Multi-scale non-uniform hierarchical filtering model based on fractal theory

Gasoline particulate filters (GPF) are widely used due to their superior environmental benefits, but its trapping efficiency is affected by many factors. We established a multi-scale non-uniform hierarchical filtering model (MNHF) based on the fractal theory to accurately analyze the dynamic changes of trapping efficiency during GPF operation. The multi-scale characteristics of the filter wall about trap diameter and pore size are presented. Additionally, filter theory and Brownian kinematics are used to precisely predict particle motion. The study focuses on the dynamic change of trapping efficiency of MNHF in different particle size ranges. The results indicate the following: By comparing the numerical simulation results of the model with experimental data, the maximum relative error range is found to be within 0.7%. The MNHF model accurately predicts the change in trapping performance at different times when particles move in the trap. The trapping efficiency of the upper layer of the single-layer trap is higher than that of the lower layer based on the particles' moving distance in unit time, and the trapping efficiency of the next layer is reduced by up to 29.34% compared to that of the upper layer. Additionally, it provides a more accurate simulation of the trapping efficiency for particles with sizes ranging from 0.01 μm to 0.5 μm under conditions of low wall flow velocity.