Modeling of the turbulent burning velocity using Lagrangian statistics of propagating surfaces

We develop a model for estimating the turbulent burning velocity based on Lagrangian statistics of propagating surfaces. An ensemble of propagating surface elements with a constant displacement speed is initially arranged on a plane in non-reacting homogeneous isotropic turbulence (HIT) to model the propagation of a planar premixed flame front. The turbulent burning velocity is estimated by the area ratio of the global propagating surface at a truncation time when the statistical geometry of propagating surfaces reaches a stationary state. This model is validated by the direct numerical simulation (DNS) of hydrogen/air turbulent premixed flames propagating in stationary HIT with detailed chemistry. We demonstrate that the modelled turbulent burning velocity agrees well with DNS at small and moderate Karlovitz numbers. The probability density functions (PDFs) of the area-weighted tangential strain rate in flames and propagating surfaces are quantitatively similar with positive means to increase the flame area, and the PDFs of the area-weighted mean curvature in propagating surfaces are wider than those in flames. In addition, the computational cost of the proposed model is much lower than the corresponding combustion DNS.