Multi-zone reaction-based modeling of combustion for multiple-injection diesel engines

As the requirements for performance and restrictions on emissions become stringent, diesel engines are equipped with advanced air, fuel, exhaust gas recirculation techniques, and associated control strategies, making them incredibly complex systems. To enable model-based engine control, control-oriented combustion models, including Wiebe-based and single-zone reaction-based models, have been developed to predict engine burn rate or in-cylinder pressure. Despite model simplicity, they are not suitable for engines operating outside the normal range because of the large error beyond calibrated region with extremely high calibration effort. The purpose of this article is to obtain a parametric understanding of diesel combustion by developing a physics-based model which can predict the combustion metrics, such as in-cylinder pressure, burn rate, and indicated mean effective pressure accurately, over a wide range of operating conditions, especially with multiple injections. In the proposed model, it is assumed that engine cylinder is divided into three zones: a fuel zone, a reaction zone, and an unmixed zone. The formulation of reaction and unmixed zones is based on the reaction-based modeling methodology, where the interaction between them is governed by Fick's law of diffusion. The fuel zone is formulated as a virtual zone, which only accounts for mass and heat transfer associated with fuel injection and evaporation. The model is validated using test data under different speed and load conditions, with multiple injections and exhaust gas recirculation rates. It is shown that the multi-zone model outperformed the single-zone model in in-cylinder pressure prediction and calibration effort with a mild penalty in computational time.