On an Integrated Transfer Matrix method for multiply connected mufflers

The commercial automotive mufflers are generally of a complicated shape with multiply connected parts and complex acoustic elements. The analysis of such complex mufflers has always been a great challenge. In this paper, an Integrated Transfer Matrix method has been developed to analyze complex mufflers. Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The paper presents a generalized one-dimensional (1-D) approach, using the transfer matrices of simple acoustic elements, which are available from the literature. The present approach is robust and flexible owing to its capability to construct an overall matrix of the muffler with the transfer matrices of individual acoustic elements and boundary conditions, which can then be used to evaluate the transmission loss, insertion loss, etc. Results from the present approach have been validated through comparisons with the available experimental and three-dimensional finite element method (FEM) based results. The results show good agreement with both measurements and FEM analysis up to the cut-off frequency.     

An inherently stable boundary-condition-transfer algorithm for muffler analysis

Wave coupling exists in the wave propagation in multiple interacting ducts within a waveguide. One may use the segmentation approach, decoupling approach, eigenvalue approach, or the matrizant approach to derive the overall transfer matrix for the muffler section with interacting ducts, and then apply the terminal boundary conditions to obtain a two-by-two transfer matrix. In such instances, a boundary condition applied to a vector is given as a linear combination of its components. Spatial dimensions along with parameters like impedance of the perforated interface may yield numerical instability during computation leading to inaccurate prediction of the acoustic performance of mufflers. Here, an inherently stable boundary-condition-transfer approach is discussed to analyze the plane wave propagation in suchlike mufflers and applied to waveguides of variable cross-sectional area. The concept of pseudo boundary conditions applied to the state vector at an intermediate point is outlined. The method is checked for self-consistency and shown to be stable even for extreme geometries.     

Sound attenuation of a periodic array of micro-perforated tube mufflers

The wave propagation in a periodic array of micro-perforated tube mufflers is investigated theoretically, numerically and experimentally. Because of the high acoustic resistance and low mass reactance due to the sub-millimeter perforation, the micro-perforated muffler can provide considerable sound attenuation of duct noise. Multiple mufflers are often used to enhance attenuation performance. When mufflers are distributed periodically in a duct, the periodic structure produces special dispersion characteristics in the overall sound transmission loss. The Bloch wave theory and the transfer matrix method are used to study the wave propagation in periodic micro-perforated tube mufflers and the dispersion characteristics of periodic micro-perforated mufflers are examined. The results predicted by the theory are compared with finite element method simulation and experimental results. The results indicate that the periodic structure can influence the performance of micro-perforated mufflers. With different periodic distances, the combination of the periodic structure and the micro-perforated tube muffler can contribute to the control of lower frequency noise with a broader frequency range or improvement of the peak transmission loss around the resonant frequency.     

充液管路噪声辐射控制研究

设计了三种水管路消声器，建立了一套水管路模拟实验系统，对所设计的消声器消减管口辐射躁声的性能进行了实验测试。     

阻抗复合消声器声学性能有限元预测方法及分析

为计算和分析具有复杂结构的阻抗复合式消声器的宽频消声性能,建立了一种高效声学有限元方法,给出了不同边界条件下的边界积分处理细节,得到有限元全局系数矩阵表达式,设计出计算程序框架以实现这些算法,其求解规模和计算速度与商业软件相比有优势。为计算阻抗复合式消声器的传递损失,通过阻抗管测量和数据拟合得到了吸声材料声学特性的经验公式。计算和测量了两通穿孔阻抗复合式消声器的传递损失,二者良好的吻合验证了声学有限元方法和计算程序的正确性。研究表明,插管长度影响消声器在中高频段的消声特性,右侧隔板上穿孔会消除共振峰,中高频消声性能随着出口管穿孔率的增加而提升。      

Transverse plane wave analysis of short elliptical chamber mufflers: An analytical approach

