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.     

Numerical studies on venting system with multi-chamber perforated mufflers by GA optimization

Research on new techniques of perforated silencers has been well addressed and developed; however, the research work in shape optimization for a volume-constrained silence requested upon the demands of operation and maintenance inside a constrained machine room is rare. Therefore, the main purpose of this paper is to not only analyze the sound transmission loss of a multi-chamber perforated muffler but also to optimize the best design shape under space-constrained condition.In this paper, both the generalized decoupling technique and plane wave theory are used. The four-pole system matrix in evaluating the acoustic performance of sound transmission loss (STL) is also deduced in conjunction with a genetic algorithm (GA). To demonstrate the precision of the tuning ability in a muffler, various targeted pure tones are proposed in numerical cases. Results reveal that the maximal acoustical performance precisely occurred in the desired frequency. Furthermore, a noise reduction with respect to full-band exhausted noise emitted from a diesel engine is also introduced and assessed. To achieve a better optimization in GA, several test parameter values were used. Before a GA operation can be carried out, the accuracy of the mathematical models have to be checked by experimental data.The optimal result in eliminating full-band noise reveals that the overall noise reduction of a multi-chamber muffler can achieve 68 dB under space-constraint conditions. Consequently, the approach used for the optimal design of the STL proposed in this study is indeed easy, economical and quite effective.     

Finite element acoustic simulation based shape optimization of a muffler

This paper describes a methodology which combines finite element analysis and Zoutendijk’s feasible directions method for mufflers shape design. The main goal is to obtain the dimensions of the acoustic muffler with the transmission loss (TL), being maximized in the frequency range of interest. The improved four parameters method is used for TL evaluations and the Helmholtz’s equation is solved numerically with the finite element method (FEM). The quadratic triangular finite element meshes are adequately constructed to control the pollution error and the optimization problem is solved using the Zoutendijk’s feasible directions method due to robustness and efficiency for problems with nonlinear constraints. Numeric experiments performed with circular expansion chambers with extended inlet and outlet show results for constrained and unconstrained shape optimization.     

GA optimization on multi-segments muffler under space constraints

Whilst the space volume of muffler in noise control system is often constrained for maintenance in practical engineering work, the maximization on muffler’s performance becomes important and essential. In this paper, a novel approach genetic algorithms (GAs) based on the principles of natural biological evolution will be used to tackle this optimization of muffler design [M. Mitchell, An Introduction to Genetic Algorithms, The MIT Press, Cambridge, MA, 1996]. Here, the shape optimization of multi-segments muffler coupled with the GA searching technique is presented. The techniques of binary genetic algorithms (BGA) together with the commercial MATLAB package [G. Lindfield, J. Penny, Numerical Method Using Matlab, second ed., Prentice Hall, Englewood Cliffs, NJ, 2000] are applied in GA searching. In addition, a numerical case of pure tone elimination with 2-5 segments on muffler is introduced and fully discussed. To achieve the best optimization in GA, several GA parameters are on trial in various values. Results show that the GA operators, including crossover mutation and elitism, are essential in accuracy. Consequently, results verify that the optimal sound transmission loss at the designed frequency of 500 Hz is exactly maximized. The GA optimization on multi-segments muffler proposed in this study surely provides a quick and correct approach.     

Multiobjective muffler shape optimization with hybrid acoustics modeling

This paper considers the combined use of a hybrid numerical method for the modeling of acoustic mufflers and a genetic algorithm for multiobjective optimization. The hybrid numerical method provides accurate modeling of sound propagation in uniform waveguides with non-uniform obstructions. It is based on coupling a wave based modal solution in the uniform sections of the waveguide to a finite element solution in the non-uniform component. Finite element method provides flexible modeling of complicated geometries, varying material parameters, and boundary conditions, while the wave based solution leads to accurate treatment of non-reflecting boundaries and straightforward computation of the transmission loss (TL) of the muffler. The goal of optimization is to maximize TL at multiple frequency ranges simultaneously by adjusting chosen shape parameters of the muffler. This task is formulated as a multiobjective optimization problem with the objectives depending on the solution of the simulation model. NSGA-II genetic algorithm is used for solving the multiobjective optimization problem. Genetic algorithms can be easily combined with different simulation methods, and they are not sensitive to the smoothness properties of the objective functions. Numerical experiments demonstrate the accuracy and feasibility of the model-based optimization method in muffler design.     

