This paper presents a comparative study of the premixed conditional moment closure (CMC) model for modelling ignition of thermally stratified mixtures under homogeneous charge compression ignition (HCCI) conditions. For this purpose, the CMC model is applied to two sets of direct numerical simulations (DNSs) modelling ignition of lean n-heptane/air and iso-octane/air mixtures with various levels of thermal stratification. The results show excellent agreement for all n-heptane cases with thermal stratification of 15-60 K. However, an advanced ignition is predicted by the CMC model for the iso-octane case with thermal stratification of 60 K in comparison with the DNS data. Inspection of homogeneous ignition delay demonstrates that the ignition delay time fluctuations are much higher in the iso-octane cases compared with the n-heptane cases having same level of temperature inhomogeneities. This is because of the differing ignition responses to temperature between these two fuels. The observed discrepancies in the iso-octane case with T′ = 60 K are due to the dominance of deflagration mode of combustion resulting in large conditional fluctuations, which occurs in the iso-octane case and not the n-heptane case because the temperature dependence of ignition delay is stronger for iso-octane. To further investigate the reasons for the observed discrepancies, a transport equation for the conditional variance is derived for premixed combustion. Assessment of the conditional variance equation using the DNS data shows that correlations between dissipation and conditional fluctuation and correlations between reaction and conditional fluctuations are the dominant sources of conditional fluctuations.
- Conditional moment closure
- Thermal stratification