Circular Expansion Chamber Research Articles

An Investigation of Acoustic Attenuation Performance of Silencers with Mean Flow Based on Three-Dimensional Numerical Simulation

Transmission loss (TL) is often used to evaluate the acoustic attenuation performance of a silencer. In this work, a three-dimensional (3D) finite element method (FEM) is employed to calculate the TL of some representative silencers, namely, circular expansion chamber silencer and straight-through perforated pipe silencer. In order to account for the effect of mean flow that exists inside the silencer, the 3D FEM is used in conjunction with the Computational Fluid Dynamics (CFD) simulation of the flow field. More concretely, the 3D mean flow field is computed by firstly using CFD, and then the obtained mean flow data are imported to an acoustic solution undertaken using FEM. The data transfer between the two steps is accomplished by mesh mapping. The results presented demonstrate good agreement between present TL predictions and previously published experimental and numerical works. Also, the details of the flow inside the silencers may be studied. Furthermore, the effect of mean flow velocity on acoustic attenuation performance of the silencers is investigated. It is concluded that for the studied silencers, in general, increasing flow velocity increases the TL and decreases the resonance peaks.

Experimental Investigation of a Double Expansion Chamber Reactive Muffler for Stationary Diesel Engine

The increasing need to control noise levels in our environment produced by internal combustion engines, demands the accurate designing of mufflers to meet specific noise emission norms. This paper describes a theoretical and experimental study of a circular double expansion chamber reactive muffler designed specifically for a stationary generator engine. For the theoretical approach, the equations are solved by four pole transfer matrix method using MATLAB software to obtain optimized dimensions of three mufflers at desired maximum transmission loss and at frequencies at which highest sound level is observed. MATLAB software is also used to obtain the graphs for transmission loss versus frequency. In the experimental method a white noise 1D plane wave is generated in the impedance tube attached on both sides of the muffler to obtain the transmission loss. The theoretical results obtained are then compared with experimental results for validation. The theoretical results are well correlated with the experimental results.

Acoustic attenuation analysis of expansion chambers with extended inlet/outlet

Numerical mode matching (NMM) method is developed to predict and analyze the acoustic attenuation performance of expansion chambers with extended inlet/outlet. The two-dimensional finite element method is employed to extract the transversal eigenvalues and eigenvectors, and the mode matching technique is used to determine the modal amplitudes and transmission loss of expansion chamber silencers by combining the boundary conditions at inlet and outlet. The transmission loss results from the NMM method, three-dimensional finite element method (FEM), and experiment showed good agreements for circular expansion chambers with extended inlet and outlet ducts, which verified the accuracy of the present NMM method in calculating the acoustic attenuation performance of expansion chamber. Then theNMMmethod is used to investigate the effects of arrangements, extended lengths and locations of inlet and outlet ducts on the acoustic attenuation performance of elliptical expansion chambers.

Time accurate finite difference method for performance prediction of a silencer with mean flow and nonlinear incident wave

Transmission losses of various reactive silencers are predicted, using a time accurate finite difference method. The numerical scheme is the 3rd order upwind scheme for axisymmetric Euler equations. Main advantage of the present method is that it can simulate linear and nonlinear wave propagation phenomena in a flow field directly with minimum numerical oscillation errors. The special treatments of incident wave condition, i.e. multiple harmonics of the transparent acoustic condition are applied to the transmission loss prediction for calculation efficiency. For the validation of the present approach, circular expansion chamber silencers without mean flow and an exponential pipe with mean flow are simulated in case of linear incident wave. The computed transmission losses have quite good agreements with those of the others. The nonlinear incident wave case is also investigated to check the usefulness of this method. The periodicN wave is clearly captured without numerical oscillation errors, and the insertion losses of two different incident frequencies are compared.

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.

Analytical approach for sound attenuation in perforated dissipative silencers with inlet/outlet extensions

The acoustic attenuation performance of perforated dissipative circular expansion chambers with inlet/outlet extensions is investigated. The eigenvalues and eigenfunctions of the sound field are analytically determined in the extended inlet/outlet circular ducts, upstream/downstream end annular dissipative chambers, and the central perforated dissipative expansion chamber. Utilizing the continuity conditions of velocity/pressure at the interfaces the transmission loss is predicted by a two-dimensional analytical approach. For a specific configuration, such predictions are compared with both experiments and a three-dimensional computational solution based on the substructure boundary element technique, showing a reasonable agreement. The analytical results for the effect of the absorbent resistivity, duct porosity, and geometryon the acoustic attenuation performance are discussed in detail.

