Evolution of local flame displacement speeds in turbulence

In this study, we assess the veracity of models for density-weighted local flame displacement speed of turbulent premixed flames. It will be shown that a combination of two models, one for the weakly stretched laminar flame state and another derived for a configuration where a curved laminar flame interacts with itself to annihilate, can describe most local realizations of a turbulent premixed flame. To that end, we have performed direct numerical simulations of a reactive mixture of hydrogen-air at atmospheric pressure using a detailed chemical reaction mechanism and analysed the dataset with recently developed flame particle tracking techniques. Forward tracking a large number of flame particles from the generating locations of the corresponding flame surfaces (given by backward tracking) to the corresponding annihilating locations, creates a manifold of local states that can represent nearly all possible states realizable for the turbulent premixed flame under consideration. With all the states of the flame accessible over time, we first assess the applicability of the two-parameter Markstein length based flame speed model. It is found that the model prediction is reasonably accurate for a significant part of the flame particles' lifetime, for turbulent premixed flames with Karlovitz number O(10) However, during the final stage of annihilation of the flame particles in the negatively curved trailing regions, the local structure of the flame no longer resembles a standard premixed flame, even qualitatively. A new interaction model for the flame displacement speed, during these final stages of annihilation of the flame elements, has been derived.