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.

A predictive model of the turbulent burning velocity for planar and Bunsen flames over a wide range of conditions

“…At p = 1 atm, the validation with several DNS datasets showed that the model in Eq. ( 11) captures the variation of s T with u ′ , outperforming previous models [30].…”

“…To estimate the flame surface ratio A T /A L in Eq. ( 3), we apply the modeling approach developed by You and Yang [30] based on theoretical analysis on Lagrangian statistics of propagating surfaces [31,32]. The essence of this modeling framework is summarized below.…”

“…The flame area model in Eq. ( 11) captures the dependence of A T on u ′ in very weak and strong turbulence [25,30]. As u ′ → 0, the Taylor expansion of Eq.…”

“…The model application is, however, restricted to a simple flame geometry, i.e., statistically planar flame propagation in HIT. Additionally, the ratio between the turbulence integral length and the flame thermal thickness is close to unity, and fuels are relatively simple such as hydrogen and methane in previous works [25,30].…”

“…Recently, You and Yang [30] proposed a model of s T from the Lagrangian perspective. This model predicts s T for flames of several simple fuels at 1 atm, with universal turbulencerelated model constants based on Lagrangian statistics of propagating surfaces [31,32] in non-reacting homogeneous isotropic turbulence (HIT).…”