Combining the Classical and Lumped Diesel Particulate Filter Models

The growing presence of Spark Ignition Direct Injection (SIDI) engines along with the prevalence of direct injected Compression Ignition (CI) engines results in the requirement of Particulate Matter (PM) exhaust abatement. This occurs through the implementation of Gasoline Particulate Filters (GPFs) and Diesel Particulate Filters (DPFs). Modeling of GPFs and DPFs are analogous because of the similar flow patterns and wall flow PM capture methodology. Conventional modeling techniques include a two-channel (inlet/outlet) formulation that is applicable up to three-dimensions. However, the numerical stiffness that results from the need to couple the solution of these channels in compressible flow can result in relatively long run times. Previously, the author presented a lumped DPF model using dynamically incompressible flow intended for an Engine Control Unit (ECU) in order to generate a model that runs faster than real time using a high-level programming language. Building on the favorable outcomes of temperature evolution from this prior effort, this work enhances the model to predict compressible flow gas dynamics in order to match the evolution of pressure drop. Another enhancement is the inclusion of deep bed filtration within the wall, and the transition to the cake layer. Results show comparable temperature profiles with the dynamically incompressible model with a pressure drop that follows appropriately by linking through the ideal gas model. However, solving chemical species as an independent equation separate from compressible flow still deviates significantly from the classical two-channel approach.