Analysis of Three Dimensional Muffler with Boundary Element Method

Abstract A numerical scheme for solving the three dimensional interior acoustic problem governed by the Helmholtz equation has been developed. The main feature of this formulation is that the singularity can be removed analytically. The boundary integral equation is solved for a specific geometry by using second-order quadrilateral surface elements and does not have the difficulty of non-uniqueness associated with the boundary integral equation formulation in an exterior problem. The transmission loss of a muffler is computed by using the derived four-pole parameters. The effects of higher-order modes due to the area discontinuity as well as the various inlet/outlet alignment on the acoustic performance of a muffler are also studied. The case of a muffler with elliptic cross-section, which is troublesome in analytical solution, can be treated easily by the present scheme. Finally, the transmission loss characteristics of a muffler with extended inlet/outlet are investigated. All the numerical results are compared with experimental measurement and agreement is good.

[1]  Allan D. Pierce,et al.  Acoustics , 1989 .

[2]  Walter Eversman.  A Systematic Procedure for the Analysis of Multiply Branched Acoustic Transmission Lines , 1987 .

[3]  Kenneth A. Cunefare,et al.  A boundary element method for acoustic radiation valid for all wavenumbers , 1989 .

[4]  S. Mukherjee,et al.  Boundary element techniques: Theory and applications in engineering , 1984 .

[5]  Y. Kagawa,et al.  Finite element simulation of an axisymmetric acoustic transmission system with a sound absorbing wall , 1977 .

[6]  Jeong-Guon Ih,et al.  Analysis of higher-order mode effects in the circular expansion chamber with mean flow , 1985 .

[7]  F. J. Rizzo,et al.  A special integral equation formulation for acoustic radiation and scattering for axisymmetric bodies and boundary conditions , 1986 .

[8]  J. S. Lamancusa.  The transmission loss of double expansion chamber mufflers with unequal size chambers , 1988 .

[9]  L. J. Eriksson,et al.  The effect of inlet/outlet locations on higher order modes in silencers , 1981 .

[10]  Frank J. Rizzo,et al.  An advanced boundary integral equation method for three‐dimensional thermoelasticity , 1977 .

[11]  D. A. Blaser,et al.  Transfer function method of measuring in-duct acoustic properties. I - Theory. II - Experiment , 1980 .

[12]  A. Craggs,et al.  A finite element method for damped acoustic systems: An application to evaluate the performance of reactive mufflers , 1976 .

[13]  A. Seybert,et al.  An advanced computational method for radiation and scattering of acoustic waves in three dimensions , 1985 .

[14]  H. Utsuno,et al.  A Method for the Analytical Prediction of Insertion Loss of a Two-Dimensional Muffler Model Based on the Transfer Matrix Derived from the Boundary Element Method , 1985 .

[15]  A. F. Seybert,et al.  Application of the Boundary Element Method to Acoustic Cavity Response and Muffler Analysis , 1987 .

[16]  H. A. Schenck.  Improved Integral Formulation for Acoustic Radiation Problems , 1968 .