The propagation of premixed flames in turbulent flows is a problem of wide physical and technological interest, with a significant literature on their propagation speed and front topology. While certain scalings and parametric dependencies are well understood, a variety of problems remain. One major challenge, and focus of this study, is to model the influence of fuel/oxidizer composition on turbulent burning rates: these effects are related to Lewis number and species differential diffusion that cause local variations in flame front propagation speed, which then influence the overall turbulent flame propagation.
Among various approaches, several studies have utilized leading points concepts to explain the observed trends. Leading point concepts suggest that the turbulent burning velocity of premixed flames is controlled by the velocity of the points on the flame that propagate farthest out into the reactants - thus, they de-emphasize the classical idea that burning velocity enhancement is due to increases in flame surface area: rather, flame area creation is the effect, not the cause, of augmented turbulent burning velocities. In this framework, it is also postulated that modifications in the overall turbulent combustion speed depend solely on modifications of the burning rate at the leading points since an increase (decrease) in the average propagation speed of these points causes more (less) flame area to be produced behind them. Then, modeling of turbulent burning rates can be thought as consisting of two sub-problems: the modeling of burning rates at the leading points and the modeling of the dynamics/statistics of the leading points in the turbulent flame. Main objective of this proposal is to address both aspects, providing validation and development of the physical description put forward by the leading point concepts.
First, a comparison between numerical simulations of quasi-steady 1D flames in different configurations and statistics from a database of direct numerical simulations (DNS) is detailed. Second, the dynamics of flame propagation in simplified flow geometries is studied theoretically by means of the G-equation: utilizing results for Hamilton-Jacobi equations from the Aubry-Mather theory, it is shown how the large-time behavior of the solutions under certain conditions is controlled only by discrete points on the flame. Based on these results, definitions of leading points are proposed and their dynamics is studied.