of multi-orifice perforated plates. Additionally, the hole-to-hole interaction end correction from a series of perforated plates with different orifice radii and spacings is obtained via the finite element method. Perforated plate specimens with different center-to-center hole spacing are tested using an impedance tube. Experimental results show that the resonance frequency is shifted toward a lower frequency with decreasing holes' spacing. The resulting model is compared with the experiments and the end-correction models available in the literature. The comparison shows that the available end-correction models cannot capture the hole-to-hole interaction effect, which is observed in experiments. In contrast, the proposed model can reproduce measurements with high quality. The resulting model demonstrates that the acoustic end-correction length for orifices is closely related to the perforated plate's porosity ratio and orifice radius. The proposed model is readily applicable in the design of multi-orifice perforated plates.

Effect of source direction on liner impedance eduction with consideration of shear flow

Acoustic lining treatments are widely used in modern aircraft engines for noise reduction. The key to the successful application of this technique is to establish a link between the geometry parameters (thickness, hole diameters, etc.) and the acoustic impedance. To achieve this goal, the impedance eduction technique is widely used by the aircraft engine noise research community. The technique iteratively finds an impedance value that leads to the best fit between the predicted and experimental results. More recently, comparative studies have shown that, in the presence of flow, the acoustic impedance educed from a liner test-rig with an upstream acoustic excitation is different from that of the same liner subject to a downstream acoustic excitation. This discrepancy is surmised to be attributed to the Ingard-Myers boundary condition. The current work attempts to provide more information about the influence of boundary layer effect on the educed impedance when the acoustic source is exerted either upstream or downstream. A duct acoustic model for a non-uniform flow with a thin but finite-thickness sheared boundary layer over the liner is developed for impedance eduction. An alternative boundary condition is derived from the Pridmore-Brown equation using the perturbation method that gives rise to an effective impedance to be enforced at the interface between the sheared boundary layer and core flow region carrying a uniform mean flow. Then, a modified impedance eduction technique procedure is developed and used to obtain the liner impedance using a flow duct facility and the result is compared with that based on the Ingard-Myers condition. Results show that considering the sheared flow effect in the impedance eduction makes no significant improvement to the educed impedance for liners used in the experiment.

IFAR liner benchmark challenge #1 – DLR impedance eduction of uniform and axially segmented liners and comparison with NASA results

This paper presents the contribution from the German Aerospace Center (DLR) to the first liner benchmark challenge under the framework of the International Forum for Aviation Research (IFAR). Therefore, two sets of acoustically damping wall treatments, called ‘liner samples’, have been produced by additive manufacturing based on the design data provided by NASA coordinating this benchmark. These liner samples have been integrated and acoustically characterized in the liner flow test facility DUCT-R at DLR Berlin as well as in the liner flow test facility GFIT at NASA Langley. Besides the dissipation coefficients and the axial pressure profiles, the liner wall impedance was educed by first determining the axial wave numbers and then applying a straightforward method based on the one-dimensional Convected Helmholtz Equation. Finally, the comparison of the liner impedance values to the NASA results show a fairly good agreement.

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.

Surface temperature measurement of acoustic liners in the presence of grazing flow and thermal gradient

The development of turbofans with larger fan diameters, shorter inlets, and thinner walls forces the acoustic liners to be placed closer to the hot parts of engines. This experimental study investigates the combined effects of large thermal gradients, grazing flow and acoustic level on the impedance of liners. Previous studies have shown that a coupling between these three effects can exist. The objective is thus to understand the underlying coupled phenomena, in order to extract the driving parameters for a more accurate impedance modeling. In the ONERA B2A grazing flow acoustic liner facility, the flow temperature can be accurately regulated and several types of acoustic excitation can be provided. For the purposes of this study, a test section with a heating device is used to obtain a thermal gradient between the backplate and the perforated plate of the liner sample. Infrared (IR) thermography is used to measure the temperature distribution on the perforated plate. The measurement is conducted for several configurations, to determine in which conditions the coupling between thermal and acoustic dissipation effects exists. In particular, a possible control of surface temperature by high sound pressure level is highlighted.Graphic abstract

Numerical simulations of perforated plate liners: Analysis of the visco-thermal dissipation mechanisms.

In the linear regime and in the absence of mean flow, the impedance of perforated liners is driven by visco-thermal effects. In this paper, two numerical models are employed for predicting these visco-thermal losses. The first model is the linearized compressible Navier-Stokes equations (LNSE), solved in the frequency domain. The second model is the Helmholtz equation with a visco-thermal boundary condition, accounting for the influence of the acoustic boundary layers. These models are compared and validated against measurements. The quantitative analysis of the dissipation rate due to viscosity, computed from the LNSE solutions of four perforated plates, highlights significant differences between the edge effects of a macro- and a micro-perforated plate. In the latter case, a jet is present at the entrances of the perforation. In contrast, the proposed numerical method to calculate the impedance of perforated liners, based on the Helmholtz equation and a visco-thermal boundary condition, is found to be computationally cheaper and to provide reliable predictions.