Short elliptical chamber mufflers are used often in the modern day automotive exhaust systems. The acoustic analysis of such short chamber mufflers is facilitated by considering a transverse plane wave propagation model along the major axis up to the low frequency limit. The one dimensional differential equation governing the transverse plane wave propagation in such short chambers is solved using the segmentation approaches which are inherently numerical schemes, wherein the transfer matrix relating the upstream state variables to the downstream variables is obtained. Analytical solution of the transverse plane wave model used to analyze such short chambers has not been reported in the literature so far. This present work is thus an attempt to fill up this lacuna, whereby Frobenius solution of the differential equation governing the transverse plane wave propagation is obtained. By taking a sufficient number of terms of the infinite series, an approximate analytical solution so obtained shows good convergence up to about 1300 Hz and also covers most of the range of muffler dimensions used in practice. The transmission loss (TL) performance of the muffler configurations computed by this analytical approach agrees excellently with that computed by the Matrizant approach used earlier by the authors, thereby offering a faster and more elegant alternate method to analyze short elliptical muffler configurations.     

A generalized scheme for analysis of multifarious commercially used mufflers

Commercial automotive mufflers are often too complex to be broken into a cascade of one-dimensional elements with predetermined transfer matrices. The one-dimensional (1-D) scheme presented in this paper is based on an algorithm that uses user-friendly visual volume elements along with the theory of transfer matrix based muffler analysis. This work attempts to exploit the speed of the one-dimensional analysis with the flexibility, generality and user-friendliness of three-dimensional analysis using geometric modeling. A code based on the developed algorithm has been employed to demonstrate the generality of the proposed method in analyzing commercial mufflers by considering three very diverse classes of mufflers with different kinds of combinations of reactive, perforated and absorptive elements. Though the examples used in the paper are not very complex for they are meant to be just representative cases of certain classes of mufflers, yet the algorithm can handle a large domain of commercial mufflers of high degree of complexity. Results from the present algorithm have been validated through comparisons with both the analytical (plane wave based) and the more general, three-dimensional FEM based results. The forte of the proposed method is its power to construct the system matrix consistent with the boundary conditions from the geometrical model to evaluate the four-pole parameters of the entire muffler and thence its transmission loss, etc. Thus, the algorithm can be used in conjunction with the transfer matrix based muffler programs to analyze the entire exhaust system of an automobile.     

通过流作用下穿孔板的声阻抗

穿孔元件在进排气消声器中广泛使用,气体流动对穿孔元件声阻抗具有较大的影响。为了获得更加精确的穿孔声阻抗模型,使用三维时域CFD方法计算通过流作用下穿孔的声阻抗。探究了通过流作用下穿孔声阻抗的获取方法,并且将无量纲小孔声阻抗的预测值与已发表的实验测量值进行了对比,两者吻合较好。分析了小孔中的通过流马赫数M_o (0.05~0.20)、穿孔的分布形式、小孔的直径d_h (2~5 mm),穿孔板的厚度t (0.8~2 mm)和穿孔率φ(4.51%~24.93%)对无量纲声阻抗的影响规律,并且通过不同参数的非线性回归分析得到了通过流作用下声阻抗的模型。作为工程计算的应用,利用Jing&Sun的声阻抗模型和本文声阻抗模型计算了横流式穿孔管消声器的传递损失,与实验测量结果比较表明,本文模型具有较高的准确性。      

Shape optimization of multi-chamber mufflers with plug-inlet tube on a venting process by genetic algorithms

Recently, research on new techniques of single-chamber plug-inlet mufflers has been amply addressed. However, research work on shape optimization of multi-chamber plug-inlet mufflers along with work on maximal back pressure has been sorely neglected. Therefore, a numerical case for eliminating broadband steam blow-off noise using multi-chamber plug-inlet mufflers in conjunction with a genetic algorithm (GA) as well as a numerical decoupling technique, all within a space-constrained pressure drop, is introduced in this paper. To verify the reliability of the GA optimization, optimal noise abatements for various pure tones on a one-chamber plug-inlet muffler are examined. Of course, the accuracy of the mathematical model must be supported by experimental data. Subsequently, optimal results then indicate that the maximal sound transmission losses are indeed located at the desired target tones. Consequently, both pressure drop and acoustical performance will increase when the diameters (at inlet tubes and perforated holes), the perforated ratio, and the length of perforated tubes are decreased.     

