Simulating Area Conservation and the Gas-Wall Interface for One-Dimensional Based Diesel Particulate Filter Models

Abstract

Researchers have been using one-dimensional based models of diesel particulate filters (DPFs) for over two decades with good success in comparison to measured experimental data. Recent efforts in literature have expanded the classical model to account for the effects of varying soot layer thickness on the flow area of the gases. However, some discrepancies exist with respect to this formulation and the physical phenomena modeled in the channel equations. In addition, there is still some discussion regarding the calculation of the gas temperature within the soot and wall layers. As a result, this paper presents a model to discuss these different phenomena to remove or validate previous assumptions. In specific, formulation of the flow equations in area-conserved format (or quasi-one-dimensional) allows the model to account for the changes in the gaseous area as a function of soot loading. In addition, imposing thermodynamic equilibrium at the interface of the channels and wall layers allows the model to capture the thermal entrance lengths. These tasks were undertaken to illustrate whether or not the results justify the effort is worthwhile and this additional complexity needs to be incorporated within the model. By utilizing linear density interpolation in the wall to increase the computational efficiency of the code, it was determined that the classical model assumptions of neglecting soot thickness and gas temperature in the wall are valid within the range of typical DPF applications.