This thesis is focused on the development and implementation of effective methods for the acoustic design and modelling of the exhaust line of internal combustion engines, and specifically for two relevant components, from the standpoint of noise control, such as mufflers and catalytic converters.

Therefore, a literature review of the one-dimensional models and their associated matrizant approach has been performed. Also a review of the existing literature regarding the characterization of perforated elements, absorbent materials and monoliths has been carried out. The limitations and deficiencies of the plane wave models show the need of multidimensional modelling tools, which are valid for high frequencies and more general muffler and catalytic converter geometries.

The finite element method is applied to solve the convective wave equation in dissipative silencers using the pressure formulation. The coupling between connected subdomains by means of perforated elements inside the muffler is studied in detail. In addition, the effect of the mean flow on the acoustic impedance is analyzed, paying particular attention to different perforate boundary conditions. The continuity conditions of velocity and displacement are applied, and the obtained results are compared with experimental results.  

The finite element method has the capacity to deal with arbitrary geometries, and for this reason it has been applied to the acoustic modelling of automotive catalysts. Two different modelling techniques are considered: (1) First, the procedure described in previous works, 3D ducts/3D monolith, in which the finite element method leads to the calculation of the three-dimensional acoustic field inside the complete catalytic converter; (2) On the other hand, the proposed technique in the Thesis, 3D ducts/1D monolith, in which the monolith is replaced by a plane wave transfer matrix, that is, only one-dimensional acoustic behaviour is allowed within the capillary ducts. The results provided by both approaches are compared with experimental measurements, showing that the latter technique exhibits a better agreement. The proposed model, 3D ducts/1D monolith, is extended to include the presence of mean flow in the capillaries. 

In response to the high computational effort associated with the finite element method, three-dimensional analytical tools have been developed using the mode-matching method. The development of such analytical techniques takes into account the modal solution of the wave equation in ducts with rectangular, circular and conical geometry. The mode-matching method has been applied to the multidimensional acoustic modelling of diverse silencers (reactive and dissipative configurations), to study their acoustic behaviour. The effect of some significant parameters, such as the relative position of the ducts, the resistivity of the absorbent material and the porosity of the perforated elements on the acoustic attenuation has been studied in detail.  

The mode-matching method has been extended to include the case of catalysts with relevant geometries, that have not been studied in the literature from a three-dimensional analytical point of view, such as the case of circular catalysts and catalysts with conical ducts. For the modelling of both geometries, 3D ducts/3D monolith and 3D ducts/1D monolith techniques have been applied. In addition, the effect of several parameters on the acoustic behaviour of the catalyst is investigated.