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The effects of tangential strain rate and curvature on the surface density function ͑SDF͒ and on different terms within the SDF transport equation in the thin reaction zone regime are studied for statistically planar turbulent premixed flames with global Lewis numbers Le= 0.8, 1.0, and 1.2 by using three-dimensional direct numerical simulations with simplified chemistry. A positive correlation is observed between the SDF and tangential strain rate, and this is explained in terms of the local statistical behaviors of tangential strain rate and dilatation rate. Curvature is shown to affect the SDF through the curvature response of both tangential strain rate and dilatation rate on a given flame isosurface. The correlation between the curvature and SDF is positive in the Le= 0.8 flame and negative in the Le= 1.2 flame. The curvature dependence of the SDF is weak in the case of unity Lewis number. Strain rate and curvature are found to have an appreciable effect on different terms of the SDF transport equation. The SDF strain rate term arising from tangential strain rate contribution in all the flames is positively correlated with tangential strain rate as expected and is also negatively correlated with curvature. For the Le= 1.0 and 1.2 flames, the SDF propagation term is found to negatively correlate with flame curvature toward the reactant side of the flame and positively toward the product side. By contrast, for the Le= 0.8 flame, the SDF propagation term is negatively correlated with curvature throughout the flame brush. The variation of the SDF curvature term with local flame curvature for all the flames is found to be nonlinear due to the additional stretch induced by the tangential diffusion component of the displacement speed. Physical explanations are provided for all of these effects, and the modeling implications are discussed in detail.

Flame surface density (FSD) based reaction rate closure is one of the most important approaches in turbulent premixed flame modeling. The algebraic models for FSD based on power laws often require information about the fractal dimension D and the inner cut-off scale ηi. In the present study, two three-dimensional direct numerical simulation (DNS) databases for freely propagating statistically planar turbulent premixed flames are analyzed among which the flame in one case belongs to the corrugated flamelet (CF) regime, whereas the other falls well within the thin reaction zone (TRZ) regime. It is found that D for the flame in the TRZ regime is greater than the value obtained for the flame in the CF regime. For the flame within the TRZ regime, the fractal dimension is found to be 7/3, which is the same as D for a material surface in a turbulent environment. For the flame in the CF regime, ηi is found to scale with the Gibson scale, whereas ηi is found to scale with the Kolmogorov length scale for the flame in the TRZ regime. Based on these observations a new algebraic model for FSD is proposed, where D and ηi are expressed as functions of Karlovitz number. The performances of the new and existing algebraic models for FSD are compared with the corresponding values obtained from DNS databases.

Here we present an evaluation of the binding affinity prediction accuracy of the free energy calculation method FEP+ on internal active drug discovery projects and on a large new public benchmark set.<br>