Comparison between a spectral and probability density function model for turbulent reacting flows

This study compares the performance of a newly developed spectral model based on the eddy damped quasi-normal Markovian (EDQNM) theory with a standard probability density function (PDF) model for the case of two initially unmixed reactants undergoing a finite-rate bimolecular reaction. The two models were chosen because they involve complementary treatments of the nonlinearities and mixing terms. That is, nonlinearities are exactly treated in the PDF and mixing is modeled, whereas the opposite is true for EDQNM. The predictions of the two models are compared to direct numerical simulations. The results show that the PDF model is capable of describing the mixing of the major species reasonably well, but fails to describe the correlations between the reactants and the products even qualitatively. This suggests that the mixing model in the PDF is adequate for describing mixing between major species, but is incapable of describing mixing of the more spatially segregated product species. The EDQNM model does a slightly better job of describing the mixing of reactant species and a much better job of describing mixing of the product species. Presumably the improvement is associated with the more accurate description of the interscale dynamics that are especially important for the segregated products. The implication is that a model that combines the strengths of the EDQNM for describing mixing and the PDF for describing the nonlinearities would yield the best of both worlds.