Four-Port Noise Model for the Diesel Particulate Filters (DPF)

This work presents a 2-d field model for the study of sound propagation in a diesel particulate filter (dpf) unit. the 2-d model is formulated using navier-stocks, energy, and continuity equations in which the normal as well as transverse component of gas velocity are retained. temperature, pressure, density, and velocities variations with time are assumed to be harmonic. by substituting these quantities in the governing navier-stock, energy, and continuity equations, a set of 2-d partial differential equations with respect to space are obtained . the obtained 2-d partial differential equations are solved using an approximate fourier series expansions. the main outcome of this approximate analytical study is a 2-d acoustic model for the exhaust gases emission, with the existence of the diesel particulate filter. the approximate 2-d model is used in this work for calculating values of wave propagation constant which includes both attenuation and phase shift, finding the acoustics impedance of the dpf unit, comparing between different types of the dpf based on sound transmission losses, soot loading and on noise and vibration damping characteristics, in addition to calculating the noise reduction factor (nrf). the obtained results are compared with those presented by other investigators and a good agreement and improvements can be noticed for the presented study.