Second-order conditional moment closure modeling of local extinction and reignition in turbulent non-premixed hydrocarbon flames

A second-order conditional moment closure (CMC) model is applied to turbulent non-premixed hydrocarbon flames with significant local extinction and reignition. Combustion of hydrocarbon fuel is described by a systematically reduced two-step mechanism. Second-order correction is made to the conditional mean reaction rates by assumed probability density function (PDF) method and Taylor expansion method. In the assumed PDF method, the conditional joint PDF of the reaction progress variables is assumed to be the maximum entropy PDF. Second-order CMC predictions show good agreement with direct numerical simulation (DNS) data for all test cases, while first-order CMC tends to overpredict the intermediate species and reaction of fuel. Results show that the intermediate species is more sensitive to accuracy of the predicted reaction rates than the major species. The predicted conditional variances and covariances of the reaction progress variables turn out to be in good agreement with DNS results during an extinction process. The onset of reignition is predicted to occur too early due to a linear fit of chemical reaction rates in the Taylor expansion method. Although the assumed PDF method generally gives better results than the Taylor expansion method, the latter may be a promising, computationally inexpensive approach for engineering problems with more complex chemistry.