The acoustic modelling of dissipative elements in automotive exhausts
The mathematical modelling and experimental testing of both dissipative silencers and catalytic converters is reported here, although dissipative silencers are of primary interest. The models examined are formulated with a view to introducing them into commercial software aimed at the acoustic design of automotive exhaust systems.The porous materials which are commonly employed in dissipative silencers are examined first, and a semi-empirical model is formulated in order to predict the bulk acoustic properties of four different fibrous materials. Perforated tubes are also commonly employed in dissipative silencers separating the central channel from the absorbent, and the effects of both grazing flow and a backing layer of porous material upon the acoustic impedance of a perforate plate are examined.Three different theoretical approaches to modelling dissipative silencers are reported, and the accuracy of each method is assessed in the light of experimental sound transmission loss data measured for five different dissipative silencers. Mean flow in the central channel is a feature of each model, in addition to the use of the new semiempirical models for the perforated tube and the absorbent. A simple fundamental mode model is examined first, employing a straightforward analytical solution. More complex models are then investigated, incorporating finite element numerical methods. First, a fully general finite element model is examined and transmission loss predictions are obtained using both two and three dimensional meshes. A less complex eigenvalue solution, which also employs the finite element method, is examined next but this does not require such a high degree of computational effort. Predictions for finite length silencers are subsequently obtained using three different mode matching formulations. An examination of the accuracy of the predictions obtained using the different mathematical models is then carried out, from which conclusions are made concerning the future usefulness of each model in commercial design software. Finally, the effects of both mean flow and an axial temperature gradient upon the transmission loss of catalytic converters are examined. The relative influence the catalytic converter exerts sound attenuation, as compared to dissipative silencers, is also discussed.