Failure of the Ingard-Myers boundary condition for a lined duct: an experimental investigation

This paper deals with experimental investigation of the lined wall boundary condition in flow duct applications such as aircraft engine systems or automobile mufflers. A first experiment, based on a microphone array located in the liner test section, is carried out in order to extract the axial wavenumbers with the help of an "high-accurate" singular value decomposition Prony-like algorithm. The experimental axial wavenumbers are then used to provide the lined wall impedance for both downstream and upstream acoustic propagation by means of a straightforward impedance education method involving the classical Ingard-Myers boundary condition. The results show that the Ingard-Myers boundary condition fails to predict with accuracy the acoustic behavior in a lined duct with flow. An effective lined wall impedance, valid whatever the direction of acoustic propagation, can be suitably found from experimental axial wavenumbers and a modified version of the Ingard-Myers condition with the form inspired from a previous theoretical study [Aure?gan et al., J. Acoust. Soc. Am. 109, 59-64 (2001)]. In a second experiment, the scattering matrix of the liner test section is measured and is then compared to the predicted scattering matrix using the multimodal approach and the lined wall impedances previously deduced. A large discrepancy is observed between the measured and the predicted scattering coefficients that confirms the poor accuracy provided from the Ingard-Myers boundary condition widely used in lined duct applications.     

A comparison of measured and computed sound pressure levels in a non-uniform acoustically lined duct

A comparison of measured and numerically calculated acoustical fields is presented for a non-uniform lined duct in the absence of appreciable mean flow. The frequency range investigated includes the “cut-on” frequencies of several transverse modes in certain portions of the duct. Measured pressure fields are compared to those predicted by one and two dimensional numerical models. The validity of the one dimensional model is confirmed for frequencies below cut-on of the first transverse mode. For higher frequencies the one dimensional model is clearly unsatisfactory, as might be expected. The two dimensional model gives reasonable results for frequencies below and above cut-on of the transverse modes, although it indicates a very strong sensitivity, of acoustical fields, to small variations in local wall impedance data.     

流管实验装置中声传播计算的模态方法

流管实验装置是测量有流动情况下航空发动机消声短舱内声衬声阻抗的主要装置。本文发展了一种解析的模态匹配方法进行在平均流有声衬条件下矩形流管中声传播的计算。用同伦方法求解特征值问题,并与用环绕积分求解的结果进行比较。声场通过轴向阻抗间断面的声压和声质点速度积分相等计算。第一个算例是无流动、硬壁、有限长、考虑端口反射的情况,并与北航流管实验台测量数据进行了对比;第二个算例为有流动情况下有限长声衬管道不考虑端口反射的声场计算,它与文献中NASA流管实验结果和CAA计算结果符合得很好。     

Comparison of measured broadband noise attenuation spectra from circular flow ducts and from lined engine intakes with predictions

Sound propagation in lined circular ducts is investigated in the presence of uniform and sheared flow. The modal solutions are obtained by solving an eigenvalue equation which, in the case of sheared flow, is derived by using finite differences and by matching the pressure and the radial component of the particle velocity at the interface of the regions of uniform and sheared flow. For the uniform flow region, standard Bessel function solutions are used. The attenuation of acoustic energy at a given frequency and for a given liner length is computed on the assumption that at the inlet to the lined duct, the acoustic energy is equally distributed among the propagating modes. The total number of propagating modes is determined from the hard wall “cut off” condition. The failure to find some of the modal solutions on the attenuation computed in this way is discussed. It is shown that the reliability of this method of computing liner attenuation depends on the ability to successfully compute most of the modal solutions over a large range of frequencies, flow conditions and duct wall impedance values. A numerical technique is developed which uses a fraction of the total number of solutions to compute the total attenuations without appreciable loss of accuracy. Measured attenuation spectra from a flow duct facility and from lined intake ducts of the RB.211 engine are compared with predictions. In general very good agreement between predictions and measurements is obtained.     

