Bulk reaction modeling of ducts with and without mean flow

A general formulation for analysis of sound field in a uniform flow duct lined with bulk-reacting sound-absorbing material is presented here. Presented theoretical model predicts the rate of attenuation for symmetric as well as asymmetric modes in rectangular duct lined with loosely bound (bulk-reacting) sound-absorbing material, which allows acoustic propagation through the lining. The nature of attenuation in rectangular ducts lined on two and four sides with and without mean flow is discussed. Computed results are compared with published theoretical and experimental results. The presented model can be used as guidelines for the acoustic design of silencers, air-conditioning ducts, industrial fans, and other similar applications.     

On the effect of viscosity and thermal conductivity on sound propagation in ducts: A re-visit to the classical theory with extensions for higher order modes and presence of mean flow

The dispersion equation for the axisymmetric modes of viscothermal acoustic wave propagation in uniform hard-walled circular ducts containing a quiescent perfect gas is classical. This has been extended to cover the non-axisymmetric modes and real fluids in contemporary studies. The fundamental axisymmetric mode has been the subject of a large number of studies proposing approximate solutions and the characteristics of the propagation constants for narrow and wide ducts with or without mean flow is well understood. In contrast, there are only few publications on the higher order modes and the current knowledge about their propagation characteristics is rather poor. On the other hand, there is a void of papers in the literature on the effect of the mean flow on the quiescent modes of propagation. The present paper aims to contribute to the filling of these gaps to some extent. The classical theory is re-considered with a view to cover all modes of acoustic propagation in circular ducts carrying a real fluid moving axially with a uniform subsonic velocity. The analysis reveals a new branch of propagation constants for the axisymmetric modes, which appears to have escaped attention hitherto. The solution of the governing wave equation is expressed in a modal transfer matrix form in frequency domain and numerical results are presented to show the effects over wide ranges of frequency, viscosity and mean flow parameters on the propagation constants. The theoretical formulation allows for the duct walls to have finite impedance, but no numerical results are presented for lined ducts or ducts carrying a sheared mean flow.     

A displacement-pressure finite element formulation for analyzing the sound transmission in ducted shear flows with finite poroelastic lining

In the present work, the propagation of sound in a lined duct containing sheared mean flow is studied. Walls of the duct are acoustically treated with absorbent poroelastic foams. The propagation of elasto-acoustic waves in the liner is described by Biot's model. In the fluid domain, the propagation of sound in a sheared mean flow is governed by the Galbrun's equation. The problem is solved using a mixed displacement-pressure finite element formulation in both domains. A 3D implementation of the model has been performed and is illustrated on axisymmetric examples. Convergence and accuracy of the numerical model are shown for the particular case of the modal propagation in a infinite duct containing a uniform flow. Practical examples concerning the sound attenuation through dissipative silencers are discussed. In particular, effects of the refraction effects in the shear layer as well as the mounting conditions of the foam on the transmission loss are shown. The presence of a perforate screen at the air-porous interface is also considered and included in the model.     

Sound wave propagation in ducts whose walls are lined with a porous layer backed by cellular cavities

This paper concerns propagation and attenuation of sound waves through acoustically lined ducts. For a cylindrical duct whose liner consists of a point-reacting porous material layer backed by cellular cavities, the admittance formula derived by taking into account a wave motion within the liner is applied to an analysis of waves propagating downstream. For the point-reacting liner of fixed porous material properties, influences of the porous layer thickness, cellular cavity depth, mean flow profile, and three dimensionality of the duct (i.e., cylindrical or plane) on the attenuation are examined. The results show a significant role of the porous layer thickness. For the cylindrical duct, attenuation spectra evaluated from this analysis are compared with those given by the widely used semi-empirical formula.     

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.     

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.     

发动机圆形管道内噪声衰减谱模态分析

本文应用模态分析方法建立了剪切流存在条件下,发动机多段声衬圆形管道声传播工程计算模型,对管内各模态频谱和总噪声衰减频谱进行了算例计算,并与有关文献试验数据进行了对比。结果表明,多段声衬圆形管道中声传播工程计算方法是可行的,从而为发动机前短舱管内声传播研究提供了一种模态分析工程预测方法。     

On the prediction of “buzz-saw” noise in acoustically lined aero-engine inlet ducts

Aero-engines operating with supersonic fan tip speeds generate an acoustic signature containing energy spread over a range of harmonics of the engine shaft rotation frequency. These harmonics are commonly known as the “buzz-saw” tones. The pressure signature attached to a supersonic ducted fan will be a sawtooth waveform. The non-linear propagation of a high-amplitude irregular sawtooth upstream inside the inlet duct redistributes the energy amongst the buzz-saw tones. In most modern aero-engines the inlet duct contains an acoustic lining, whose properties will be dependent on the mode number and frequency of the sound, and the speed of the oncoming flow. Such effects may not easily be incorporated into a time-domain approach; hence the non-linear propagation of an irregular sawtooth is calculated in the frequency domain, which enables liner damping to be included in the numerical model. Results are presented comparing noise predictions in hard-walled and acoustically lined inlet ducts. These show the effect of an acoustic liner on the buzz-saw tones. These predictions compare favourably with previous experimental measurements of liner insertion loss (at blade passing frequency), and provide a plausible explanation for the observed reduction in this insertion loss at high fan operating speeds.     

