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 $\left(\mathrm{\Delta }\beta \right)$ are examined. The multifractal complexity is characterized by the singularity spectrum of the heat release time series in terms of the Hölder 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 $\mathrm{\Delta }\beta =30°$ followed in order by $\mathrm{\Delta }\beta =15°$ and $5°$ . 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, $\mathrm{\Delta }\beta =5°$ , 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 $\mathrm{\Delta }\beta =15°$ and $30°$ , 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.

We analyze the experimental time series of internal pressure in a four cylinder spark ignition engine. In our experiment, performed for different spark advance angles, apart from the usual cyclic changes of engine pressure we observed additional oscillations. These oscillations are with longer time scales ranging from one to several hundred engine cycles depending on engine working conditions. Based on the pressure time dependence we have calculated the heat released per combustion cycle. Using the time series of heat release to calculate the correlation coarse-grained entropy we estimated the noise level for internal combustion process. Our results show that for a larger spark advance angle the system is more deterministic.