Stiffness control of low frequency acoustic transmission through the walls of rectangular ducts

An investigation is reported here on the use of “stiffness control” to reduce low frequency acoustic “breakout” through the walls of rectangular air-moving ducts; in this, attempts are made to increase the fundamental transverse resonance frequency of the duct walls (by using materials with a high stiffness/mass ratio) so that the capacitive (stiffness) controlled nature of the wall impedance below this frequency may be exploited to raise the wall transmission loss and remove low frequency resonances. Some degree of success is achieved in this, and the results appear encouraging. As a necessary part of the work, the nature of the acoustic/structural wave combinations is explored in more detail than hitherto, and a simplified low frequency approximate method of determining the transmission loss of ducts is also given.     

The effects of external lagging on low frequency sound transmission through the walls of rectangular ducts

Previous work by the author [1], on the transmission of internally propagated acoustic noise through the walls of rectangular ducts, is extended here in an investigation of the effects of external “lagging” (consisting of a layer of porous sound-absorbing material, and an impervious external covering) on the duct walls; this type of treatment is commonly applied as a noise control measure. A simple theoretical model, based, as before, on a coupled acoustic/structural wave system, is devised and shown to give reasonably accurate predictions in comparison with measurements of the wall transmission loss (though not in the case of lagging in which an external covering of very non-uniform thickness is incorporated). The conclusion is reached that external lagging used as an acoustic treatment is not, in general, particularly satisfactory.     

Low frequency acoustic transmission through the walls of rectangular ducts

A simple theory is described for the transmission of low frequency sound through the walls of rectangular ducts, particularly those in air conditioning systems. The model is based on a coupled acoustic/structural wave system, and it is assumed that the duct radiates in the same way as a finite-length line source incorporating a single travelling wave. Measurements of wall transmission loss on two types of duct system are compared to theoretical predictions, and good agreement is obtained within the frequency range of validity of the theory. It is concluded that the present approach should give reliable estimates of noise transmission in practical situations.     

Sound transmission at low frequencies through the walls of distorted circular ducts

A theoretical treatment of sound transmission through the walls of distorted circular ducts is given, for plane mode transmission within the duct. The transmission mechanism is essentially that of “mode coupling”, whereby higher structural modes in the duct walls are excited, because of the wall distortion, by the internal sound field. The theory is in two parts: an approximate analytical model for the structural response of the walls to the internal sound field, and a structural radiation model. Computed results, based on the theory, are compared to measurements on “long-seam” air conditioning ducts. Where the duct geometry can be reliably specified, reasonably good agreement is obtained between theoretical and experimental data. It is concluded that mode coupling effects serve to account for the discrepancies between ideal and observed behaviour in sound transmission through duct walls.     

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.     

The three-measurement two-calibration method for measuring the transfer matrix

Extensive use of transfer matrices (TMs) is made in determining the acoustic properties of a duct and in in-duct acoustic propagation models in the automotive industry and for musical acoustics purposes. The experimental apparatuses of classical TM measurement methods feature two measurement heads. Two microphones are flush with the walls of each head. The pressure signals are processed following the transfer function method constructed on an analytical model of acoustic propagation in measurement heads. The present paper aims at presenting a measurement method based on a three-microphone experimental apparatus and on its acoustic calibration through two reference measurements: the three-measurement two-calibration method for measuring the TM (3M2C-TM). Two microphones are flush with the measurement head walls and one is in the cap closing one side of the measured duct. 3M2C-TM proved essential for an accurate measurement of the four TM elements of two different ducts: a cylindrical duct and an expansion chamber.     

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.     

Approximate asymptotic solutions for acoustic transmission through the walls of rectangular ducts

Approximate expressions—valid at sufficiently high frequencies—are obtained for the acoustic transmission loss of the walls of rectangular ducts. Single mode propagation inside the duct, both in the fundamental mode and in higher order modes, is considered and a multimode model is also proposed. These theories lead to very simple formulae for the transmission loss, which prove to be in tolerably good agreement with measurements.     

