Conditional moment closure modelling for HCCI with temperature inhomogeneities

This paper presents an approach for modelling combustion in homogeneous charge compression ignition (HCCI) conditions based on the first order conditional moment closure (CMC) method. The model is implemented into the open source C++ computational fluid dynamic (CFD) code known as OpenFOAM. Direct numerical simulations (DNSs) are used to evaluate the performance of the CFD-CMC solver. In the two-dimensional (2D) DNS cases, ignition of a lean n-heptane/air mixture with thermal inhomogeneities is simulated for nine cases, with two different mean temperatures and several different levels of thermal stratification. Results from the CFD-CMC solver are in excellent agreement with the DNS for cases which exhibit a spontaneous sequential ignition mode of combustion whereas for the cases in which a mixed mode of deflagration and spontaneous ignition exists, the CMC underpredicts the ignition delay. Further investigation using the DNS data demonstrates that this discrepancy is primarily attributed to the first order closure assumption. Conditional fluctuations are found to be more significant in the case with deflagrations. Further analysis of the DNS shows that scalar dissipation fluctuations are the cause of conditional fluctuations.