Correlations for Wiebe function parameters for combustion simulation in two-stroke small engines

Combustion simulation in two-stroke engines becomes necessary not only for engine performance prediction but also for scavenge evaluation, since in-cylinder pressure and temperature are highly influenced by combustion process evolution. Combustion simulation by using a Wiebe function is appropriate to be included in a 1D engine code for providing design criteria with fast and accurate calculations; the main drawback is the determination of the four Wiebe parameters needed to build up the in-cylinder heat release. This paper deals with a detailed methodology for heat release determination in two-stroke engines under a wide range of running conditions; obtained empirical data will serve for building ad-hoc Wiebe functions, whose four parameters will be finally correlated with engine related parameters derived from 1D simulations. Two different engines, with three exhaust systems each, varying engine speed and spark-ignition timing were used to obtain correlations far from particular situations. A multiple regression analysis stated that charge density, residual gas fraction, spark timing and mean piston speed were the significant engine parameters that influence on Wiebe parameters. Finally, two scenarios were considered regarding Wiebe parameters: (a) specific correlations different for each engine gave coefficient of multiple determination values higher than 98% when predicting indicated mean effective pressure, (b) a global correlation used for both engines provided R2 values of 93% in the 50 cc and 91% in the 125 cc engine.