Numerical mode matching for sound propagation in silencers with granular material

Abstract

This work presents an efficient numerical approach based on the combination of the mode matching technique and the finite element method (FEM) to model the sound propagation in silencers containing granular material and to evaluate their acoustic performance through the computation of transmission loss (TL). The methodology takes into account the presence of three-dimensional (3D) waves and the corresponding higher order modes, while reducing the computational expenditure of a full 3D FE calculation. First, the wavenumbers and transversal pressure modes associated with the silencer cross section are obtained by means of a two-dimensional FE eigenvalue problem, which allows the consideration of arbitrary transversal geometries and material heterogeneities. The numerical approach considers the possibility of using different filling levels of granular material, giving rise to cross sections with abrupt changes of properties located not only in the usual central perforated passage, but also in the transition between air and material, that involves a significant change in porosity. After solving the eigenvalue problem, the acoustic fields (acoustic pressure and axial velocity) are coupled at geometric discontinuities between ducts through the compatibility conditions to obtain the complete solution of the wave equation and the acoustic performance (TL). The granular material is analysed as a potential alternative to the traditional dissipative silencers incorporating fibrous absorbent materials.Sound propagation in granular materials can be modelled through acoustic equivalent properties, such as complex and frequency dependent density and speed of sound. TL results computed by means of the numerical approach proposed here show good agreement with full 3D FE calculations and experimental measurements. As expected, the numerical mode matching outperforms the computational expenditure of the full 3D FE approach. Different configurations have been studied to determine the influence on the TL of several parameters such as the size of the material grains, the filling level of the chamber, the granular material porosity and the geometry of the silencer cross section.

Computational approach for the acoustic modelling of large aftertreatment devices with multimodal incident sound fields

“…The complete acoustic field of the system requires the computation of the wave amplitudes A n ± , B n ± , D n ± and E n ± in all the ducts. First, the compatibility conditions of the acoustic fields are taken into account, being applied at the interfaces between duct A and central chamber B (inlet expansion), duct D and central chamber E (outlet contraction), 24 as well as the coupling of acoustic pressures and axial velocities at both sides of the monolith through the aforementioned plane wave four-pole transfer matrix. These can be expressed as detailed next.…”

“…Basically, a weighted integration procedure is applied whose weighting functions are the transversal modal functions of the ducts. [3][4][5]10,23,24 Hereinafter, N m is the number of higher order modes considered to expand the acoustic pressure and velocity fields (see equations ( 1) and ( 2)) for regions B and D, associated with the central chambers, while N a and N e higher order modes are taken into account for the inlet and outlet ducts A and E, respectively. The algebraic system of equations required to compute the unknown wave amplitudes is generated next.…”

Analysis of high-duty dual exhaust silencer system based on acoustic field and flow field

“…Mok J C's study focused on a silencer built within the thick portion of a door edge and reports on the results of evaluating silencers by determining sound transmission loss via theoretical analysis and experiments on three types of silencers [7]. EM Sánchez-Orgaz et al presented an efficient numerical approach based on the combination of the mode matching technique and the finite element method (FEM) to model the sound propagation in silencers containing granular material and to evaluate their acoustic performance through the computation of transmission loss (TL) [8]. Arslan H, Ranjbar M designed a silencer system to reduce the exhaust noise.…”