An investigation on noise attenuation by acoustic liner constructed by Helmholtz resonators with extended necks.

The noise attenuation properties of an acoustic liner consisting of Helmholtz resonators with extended necks (HRENs) are investigated. An optimal liner constructed by 16 inhomogeneous HRENs is designed to be effective in sound absorption in a prescribed frequency range from 700 to 1000 Hz. Its quasi-perfect absorption capability (average absorption coefficient above 0.9) is validated by measurements and simulations. The resonance frequencies of the individual resonators in the designed liner are just located within the effective absorption bandwidth, indicating the overlapping phenomenon of absorption peaks. In addition, the liner maintains a thin thickness, about 1/25th with respect to the longest operating wavelengths. To assess the acoustic performance of the designed liner in the presence of mean flow, experimental investigations are performed in a flow tube. Results show a near flat transmission loss is attained in the target frequency range by the designed liner. Additionally, the impedance of the uniform HREN-based liner is extracted at flow condition. In all, the inhomogeneous HREN-based liner is featured by the thin thickness and the excellent wide-band noise attenuation property. These features make the designed liner an promising solution for noise attenuation in both static and flow conditions.

INVESTIGATION OF THE REASON FOR THE DIFFERENCE IN THE ACOUSTIC LINER IMPEDANCE DETERMINED BY THE TRANSFER FUNCTION METHOD AND DEAN´S METHOD

The article considers the reason for the difference in the results of determining the impedance of the single-layer acoustic liner samples by different methods during the operation in a normal incidence impedance tube. The operation of the normal incidence impedance tube was simulated by numerical solution of the Navier-Stokes equations. The data obtained from the numerical simulation were processed by the transfer function method and Dean’s method. A direct determination of the liner impedance, based on the ratio of the acoustic pressure to the acoustic normal velocity, was used to find out the reasons for the difference in impedance values. The analysis was carried out in the frequency range close to the resonance. It was shown that the transfer function method determines the impedance of the sample face, and the Dean’s method determines the impedance of the one cell only.

Experimentally testing impedance boundary conditions for acoustic liners with flow: Beyond upstream and downstream

Impedance eduction experiments on acoustic liners with flow have systematically shown the educed impedance depending on the direction of the incident wave. Recent attempts to model this dependence include impedance boundary conditions with an additional degree of freedom. In this case, both upstream and downstream acoustic sources must be used to educe both the liner impedance and the extra degree of freedom of the model, which implies two different axial wavenumber conditions are used, and always result in a perfect collapse of the educed impedances; this would be true whether or not the model itself is correct. In this work, we describe a novel experimental setup that allows for four different axial wavenumbers per frequency to be measured: two upstream and two downstream. We use this experiment to investigate three different impedance boundary conditions, namely inviscid sheared, viscous, and momentum transfer conditions, in addition to the classical Ingard–Myers boundary condition, using an inverse eduction technique based on the mode matching method. The additional degree of freedom in each of the first three models is best fitted to experimental data, and then compared to the theoretically predicted values. Unphysical or unrealistic values are found at certain frequencies for each model, and therefore the validity of such models is questionable. The predictive capabilities of the models are tested and compared by means of the plane-wave scattering matrix, and no model is found to be truly predictive. Under certain conditions, educed impedances using the Ingard–Myers boundary condition show similar accuracy in terms of transmission coefficients when compared to the other models.

On the role of acoustic reflections from duct boundaries in fan flutter

The role that acoustic reflections from duct boundaries play in aeroengine fan flutter is theoretically investigated. To make a systematic parametric study attainable, a three-dimensional semi-analytical approach is employed. Based on the transfer element method combined with a boundary integral equation method, this approach effectively captures the acoustic coupling effect of an annular rotor undergoing incipient oscillation and a finite-length non-rigid duct in subsonic flow. For a given vibration mode, the disturbances generated both inside and outside the duct are determined by a simultaneous solution. The flutter likelihood is subsequently evaluated through the energy method. Results reveal that near the flutter boundary, the aeroelastic impact of duct boundary reflections becomes evident and critical when propagating (cut-on or weakly damped) acoustic modes exist in the flow duct. Under such condition the aerodynamic interaction between both duct openings strongly affects the sound field distribution, thus contributing to the notable installation effect on aeroelastic stability. Moreover, the flutter-driven acoustic field is also susceptible to the sound reflection effect of the partially lined duct wall. It is found that the variation of the blade aerodynamic damping with the liner impedance is markedly different when the duct end reflections come into play. Under appropriate conditions the mutual effect of the lined wall and the duct openings significantly strengthens their acoustic couplings with the ducted fan, where a reasonable estimate of aeroelastic stability can only be provided with an adequate consideration of the realistic acoustic boundary conditions for the entire duct.