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。     

A critical survey of basic theories used in muffler design and analysis

The acoustic equations are derived for the general case of sound wave propagation in circular ducts. The exact and approximate methods for solution are reviewed, analyzed and compared for the purpose of ICE muffler design. Different types of mufflers are also presented; their attenuation properties are estimated according to different theoretical approaches.     

The nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores

Based on an equivalent medium approach, this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation, sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of micropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore, multiple scattering has been taken into account, which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%.     

声波在含气泡液体中的线性传播

为了探讨含气泡液体对声波传播的影响, 研究了声波在含气泡液体中的线性传播. 在建立含气泡液体的声学模型时引入气泡含量的影响,建立气泡模型时引用 Keller的气泡振动模型并同时考虑气泡间的声相互作用,得到了经过修正的气泡振动方程. 通过对含气泡液体的声传播方程和气泡振动方程联立并线性化求解,在满足 (ω R₀)/c << 1 的前提下,得到了描述含气泡液体对声波传播的衰减系数和传播速度. 通过数值分析发现,在驱动声场频率一定的情况下,气泡含量的增加及气泡的变小均会导致衰减系数增加和声速减小;气泡的体积分数和大小一定时, 驱动声场频率在远小于气泡谐振频率的情况下,声速会随驱动频率的增加而减小; 气泡间的声相互作用对声波传播速度及含气泡液体衰减系数的影响不明显.最终认为气泡的大小、 数量和驱动声场频率是影响声波在含气泡液体中线性传播的主要因素. 关键词： 含气泡液体 线性声波 声衰减系数 声速     

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.     

Scattering of sound in a moving viscous microinhomogeneous medium at large Reynolds numbers

A generalization of the Rayleigh law of a low-frequency sound attenuation in a microinhomogeneous medium to the case of scattering particles moving in a viscous liquid at a large Reynolds numbers is proposed. It is shown that, under these conditions, the attenuation may be independent of the scattering by the moving particles themselves but be only determined by the flow caused by these particles, the maximum attenuation being observed in the direction across the particle motion. The corresponding corrections proportional to the first power of the hydrodynamic Mach number are compared with the corrections lying at the basis of the modified Rayleigh law, which was proposed earlier for the potential flow of an ideal liquid around inhomogeneities, and also with the laws of scattering in a moving viscous microinhomogeneous medium at a small Reynolds numbers. As an example of the operation of the generalized law, characteristics of the sound scattering by rain are refined.     

含少量气泡流体饱和孔隙介质中的弹性波

考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.     

Properties of sound attenuation around a two-dimensional underwater vehicle with a large cavitation number

Due to the high speed of underwater vehicles,cavitation is generated inevitably along with the sound attenuation when the sound signal traverses through the cavity region around the underwater vehicle.The linear wave propagation is studied to obtain the influence of bubbly liquid on the acoustic wave propagation in the cavity region.The sound attenuation coefficient and the sound speed formula of the bubbly liquid are presented.Based on the sound attenuation coefficients with various vapor volume fractions,the attenuation of sound intensity is calculated under large cavitation number conditions.The result shows that the sound intensity attenuation is fairly small in a certain condition.Consequently,the intensity attenuation can be neglected in engineering.     

One-dimensional numerical simulations of random sound impulses

Abstract

We perform one-dimensional numerical simulations of small-amplitude acoustic pulses in space- and time-dependent random mass density and time-dependent velocity fields. Numerical results reveal that: (a) random fields affect the speeds, amplitudes and, consequently, shapes of sound pulses; (b) for weak random fields and short propagation times the numerical data converge with the analytical results of the mean field theory which says that a space-dependent (time-dependent) random field leads to wave attenuation (amplification) and all random fields speed up sound pulses; (c) for sufficiently strong random fields and long propagation times numerical simulations reveal pulse splitting into smaller components, parts of which propagate much slower than a wave pulse in a non-random medium. These slow waves build an initial stage of a wave localization phenomenon. However, this effect can be very weak in a real three-dimensional medium.     