A finite element method for damped acoustic systems: An application to evaluate the performance of reactive mufflers

The approximate equations governing the forced harmonic motion of a damped acoustic system are set up by using a variational principle. Acoustic finite elements are then used in a computer program to study the transmission loss and insertion loss performance of some expansion chamber mufflers. The manner in which the equations are set up allows a number of input and output nodes, and two-dimensional effects involving the influence of transverse acoustic modes to be taken into account. Although only the simplest of elements and coarse mesh sizes are used the resulting accuracy of the solutions is extremely good; thus the method should be a viable one for studying the performance of more complicated mufflers, having variable cross-sections and internal energy dissipation.     

Investigations on mufflers for internal combustion engines

This paper deals with experimental studies on reactive types of muffler—and their combinations with absorption types—in order to determine their noise attenuation characteristics. Tests were carried out on a test rig, with a loudspeaker as the input source, as well as on a four cylinder diesel engine. The frequency spectra of attenuation levels, obtained experimentally, were compared with corresponding theoretical predictions. In addition, the effect on the performance of the engine itself was studied.The results showed, in general, a fairly good agreement between experimental results from test rig and theoretical predictions in the frequency range for which the latter is valid. The attenuation levels obtained from the mufflers fitted on the engine were, in general, lower. The effect on the performance of the engine was marginal. It was seen that the combination mufflers offer a good solution when high noise attenuation is desired.     

Shape optimization of multi-chamber cross-flow mufflers by SA optimization

It is essential when searching for an efficient acoustical mechanism to have an optimally shaped muffler designed specially for the constrained space found in today's plants. Because the research work of optimally shaped straight silencers in conjunction with multi-chamber cross-flow perforated ducts is rarely addressed, this paper will not only analyze the sound transmission loss (STL) of three kinds of cross-flow perforated mufflers but also will analyze the optimal design shape within a limited space.In this paper, the four-pole system matrix used in evaluating acoustic performance is derived by using the decoupled numerical method. Moreover, a simulated annealing (SA) algorithm, a robust scheme in searching for the global optimum by imitating the softening process of metal, has been adopted during shape optimization. To reassure SA's correctness, the STL's maximization of three kinds of muffles with respect to one-tone and dual-tone noise is exemplified. Furthermore, the optimization of mufflers with respect to an octave-band fan noise by the simulated algorithm has been introduced and fully discussed. Before the SA operation can be carried out, an accuracy check of the mathematical model with respect to cross-flow perforated mufflers has to be performed by Munjal's analytical data and experimental data.The optimal result in eliminating broadband noise reveals that the cross-flow perforated muffler with more chambers is far superior at noise reduction than a muffler with fewer chambers. Consequently, the approach used for the optimal design of noise elimination proposed in this study is certainly easy and efficient.     

Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

Transfer matrices are commonly considered in the numerical modelling of the acoustic behaviour associated with exhaust devices in the breathing system of internal combustion engines, such as catalytic converters, particulate filters, perforated mufflers and charge air coolers. In a multidimensional finite element approach, a transfer matrix provides a relationship between the acoustic fields of the nodes located at both sides of a particular region. This approach can be useful, for example, when one-dimensional propagation takes place within the region substituted by the transfer matrix. As shown in recent investigations, the sound attenuation of catalytic converters can be properly predicted if the monolith is replaced by a plane wave four-pole matrix. The finite element discretization is retained for the inlet/outlet and tapered ducts, where multidimensional acoustic fields can exist. In this case, only plane waves are present within the capillary ducts, and three-dimensional propagation is possible in the rest of the catalyst subcomponents. Also, in the acoustic modelling of perforated mufflers using the finite element method, the central passage can be replaced by a transfer matrix relating the pressure difference between both sides of the perforated surface with the acoustic velocity through the perforations. The approaches in the literature that accommodate transfer matrices and finite element models consider conforming meshes at connecting interfaces, therefore leading to a straightforward evaluation of the coupling integrals. With a view to gaining flexibility during the mesh generation process, it is worth developing a more general procedure. This has to be valid for the connection of acoustic subdomains by transfer matrices when the discretizations are nonconforming at the connecting interfaces. In this work, an integration algorithm similar to those considered in the mortar finite element method, is implemented for nonmatching grids in combination with acoustic transfer matrices. A number of numerical test problems related to some relevant exhaust devices are then presented to assess the accuracy and convergence performance of the proposed procedure.     

