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Laminar premixed flame profiles of methane/air free flames and strained flames at different fuel/air ratios and strain rates are analysed using detailed chemistry with Lewis numbers equal to one. It is shown that the detailed chemistry flame profiles of progress variables CO2+CO and H2O+H2 in canonically stretched coordinates can be fitted accurately by a slight generalization of recently proposed analytical presumed flame profiles over a wide range of fuel/air ratios through adaptation of a single model parameter. Strained flame profiles can be reproduced using an additional linear coordinate transformation, emulating the compression of the preheat zone by strain as predicted by premixed flame theory. The model parameter can alternatively be determined using only the laminar flame speeds and the fully burnt temperatures from the laminar flame calculations. The stretch factor of the coordinate transformation is proportional to cp/lambda, which drops by factor up to 4 across the laminar flame.It is shown how the non-constant cp/lambda modifies the laminar flame probability density function (pdf), a polynomial fit to cp/lambda as function of progress variable allows analytical results for the laminar flame pdf, the mean value of progress variable and of the reaction source term. An analytic pdf for partially premixed flames is proposed based on Bayes theorem as a combination of a beta pdf for the mixture fraction and the laminar flame pdf's evaluated at the respective fuel/air ratio.

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In this work, reaction-diffusion manifold (REDIM) reduced chemistry is used in the simulation of turbulent non-premixed flames based on a transported-probability density function model. Differential molecular diffusion is applied in the generation of the manifolds. This is the first work to consider the gradients of the reduced variables as additional parameters in the REDIM model, and one-directional gradients are utilized to generate the REDIM reduced chemistry. Hereby, the influence of turbulence on differential molecular diffusion is automatically considered in terms of reduced variable gradients, and the physical transport properties (e.g., diffusion coefficients) are used in a detailed way, without any additional modeling (e.g., unity-Lewis number assumption). Although the scalar gradients appear as multi-directional in a general turbulent reacting flow, previous direct numerical simulation analysis reveals that REDIMs generated from one-directional gradients can accurately describe the system featuring multi-directional gradients, if this one-directional gradient has a major effect on the chemistry. Here, it is proposed to obtain such gradients under the hypothesis that the flame structure is locally one-dimensional at each spatial position. In order to retrieve the gradients of the reduced variables for the interpolation of the thermo-kinetic states from the REDIM table, the sub-grid gradient is evaluated here from the particle fields. The well-known Sandia series of flames is selected to validate the proposed algorithm. The results show that the new algorithm can reproduce the thermo-kinetic quantities with high accuracy for all investigated flames.