Higher-order conditional moment closure modelling of local extinction and reignition in turbulent combustion

Higher-order, conditional moment closure approaches to modelling local extinction and reignition in turbulent, non-premixed combustion are investigated. This is done by studying closure strategies of the conditional source term itself. Feasibility studies are done using direct numerical simulation (DNS) experiments which exhibit varying degrees of local extinction. The higher-order conditional moments are taken directly from the DNS experiments as opposed to solving modelled transport equations for them. Results show that with moderate levels of extinction, the conditional probability density function (pdf) of the reduced temperature is unimodal, but skewed, and at least third-order terms in a series expansion of the nonlinear chemical source term conditional on the mixture fraction are required to predict the conditional means. With higher levels of local extinction, the conditional pdf shapes can be bimodal and third-order closure breaks-down. The success of a presumed beta pdf shape for conserved scalars is well known. A beta probability distribution for the conditional reactive scalar cannot describe either the unimodal or bimodal pdf shapes which result from the local extinction and reignition events. However, predictions of the conditional means are excellent with the beta pdf model incorporated into a conditional moment closure modelling framework. The modelling results show little sensitivity to the conditional variances.