Revisiting the Single Equation Pressure Drop Model for Particulate Filters

Particulate filters (PF) are a highly effective after-treatment device that reduces particulate matter emissions, a rising environmental concern in the automotive industry. However, accumulation of solid particles during the PF filtration process increases engine backpressure considerably, which can have a negative impact on engine efficiency, acoustics, and gaseous emissions. In this area, an accurate pressure drop model helps to better understand the effect of accumulated solid particles in the PF on engine backpressure, aiding in design and regeneration considerations without physical testing. These effects are further improved on board the vehicle using a single equation pressure drop model with a relatively low computational cost. This article presents a thorough history of PF pressure drop models and their advancements. Specifically, this review highlights that numerous authors have derived single pressure drop equations for dynamically incompressible flow and several have formulated models for compressible flow. Then, this effort builds on this history by presenting a revised single equation PF pressure model derived for pseudo-compressible flow. This updated model improves the predictions under varying PF temperature profiles when compared to dynamically incompressible flow. As a result, computation of the pressure drop for non-isothermal flow is now possible via a single algebraic equation, reducing computational costs in comparison to the previous compressible numerical approaches.