Boundary Element Analysis of Reactive Mufflers and Packed Silencers with Catalyst Converters

Abstract

This paper reviews recent developments in the application of the boundary element method (BEM) to muffler and silencer analysis. Initial results of modeling built-in catalyst converters are also presented. A so-called "direct mixed-body boundary element method" has been developed for muffler and silencer analysis since 1996. The idea of the method is to integrate all kinds of different boundary and internal surfaces into a single integral equation set without using the conventional multi-domain approach, even though there may be different media in the domain. A key ingredient in this method is the hypersingular integral equation. The concept of the direct mixedbody BEM is not totally against the conventional multi-domain BEM, though. For very large structures or at high frequencies, a multi-domain or substructuring approach is still necessary in order to reduce the memory usage as well as the computation time. With the direct mixed-body BEM, each substructure does not need to be a well-defined and homogeneous subdomain. As such, substructuring can be done more naturally along the longitudinal direction. Catalyst converters may also be modeled as a modular in the general framework of substructuring. Several test cases are presented with experimental verification, including two cases with built-in converters.

Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

“…The application of FE/BE approaches to catalytic converters has been presented in a number of investigations [2,[10][11][12]. Two alternative modelling techniques are available for the monolith.…”

“…In this case, the numerical approach computes three-dimensional acoustic fields inside all the catalytic converter components, including the inlet/outlet ducts and the monolith [2]. The second model replaces the monolith by a plane wave connection or a "element-to-element four-pole transfer matrix" [10][11][12]. This approach provides a relationship between the acoustic fields associated with the discretizations located at both sides of the monolithic region.…”

“…The coupling between the interfaces Γ 1c and Γ 2c associated with both sides of the connecting subdomain W c is carried out by using a transfer matrix T [10][11][12]. Details of the particular expressions for T considered in the current investigation will be provided in Sec.…”

On Theoretical of Transmission Loss in Exhaust Muffler System

“…Numerical methods, such as the Finite Element Method (FEM), Z.Toa et al [7] and J. Middleberg et al [4], [5], and the Boundary Element Method (BEM), A.Aubert et al [8], and T.W. Wu et al [9], are introduced and have been proven to be convenient for complex muffler geometries S.N.Y.Gerges et al [6]. Although these methods are applicable to any muffler configuration, when the silencer shape becomes complex, this procedure is difficult to apply.…”

Contribución al modelado acústico de la línea de escape en motores de combustión. Aplicación a silenciadores y catalizadores

“…En segundo lugar, es necesario disponer de modelos de acoplamiento entre el monolito y los conductos de entrada y salida. Si bien una posibilidad es recurrir a los modelos de onda plana en los conductos de entrada y salida, se puede lograr una mayor precisión recurriendo a modelos basados en métodos numéricos, tales como el método de elementos finitos [123] y el de elementos de contorno [145]. Debe tenerse en cuenta que para geometrías comerciales y para frecuencias suficientemente altas, el campo acústico real es tridimensional, con lo que las predicciones basadas en modelos de onda plana pueden presentar un error considerable.…”