Assessment of Damköhler's hypotheses in the thin reaction zone regime using multi-step chemistry direct numerical simulations of statistically planar turbulent premixed flames

Abstract

The effects of the definition of the reaction progress variable and equivalence ratio on the validity of Damköhler's hypotheses for turbulent premixed flames belonging to the thin reaction zone regime have been studied using multi-step chemistry direct numerical simulations of statistically planar CH4–air premixed flames with equivalence ratios of 0.8 and 1.0. Although CH4–air premixed flames with equivalence ratios of 0.8 and 1.0 have effective Lewis numbers close to unity, local differential diffusion effects can play a non-negligible role in determining the turbulent burning velocity and flame surface area in all cases. However, the augmentations of burning rate and flame surface area under turbulence do not occur in equal proportion, but their ratio remains of the order of unity. This conclusion holds irrespective of the definition of the reaction progress variable for the cases considered here. Damköhler's second hypothesis, which relates the ratio of turbulent burning velocity and the unstretched laminar burning velocity to the ratio of turbulent diffusivity and molecular diffusivity, has been found not to hold in the sense of equality, but it is valid in an order of magnitude sense for all choices of reaction progress variable definition. The findings of the current analysis indicate that Damköhler's first and second hypotheses should only be interpreted in an order of magnitude sense in the thin reaction zone regime even when the effective Lewis number remains close to unity.