J-L. Consalvi, F. Nmira and C. Devaud
The main difficulty in modeling turbulence/soot production interaction (TSI) in non-premixed flames stems from the strong correlation between soot quantities and mixture fraction in the soot oxidation region. This is due to the fast nature of the oxidation process, which limits the coexistence of soot and oxidative species in mixture fraction space. Consequently, the “uncorrelated” model, which neglects this correlation, overestimates soot oxidation rates by more than an order of magnitude. In the RANS context, a presumed-probability density function (PDF) model is proposed. This model combines the flamelet approach to express the gas-phase part of soot production rates as a function of a reduced set of parameters, with the conditional source-term estimation (CSE) model to obtain the conditional mean of soot mass fraction in mixture fraction space. This model is more general than existing presumed PDF models in the literature because the conditional means of soot mass fraction are retrieved from the CSE inverse problem without presuming their shape. It is, therefore, applicable to situations with both infinitely fast and finite-rate soot oxidation. The model relies on several hypotheses: 1) The first-order conditional moment closure (CMC) hypothesis; 2) A presumed-PDF for the flamelet parameters; 3) The conditional mean of the number density of soot primary particles is set equal to its mean value; 4) The conditional mean of soot mass fraction is decomposed into Bernstein basis polynomials and 5) A strategy based on temporal samples at a fixed location is proposed to build the CSE ensembles used to retrieve the Bernstein coefficients from the CSE inverse problem. This alternative definition of the CSE ensemble substitutes the classical one based on the radial homogeneity assumption, as soot does not strictly satisfy this assumption. These assumptions, along with the accuracy of the corresponding predicted mean soot oxidation by 𝑂𝐻 and soot surface growth rates, are assessed in the case of the Sandia ethylene non-premixed turbulent jet flame by comparison with reference solutions obtained from RANS/TPDF simulations. The hybrid flamelet/CSE-based model predicts reasonably well the mean soot oxidation and surface growth rates within about 30% and 20% of the TPDF solutions, respectively. It significantly improves the prediction of the “uncorrelated” model and outperforms flamelet-based presumed PDF models from the literature, while being more flexible. The model can be readily extended to large eddy simulation