Genesis and evolution of premixed flames in turbulence

Flames interacting with turbulence are continuously generated and annihilated by stretching and folding processes over a range of length-scales and time-scales. In this paper, we address: from where and how do the complex topology and physico-chemical state of a fully developed turbulent premixed flame generate and evolve in time by analyzing the motion of flame particles. Flame particles are points that co-move with reactive isoscalar surfaces which are representative of turbulent premixed flames. Direct Numerical Simulation (DNS) of H2-air turbulent premixed flame with detailed chemistry is combined with a computational methodology called the Backward Flame Particle Tracking (BFPT) algorithm. Uniform distribution of flame particles that entirely span isotherms at time tf is tracked backwards to an earlier time ti (ti < tf). On backtracking, the once uniformly distributed flame particles form multiple clusters in the leading locations of the corresponding isotherms. Since Zeldovich, such leading locations or leading points have remained an enigmatic concept in combustion literature inducing strong hypotheses without concrete proofs on their role. The critical observation that entire flame surface evolves from multiple clusters of leading points at earlier time allows a Finite Strain Theoretic description of the turbulent flame in terms of these points. Stretching is initiated by flame propagation along the direction of maximum curvature. Using Finite Strain Theory, we observe that at the flame surface around the leading points, the direction of minimum curvature gets preferentially aligned with the most extensive direction of the left Cauchy-Green strain-rate tensor and vorticity. These two stretching mechanisms cause the leading regions to become finite sized surfaces, several of which subsequently join together generating the complete surface at tf. A relationship is developed between the turbulent flame speed at time tf and the flame displacement speed and flow-flame properties like stretch-rate of the leading points from an earlier time. Finally, we have used two distinct sets of flame particles: Set-G and Set-D, which generate and destroy the flame surface, respectively. Using the observations that the flame particles in these sets follow a modified Batchelor's pair dispersion law, we have identified an important length-scale known as the Gibson scale. Curved flame propagation dominates dispersion of flame particles upto Gibson scale, while turbulence dominates dispersion of flame particles beyond this scale.