High amplitude acoustic transmission through duct terminations: Theory

Recent experimental measurements have demonstrated that net acoustic energy dissipation can occur when sound waves interact with free shear layers, which are produced either by boundary layer separation in mean fluid flow at sharp edges, or by separation of the boundary layer in the acoustic flow at an edge in the absence of mean flow. This paper presents theoretical results which are offered in an attempt to explain these observations quantitatively. Comparison is made between the predicted and measured net energy loss which occurs upon transmission of high amplitude impulsive acoustic waves through various duct terminations, and also between calculated and measured reflection coefficients in the duct. The agreement is generally at least qualitatively good, and would appear to justify the physical assumptions on which the theoretical arguments are based.     

Time-domain characterization of the acoustic damping of a perforated liner with bias flow

Combustion instabilities are caused by the interaction of unsteady heat releases and acoustic waves. To mitigate combustion instabilities, perforated liners, typically subjected to a low Mach number bias flow (a cooling flow through perforated holes), are fitted along the bounding walls of a combustor. They dissipate the acoustic waves by generating vorticity at the rims of perforated apertures. To investigate the absorption of plane waves by a perforated liner with bias flow, a time-domain numerical model of a cylindrical lined duct is developed. The liners' damping mechanism is characterized by using a time-domain "compliance." The development of such time-domain compliance is based on simplified or unsimplified Rayleigh conductivity. Numerical simulations of two different configurations of lined duct systems are performed by combining a 1D acoustic wave model with the compliance model. Comparison is then made between the results from the present models, and those from the experiment and the frequency-domain model of previous investigation [Eldredge and Dowling, J. Fluid Mech. 485, 307-335(2003)]. Good agreement is observed. This confirms that the present model can be used to simulate the propagation and dissipation of acoustic plane waves in a lined duct in real-time.     

Acoustic transmission in non-uniform ducts with mean flow,part II: The finite element method

This second paper in a two part series describes the implementation of the finite element method for the solution of the problem of acoustic transmission through a non-uniform duct carrying a high speed subsonic compressible flow. A finite element scheme based on both the Galerkin method and the residual least squares method and with eight noded isoparametric elements is described. Multi-modal propagation is investigated by coupling of the solution in the duct non-uniform section to modal expansions in uniform sections. The accuracy of the finite element results for both the eigenvalue and transmission problems is assessed by comparison with exact solutions and with results from the method of weighted residuals in the form of a modified Galerkin method as introduced in Part I of this pair of papers. The results of calculations show that modal interactions, particularly in transmitted modes, become increasingly important with increasing duct flow Mach number. Power transmission coefficient calculations for the geometries studied reveal no indication of a linear basis for the phenomenon of subsonic acoustic choking.     

Structural acoustic silencers--design and experiment

The effectiveness of introducing flexible structural layers into air conveying ducts for controlling noise is investigated through theoretical and experimental means, focusing at low frequencies where conventional passive silencing technology is least effective. Previous theoretical work has shown that using flexible rather than rigid walls has the potential to achieve high transmission losses. The physical mechanisms responsible for structural acoustic silencing, including the relation between transmission loss peaks and structural resonance corresponding to different transverse structural modes, are presented. Sensitivity of the performance to acoustic and structural boundary conditions is discussed. To eliminate radiated noise from these walls (breakout noise), a rigid walled cavity is introduced under the flexible plate. The challenge is to find means to reject plane waves in the two-duct system. Designs that overcome these issues and achieve appreciable transmission loss are investigated. Results based on three-dimensional finite element simulations are compared with experimental results.     

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.     

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.     

Side-branch resonators modelling with Green׳s function methods

This paper deals with strategies for computing efficiently the propagation of sound waves in ducts containing passive components. In many cases of practical interest, these components are acoustic cavities which are connected to the duct. Though standard Finite Element software could be used for the numerical prediction of sound transmission through such a system, the method is known to be extremely demanding, both in terms of data preparation and computation, especially in the mid-frequency range. To alleviate this, a numerical technique that exploits the benefit of the FEM and the BEM approach has been devised. First, a set of eigenmodes is computed in the cavity to produce a numerical impedance matrix connecting the pressure and the acoustic velocity on the duct wall interface. Then an integral representation for the acoustic pressure in the main duct is used. By choosing an appropriate Green?s function for the duct, the integration procedure is limited to the duct–cavity interface only. This allows an accurate computation of the scattering matrix of such an acoustic system with a numerical complexity that grows very mildly with the frequency. Typical applications involving Helmholtz and Herschel–Quincke resonators are presented.     

