On the application of Wiebe functions to simulate normal and knocking spark-ignition combustion

Employing a Wiebe function is a very convenient method to simulate fuel burning in internal combustion engines. The present study examines the various forms of the Wiebe functions and presents a methodology which optimises the Wiebe parameters for simultaneously best fit of the cumulative heat release and the rate of heat release histories. The accuracy of the results of the Wiebe function when solving for two parameters and for four parameters is compared; the former is done in closed form, whereas the latter is done by using an optimisation routine. The latter methodology was applied for the simulation of combustion in spark-ignition engines under normal and knocking conditions. For the knocking cycles, a linear weighted combination of two Wiebe functions, one enabling the modelling of the flame-propagation combustion and the other that of the autoignition combustion was found to give excellent results.