Lumped Approach for Flow-Through and Wall-Flow Monolithic Reactors Modelling for Real-Time Automotive Applications

The increasingly restrictive legislation on pollutant emissions is involving new homologation procedures driven to be representative of real driving emissions. This context demands an update of the modelling tools leading to an accurate assessment of the engine and aftertreatment systems performance at the same time as these complex systems are understood as a single element. In addition, virtual engine models must retain the accuracy while reducing the computational effort to get closer to real-time computation. It makes them useful for pre-design and calibration but also potentially applicable to on-board diagnostics purposes. This paper responds to these requirements presenting a lumped modelling approach for the simulation of aftertreatment systems. The basic principles of operation of flow-through and wall-flow monoliths are covered leading the focus to the modelling of gaseous emissions conversion efficiency and particulate matter abatement, i.e. filtration and regeneration processes. The model concept is completed with the solution of pressure drop and heat transfer processes. The lumped approach hypotheses and the solution of the governing equations for every sub-model are detailed. While inertial pressure drop contributions are computed from the characteristic pressure drop coefficient, the porous medium effects in wall-flow monoliths are considered separately. Heat transfer sub-model applies a nodal approach to account for heat exchange and thermal inertia of the monolith substrate and the external canning. In wall-flow monoliths, the filtration and porous media properties are computed as a function of soot load applying a spherical packed bed approach. The soot oxidation mechanism including adsorption reactant phase is presented. Concerning gaseous emissions, the general scheme to solve the chemical species transport in the bulk gas and washcoat regions is also described. In particular, it is finally applied to the modelling of CO and HC abatement in a DOC and DPF brick. The model calibration steps against a set of steady-state in-engine experiments allowing separate certain phenomena are discussed. As a final step, the model performance is assessed against a transient test during which all modelled processes are taking place simultaneously under highly dynamic driving conditions. This test is simulated imposing different integration time-steps to demonstrate the model’s potential for real-time applications.