‘Hybrid’ multiple mapping conditioning on passive and reactive scalars

A two-dimensional, hybridized multiple mapping conditioning (MMC) model is used to model local extinction and reignition phenomena in homogeneous, isotropic decaying turbulence. The equations are solved in a prescribed, jointly Gaussian reference space with stochastic reference variables emulating the fluctuations of the mixture fraction and normalized sensible enthalpy conditioning variables. In “pure” MMC the joint PDF of the conditioning scalars is a solved quantity. Here we use a hybrid method where the time evolution of the marginal PDF for mixture fraction is solved and a presumed β-PDF is used for the conditional distribution of the normalized sensible enthalpy. Model results are compared with DNS in three flame cases with varying levels of local extinction, up to global extinction. Results for principal chemical species are in very good agreement with DNS and those for intermediate species are also satisfactory. The doubly conditioned MMC yields results which are considerably more accurate than those by modeling with conditioning on mixture fraction alone. A transformation of the Gaussian reference space casts the MMC model in the same form as conditional moment closure (CMC). The great advantage is that the MMC model contains the doubly conditioned scalar dissipation terms in closed form and these are generally found to be in good agreement with the DNS data.