Muffler Performance Studies Using a Direct Mixed-Body Boundary Element Method and a Three-Point Method for Evaluating Transmission Loss

1996 ◽  
Vol 118 (3) ◽  
pp. 479-484 ◽  
Author(s):  
T. W. Wu ◽  
G. C. Wan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Velocity Potential ◽  
Transmission Loss ◽  
Point Method ◽  
Integral Formulation ◽  
Pressure Jump ◽  
Direct Integral ◽  
Body Boundary ◽  
Element Method

In this paper, a single-domain boundary element method is presented for muffler analysis. This method is based on a direct mixed-body boundary integral formulation recently developed for acoustic radiation and scattering from a mix of regular and thin bodies. The main feature of the mixed-body integral formulation is that it can handle all kinds of complex internal geometries, such as thin baffles, extended inlet/outlet tubes, and perforated tubes, without using the tedious multi-domain approach. The variables used in the direct integral formulation are the velocity potential (or sound pressure) on the regular wall surfaces, and the velocity potential jump (or pressure jump) on any thin-body or perforated surfaces. The linear impedance boundary condition proposed by Sullivan and Crocker (1978) for perforated tubes is incorporated into the mixed-body integral formulation. The transmission loss is evaluated by a new method called “the three-point method.” Unlike the conventional four-pole transfer-matrix approach that requires two separate computer runs for each frequency, the three-point method can directly evaluate the transmission loss in one single boundary-element run. Numerical results are compared to existing experimental data for three different muffler configurations.

A Novel Displacement Gradient Boundary Element Method for Elastic Stress Analysis With High Accuracy

1988 ◽  
Vol 55 (4) ◽  
pp. 786-794 ◽  
Author(s):  
H. Okada ◽  
H. Rajiyah ◽  
S. N. Atluri
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Numerical Differentiation ◽  
Boundary Integral ◽  
Displacement Gradient ◽  
Direct Integral ◽  
Displacement Boundary ◽  
Element Method

The boundary element method (BEM) in current usage, is based on the displacement boundary integral equation. The current practice of computing stresses in the BEM involves the use of a two-tier approach: (i) numerical differentiation of the displacement field at the boundary, and (ii) analytical differentiation of the displacement integral equation at the source point in the interior. A new direct integral equation for the displacement gradient is proposed here, to obviate this two-tier approach. The new direct boundary integral equation for displacement gradients has a lower order singularity than in the standard formulation, and is quite tractable from a numerical view point. Numerical results are presented to illustrate the advantages of the present approach.

Application of the Boundary Element Method to Acoustic Cavity Response and Muffler Analysis

1987 ◽  
Vol 109 (1) ◽  
pp. 15-21 ◽  
Author(s):  
A. F. Seybert ◽  
C. Y. R. Cheng
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Transmission Loss ◽  
Radiation Condition ◽  
Boundary Integral ◽  
Exterior Problems ◽  
Integral Equation Formulation ◽  
Element Method

This paper is concerned with the application of the Boundary Element Method (BEM) to interior acoustics problems governed by the reduced wave (Helmholtz) differential equation. The development of an integral equation valid at the boundary of the interior region follows a similar formulation for exterior problems, except for interior problems the Sommerfeld radiation condition is not invoked. The boundary integral equation for interior problems does not suffer from the nonuniqueness difficulty associated with the boundary integral equation formulation for exterior problems. The boundary integral equation, once obtained, is solved for a specific geometry using quadratic isoparametric surface elements. A simplification for axisymmetric cavities and boundary conditions permits the solution to be obtained using line elements on the generator of the cavity. The present formulation includes the case where a node may be placed at a position on the boundary where there is not a unique tangent plane (e.g., at an edge or a corner point). The BEM capability is demonstrated for two types of classical interior axisymmetric problems: the acoustic response of a cavity and the transmission loss of a muffler. For the cavity response comparison data are provided by an analytical solution. For the muffler problem the BEM solution is compared to data obtained by a finite element method analysis.