Effect of Mean Flow on Acoustic Wave Propagation in a Duct with a Periodic Array of Helmholtz Resonators

Sound propagation properties of a duct system with Helmholtz resonators(HRs) are affected by mean flow.Previous studies have tended to focus on the effects of mean flows on acoustic response of a duct system with a finite number of HRs. Employing an empirical impedance model, we present a modified transfer matrix method for studying the effect of mean flow on the complex band structure of an air duct system with an infinite periodic array of HRs. The efficiency of the modified transfer matrix is demonstrated by comparison between an example of transmission response calculation for a finite single HR loaded duct and the finite element simulation result calculated using the COMSOL software. Numerical results are presented to analyze the effect of mean flow on the band structure and transmission loss of the sound wave in the duct system. It is hoped that this study will provide theoretical guidance for acoustic wave propagation of HR silencer in the presence of mean flow.     

Broadband noise reduction by circular multi-cavity mufflers operating in multimodal propagation conditions

In this study, sound propagation through a circular duct with non-locally lining is investigated both numerically and experimentally. The liner concept is based on perforated screens backed by air cavities. Dimensions of the cavity are chosen to be of the order or bigger than the wavelength so acoustic waves within the liner can propagate parallel to the duct surface. This gives rise to complex scattering mechanisms among duct modes which renders the muffler more effective over a broader frequency range. This work emanates from the Cleansky European HEXENOR project which aim is to identify the best multi-cavity muffler configuration for reduction of exhaust noise from helicopter turboshaft engines. Here, design parameters are the cavity dimensions in both longitudinal and azimuthal directions. The best cavity configuration must in addition fit weight specifications which implies that the number of walls separating each cavity should be chosen as small as possible. To achieve these objectives, the scattering matrix of the lined duct section is obtained experimentally for two specific muffler configurations operating in multimodal propagation conditions. The good agreement with numerical predictions serves to validate the perforate plate impedance model used in our calculation. Finally, given an incident acoustic pressure which is representative of typical combustion noise spectrum, the best cavity configuration achieving the maximum overall acoustic Transmission Loss is selected numerically. The study also illustrates how the acoustic performances are dependent on the nature of the incident field.     

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。     

Identification of aero-acoustic scattering matrices from large eddy simulation. Application to a sudden area expansion of a duct

A methodology is presented which allows to determine the coefficients of transmission and reflection of plane acoustic waves at flow discontinuities in piping systems by combining large eddy simulation (LES) of turbulent compressible flows with system identification. The method works as follows. At first, an LES with external, broadband excitation of acoustic waves is carried out. Time series of acoustic data are extracted from the computed flow field and analyzed with system identification techniques in order to determine the acoustic scattering coefficients for a range of frequencies. The combination of broadband excitation with highly parallelized LES makes the overall approach quite efficient, despite the difficulties associated with simulation of low-Mach number compressible flows. The method is very general, here it is applied to study the scattering behavior of acoustic waves at a sudden change in cross-section in a duct system. The complex aero-acoustic interactions between acoustic waves and free shear layers are captured in detail by high resolution compressible LES, such that the scattering coefficients can be determined accurately from first principles. In order to demonstrate the reliability and accuracy of the method, the results for the scattering behavior and the acoustic impedance are presented and physically interpreted in combination with several analytical models and experimental data.     

压电声透通信的研究进展*

由于电磁屏蔽效应,传统的无线通信技术受限于金属障碍物的遮挡而无法应用。压电声透通信能够克服电磁无线通信方式的这一缺陷,在不破坏金属障碍物物理结构的前提下,通过声波穿透障碍物实现通信。本文在介绍金属隔物通信的基本原理和实现方式的基础上,总结阐述了压电声透通信目前国内外的研究进展,包括传输系统模型的建立、参数的设计、系统的搭建以及该技术中独特的能量传输方式,最后对影响压电声透通信系统性能的因素进行了分析。