Efficient finite element modelling of sound propagation in after treatment devices with arbitrary cross section

Abstract

[EN] The acoustic modelling of exhaust after-treatment devices, such as catalytic converters (CC) and diesel particulate filters (DPF), usually requires the use of multidimensional numerical techniques to assess the influence of higher order modes on the sound attenuation performance. Three-dimensional (3D) wave propagation can be considered through the finite element method (FEM). With a view to improving the computational expenditure of full 3D FEM, an efficient modelling technique is presented in this work to speed up transmission loss (TL) calculations in after-treatment devices with arbitrary cross section incorporating monoliths. The efficient modelling approach is based on the mode matching method, combining: (1) transversal pressure modes computed through a 2D FEM approach for devices with arbitrary but axially uniform cross section; (2) compatibility conditions of the acoustic fields at the device geometric discontinuities. For the acoustic modelling of monoliths, these are replaced by four pole transfer matrices relating the acoustic fields at both sides of the monolithic region. Mode matching TL results are compared with full 3D FE simulations and experimental measurements for some selected configurations, showing a good agreement. For a given accuracy, the computational efficiency of the mode matching technique proposed in this work improves that of full 3D FE calculations. TL improvements are achieved by suitable locations of a DPF inlet/outlet ducts. Next, a Genetic Algorithm (GA)-based optimization approach is used in order to improve the attenuation performance of the after-treatment device by varying the geometry as well as the monolith properties. Results show that the optimized configuration outperforms the initial design at target frequencies.