The effect of grazing mean flow on acoustical characteristics of the micro-perforated panel absorber

There are three effects of grazing mean flow on acoustical characteristics of the micro-perforated panel absorber(1) on radiation impedance of the orifice,(2) on acoustical impedance of the construction at sound wave angle incidence,(3) on sound propagation property in a duct lined by absorber.Based on the acoustical fundamental principle,these effects were analyzed respectively,and relative formulas were derived. Some qualitative tendencies were shown that radiation impedance of an orifice,value ofξin function coth(ξ) which estimates cavity impedance,and transmission loss in a lined duct all will decrease with flow speed increases as well as the resonant frequency will move to lower frequency caused by Doppler Effect,when sound wave propagation direction is the same with flow direction. The discussion was also supported by a relative experimental study.     

Sound source in the presence of wall shear layers

Numerical solution techniques for evaluating the acoustic field generated by a single line source located inside or outside a wall shear layer of an infinitely long lined rectangular duct are presented. A formula for calculating wave attenuation due to an acoustic lining is given.     

切向流对微穿孔共振吸声结构声学性能的影响

切向流对微穿孔共振吸声结构声学性能的影响可以分成三类:(1)对小孔辐射声抗的影响;(2)对结构斜入射吸声性能的影响;(3)对消声通道消声性能的影响。根据声学基本理论,详细讨论这些影响,得到对应的理论分析公式。定性而言,若声波的传播方向与气流的运动方向一致,小孔外侧的辐射声抗、空腔声阻抗函数coth (ξ)的宗量ξ赋值和消声通道的消声系数都会减小;同时呈现多普勒效应,使得结构的吸声系数共振峰频率向低频移动。理论分析得到相应实验研究的支持。      

Thermal effect on the acoustic behavior of an axisymmetric lined duct

This paper deals with the effect of the temperature and the frequency on the acoustic behavior of lined duct partially treated with usual material used in acoustic insulation.First, the effect of frequencies and temperature on the acoustic impedance of usual materials used in lined duct such as glass or rock wools in order to reduce acoustic level is investigated.Secondly, the variational formulation of the acoustic duct problem taking into account velocity and temperature effects is established. Then, a numerical model is derived which permits to compute the reflection and the transmission coefficients of such duct for different temperatures and several flow velocities. The acoustic power attenuation is then computed from these coefficients and the effect of the temperature and flow velocities on this energetic quantity is evaluated.The numerical results are obtained for three configurations of a lined duct treated for different temperature ranges and several velocities. Numerical coefficients of transmission and reflection as well as the acoustic power attenuation show the relative influence of temperature.     

An improved multimodal method for sound propagation in nonuniform lined ducts

An efficient method is proposed for modeling time harmonic acoustic propagation in a nonuniform lined duct without flow. The lining impedance is axially segmented uniform, but varies circumferentially. The sound pressure is expanded in term of rigid duct modes and an additional function that carries the information about the impedance boundary. The rigid duct modes and the additional function are known a priori so that calculations of the true liner modes, which are difficult, are avoided. By matching the pressure and axial velocity at the interface between different uniform segments, scattering matrices are obtained for each individual segment; these are then combined to construct a global scattering matrix for multiple segments. The present method is an improvement of the multimodal propagation method, developed in a previous paper [Bi et al., J. Sound Vib. 289, 1091-1111 (2006)]. The radial rate of convergence is improved from O(n(-2)), where n is the radial mode indices, to O(n(-4)). It is numerically shown that using the present method, acoustic propagation in the nonuniform lined intake of an aeroengine can be calculated by a personal computer for dimensionless frequency K up to 80, approaching the third blade passing frequency of turbofan noise.     

Non-linear effect of wall linings on sound attenuation in ducts

The equivalent surface source method is extended to the analysis of high intensity sound propagation in a duct whose wall is partially treated with a sound absorbing material. The propagation of sound in the gas is assumed to be linear, but the acoustic resistance of the sound absorbing material is assumed to be a function of the normal acoustic velocity. The problem is reduced to a non-linear integro-differential equation for the fluid particle displacement at the lined wall surface, which can be solved by a successive approximation method. Numerical examples show that the non-linear effect decreases or increases the peak sound attenuation rate of the lowest mode depending upon the linear component of the resistance. The dependence of the attenuation spectrum on modal phase difference of multi-mode incident waves is heavily affected by the non-linear effect. In the case of incident waves of multi-circumferential modes, different circumferential modes are generated by the non-linear effect.     

