ABSTRACT
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 the field Navier-stocks,
energy, and continuity equations and retains the normal as well as transverse
component of gas velocity. Temperature, pressure, density, and velocities are taken to
be as plane and time harmonic variations. By substituting the differentials of these
quantities with respect to both plane and time in field equations, a set of three coupled
linear 2-D field variation equations for pressure, axial and transverse velocities is
obtained. The obtained model is solved analytically using Fourier series
approximations. The approximate solution is used to build a 2D acoustic model for the
exhaust gases emission, with the existence of the diesel particulate filter, which
accounts for both attenuation and phase shift defining the propagation wave constant.
In addition the obtained approximate solution is used to determine the acoustics
impedance of the DPF unit, comparing between different types of DPF based on sound
transmission losses performance, soot loading, noise and vibration damping, in addition
to calculating the noise reduction factor (NRF). In the present study, unlike previous
ones, six, rather than four, roots for wave propagation constant are obtained
corresponding to the obtained six port acoustic DPF model. The results obtained using
the present six -port model, for selected system parameters are graphically displayed
and compared with those available in the open literature using four- port models. The
present model results show, in general, similar qualitative behavior and a significant
quantitative improvement of the available results in the open literature obtained using a
four port model.