Conditional moment closure for SCCI combustion

Abstract

Homogeneous charge compression ignition (HCCI) and stratified charge compression ignition (SCCI) engines potentially offer high fuel economy and low emissions. Practical problems need to be overcome, however, and several of them are affected by or may be alleviated/controlled by stratification of the charge, whether deliberate mixture-stratification by direct injection, or thermal stratification resulting from wall-heat transfer. This thesis therefore seeks to develop and evaluate a computational model of the combustion process in HCCI and SCCI engines that is capable of simulating the effects of charge stratification. The basis of the modelling is an approach known as conditional moment closure (CMC), originally developed for nonpremixed jet flames, which reduces errors associated with closure of chemical source terms by conditioning them on a variable upon which they principally depend. This thesis builds on previous work to adapt CMC to HCCI and SCCI engines which considered thermally stratified ignitions in an environment free of walls. In two important steps towards a complete CMC model of an SCCI engine, the present thesis considers first mixture-stratified ignition and second thermally stratified ignitions in the presence of walls. In the former case the baseline CMC model considers mixture fraction as the conditioning variable, while in the latter it considers total enthalpy. Extensions of these models by considering second order closure, double conditioning, and conditioning on reacting scalars are also considered. Two sets of two-dimensional direct numerical simulation (DNS) are employed to evaluate performance of the CMC models. The first DNS data-set simulate ignitions in SCCI-like thermochemical conditions with compositionally stratified n-heptane / air mixtures in a constant volume representing the bulk gas at top dead centre (TDC) of an SCCI engine. The second DNS data-set considers the effect of wall heat transfer on auto-ignition of thermally stratified hydrogen/air mixtures in a two-dimensional channel representing the TDC of an HCCI engine. The first DNS data-set is parametrised by fluctuations in mixture composition and temperature, whereas the second set is parametrised by temperature fluctuations. Using the first DNS data-set, and the mixture-fraction CMC model, a posteriori tests of the model, which is implemented in an open-source computational fluid dynamics (CFD) package known as OpenFOAM R , reveals an excellent agreement between the CFD-CMC solver and the DNS data-set for the cases with low levels of stratification, whereas deviations from the DNS are observed in cases which exhibit high level of stratifications. A subsequent a priori analysis reveals that the reason for disagreement is failure of the first-order closure due to the high level of conditional fluctuations. A second-order closure is also shown to fail to improve the results and it is only double conditioning that provides a satisfactory closure for the reaction rates. Using the second DNS data-set modelling ignition in a channel with wall heat transfer, the entrainment of fluid from the cold near-wall region into the bulk gas is shown to support temperature fluctuations in the bulk, thus leading to more highly stratified conditions relative to a corresponding case without walls. The CMC equation itself is first examined in a priori tests with total enthalpy as the conditioning variable. The error committed by the primary closure hypothesis is shown to be small, as is the error induced by neglecting correlations of the source term of the conditioning scalar with species mass fractions. The main error needing addressing is shown to be the first-order closure of reaction rates. An a priori analysis is used to show that first-order closure fails for high levels of stratification for all species. At lower stratification levels, errors are acceptable for major species but large for radical species. However, unlike n-heptane cases, here the secondorder closure improves the CMC predictions, but only for major species. Switching to sensible enthalpy as the conditioning variable for a first-order closure, yields similar results to second-order approach with total enthalpy. The implications of using total enthalpy or sensible enthalpy as conditioning variable are discussed to provide future directions for a posteriori implementation of the CMC model.