Gradient and counter-gradient scalar transport in turbulent premixed flames

Abstract

In premixed turbulent combustion, the modelling of the turbulent flux of the mean reaction progress variable remains somewhat controversial. Classical gradient transport assumptions based on the eddy viscosity concept are often used while both experimental data and theoretical analysis have pointed out the existence of countergradient turbulent diffusion. Direct numerical simulation (DNS) is used in this paper to provide basic information on the turbulent flux of and study the occurrence of counter-gradient transport. The numerical configuration corresponds to twoor three-dimensional premixed flames in isotropic turbulent flow. The simulations correspond to various flame and flow conditions that are representative of flamelet combustion. They reveal that different flames will feature different turbulent transport properties and that these differences can be related to basic dynamical differences in the flame-flow interactions: counter-gradient diffusion occurs when the flow field near the flame is dominated by thermal dilatation due to chemical reaction, whereas gradient diffusion occurs when the flow field near the flame is dominated by the turbulent motions. The DNS-based analysis leads to a simple expression to describe the turbulent flux of , which in turn leads to a simple criterion to delineate between the gradient and counter-gradient turbulent diffusion regimes. This criterion suggests that the occurrence of one regime or the other is determined primarily by the ratio of turbulence intensity divided by the laminar flame speed, and by the flame heat release factor, τ ≡ (Tb — Tu)/Tu, where Tu and Tb are respectively the temperature within unburnt and burnt gas. Consistent with the Bray-Moss-Libby theory, counter-gradient (gradient) diffusion is promoted by low (high) values and high (low) values of τ. DNS also shows that these results are not restricted to the turbulent transport of . Similar results are found for the turbulent transport of flame surface density, Σ. The turbulent fluxes of and Σ are strongly correlated in the simulated flames and counter-gradient (gradient) diffusion of always coincides with counter-gradient (gradient) diffusion of Σ.

Effects of Lewis number on vorticity and enstrophy transport in turbulent premixed flames

“…The value of u ′ /S L decayed by 50% ahead of the flame, whereas l/δ th increased by a factor of 1.7 when the statistics were extracted. The simulation time used in the current analysis remains comparable to several previous analyses, [61][62][63][64][65][66][67] which have contributed significantly to the fundamental understanding of turbulent reacting flows in the past.…”

A Direct Numerical Simulation-Based Analysis of Entropy Generation in Turbulent Premixed Flames

“…It is worth noting that Soret and Dufor effects are ignored here following several previous analyses on entropy generation in turbulent reacting flows [4][5][6][7][8][10][11][12][13][14][15]17]. Moreover, there have been several previous DNS based computational analyses [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], which ignored Dufor and Sorret effects without much loss of generality. These effects are not expected to play important roles in most hydrocarbon-air and hydrogen-air flames [35] unless extremely lean hydrogen-air flames are considered.…”

“…Single step chemistry has been used successfully to obtain fundamental physical insight and to develop high-fidelity models in several analyses in the past [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] and the same methodology has been followed here. In the context of simplified chemistry the species field is characterized by a reaction progress variable c , which can be defined in terms of a suitable reactant mass fraction R Y as follows:…”

Flame Surface Densities in Premixed Combustion at Medium to High Turbulence Intensities

“…The strain rates that would quench the flame have been quantified by Bradley et al (1998) and the results have been used to evaluate the S d =S L ratio. More conservative approaches assume that for flames with Lewis numbers close to unity, S d remains close to the laminar flame velocity (Trouvé and Poinsot, 1994;Veynante et al, 1997). Neglecting the effects of S d for the sake of discussion, assuming that it remains close to S L , then we are faced with three possibilities:…”