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This paper describes an improved mathematical model to study the emission conversion effectiveness of a three-way catalytic converter, which employed detailed chemical reaction mechanism. The model also accounts for adsorption/release of oxygen in the catalyst monolith under non-stoichiometric A/F conditions. A commercial CFD code FLUENT was utilized to solve the governing equations for flow and pressure drop and to simulate the transient process in a three-way catalytic converter in a multi-dimensional manner. A comparison between simulation results and experimental data for a three-way catalyst was conducted and a good agreement was observed. Based on the improved model, some geometric parameters were studied for an elliptic monolith catalyst, which are widely used in today's converter systems because of its advantages in packaging.