Analytical solutions for convection, diffusion and chemical reaction in Diesel Particulate Filters

Athanasios  Konstandopoulos, APT Lab, CPERI/CERTH

The goal of the present work is to derive analytical solutions for the problem of convection, diffusion and chemical reaction in wall-flow monoliths. The advantage of having an analytical solution instead of solving numerically is obvious as it not only brings full scale simulations of diesel particulate filters to the real time domain, but also enables efficient implementations on computationally limited ECUs for on-board management and control of emission control systems.  The presentation depicts 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.