Sound attenuation in circular duct using slit-like short expansion of eccentric and/or serialized configuration

Sound attenuation in a circular duct is investigated by measurement and numerical calculation for using a slit-like short circular expansion chamber, termed ‘slit’ here, that performs as a resonator muffler in the duct. Since its resonant frequency depends on its depth, some depth-varying configurations of it are introduced in order to widen its effective frequency range. First, the performance of a set of serialized slits is examined. This configuration is composed by the slits located in series in the duct, having different diameters from each other and concentric to the duct. While this type of slit basically shows the summative performance of each composing slit, a certain interaction among slits occurs if the resonant frequency of each slit comes close to each other. Second, a single slit eccentric to the duct is examined. In every case of it treated here, two resonant frequencies are obtained. While the lower resonance seems to relate to the (1,0) mode in the slit, the higher one seems to relate to the corresponding concentric slit. Finally, a set of serialized slits eccentric to the duct is considered. Its property becomes considerably complicated against the two cases mentioned above. In certain configurations of it, however, a good performance for sound reduction is obtained.

Case study: Acoustic attenuation performance of circular expansion chambers with extended end-inlet and side-outlet

Case study: Acoustic attenuation performance of circular expansion chambers with extended end-inlet and side-outlet

Optimum Design for Inlet and Outlet Locations of Circular Expansion Chamber for Improving Acoustic Performance

The acoustic characteristics of expansion chamber will be changed with the variation of inlet/outlet location due to the higher order acoustic mode in a high frequency in which the plane wave theory is not available. In this paper, the acoustic performance of reactive type expansion chamber with circular cross-section is analyzed by using the modified mode matching theory. The sensitivity analysis of four-pole parameters with respect to the location of inlet and outlet is also suggested to increase the acoustic performance. The acoustic power transmission coefficient is used as cost function, and the location of inlet and outlet is used as design variables. The steepest descent method and SUMT algorithm are used for optimization technique. Several results showed that the expansion chamber with optimally located inlet/outlet had better acoustic performance than concentric expansion chamber.

ACOUSTIC ATTENUATION PERFORMANCE OF CIRCULAR EXPANSION CHAMBERS WITH SINGLE-INLET AND DOUBLE-OUTLET

Expansion chambers with single-inlet and double-outlet provide desirable broadband acoustic attenuation similar to simple (single inlet/outlet) chambers and reduce the flow noise and back pressure in exhaust systems. The present study develops a three-dimensional analytical approach to determine the transmission loss of circular expansion chambers with single-inlet and double-outlet, which couples the continuity conditions of the acoustic pressure and particle velocity at the inlet and outlets with the orthogonality relations of Fourier–Bessel functions. The analytical results are compared with the boundary element predictions. The acoustic attenuation of the expansion chambers with single-inlet and double-outlet is then investigated in detail as a function of the chamber length and the locations of inlet and outlets.

ACOUSTIC ATTENUATION PERFORMANCE OF CIRCULAR EXPANSION CHAMBERS WITH EXTENDED INLET/OUTLET

The acoustic attenuation performance of circular expansion chambers with extended inlet/outlet is investigated. Three approaches are employed to determine the transmission loss: (1) a two-dimensional, axisymmetric analytical solution for the concentric configuration; (2) a three-dimensional computational solution based on the substructure boundary element–transfer impedance matrix technique; and (3) experiments on an extended impedance tube set-up with expansion chambers fabricated with fixed inlet, outlet, and chamber diameters, and varying lengths for the extended ducts and the chamber, and varying offset locations of the inlet and outlet. The transmission loss results from all three approaches are shown to agree well for the concentric configurations. The computational approach is also applied to determine the acoustic attenuation performance of asymmetric expansion chambers with extended inlet/outlet, which also compares well with the experiments. The effect of geometry (lengths of the extended ducts and expansion chamber, and the offset angles of the asymmetric configuration) on the multidimensional wave propagation and acoustic attenuation performance is discussed in detail.

ACOUSTIC ATTENUATION PERFORMANCE OF CIRCULAR EXPANSION CHAMBERS WITH OFFSET INLET/OUTLET: II. COMPARISON WITH EXPERIMENTAL AND COMPUTATIONAL STUDIES

This is the second of two papers investigating the acoustic attenuation performance of asymmetric, circular expansion chambers with respect to the chamber length and the relative location of the offset inlet/outlet. Three approaches are employed to determine the transmission loss: (1) the three-dimensional analytical approach developed by the authors in a companion paper (Selamet and Ji, 1998,Journal of Sound and Vibration,213, 601–617) [1]; (2) the three-dimensional computational solution based on the boundary element method; and (3) experiments on an extended impedance tube set-up with expansion chambers fabricated with fixed inlet, outlet, and chamber diameters, varying chamber length to diameter ratios, and varying offset locations of the inlet and outlet. The results from the three approaches are shown to agree well. The effect of geometry, particularly that of the offset angles of the asymmetric configurations, on the multidimensional wave propagation and acoustic attenuation performance is discussed in detail.

