Semi-empirical estimation model of in-cylinder pressure for compression ignition engines

There have been significant efforts in recent years to comply with automotive emission regulations. To resolve the issue, researchers have strived to reduce the emissions through combustion control. The heat release rate, or in-cylinder pressure information, is necessary to model engine-out emissions, and can also be used to optimize efficiency and emissions by controlling combustion and estimating torque for torque-based engine dynamic control. Piezoelectric pressure sensors are widely used. However, because of cost and durability issues, there have been studies which estimate the in-cylinder pressure using data available only from the engine control unit to reduce engine costs. Therefore, in this study, in-cylinder pressure was predicted, without additional pressure sensors, in light-duty diesel engines. A variable polytropic exponent model was first adopted during the compression stroke, assuming a polytropic process. A Wiebe function was then applied for describing cumulative heat release rate during the combustion phase. Using the in-cylinder pressure model, it was possible to calculate combustion-related parameters which are frequently used such as ignition delay, combustion duration, peaked pressure, and MFB50 (mass fraction burned: timing when 50% of the fuel is burned) without pressure sensors. Notwithstanding the simplification of the model which is targeting real-time applications, the model can predict the in-cylinder pressure at steady-state conditions. The pressure at the end of compression stroke, at start of main combustion timing, and when it has a peaked value by the main combustion were estimated with accuracy of R² 0.996, 0.993, and 0.956, respectively, in test engine. The model was also validated against a second engine. This study can contribute to emission models that need to calculate in-cylinder temperature using pressure data, and other studies to establish engine control strategies, including optimization through combustion control and torque prediction, which can be applied to engine dynamic control.