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

The influence of multimodal incident sound fields on the acoustic behaviour of large aftertreatment devices incorporating a monolith is modelled and analysed in detail. The analytical mode matching method is applied to the compatibility conditions of the three-dimensional acoustic fields at the device geometric discontinuities, leading to the computation of the complex wave amplitudes in all the subdomains involved and the corresponding device transmission loss. To have a realistic model, three-dimensional propagation must be considered in the inlet/outlet ducts and chambers, while one-dimensional wave propagation has to be assumed along the small capillaries of the aftertreatment device monolith (such catalytic converters and particulate filters); therefore, the monolith can be replaced by a plane wave four-pole transfer matrix from an acoustical point of view. On the other hand, for large aftertreatment device inlet ducts such as those found in heavy-duty and off-road engines, the usual models with plane incident wave excitation are not accurate since the onset of higher order incident modes in the inlet duct is expected for the frequency range of interest. Therefore, a variation of the acoustic attenuation performance is likely to occur depending on these modes, similar to the results previously found in the case of large dissipative silencers. Results are presented for three different multimodal incident sound field hypotheses: equal modal amplitude, equal modal power and equal modal energy density. A relevant influence on the sound attenuation is found for the test problems considered in the current investigation.