ACOUSTIC ATTENUATION PERFORMANCE OF CIRCULAR EXPANSION CHAMBERS WITH OFFSET INLET/OUTLET: I. ANALYTICAL APPROACH

The inlet and outlet locations of expansion chambers can significantly affect the acoustic attenuation performance of the silencer, due to their control over the excitation and suppression of higher order modes. By combining the continuity conditions of the acoustic pressure and particle velocity with the orthogonality relations of Fourier–Bessel functions at the inlet and outlet discontinuities, the present study develops a three-dimensional analytical approach to determine the transmission loss of circular expansion chambers with offset inlet and outlet ducts. The results obtained from the present approach are compared with the classical one-dimensional predictions and the earlier multidimensional works.

Green’s solution of the acoustic wave equation for a circular expansion chamber with arbitrary locations of inlet, outlet port, and termination impedance

The acoustic characteristics of a circular expansion chamber whose inlet and outlet are situated on arbitrary locations of the chamber, i.e., the side wall or the face of the chamber, are analyzed based on the Green’s function of a chamber with homogeneous boundary conditions. The Green’s function is found by considering the boundary condition of the walls as rigid except at the location of the source, which is assumed to be a uniform volumetric acoustic source. The complete solution that determines the sound pressure distribution, intensity, and sound power pattern inside of the chamber are found. The solutions are compared with those based on the modal expansion techniques for the aforementioned cases. To verify the solutions, experiments were also performed, which determines the transmission loss of the expansion chamber. Side-inlet/side-outlet, face-inlet/side-outlet chambers were tested. A two-microphone method was used to accurately determine the transmission losses of the chambers. The Green’s solutions are verified by comparison with the experimental results and the solutions based on the modal expansion techniques.

Acoustic Characteristics of an Expansion Chamber With Constant Mass Flow and Steady Temperature Gradient (Theory and Numerical Simulation)

The governing equation of acoustic wave propagation in a circular expansion chamber with mean flow and temperature gradient is solved. The circular chamber is divided into N segments and the flow speed and temperature are assumed to be constant in each segment. The solution is obtained in recursive form by applying the matching condition on the boundary of adjacent elements. The solution is verified by comparing it with the experimental results. The results demonstrate that the present theory can well predict the transmission loss of an expansion chamber which has offset, a twisting angle, mean flow, and temperature gradient.

Three-dimensional acoustic analysis of a circular expansion chamber with side inlet and end outlet

Noise attenuation characteristics of a simple expansion chamber with a side inlet and an end outlet are studied. A theoretical method is derived to investigate the influences caused by higher-order modes, using a three-dimensional analysis in which the chamber is considered as a piston-driven circular cylinder. Also, quantitative estimation for the transmission loss can be performed, using the derived four-pole parameters. Accordingly, the characteristics of the chamber, as a result of the interactions between the plane wave and the transverse waves, can be investigated easily with respect to the relative locations of the inlet/outlet and chamber length. Experiments are performed for the verification of the theory. In the case of the chamber with a concentric end outlet, plane-wave theory agrees with the theoretical and experimental results below the rather high frequency range, but not for the case of the chamber with an offset end outlet. Experimental results are in good agreement with the theoretical results obtained.

Three-dimensional acoustic analysis of circular expansion chambers with a side inlet and a side outlet

The effects of higher-order acoustic modes upon the performance of a circular expansion chamber with its inlet and outlet located on the cylinder wall are investigated. The sound distribution in the expansion chamber is obtained, theoretically, considering the influences of the diffracted sound pressure generated by the presence of end plates in the chamber. A theoretical method for the estimation of the transmission loss is suggested by using the derived four pole parameters, assuming that the chamber can be modeled as a piston-driven circular rigid cylinder. A series of experimental observations are taken for verification, and it is found that they are in good agreement with the theoretical results. The influences of those modes are studied for a variety of chamber lengths and combined inlet/outlet locations. As a result of this study, it is concluded that the diffracted sound pressure affects the performance of the expansion chamber considerably in the range above the cutoff frequency of the n=1, m=0 asymmetric mode, and that the plane-wave theory can hardly be adopted even in the low-frequency range where the fundamental mode prevails.

Analysis of higher-order mode effects in the circular expansion chamber with mean flow

The effects of higher-order acoustic modes produced by the areal discontinuities of the simple expansion chamber with mean flow on the acoustic performance are studied. The chamber is modeled as a piston-driven circular rigid tube with no losses and, by using the Fourier–Bessel expansion, a general expression of the output pressure to the given input uniform volume velocity is obtained for a whole chamber. Quantitative estimation for the transmission loss can be performed using the derived four-pole parameters, whereas the characteristics of the chamber, as a result of the interactions between the plane wave and the transverse waves, can be easily investigated with respect to the relative locations of the inlet/outlet, the chamber length, and the mean flow. The expression as a form of C in four-pole parameters is adopted to describe the chamber characteristics for computational convenience. All the parameters involved in the experimental works by Eriksson [L. J. Eriksson, J. Acoust. Soc. Am. 72, 1208–1211 (1982)] are taken in the examples. Using the derived four-pole parameters, the transmission losses for both the concentric and offset inlet/outlet configurations are predicted and compared with the experimental results. The theoretical results of the present study are in good agreement with the experiments of the authors and the previous works.