Development of a Particulate Filter Model for the Prediction of Backpressure: Improved Momentum Balance and Entrance and Exit Effect Equations

The development of a one-dimensional model for the prediction of backpressure across a gasoline or diesel particulate filter (PF) is presented. The model makes two innovations: Firstly, the term for momentum convection in the gas momentum balance equations includes the loss (or gain) of axial momentum in the direction perpendicular to the channels; neglecting this results in the momentum convection term being too large. Secondly, equations for the pressure change due to the abrupt contraction at the PF entrance and for abrupt expansion at the exit are derived which take into account the fact that the velocity profile across the channels is not flat; often workers have used equations appropriate for high Reynolds numbers which assume flat velocity profiles. The model has been calibrated/tested against cold flow data for more than one length of PF. The use of more than one length allows along-filter pressure losses to be separated from entrance and exit effects. A simulation study has been carried out to investigate the relative magnitude of the different contributions to backpressure, viz. across-wall losses (Darcy and Forchheimer), along-channel losses (viscous and inertial) and entrance and exit effects. Finally, other workers have recently published a PF model in which the effect of the wall Reynolds number on the friction factors, Nusselt numbers and momentum transport has been included. The influence of these modifications on the backpressure and outlet temperature prediction has been investigated and found not to be significant over the range of conditions tested.