In the last decade, gaseous fuels, such as liquefied petroleum gas (LPG) and natural gas (NG), widely spread in many countries, thanks to their prerogative of low cost and reduced environmental impact. Hence, bi-fuel engines, which allow to run either with gasoline or with gas (LPG or NG), became very popular. Moreover, as experimentally demonstrated by the authors in the previous works, these engines may also be fueled by a mixture of gasoline and gas, which, due to the high knock resistance of gas, allow to use stoichiometric mixtures also at full load, thus drastically improving engine efficiency and pollutant emissions with respect to pure gasoline operation without noticeable power loss. This third operation mode, called double fuel combustion, can be easily introduced in series production engine, since a simple electronic control unit (ECU) programing is required. The introduction into series production would require the availability of proper models for thermodynamic simulations, nowadays widely adopted to reduce research and development efforts and costs. To this purpose, the authors developed a quite original knock onset prediction model for knock-safe performances optimization of engines fueled by propane, gasoline, and their mixtures. The ignition delay model has been properly modified to account for the negative temperature coefficient (NTC) behavior exhibited by many hydrocarbon fuels such as gasoline and propane. The model parameters have been tuned by means of a considerable amount of light knocking in-cylinder pressure cycles acquired on a modified cooperative fuel research (CFR) engine, fueled by gasoline–propane mixtures. The adoption of many different compression ratios (CRs), inlet mixture temperatures, spark advances (SAs), and fuel mixture compositions allowed to use a very differentiated set of pressure and temperature curve, which gives the calibrated model a general validity for using different kinds of engines, i.e., naturally aspirated or supercharged. As a result, the model features a maximum knock onset prediction error around four crank angle degrees (CAD) and a mean absolute error always lower than 1 CAD, which is a negligible quantity from an engine control standpoint.

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