Modelling of the turbulent burning velocity based on Lagrangian statistics of propagating surfaces

Abstract

We propose a predictive model of the turbulent burning velocity $S_T$ in homogeneous isotropic turbulence (HIT) based on Lagrangian statistics of propagating surfaces. The propagating surfaces with a constant displacement speed are initially arranged on a plane, and they evolve in non-reacting HIT, behaving like the propagation of a planar premixed flame front. The universal constants in the model of $S_T$ characterize the enhancement of area growth of premixed flames by turbulence, and they are determined by Lagrangian statistics of propagating surfaces. The flame area is then modelled by the area of propagating surfaces at a truncation time. This truncation time signals the statistical stationary state of the evolutionary geometry of propagating surfaces, and it is modelled by an explicit expression using limiting conditions of very weak and strong turbulence. Another parameter in the model of $S_T$ characterizes the effect of fuel chemistry on $S_T$, and it is pre-determined by very few available data points of $S_T$ from experiments or direct numerical simulation (DNS) in weak turbulence. The proposed model is validated using three DNS series of turbulent premixed flames with various fuels. The model prediction of $S_T$ generally agrees well with DNS in a wide range of premixed combustion regimes, and it captures the basic trends of $S_T$ in terms of the turbulence intensity, including the linear growth in weak turbulence and the `bending effect' in strong turbulence.