Transported and presumed probability density function modeling of the Sandia flames with flamelet generated manifold chemistry

Abstract

The first modeling results for Sandia flames D, E, and F using the flamelet generated manifold reduced chemistry model with a transported probability density function (TPDF) closure model are presented. The micro-mixing is modeled with the simple “interaction by exchange with the mean” model and mean molecular diffusion is accounted for through a mean drift term. By accounting for mean molecular diffusion, stable burning flames D, E, and F could be predicted using the standard value for the mixing rate constant Cϕ=2. The TPDF results are used in an a priori analysis of the main simplifying assumptions typically used in presumed PDF (PPDF) models. A new PPDF model that accounts for the correlation between mixture fraction and progress variable in the joint PDF through a Gaussian copula is presented and included in the analysis. The analysis reaffirmed earlier findings: the marginal PDF of the progress variable is not well approximated by a β-PDF and the mixture fraction and progress variable are not statistically independent. The Gaussian copula PPDF model did show a qualitative improvement over the models that invoke the statistical independence assumption. Quantitative analysis showed that the mean progress variable source term could not be predicted accurately by any of the PPDF models. The PPDF models were then applied in actual simulations of flames D and E. The erroneous predictions of the mean progress variable source term cause relative errors in the PPDF simulation results for the conditional mean temperature exceeding 20%.