Computationally Fast Implementations of Convection, Diffusion and Chemical Reaction Phenomena in Diesel Particulate Filters

In the present work we derive analytical solutions for the problem of convection, diffusion and chemical reaction in wall-flow monoliths. The advantage of having analytical instead of numerical treatments is clear as the analytical solutions not only can be exploited to bring full scale simulations of diesel particulate filters to the real time domain, but also they enable efficient implementations on computationally limited engine control units (ECUs) for on-board management and control of emission control systems. The presentation describes the mathematical problem formulation, the governing dimensionless parameters and the corresponding assumptions. Then the analytical solution is derived and several asymptotic (for limiting values of the parameters) and approximating solutions are developed, corresponding to different physical situations. Reactant distributions in the filter are presented and discussed for several values of the parameters. The conclusion is that the classic single channel model for DPF simulation can for all practical conditions accommodate diffusive phenomena with no added computational cost and without significantly altering the structure of existing code implementations.