Exact solutions to one-dimensional acoustic fields with temperature gradient and mean flow

An exact solution for one-dimensional acoustic fields in ducts in the presence of an axial mean temperature gradient and mean flow is presented in this paper. The analysis is valid for mean Mach numbers such that the square of the mean Mach number is much less than one. The one-dimensional wave equation for ducts with axial mean temperature gradient and mean flow is derived. By appropriate transformations, the wave equation is reduced to an analytically solvable hypergeometric differential equation for the case of a linear mean temperature profile. The developed solution is applied to investigate the dependence of sound propagation in a duct on factors such as temperature gradient and mean flow. The results obtained using the analytical solution compare very well with the numerical results. The developed solution is also compared with an existing analytical solution.     

Attenuation of sound in multi-element acoustically lined rectangular ducts in the absence of mean flow

Extensions of the ordinary Wiener-Hopf technique are outlined and applied to the solution of sound attenuation in multi-element ducts with acoustically absorbing liners in series as well as in parallel combination. For demonstration purposes the simplest case of engineering interest is chosen: namely, a rectangular channel at zero convection velocity. Extensions to circular and annular geometries as well as to mean flow situations are possible. In the absence of a realistic source model acoustic power attenuation results are presented for an incoming fundamental mode only, to show the influence of major design parameters for point reacting liners. The broad band-width attenuation capacity of some liner configurations as well as the necessity to include wave reflections at liner discontinuities for multi-element liners is clearly demonstrated. For a given acoustic source a multi-mode solution can be found by summing the contributions of each incoming unattenuated mode.     

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.     

强声波作用下煤颗粒周围气体的振荡流动特性

根据二维非稳态层流的质量和动量守恒方程,研究强声波作用下煤颗粒周围气体的振荡流动特性.入射波的振幅远大于颗粒特征长度,声雷诺数小于20.根据通用微分方程的解,详细分析不同声雷诺数与斯特劳哈尔数下,颗粒壁面的流场分布、轴向压力梯度、切向应力及分离角的分布,发现在低频（~50 Hz）时,颗粒壁面轴向压力梯度、切向应力及流动分离角的分布主要受曲率效应影响,其变化规律与振荡速度的幅值变化相对应;在高频时（~5 000 Hz）,颗粒壁面轴向压力梯度、切向应力及流动分离角的分布同时受到曲率效应和流动加速度的影响.为进一步研究强声波强化煤颗粒燃烧提供理论基础.     

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.     

Noise generation by instabilities in low Reynolds number supersonic jets

An experimental investigation of noise generation by instabilities in low Reynolds number supersonic air jets has been performed. Sound pressure levels, spectra and acoustic phase fronts were measured with a traversing condenser microphone in the acoustic field of axisymmetric, perfectly expanded, cold jets of Mach numbers 1·4, 2·1 and 2·5. Low Reynolds numbers in the range from Re = 3700 to Re = 8700 were obtained by exhausting the jets into an anechoic vacuum chamber test facility. This contrasts with Reynolds numbers of over 10⁶ for similar jets exhausting into atmospheric pressure. The flow fluctuations of the instability in all three jets have been measured with a hot-wire and the results are documented in a previous paper by Morrison and McLaughlin. Acoustic measurements show that the major portion of the sound radiated by all three jets is produced by the instability's rapid growth and decay that occurs near the end of the potential core. This takes place over a relatively short distance (less than two wavelengths of the instability) in the jet. In the lower two Mach number jets the instability has a phase velocity less than the ambient acoustic velocity. In the Mach number 2·5 jet the instability phase speed is 1·11 times the ambient acoustic velocity. In this case the acoustic phase fronts indicate the possibility of a Mach wave component. It was also determined that low level excitation at the dominant frequency of the instability actually decreased the radiated noise by suppressing the broad band component.     

