BEM modeling of mufflers with diesel particulate filters and catalytic converters

The boundary element method (BEM) is used to evaluate the transmission loss (TL) of mufflers with a catalytic converter (CC) or diesel particulate filter (DPF). The CC or DPF may be modeled as a block of bulk-reacting material, or by the “element-to-element four-pole connection” in the BEM. The four-pole parameters of the block can be measured by the two-source method. To avoid cutting a small fragile sample from the brittle filter, we perform the measurement on the entire filter block connected to a pair of transition cones. A 1-D matrix inverse procedure is used to extract the four-pole parameters of the filter itself. However, the large diameter of the cross section may not justify the 1-D theory throughout the entire setup. To alleviate this restriction, we implement a 3-D BEM optimization to fine-tune the extracted four-pole parameters. This involves using the BEM to compute the impedance matrices of the substructures, and then adopting a MATLAB optimization routine to find the optimal parameters that produce the same TL as the measured TL. In our test cases with different configurations, this procedure gives better predictions than using the 1-D matrix inverse alone.