Development and validation of double and single Wiebe function for multi-injection mode Diesel engine combustion modelling for hardware-in-the-loop applications

The improvement of Diesel engine performances in terms of fuel consumption and pollutant emissions has a huge impact on management system and diagnostic procedure. Validation and testing of engine performances can benefit from the use of theoretical models, for the reduction of development time and costs. Hardware in the Loop (HiL) test bench is a suitable way to achieve these objectives. However, the increasing complexity of management systems rises challenges for the development of very reduced physical models able to run in real time applications. This paper presents an extension of a previously developed phenomenological Diesel combustion model suitable for real time applications on a HiL test bench. In the earlier study, the modelling efforts have been targeted at high engine speeds with a very short computational time window, and where the engine operates with single injection. In the present work, a modelling of in-cylinder processes at low and medium engine speeds with multi-injection is performed. In order to reach an adequate computational time, the combustion progress during the pilot and main injection periods has been treated through a double Wiebe function, while the post combustion period has required a single Wiebe function. This paper describes the basic system models and their calibration and validation against experimental data. The use of the developed correlations of Wiebe coefficients and ignition delay times for each combustion phase, included in the in-cylinder crank angle global model, is applied for the prediction of ignition delay time and in-cylinder pressure profiles at varying engine operations. As discussed in this paper, the behaviour of the simulated in-cylinder pressure confirms the good accuracy of the developed sub-models for ignition delay and of the combustion process description with double Wiebe approach. A lower but acceptable accuracy with single Wiebe function has been observed for post-injection combustion process.

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