A scaling analysis for the evolution of small-scale turbulence eddies across premixed flames with implications on distributed combustion

In this work, we propose a physics-based scaling theory for the evolution of small-scale turbulence eddies in the unburnt mixture when they travel across the preheat zone of a premixed flame. This scaling theory is developed to explicitly account for the effects of viscous diffusion on the length and velocity scales of turbulence eddies that are smaller than the inner reaction zone thickness of a premixed flame. This scaling suggests that both the length and velocity scales of the turbulence eddies are significantly altered as they pass through the preheat zone. The applicability of the scaling is assessed using a series of detailed numerical simulations of flame-vortex interactions with finite-rate chemistry and detailed molecular transport. The scaling estimates of eddy evolution are compared to simulation predictions with reasonable agreement. The proposed scaling is then applied to estimate the required length and velocity scales of turbulence eddies in the unburnt mixture of a turbulent premixed flame to potentially create significant perturbation of the reaction zone by local mixing after passing through the preheat zone. These requirements are translated into a minimum estimated Karlovitz number (Ka) of approximately 10⁴ in the unburnt mixture of a turbulent premixed flame to potentially achieve distributed combustion. This estimated minimum Ka is significantly higher than the classical scaling estimate (Ka ~ 102) for turbulent premixed flames, which supports the observations in recent experimental and Direct Numerical Simulation studies. The proposed scaling analysis implies that it is unlikely that turbulence eddies on the unburnt side of realistic turbulent premixed flames can be simultaneously sufficiently small and sufficiently strong to significantly alter the structure of the inner reaction zone.