Numerical Simulation of the Water Entry of a Wedge Based on the Complex Variable Boundary Element Method

2011 ◽  
Vol 90-93 ◽  
pp. 2507-2510 ◽  
Author(s):  
Jie Gao ◽  
Yong Hu Wang ◽  
Ke An Chen
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Complex Variable ◽  
Similarity Solution ◽  
Velocity Potential ◽  
Initial Conditions ◽  
Time Derivative ◽  
Water Entry ◽  
Variable Boundary ◽  
Element Method

The water entry problem of a wedge is simulated based on the velocity potential theory in time domain. The Complex Variable Boundary Element Method (CVBEM) is used in the stretched coordinate system. Before the simulation, the similarity solution is taken as the initial conditions. The auxiliary function scheme in conjunction with the same CVBEM is used to obtain the accurate time derivative of velocity potential and pressure distribution on wedge surface. The time marching solution is matched with the jet special treatment. Finally, the simulation results are compared with the similarity solution, which shows that the jet linear approximation can simulate the jet well.

A DIRECT MIXED-BODY BOUNDARY ELEMENT METHOD FOR MUFFLERS WITH INTERNAL THIN COMPONENTS COVERED BY LINING AND A PERFORATED PANEL

2007 ◽  
Vol 15 (01) ◽  
pp. 145-157 ◽  
Author(s):  
K. L. PAN ◽  
C. I. CHU ◽  
T. W. WU
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Experimental Comparison ◽  
Thin Body ◽  
Wall Surface ◽  
Interior Wall ◽  
Lining Material ◽  
Body Boundary ◽  
Impedance Modeling ◽  
Element Method

Thin components, such as baffles, extended inlet/outlet tubes, and internal connecting tubes, are commonly used in reactive mufflers for cancelation of sound at particular frequency peaks. To provide additional absorption effects at higher frequencies, porous sound absorbing materials may be used on the muffler interior wall surface or on any internal thin components. If the sound absorbing material is backed by a rigid surface, it is usually modeled by the local normal impedance approach. The local impedance modeling on the interior wall surface is straightforward and has been extensively used in the boundary element method, in which the boundary surface is just moved forward to the contact surface between the lining and air. On the other hand, the local impedance modeling on any internal thin components is relatively rare. This paper first presents a direct mixed-body boundary element formulation for a thin body covered by local impedance on either side or both sides of the thin body. The local impedance can be from the lining material itself, or from the lining material plus a protective perforated metal cover. Several test cases with experimental comparison are presented in this paper.

Case study: Correlation between boundary and finite element determination of large silencer transmission loss

2021 ◽  
Vol 69 (4) ◽  
pp. 276-287
Author(s):  
Kangping Ruan ◽  
T.W. Wu ◽  
D.W. Herrin
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Sections ◽  
Transmission Loss ◽  
Cutoff Frequency ◽  
Low Frequency ◽  
Cross Sectional ◽  
Element Determination ◽  
Element Method

Silencers used in the power generation industry generally have large ducts entering and leaving the silencer. With large cross-sectional dimensions, the plane wave cutoff frequency will be exceeded at a low frequency so that transmission loss can no longer be evaluated by assuming constant sound pressure over a cross-section. More sophisticated calculation and processing approaches are necessary. In this research, the boundary element method is used in conjunction with a reciprocal identity method to determine the transmission loss for rectangular and circular cross-sections: the two configurations that cover most real-world designs. The boundary element method is compared to a finite element method strategy where the transmission loss is determined using an automatically matched layer boundary condition at the inlet and outlet. This approach can be used in most commercial software. Although these two approaches have little in common, transmission loss results compare well with one other. Validation by comparison is helpful because analytical solutions are only available for simple axisymmetric cases. Methods are compared for practical configurations like parallel-baffle silencers and reactive silencers.

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