On the acoustic modes in a cylindrical duct with an arbitrary wall impedance distribution

The present paper considers the propagation of sound in a cylindrical duct, with a wall section of finite length covered by an acoustic liner whose impedance is an arbitrary function of position. The cases of (i) uniform wall impedance, and wall impedance varying along the (ii) circumference or (iii) axis of the duct, or (iv) both simultaneously, are explicitly considered. It is shown that a nonuniform wall impedance couples modes with distinct azimuthal l or axial m wave numbers, so that their radial wave numbers k can no longer be calculated separately for each pair (m,l). The radial wave numbers are the roots of an infinite determinant, in the case when the wall impedance varies either (i) circumferentially or (ii) radially. If the wall impedance varies (iv) both radially and circumferentially, then the radial wave numbers are the roots of a doubly infinite determinant, i.e., an infinite determinant in which each term is an infinite determinant. The infinite determinants specifying the radial wave numbers are written explicitly for sound in a cylindrical nozzle with a uniform axial flow, in which case the radial eigenfunctions are Bessel functions; the method of calculation of the radial wave numbers applies equally well to a cylindrical nozzle with shear flow and/or swirling flows, with the Bessel functions replaced by other eigenfunctions. The radial wave numbers are calculated by truncation of the infinite determinants, for several values of the aspect ratio, defined as the ratio of length to diameter. It is shown that a nonuniform wall impedance will give rise to additional modes compared with a uniform wall impedance. The radial wave numbers specify the eigenfrequencies for the acoustic modes in the duct; the imaginary parts of the eigenfrequencies specify the decay of the sound field with time, and thus the effectiveness of the acoustic liner.     

Propagation and radiation of sound from flanged circular ducts with circumferentially varying wall admittances,II: Finite ducts with sources

The radiation of sound from a flanged duct system containing various hard-walled pressure sources and a finite length of non-uniformly lined duct is considered. Reflection coefficients, transmission losses and the directivity of the radiated field are evaluated. Direct comparisons between the results for the non-uniformly lined ducts, a uniformly lined duct and a hard-walled duct are made for fixed values of admittance, liner length and source distributions. Several interesting wave scattering characteristics which relate to the design of aircraft turbofan inlet liners are uncovered.     

On the causes of negative source impedance in the measurement of intake and exhaust noise sources

In order to evaluate the acoustic field within a duct system some knowledge is required about the acoustic source, which is characterized by frequency-dependent values of both strength and impedance. However, in using various experimental techniques for various types of source to obtain these values, negative real parts of the source impedance have been measured. Negative source resistance is physically implausible. In some instances, one measurement method gives positive values of source resistance where another gives negative values. This paper reviews the possible causes of the problem, with reference to experimental and theoretical results, in an attempt to clarify the issue. Various possible origins of a negative source resistance have been investigated. It is noted that, for the time being, the violation of the assumption of a time-invariant source and the defect in the inherent algorithm of the load method are the most probable origins of the negative source resistance.     

A possible approach to optimization of parameters of sound-absorbing structures for multimode waveguides

A method of allowing for the spatial sound field structure in designing the sound-absorbing structures for turbojet aircraft engine ducts is proposed. The acoustic impedance of a duct should be chosen so as to prevent the reflection of the primary sound field, which is generated by the sound source in the absence of the duct, from the duct walls.     

A finite element method for modelling dissipative mufflers with a locally reactive lining

The transmission loss of a lined expansion chamber muffler with zero mean flow is studied by using a finite element model of the system. In the cases considered the lining is arranged in small cells so that it is reasonable to assume a locally reacting effect. An existing empirical relationship is used to calculate the lining impedance. The results show that the lining always increases the transmission loss over the unlined chamber valuys; with a thin lining its effect is similar to that of a side branch filter. However, as the thickness increases and the lining impedance approaches the characteristic impedance for the absorption material, the transmission loss develops a single maximum similar to the attenuation produced by a thick lining on the primary mode in a lined duct.     

