0D Modelling: a Promising Means for After-treatment Issues in Modern Automotive Applications

Abstract

For modern automotive applications, after-treatment systems have become essential to respect the new emission standards. All the automotive world's attention is focused on catalysis systems because they seem to be one of the best ways to reach the future standards. As a result, after-treatment issues are more and more significant in the cost of the whole engine and vehicle development process. For example, the Euro 6 Diesel after-treatment line might for some applications be composed of nothing less than five distinct after-treatment bricks. This complex architecture implies developing advanced tools to help the exhaust line conception and also the design of associated control strategies. The present paper demonstrates that zero-dimensional (0D) simulation can be a relevant approach to develop exhaust line simulators compatible with accuracy and CPU time required performances. This paper proposes an original zero-dimensional model of the monolith. This approach is based on resistive and capacitive elements according to the bond graph theory [Karnopp D.C., Margolis D.L., Rosenberg R.C. (1990) Systems dynamics: a unified approach, Second Edition, John Wiley & Sons, New-York]. The described dynamic model takes into account the pneumatic flow and the thermal behaviour of the monolith. Models of several catalysts are built by plugging this monolith model with some well-known simplified chemical reaction schemes [Koltsakis G.C., Konstandinis P.A., Stamatelos A.M. (1997) Development and application range of mathematical models for 3-way catalytic converters, Appl. Catal. B: Environ. 12, 161-191]. Splitting a monolith model into several elementary zero-dimensional blocks in series allows having a good representation of the specific internal dynamic of one catalyst and to access some local information as in conventional well-known one-dimensional models with low CPU time cost [Koltsakis G.C., Konstandinis P.A., Stamatelos A.M. (1997) Development and application range of mathematical models for 3-way catalytic converters, Appl. Catal. B: Environ. 12, 161-191]. Such an approach can be used as a way to get a phenomenological understanding of the catalytic system, which is known to be a very complex multi-physical system. It also represents a relevant simulation tool for the definition of after-treatment line architecture and pollutant emission control. The approach's potential to deal with all modern after-treatment bodies is illustrated by results for a Three-Way Catalyst (3WC), a Diesel Oxidation Catalyst (DOC), a Lean NOx Trap (LNT) system, a Selective Catalyst Reduction of NOx (SCR) system and a Diesel Particulate Filter (DPF). This ability to give, with a good compromise between accuracy/low CPU time cost, some interesting information to help the development of more and more complex exhaust system makes zero-dimensional simulation relevant.