Multifractal and statistical analyses of heat release fluctuations in a spark ignition engine

Using multifractal and statistical analyses, we have investigated the complex dynamics of cycle-to-cycle heat release variations in a spark ignition engine. Three different values of the spark advance angle (Delta beta) are examined. The multifractal complexity is characterized by the singularity spectrum of the heat release time series in terms of the Holder exponent. The broadness of the singularity spectrum gives a measure of the degree of mutifractality or complexity of the time series. The broader the spectrum, the richer and more complex is the structure with a higher degree of multifractality. Using this broadness measure, the complexity in heat release variations is compared for the three spark advance angles (SAAs). Our results reveal that the heat release data are most complex for Delta beta=30 degrees followed in order by Delta beta=15 degrees and 5 degrees. In other words, the complexity increases with increasing SAA. In addition, we found that for all the SAAs considered, the heat release fluctuations behave like an antipersistent or a negatively correlated process, becoming more antipersistent with decreasing SAA. We have also performed a statistical analysis of the heat release variations by calculating the kurtosis of their probability density functions (pdfs). It is found that for the smallest SAA considered, Delta beta=5 degrees, the pdf is nearly Gaussian with a kurtosis of 3.42. As the value of the SAA increases, the pdf deviates from a Gaussian distribution and tends to be more peaked with larger values of kurtosis. In particular, the kurtosis has values of 3.94 and 6.69, for Delta beta=15 degrees and 30 degrees, respectively. A non-Gaussian density function with kurtosis in excess of 3 is indicative of intermittency. A larger value of kurtosis implies a higher degree of intermittency.