Sound attenuation in acoustically lined curved ducts in the absence of fluid flow

A study has been made of the sound attenuation in a lined curved duct with rectangular cross-section. In this study, the derivation of the eigenvalue equation was based on the continuity of the normal component of the particle displacement and the matching of the acoustic pressure on the acoustic lining surface. The sound attenuation was calculated by using the acoustic energy expression for the waves propagating in a curved duct. For a given duct geometry and known acoustic lining impedances, a computer program was developed to solve for the eigenvalues and to obtain the sound attenuation of the propagating waves in the lined curved duct. It was found that in the case studied here the fundamental mode was least attenuated. The total sound attenuation was calculated on the assumption that the amplitudes for all propagating waves were equal at a given frequency. Effects of aspect ratio, bend angle and the acoustic impedance on the sound attenuation were investigated in the present work.     

On the selection of loads in the multiload method for measuring the acoustic source parameters of duct systems

The in-duct source can be characterized by two acoustical parameters such as the source strength and the source impedance, which permit the prediction of radiated sound pressure or insertion loss of the whole duct system. One-port acoustic characteristics of an in-duct source can be measured by the multiload method using an overdetermined set of open pipes or side-branch pipes with different lengths as applied loads. The input data, viz. load pressure and load impedance, are usually contaminated by measurement error in the actual measurements, which result in errors in the calculated source parameters. In this paper, the effects of the errors in the input data on the results have been studied numerically, varying the number of loads and their impedances in order to determine what combination of the loads will yield the best result. It is noted that, frequently, only a set of open pipes is used when applying the multiload method to the internal combustion engine sources. A set of pipe lengths, which cause the calculated results to be least sensitive to the input data error, can be found when using open pipe loads. The present work is intended to produce guidelines for preparing an appropriate load set in order to obtain accurate source properties of fluid machines.     

Analysis and design of pod silencers

Parallel baffle mufflers or split silencers are used extensively in heating, ventilation and air conditioning systems for increased attenuation of noise within a short or given length. Acoustic analysis of rectangular parallel baffle mufflers runs on the same lines as that of a rectangular duct lined on two sides. This simplification would not hold for circular configurations. Often, a cylindrical pod is inserted into a circular lined duct to increase its attenuation (or transmission loss), thereby making the flow passage annular and providing an additional absorptive layer on the inner side of this annular passage. This configuration, called a pod silencer, is analyzed here for the four-pole parameters as well as transmission loss, making use of the bulk reaction model.The effect of thin protective film or a highly perforated metallic plate is duly incorporated by means of a grazing-flow impedance. Use of appropriate boundary conditions leads to a set of linear homogeneous equations which in turn lead to a transcendental frequency equation in the unknown complex axial wave number. This is solved by means of the Newton-Raphson method, and the axial wave number is then used in the expressions for transmission loss as well as the transfer matrix parameters. Finally, results of a parametric study are reported to help the designer in optimization of a pod silencer configuration within a given overall size for minimal cost.     

A straightforward method for wall impedance eduction in a flow duct

The development of the advanced liner technology for aeroengine noise control necessitates the impedance measurement method under realistic flow conditions. Currently, the methods for this need are mainly based on the inverse impedance eduction principle, confronting with the problems of initial guess, high computation cost, and low convergence. In view of this, a new strategy is developed that straightforwardly educes the impedance from the sound pressure information measured on the duct wall opposing to the test acoustic liner embedded in a flow duct. Here, the key insight is that the modal nature of the duct acoustic field renders a summed-exponential representation of the measured sound pressure; thus, the characterizing axial wave number can be readily extracted by means of Prony's method, and further the unknown impedance is calculated from the eigenvalue and dispersion relations based on the classical mode-decomposition analysis. This straightforward method is simple in its basic principle but remarkably has the advantages of ultimately overcoming the drawbacks inherent to the inverse methods, incorporating the realistic multimode nonprogressive wave effects, high computational efficiency, possibly reducing the measurement points, and even avoiding the necessity of the duct exit impedance that bothers perhaps all the existing waveguide methods.