Sound propagation in an array of narrow porous channels with application to diesel particulate filters

In an earlier work the authors have presented a 1-D acoustic model for diesel particulate filters (DPFs). One shortcoming of this first model is the approximate treatment of the viscous and thermal losses along the narrow channels. In the present paper this issue is analyzed in more detail, by solving the convective acoustic wave equations for two neighboring channels simplified in the manner of the Zwikker and Kosten theory. From the solution the acoustic two-port has been calculated to predict the sound transmission losses for an entire DPF unit. The theoretical results are compared with experimental data for clean filter units at room temperature and the agreement is very good and better, in particular for very small Mach numbers, than for the earlier presented 1-D model. A modified 1-D model using the classical (exact) Kirchhoff solution for a plane wave in a narrow tube is also presented. This modified 1-D model is in close agreement with the predictions of the new model. Furthermore, the earlier proposed 1-D model, which assumes isothermal sound propagation, works satisfactorily up to 800–1000 Hz for a typical filter at operating (hot) conditions.