The influence of differential diffusion on the statistical behavior of the local displacement speed (Sd) in relation to flame curvature is studied based on three-dimensional compressible direct numerical simulations (DNS) of statistically planar flames with single-step Arrhenius-type chemistry. Three different Lewis number cases (Le=0.8, 1.0, and 1.2) are considered. In order to study the influence of differential diffusion on curvature effects in flame propagation, temperature statistics are presented in terms of standard probability density functions (pdfs) and also joint pdfs with curvature for the nonunity Lewis number cases. Temperature statistics are found to be consistent with previous incompressible combustion DNS studies. It is found that both dilatation and tangential strain rate are negatively correlated with curvature. The relative strength of these two correlations determines the nature of the correlation between surface density function (SDF) (∣∇c∣) and curvature. It is also found that the variations of temperature and SDF on an isosurface of reaction progress variable (c) have significant influence on local displacement speed behavior. Displacement speed statistics are presented in terms of standard pdfs as well as joint pdfs with curvature for the three Lewis number cases. The curvature response of the displacement speed and its different components is found to be nonlinear which is consistent with previous two-dimensional DNS with detailed chemistry. The observed nonlinear behavior in the present study in the absence of a detailed chemical mechanism is explained through the influence of differential diffusion.

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Strain rate and curvature effects on Surface Density Function (SDF) transport in the thin reaction zones regime are studied using a three-dimensional direct numerical simulations (DNS) with a single-step Arrhenius type chemistry. It is shown that if the tangential strain rate on a flame isosurface exceeds a critical value, then a negative normal strain rate is induced, which acts to bring the isoscalar lines closer to each other and hence leads to a higher value of SDF. This is reflected in a positive correlation between SDF and tangential strain rate. Curvature is also found to affect SDF through the correlation between tangential strain rate and curvature on a given flame isosurface. Strain rate and curvature are found to have an appreciable effect on various terms of the SDF transport equation. The SDF straining term is correlated positively with tangential strain rate as expected and is also correlated negatively with the curvature. The combined SDF curvature and propagation terms operate as a source near the fresh gas side of the flame and as a sink towards the burned gas side. The SDF propagation term is found to correlate negatively with flame curvature towards the fresh gas side and positively towards the burned gas side. The variation of the SDF curvature term with local flame curvature is found to be nonlinear due to the additional stretch induced by the tangential diffusion component of the displacement speed.

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