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.     

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。     

Optimization of reactive mufflers

A new approach to optimization of reactive mufflers, which is based on use of muffler prototype with nondimensional geometrical parameters and integral criterion of acoustic performance of mufflers, is proposed. Implementation of the approach using the example of chamber mufflers is considered.     

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.     

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.     

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.     

基于低频吸声超构材料的复合消声器研究*

针对管道内低频噪声难以抑制的问题，本文基于亥姆霍兹共振腔（HR）阵列吸声板和穿孔管消声器组合，设计了一种复合式宽带消声器。首先利用有限元法仿真分析传统穿孔管消声器，发现中低频消声能力较差，通过嵌入HR阵列吸声板吸收中低频噪声。采用仿真与实验的方式研究吸声板的声学性能：在400-1000 Hz频段内的平均吸声系数达到了0.88。然后对复合式消声器进行数值模拟及3D打印阻抗管实验测试对比：复合式消声器在400-1718Hz频率范围内的平均传递损失为18.15 dB ，最终实现了管道内全频带噪声有效控制。     

The study of reactive silencers by shape and parametric optimization techniques

The aim of this work is to show the application of shape and parametric optimization techniques in the study of reactive silencers with extended inlet and outlet ducts. Parametric optimization is employed to evaluate the appropriate size of the inlet and outlet ducts. Shape optimization is employed to establish the proper profile of these ducts in order to improve the acoustic features of these mufflers in a specific frequency range. The objective function used in the optimization processes is defined through the average transmission loss (TL) for the desired frequency range. This type of objective function is strongly non-linear and the genetic algorithm, GA, was chosen as a mathematical method for determining the maximum of this function. The Finite Element Method with an axisymmetric formulation along with the modified four-parameter method are used to calculate the TL(ω). The Hermite polynomials were used in the shape optimization in order to obtain local boundary approximations with C¹ continuity. The results showed the optimization efficiency of the inlet ducts profile for acting in specific frequency ranges with gains up to 20 dB with respect to silencers without shape optimization. The numerical analyses agree well with experimental results.     

Model-based optimization of ultrasonic transducers

Numerical simulation and automated optimization of Langevin-type ultrasonic transducers are investigated. These kind of transducers are standard components in various applications of high-power ultrasonics such as ultrasonic cleaning and chemical processing. Vibration of the transducer is simulated numerically by standard finite element method and the dimensions and shape parameters of a transducer are optimized with respect to different criteria. The novelty value of this work is the combination of the simulation model and the optimization problem by efficient automatic differentiation techniques. The capabilities of this approach are demonstrated with practical test cases in which various aspects of the operation of a transducer are improved.     

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.     

新型高频消音器对Whoosh噪声的优化

为了诊断匹配涡轮增压器的汽油车型急加速过程中产生的Whoosh噪声,并分析噪声产生的原理,确定噪声的频率特性以及噪声产生的工况,本文通过对Whoosh噪声在进气系统中贡献量的分析,按照"源-路径-响应"原则,设计出频率相应的高频穿孔消音器并将其插入到进气系统中,从噪声传递路径上进行优化与控制。通过整车道路客观数据分析和主观驾评,确定该方案切实可行,可推广至多款增压车型上应用。     

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.     

Optimization of constrained composite absorbers using simulated annealing

Sound reverberation is an important problem in some industrial environments. As indicated by the Occupational Safety and Health Act of 1970, noise is responsible for the psychological and physiological ills of workers. Therefore reduction of reverberation becomes essential. For maintenance and other reasons, the thickness of sound absorbers used for reverberation control may be constrained. Consequently there is interest in minimizing noise using sound absorbers with constrained thickness. Optimization of a composite absorber using a simulated annealing algorithm is presented. Simulated annealing is a stochastic relaxation technique based on analogy with the physical process of annealing metal. The algorithm requires a mathematical model for the acoustical properties of the absorber. Before optimization, the accuracy of the mathematical model was checked against experimental data. A program for optimizing in respect of broad band noise at a specified receiver has been created and run. Results prove that SA optimization provides a quick and efficient approach in designing constrained thickness composite sound absorbers.     

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。