Reflection of sound at area expansions in a flow duct

An analytical model for scattering at area discontinuities and sharp edges in flow ducts and pipes is presented. The application we have in mind is large industrial duct systems, where sound attenuation by reactive and absorptive baffle silencers is of great importance. Such devices commonly have a rectangular cross-section, so the model is chosen as two-dimensional. Earlier solutions to this problem are reviewed in the paper. The modelling of the flow conditions downstream of the area expansion, with and without extended edges, and its implications for the resulting acoustic modes are discussed. Here, the scattering problem is solved with the Wiener-Hopf technique, and a Kutta condition is applied at the edge. The solution of the wave equation downstream of the expansion includes hydrodynamic waves, of which one is a growing wave. Theoretical results are compared with experimental data for the reflection coefficient for the plane wave, at frequencies below the cut-on for higher order modes. Influence of the interaction between the sound field and the flow field is discussed. A region where the reflection coefficient is strongly Strouhal number dependent is found.     

Influence of viscosity on aerodynamic sound emission in free space

The theory of aerodynamic sound is reformulated with account taken of the influence of viscosity in the source flow on the sound emission in free space. This is based on the Ffowcs Williams form of the Lighthill equation. The source flow is assumed to be determined by a localized vorticity field and characterized by low Mach numbers and high Reynolds numbers. It is found that the acoustic pressure emitted by the viscous vortex motion is composed of a quadrupole and two kinds of monopole. The Reynolds stress in the source flow is decomposed into isotropic and non-isotropic parts. The non-isotropic part leads to the quadrupole wave derived by Möhring, while the isotropic part is related to one of the monopole-like waves radiated when the total kinetic energy changes. The other monopole wave is associated with entropy production by viscous dissipation of the kinetic energy. All three components are influenced by viscosity.     

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.     

Propagation of acoustic wave in viscoelastic medium permeated with air bubbles

Based on the modification of the radial pulsation equation of an individual bubble, an effective medium method (EMM) is presented for studying propagation of linear and nonlinear longitudinal acoustic waves in viscoelastic medium permeated with air bubbles. A classical theory developed previously by Gaunaurd (Gaunaurd GC and \"{U}berall H, {\em J. Acoust. Soc. Am}., 1978; 63: 1699--1711) is employed to verify the EMM under linear approximation by comparing the dynamic (i.e. frequency-dependent) effective parameters, and an excellent agreement is obtained. The propagation of longitudinal waves is hereby studied in detail. The results illustrate that the nonlinear pulsation of bubbles serves as the source of second harmonic wave and the sound energy has the tendency to be transferred to second harmonic wave. Therefore the sound attenuation and acoustic nonlinearity of the viscoelastic matrix are remarkably enhanced due to the system's resonance induced by the existence of bubbles.     

Characterization of acoustic disturbances in linearly sheared flows

The equation describing the plane wave propagation, the stability, or the rectangular duct mode characteristics in a compressible inviscid linearly sheared parallel, but otherwise homogeneous, flow, is shown to be reducible to Whittaker's equation. The resulting solutions, which are real, viewed as functions of two variables, depend on a parameter and an argument the values of which have precise physical meanings depending on the problem. The exact solutions in terms of Whittaker functions are used to obtain a number of known results of plane wave propagation and stability in linearly sheared flows as limiting cases in which the speed of sound goes to infinity (incompressible limit) or the shear layer thickness, or wave number, goes to zero (vortex sheet limit). The usefulness of the exact solutions is then discussed in connection with the problems of plane wave propagation and stability of a finite thickness shear layer with a linear velocity profile. With respect to the plane wave propagation it is shown that, unlike the compressible vortex sheet, the shear layer possesses no resonances and no Brewster angles, whereas with respect to the stability problem it is shown that, again unlike the compressible vortex sheet, the thin layer is unstable to long wavelength disturbances for all Mach numbers. These results imply that the reflection and stability characteristics of a non-zero thickness but thin shear layer (i.e., the long wavelength characteristics) do not go over smoothly into the results of the compressible vortex sheet as the wave number approaches zero, except for a limited range of generally subsonic relative flow of the two parallel streams bounding the shear layer.