Non-linear attenuation of sound in circular lined ducts

The attenuation of high intensity sound in circular ducts lined with fibrous material has been investigated. With no mean flow, the sound pressure levels are varied to illustrate the linear and non-linear absorption characteristics of the liner. Effects of liner thickness, perforation ratio of the duct wall and the $\text{d}\text{t}$ ratio are analysed.Optimum combinations of the perforation geometry and liner thickness are found to be of stable attenuation characteristics over a wide frequency range and at high sound levels.     

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.     

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.     

Analysis of liner performance using the NASA Langley Research Center Curved Duct Test Rig

The NASA Langley Research Center Curved Duct Test Rig (CDTR) is designed to test aircraft engine nacelle liner samples in an environment approximating that of the engine on a scale that approaches the full scale dimensions of the aft bypass duct. The modal content of the sound in the duct can be determined and the modal content of the sound incident on the liner test section can be controlled. The effect of flow speed, up to Mach 0.5 in the test section, can be investigated. The results reported in this paper come from a study to evaluate the effect of duct configuration on the acoustic performance of single degree of freedom (SDOF) perforate-over-honeycomb liners. Variations of duct configuration include: asymmetric (liner on one side and hard wall opposite) and symmetric (liner on both sides) wall treatment; inlet and exhaust orientation, in which the sound propagates either against or with the flow; and straight and curved (outlet is offset from the inlet by one duct width) flow path. The effect that duct configuration has on the overall acoustic performance is quantified. The redistribution of incident mode content is shown, in particular the mode scatter effect that liner symmetry has on symmetric and asymmetric incident mode shapes. The Curved Duct Test Rig is shown to be a valuable tool for the evaluation of acoustic liner concepts.     

A modal separation measurement technique for broadband noise propagating inside circular ducts

A measurement technique which separates broadband noise propagating inside circular ducts into the acoustic duct modes is developed. The technique is also applicable to discrete frequency noise. The acoustic modes are produced by weighted combinations of the instantaneous outputs of microphones spaced around the duct circumference. The technique is compared with the cross spectral density approach presently available and found to have certain advantages, and disadvantages. Considerable simplification of both the new technique and the cross spectral density approach occurs when no correlation exists between different circumferential mode orders. The properties leading to uncorrelated modes and experimental tests which verify this condition are discussed. The modal measurement technique-is applied to the case of broadband noise generated by flow through a coaxial obstruction (nozzle or orifice) in a pipe. Different circumferential mode orders are shown to be uncorrelated for this type of noise source.     

Effects of wall admittance changes on duct transmission and radiation of sound

This paper is concerned with the effect of changes in duct wall acoustic properties on the transmission of sound through ducts. Two special problems are considered. The first problem is that of a rectangular infinite-length duct with airflow and a single change in duct wall acoustic admittance. The second problem is that of an axisymmetric field in a finite circular duct without airflow and with an arbitrary number of duct wall acoustic admittance changes. Results for the first problem show the effect of wall admittance change and flow on the acoustic power transmission within the duct. Results for the second problem show the interactive effects of multiple duct liner sections on power radiated from a finite duct.     

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.     

Calculations of modes in circumferentially nonuniform lined ducts

This paper proposes a computationally efficient method of determining eigenfunctions and eigenvalues of acoustic modes propagating in circular lined ducts with zero or uniform flow. Linings with circumferentially nonuniform impedance, as found in nacelle acoustics, are the focus. The method of solution adapts in two important respects--the presence of flow and the imposition of impedance boundary conditions--the series expansion method first proposed by Pagneux et al. [J. Acoust. Soc. Am. 110, 1307-1314 (2001)] to calculate the eigenvalues of Lamb modes. The inclusion of flow, and a corresponding different method of solution leading to an improved convergence of eigenvalues (O(N(-5)), N is the truncation of radial basis of expansion), is the important new feature as compared to the previous adaptation by Bi et al. [J. Acoust. Soc. Am. 122, 280-291 (2007)]. As a result, it becomes possible to safely determine and in a simple manner the eigenvalues and eigenfunctions of circumferentially nonuniform lined ducts in the presence of uniform flow, up to relatively high frequencies (e.g., 30相似文献   

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.     

Acoustic energy in ducts: Further observations

The transmission of acoustic energy in uniform ducts carrying uniform flow is investigated with the purpose of clarifying two points of interest. The two commonly used definitions of acoustic “nergy” flux are shown to be related by a Legendre transformation of the Lagrangian density exactly as in deriving the Hamiltonian density in mechanics. In the acoustic case the total energy density and the Hamiltonian density are not the same which accounts for two different “energy” fluxes. When the duct has acoustically absorptive walls neither of the two flux expressions gives correct results. A re-evaluation of the basis of derivation of the energy density and energy flux provides forms which yield consistent results for soft walled ducts.