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.

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This article presents a control-oriented two-zone reaction-based zero-dimensional model to accurately describe the combustion process of a spark-ignited engine for real-time simulations, and the developed model will be used for model-based control design and validation. A two-zone modeling approach is adopted, where the combustion chamber is divided into the burned (reaction) and unburned (pre-mixed) zones. The mixture thermodynamic properties and individual chemical species in two zones are taken into account in the modeling process. Instead of using the conventional pre-determined Wiebe-based combustion model, a two-step chemical reaction model is utilized to predict the combustion process along with important thermodynamic parameters such as the mass-fraction-burned, in-cylinder pressure, temperatures, and individual species mass changes in both zones. Sensitivities of model parameters are analyzed during the model calibration process. As a result, one set of calibration parameters is used to predict combustion characteristics over all engine operating conditions studied in this article, which is the major advantage of the proposed method. Also, the proposed modeling approach is capable of modeling the combustion process under different air-to-fuel ratios, ignition timings, and exhaust-gas-recirculation rates for real-time simulations. As the by-product of the model, engine knock can also be predicted based on the Arrhenius integral in the unburned zone, which is valuable for model-based knock control. The proposed combustion model is intensively validated using the experimental data with a peak relative prediction error of 6.2% for the in-cylinder pressure.

As requirements for continuously improving internal combustion engine fuel economy with satisfactory emissions, model-based control strategies are often used to optimize the combustion process. To apply advanced control techniques for closed-loop engine combustion control, control-oriented engine combustion models are necessary and they are physics-based, accurate enough for model-based control, computationally low cost, and capable of real-time simulations. In addition, control-oriented combustion model with adequate fidelity may need to adapt to physical system and environment changes over time to maintain model-based control performance, such as model-reference (guided) control, where the control-oriented combustion model runs in real-time to generate an error signal between physical system and reference-model output for feedback control. This paper provides a review of existing control-oriented engine combustion models, along with their associated applications. Three main groups of control-oriented combustion models are reviewed from simple to sophisticated physics-based dynamic models, including mean-value, Wiebe function-based, and reaction-based models. The fundamental principle of each model group is reviewed briefly and its applications are also addressed. At the macro level, a control-oriented engine model can be used for crank angle-based and/or cycle-based control. As the engine control hardware performance continuous improving with reduced cost, model-reference (guided) combustion control shall become reality since now it is feasible to run a physics-based control-oriented engine combustion model inside an engine control module. On the other hand, each model group, even for the simple mean-value model, has its own applicable scenarios.