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It has been shown that lean burn is effective for improving the thermal efficiency of gasoline SI engines. This happens because the reduction of heat loss by decrease of flame temperature. On the other hand, the fuel dilution of the premixed gas makes the combustion speed low, and cycle-to-cycle variations of combustion are increased by excessive dilution, it is difficult to increase the thermal efficiency of the gasoline SI engine. Influence of ignition by spark discharge is considered as a factor of combustion variation, and it is necessary to understand the effects of spark discharge characteristics on the lean combustion process. Spark discharge in the SI engines supplies energy to the premixed-gas via a discharge channel in the spark plug gap which ignites the premixed-gas. The discharge channel is elongated by in-cylinder gas flow and its behavior varies in each cycles.

A simulation study was conducted to examine the transition from SI combustion to HCCI combustion in a two-stroke free piston engine fuelled with propane. Operation of the free piston engine was simulated based on the combination of three mathematical models including a dynamic model, a linear alternator model and a thermodynamic model. The dynamic model included an analysis of the piston motion, based on Newton's second law. The linear alternator model included an analysis of electromagnetic force, which was considered to be a resistance force for the piston motion. The thermodynamic model was used to analysis thermodynamic processes in the engine cycle, including scavenging, compression, combustion, and expansion processes. Therein, the scavenging process was assumed to be a perfect process. These mathematical models were combined and solved by a program written in Fortran.