A 2-D computational model was developed to describe the flow and filtration processes, in a honeycomb structured ceramic diesel particulate trap. This model describes the steady state trap loading, as well as the transient behavior of the flow and filtration processes. The theoretical model includes the effect of a copper fuel additive on trap loading and transient operation.
The convective terms were based on a 2-D analytical flow field solution derived from the conservation of mass and momentum equations. The filtration theory incorporated in the time dependent numerical code included the diffusion, inertia, and direct interception mechanisms. Based on a measured upstream particle size distribution, using the filtration theory, the downstream particle size distribution was calculated. The theoretical filtration efficiency, based on particle size distribution, agreed very well (within 1%) with experimental data for a number of different cases. The filtration model was used to predict the overall as well as individual (particulate layer and porous wall) filtration efficiency. These results indicated that the first 30-45 minutes of trap loading represent a transient state for the filtration characteristics of the trap. In the beginning, when the trap is clean, the filtration efficiency is based on the filtration characteristics of the clean wall. As particles are being deposited on the wall surface, as well as within the wall, the filtration characteristics change to the point where the particulate layer (or filter cake) becomes the dominant filtration medium.
While the mass model gives a bulk analysis of the particulate matter in the trap, the developed filtration model was used to determine the change in porous wall porosity and permeability as a function of particles retained in the wall, and on the wall surface. This analysis allows for a better description of where the particulate matter is deposited, which in turn is crucial for the discrete definition of the reaction (source) term in the energy equation.
A general semiheuristic power law approach for determining the particulate matter properties was developed. This relationship relates the particulate layer porosity to the amount of mass present in the trap and the trap pressure drop. Based on the calculated particulate layer porosity, analytical relationships can be used to determine the particulate layer permeability and density.
A general analytical solution for the trap pressure drop was developed. This analytical relationship can be used to determine the clean trap pressure drop. The loaded trap pressure drop can also be determined using this analytical relationship in conjunction with knowledge about the trapped particulate matter and its properties as given by the power law relationship for particulate layer porosity.
The parametric study indicated that the trap wall porosity, pore size, and wall thickness are the main parameters controlling the trap pressure drop and filtration processes.
The particulate layer permeability was determined using the Rumpf and Gupte's analytical relationship, which relates the permeability of a porous layer to its porosity and pore size. Results obtained with this model indicated that the particulate layer permeability follows a similar trend as its porosity, and, on average, is approximately 3 orders of magnitude lower than the permeability of a clean trap. This finding indicates that the pressure drop across the trap is extremely sensitive to the amount of particulate matter in the trap. The particulate layer porosity during steady state loading was on average 45-50%, but varied nonlinearly from 20% to approximately 65% with the copper fuel additive and from 10% to approximately 60% without the fuel additive. Based on these values, it was determined that the particulate layer density ranges from 1600 kg/m3 (initially, when the trap is clean) to 700 kg/m3 with the fuel additive, and from 1800 kg/m3 to 800 kg/m3 without the copper fuel additive.