A note on various formulations for four-pole parameters of a pipe with mean flow

This note is concerned with an examination of various formulations for the determination of four-pole parameters of a uniform pipe containing a moving medium. The correct four-pole parameters are identified. Their limitations in applications to the acoustic simulation of exhaust mufflers and piping systems are discussed.     

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.     

Generalized analysis of a muffler with any number of interacting ducts

The muffler elements that use perforated elements for acoustic attenuation are common in practice. In typical commercial mufflers perforated elements are used involving two, three, four or more interacting ducts. Analysis of such configurations involves writing down the basic governing equations of mass continuity, momentum balance, etc., and then elimination of velocity variables to obtain the coupled ordinary differential equations in terms of acoustic pressure variables. Mathematical modelling and the consequent analytical derivation of the transmission loss for these multi-duct acoustical elements become increasingly tedious, as just not the number of ducts, but also their relative arrangement along with the boundary conditions dictate the analysis considerably. In the present paper, authors have proposed a generalization and thus an algebraic algorithm to directly produce the system matrix, eliminating the tedium of writing the basic governing equations and elimination of velocity variables. Also, a convenient approach for applying the boundary conditions is outlined here.     

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.     

On the attached length of orifices

The attached length of orifices in reactive mufflers has been estimated based on numerical calculations by the finite-element method. The numerical results for a diaphragm in a duct are compared with the theoretical data obtained by Rayleigh, Fock, Karal, and Ingard. The dependence of the attached length on the diaphragm thickness is given. The results obtained are generalized for the case in which the orifice is a Helmholtz resonator neck. The effect of the resonator length on the attached length of the neck is analyzed.     

Multi-mode sound transmission in ducts with flow

Exhaust mufflers, large exhaust stacks, and turbofan engines are common examples of ducted noise. The most useful measure of the sound produced by these noise sources is the sound power transmitted along the duct. When airflow is present, sound power flow can no longer be uniquely determined from the usual measurements of acoustic pressure and particle velocity.One approach to sound power determination from in-duct pressure measurement, and the one discussed in this paper, is to predict the relationship between the sound power and pressure based upon an assumed mode amplitude distribution. This paper investigates the relationship between acoustic pressure and power for a family of idealized source distributions of arbitrary temporal and spatial order. Incoherent monopole and dipole sources uniformly distributed over a duct cross-section can be obtained as special cases. This paper covers the sensitivity of the pressure-power relationship to source multipole order, frequency and, in particular, flow speed. It is shown that the introduction of flow in a hard-walled duct can have a substantial effect on the behavior of the pressure-power relationship for certain source distributions. Preliminary experimental results in a no-flow facility are presented in order to verify some of the main results.     

基于扩张室消声器的座便器噪声控制研究

本文以虹吸式座便器为研究对象,将扩张室消声器应用于座便器管道结构设计中,采用CFD (computational Fluid Dynamics)软件对加装不同长度扩张室消声器的座便器模型进行了冲水过程数值模拟。在研究座便器噪声产生机理及扩张室消声器声学性能的基础上,进行座便器冲洗性能试验及噪声测量试验,分别研究了冲水量与冲洗噪声、冲水量与冲洗性能之间的关系。研究表明,安装扩张室消声器,不仅可以提高座便器的冲洗性能,还可以降低冲洗噪声,达到降噪节水的目的。