Browse Publications Technical Papers 2002-01-1019
2002-03-04

# Modeling and Numerical Simulation of Diesel Particulate Trap Performance During Loading and Regeneration 2002-01-1019

A 2-dimensional numerical model (MTU-FILTER) for a single channel of a honeycomb ceramic diesel particulate trap has been developed. The mathematical modeling of the filtration, flow, heat transfer and regeneration behavior of the particulate trap is described. Numerical results for the pressure drop and particulate mass were compared with existing experimental results. Parametric studies of the diesel particulate trap were carried out. The effects of trap size and inlet temperature on the trap performance are studied using the trap model.
An approximate 2-dimensional analytical solution to the simplified Navier-Stokes equations was used to calculate the velocity field of the exhaust flow in the inlet and outlet channels. Assuming a similarity velocity profile in the channels, the 2-dimensional Navier-Stokes equations are approximated by 1-dimenisonal conservation equations, which is similar to those first developed by Bissett. The 1-dimensional conservation equations are then solved by the approach of Konstandopoulos and Johnson. In order to validate the analytical solution, pressure drop across the porous wall is compared with that of 1-dimensional solution and shows good agreement.
The filtration efficiency of the porous wall is calculated from the collection efficiency, and the filtration efficiency of the particulate matter layer is calculated from the so-called percolation factor. A unit cell collector model is used to update the porosity and permeability of the porous wall. A pressure drop model derived from the previous flow field solution is used to determine the transient pressure drop of the particulate trap.
The temperature field is found by solving the energy equation numerically. A global reaction mechanism is used for the oxidation of the particulate matter. The reaction kinetics for both catalyzed and uncatalyzed traps is considered, and it is described by an Arrhenius equation. The mass conservation of particulate matter is added to the energy equation as a source term. The energy equation is solved using an Alternate-Direction-Implicit (ADI) scheme coupled with upwind scheme.
This numerical model is capable of interacting with time varying input data, such as transient exhaust mass flow rate, exhaust inlet temperature and particulate concentration. Numerical results for the pressure drop, particulate mass and trap temperature during both loading and regeneration processes were compared with existing experimental results and are in good agreement. A number of filtration constants are derived from the model and these filtration constants are consistent for the same type of trap. Parametric studies of the diesel particulate trap using these filtration constants were carried out. The effects of trap size and inlet temperature on the trap performance are presented and analyzed. This model can provide insights to the physical processes in the diesel particulate trap and can be used as an engineering tool for trap design.

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