The Control-Oriented Heat Release Rate Model for a Marine Dual-Fuel Engine under All the Operating Modes and Loads

Abstract

An accurate model plays an important role in control strategy development of smart ships. For the control-oriented engine models, calibration by experienced personnel is key to outputting high accuracy. However, the dual-fuel engine runs in liquid fuel mode, gas fuel mode, and fuel sharing mode. It is impossible to tune a single model or a set of parameters for the dual-fuel engine under all operating modes and loads. On the basis of our experience and practice, a Wiebe-based heat release rate model is used. To make the Wiebe model available for the dual-fuel engine, the Wiebe parameters are assumed to be linear functions. The combustion beginning angle is modeled as a function of fuel quantity in liquid fuel mode and as a look-up table in gas fuel mode for all loads. The combustion duration and the combustion distribution factor are modeled as a function of fuel quantity and engine revolution both in liquid fuel mode and in gas fuel mode. In fuel sharing mode, the heat release rate is modeled as a combination of the heat release rate models in liquid fuel mode and gas fuel mode. This model is called the SL model. For a further discussion, four types of combinations in fuel sharing mode are investigated. In addition, in liquid fuel mode and gas fuel mode, the combustion duration model and the combustion distribution factor model are replaced by the Woschni/Anisits model, which was specifically used in the diesel engine. This variation of model is called the WA model. To validate our hypothesis and models, the Wiebe parameters in liquid fuel mode and gas fuel mode are given, four types of combinations and two cases of comparisons in fuel sharing model are discussed, and the engine performance is checked and analysed. Results show that for the SL model, the average RMSE is 1.45% in the liquid fuel mode, 2.22% in the gas fuel mode, and 2.53% in the fuel sharing mode. For the WA model, the RMSE of the NOx is 9.79% in liquid fuel mode and 45.20% in gas fuel mode. Its maximum error reaches −65.54%. The proposed SL model is accurate and can generate Wiebe parameters that are better than the carefully tuned parameters. The WA model is not suitable for engine models that require NOx-emission-related parameters.