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

Abstract

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.

Real-time NOx estimation in light duty diesel engine with in-cylinder pressure prediction

“…This section describes the developed in-cylinder pressure model, which is divided into three steps: a compression process, pilot combustion process, and main combustion process. 21,22 These processes are presented in Figure 3. As shown in the figure, the prediction of the in-cylinder pressure was conducted through three steps.…”

“…The polytropic index (n) plays an important role when estimating the pressure during the compression process, and a variable polytropic index was applied in this study, reflecting various engine operating conditions to predict a more accurate in-cylinder pressure at the end of the compression. 21,22 The polytropic index was fitted as a function of in-cylinder gas composition and intake manifold temperature. 32…”

“…20 In this paper, the Wiebe function was also adopted for incylinder prediction. 21,22 Over the years, the authors have tried to estimate the engine-out NOx, and engine-out NO and NO 2 models have been established at steady-state conditions. 23,24 The NOx prediction models 23,24 proposed by the authors are physical-based models that simplified the chemical and physical relations.…”

“…26 Therefore, we also developed an in-cylinder pressure model at steady-state conditions. 21,22 Finally, study in this paper tried to estimate engine-out NOx in real time using only ECU data without a pressure sensor. Based on an NO prediction model, 24,27 NOx could be estimated with the additional NO 2 model.…”

“…23 The NO 2 model consists of both formation and decomposition mechanisms and considers the dominant pathways and reactions for each mechanism. The pressure estimation procedure could be conducted in three steps, 21,22 where the first step is assumed to be a polytropic process until there is a combustion reaction in the chamber and the second and third steps calculate the in-cylinder pressure during the pilot and main combustion periods, each using the Wiebe function. This pressure estimation was applied to the NO and NO 2 models, which require incylinder pressure information.…”