Impedance Eduction Techniques Research Articles

A comparison of in situ and impedance eduction experimental techniques for acoustic liners with grazing flow and high sound pressure level

Several techniques are available to characterize acoustic liners when subject to grazing flow and high sound pressure level (SPL). Although the in situ technique started as the primary experimental procedure, impedance eduction techniques have gained popularity over the past years. However, there is a lack of comparison between these group of methods, especially at conditions typically found in turbofan engines. In this work, in situ and impedance eduction techniques are compared at high flow velocities and SPL using typical acoustic liner test samples and considering uniform flow. Both upstream and downstream acoustic wave propagation will also be considered in view of the discrepancies recently observed by eduction methods. A new method to compensate the instrumentation effect in the in situ technique is proposed and validated. Results are obtained for bulk Mach numbers up to 0.5 and SPLs up to 145 dB for both in situ and two eduction techniques. The three methods presents good agreement in the absence of flow. Unexpected results are observed with higher flow Mach numbers using the eduction technique.

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.

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.

Design of a single degree of freedom acoustic liner for a fan noise test rig

Acoustic liners are an essential part of noise reduction technologies commonly applied in aircraft turbofan engines. Fan noise suppression can be achieved by selecting an appropriate liner design with optimal acoustic impedance at the blade passing frequency. Great efforts have been made not only to improve experimental characterization and numerical methods for acoustic liners, but also to understand noise generation mechanisms, which ultimately impacts on the liner design itself. To gain confidence in the liner design process, a liner barrel was developed and fabricated for the Fan Noise Test Rig located at the University of São Paulo. To this end, analytical methods were used to determine the optimal acoustic impedance for the Fan Noise Test Rig, and a flat test sample was fabricated for experimental characterization with flow using both in-situ and impedance eduction techniques at the Federal University of Santa Catarina. A liner barrel of same nominal geometry was fabricated and placed at the Fan Noise Test Rig, and a modal decomposition indicated that the Tyler-Sofrin mode has been successfully suppressed at the first blade passing frequency. Numerical predictions of liner transmission loss considering the flat sample impedance showed good agreement with experimental results.

Parametric Uncertainty Analysis for Impedance Eduction Based on Prony’s Method

Impedance eduction techniques are commonly employed to obtain the acoustic impedance of liner test samples in the presence of flow; but, as other experimental techniques, it is subject to measuring uncertainties. This paper investigates the main sources of uncertainty in impedance eduction techniques based on Prony-like algorithms. The Monte Carlo method is used to conduct a parametric uncertainty analysis for each input variable in an analytical model of a test rig. Results suggest that critical variables are the microphone sensitivity and positioning. Different microphone arrays are considered to reduce uncertainty levels. Also, it is observed that, in general, the Kumaresan–Tufts algorithm achieves better accuracy than the original Prony’s method. Finally, the Monte Carlo method is used to evaluate uncertainty levels on NASA benchmark data, and the results corroborate the numerical experiments analysis.

On modeling the sound propagation through a lined duct with a modified Ingard-Myers boundary condition

A duct acoustics model is an essential component of an impedance eduction technique and its computation cost determines the impedance measurement efficiency. In this paper, a model is developed for the sound propagation through a lined duct carrying a uniform mean flow. In contrast to many existing models, the interface between the liner and the duct field is defined with a modified Ingard-Myers boundary condition that takes account of the effect of the boundary layer above the liner. A mode-matching method is used to couple the unlined and lined duct segments for the model development. For the lined duct segment, the eigenvalue problem resulted from the modified boundary condition is solved by an integration scheme which, on the one hand, allows the lined duct modes to be computed in an efficient manner, and on the other hand, orders the modes automatically. The duct acoustics model developed from the solved lined duct modes is shown to converge more rapidly than the one developed from the rigid-walled duct modes. Validation against the experiment data in the literature shows that the proposed model is able to predict more accurately the liner performance measured by the two-source method. This, however, cannot be made by a duct acoustics model associated with the conventional Ingard-Myers boundary condition. The proposed model has the potential to be integrated into an impedance eduction technique for more reliable liner measurement.

An improved impedance eduction technique based on impedance models and the mode matching method

The problem of determining the acoustic impedance of liners used in turbofan engines of commercial aircraft has been a point of interest for the scientific community for decades, especially in the presence of grazing flows, similar to operational conditions. Different techniques have been developed to determine liner acoustic impedance under grazing flow. More recent research have been focused on inverse methods, which consist of two steps: (i) measurement of the acoustic field in a rectangular duct with flow and a liner sample located at one or two walls of the duct and (ii) modelling of the acoustic field and application of an optimization procedure to find the impedance that minimize the difference between experimental and analytic results. The process is usually carried on using optimization techniques and performed at each frequency step, which can lead to discontinuous impedance curves and large computational costs. In this work, the mode matching method is discussed in detail, and a new technique for impedance determination is proposed, which incorporates a mathematical impedance model to the optimization process as a mean to improve the impedance curve, therefore suppressing measurements error and convergence issues at single frequencies. The impedance models considered here are given in the frequency domain and satisfy passivity, reality and causality conditions, which allows the use of the educed impedance in time domain simulations. Three models are considered and compared regarding different liner samples, flow velocities and wave propagation direction. The results show that the impedance models can successfully suppress convergence errors close to the liner resonance frequency.

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.

Comparison of Time-Domain Impedance Boundary Conditions for Lined Duct Flows

impedance of liners. This part of the model, however, is limited to single frequency sound source in its present form. The EHR is based on the z‐transformation of the corresponding impedance function for the Extended Helmholtz Resonator in the frequency‐domain. The implementations of the two models in the numerical simulation tool with the DRP scheme are discussed in details. The results from the both models in general agree notably well with each other. However, in one case, the results from the two models dier significantly due to the presence of strongly attenuated modes, which renders the approximations of the EFI invalid. The validation and verification of both models are carried out for the latest NASA impedance tube experiment and the generic aero‐engine frequency domain results of Rienstra and Eversman. In addition, an impedance eduction technique based on the EHR and the optimization process has been developed. This further extends applications of the time‐domain models. The simultaneous optimization of all frequencies considered in the NASA’s impedance tube experiments results in a physically reasonable set of parameters for the EHR. The fitted terminal impedances and the measured mean flow profiles are used for the impedance eduction. The numerical results of both models for the generic aero‐engine inlet test case with higher azimuthal modes also compare well if the same flow assumptions and eigenvalues are used as for the frequency domain methods. Overall both models give a similar physical behavior, but the EHR requires smaller time steps in the case of small face sheet reactances.