Assessment of High Temperatures Sound Transmission Losses and Noise Reduction Factor for a DPF Using a Six-port Acoustic Model

We construct a 2-D field model as a modified version of the 1-D model formulated in [1] for the study of sound propagation in a diesel particulate filter (DPF) unit. The modified model is used to evaluate both sound transmission losses and noise reduction factors of a typical DPF unit at high temperatures. The 2-D model is formulated using linearized field Navier-Stocks, energy, and continuity equations but retains the normal as well as transverse component of gas velocity. The temperature, pressure, density, and velocities of gas profiles in the 2-D space and variation with time are assumed to be harmonic. By substituting the differentials of the assumed forms of these variables with respect to both space and time in the governing field equations, a set of three coupled linear 2-D field variation equations for pressure, axial and transverse velocities is obtained. The obtained reduced model is solved analytically using Fourier series approximations for the obtained field variable functions in the reduced model. The approximate solution is used to build a 2-D acoustic model for the exhaust gases emission which accounts for both attenuation and phase shift defining the propagation wave constant. Also the obtained approximate solution is used to determine the acoustics impedance of the DPF unit, soot loading, noise and vibration damping, in addition to calculating the noise reduction factors (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 a four- port model. 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.