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Abstract: For the calculation of nonpremixed turbulent flames with thin reaction zones the joint probability density function (PDF) of the mixture fraction and its dissipation rate plays an important role. The corresponding PDF transport equation involves a mixing model for the closure of the molecular mixing term. Here, the parameterized scalar profile (PSP) mixing model is extended to provide the required joint statistics. Model predictions are validated using direct numerical simulation (DNS) data of a passive scalar mixing in a statistically homogeneous turbulent flow. Comparisons between the DNS and the model predictions are provided, which involve different initial scalar-field lengthscales. [Copyright &y& Elsevier]

Abstract: Probability density function (PDF) methods are especially suited for turbulent combustion calculations, since the averaging of the reaction source term in the governing equation poses no closure problem. Molecular mixing and computing thereof in the presence of chemical kinetics, however, remains a major modeling challenge; not only for PDF methods. In this work we present a new model for partially premixed combustion based on the joint statistics of mixture fraction, scalar dissipation rate and a burning indicator, which is used to evolve notional fluid particles in mixture fraction-reactive scalar space (e.g., enthalpy). Therefore, the parameterized scalar profile (PSP) mixing model was extended for reactive scalars. As in the PSP mixing model for inert scalars, each fluid particle is associated with a representative profile in physical space. Different than in the standard PSP model, the reactive profiles get modified by chemical reactions. The decision whether a fluid particle is reacting or not is based on a burning indicator, the local scalar dissipation rate and the profile boundaries. The burning indicator accounts for the flame propagation in the partially premixed environment and controls extinction and re-ignition; together with the scalar dissipation rate. The solutions of the reaction–diffusion equation for different scalar dissipation rates is used to determine the state of the embedded flame associated with a reacting particle, which allows to construct reactive scalar profiles and on the other hand pure diffusion is assumed for extinct particles. The new combustion model was validated with the Sandia flame F data and comparisons demonstrate its ability to account for the relevant phenomena in partially premixed flames. [Copyright &y& Elsevier]