The relation between flame surface area and turbulent burning velocity in statistically planar turbulent stratified flames

Abstract

The relation between turbulent burning velocity and flame surface area for turbulent stratified flames has been analysed using a direct numerical simulation database. The simulations have been carried out for different initial turbulence intensities and initial integral length scales of equivalence ratio fluctuation for a given root-mean-square value in a globally stoichiometric mixture. Additionally, statistically similar turbulent premixed flames have been considered for comparison. The turbulent burning velocity and flame surface area for stratified flames are found to be significantly smaller than in premixed flames for slow mixing cases (large scalar integral length scale, low turbulence intensity), though this trend weakens in fast mixing cases (low scalar integral length scale, high turbulence intensity). In slow mixing cases, the increase of burning rate occurs at a smaller proportion than the increase of flame surface area.The contributions of the components arising from tangential diffusion of displacement speed and cross-scalar dissipation rate to the turbulent burning velocity are found to be negligible in comparison to that arising from the combined reaction and normal diffusion component for all cases. The increased probability of finding fuel-lean and fuel-rich mixture affects the contribution of turbulent burning velocity arising from the combined reaction and normal diffusion component of displacement speed for slow mixing cases. Front-supported flame elements dominate over back-supported flame elements for large scalar length scale cases, but this behaviour reverses for small scalar length scale cases. These findings suggest that increases of burning rate and flame surface area do not take place in the same proportions for turbulent stratified combustion.

Scalar Forcing Methodology for Direct Numerical Simulations of Turbulent Stratified Mixture Combustion

“…Note that the parameter defining the unburned gas cut-off point c (where c < 𝜖 c ) was tested with c = 0.0001 , 0.001 and 0.01 and it was found that there was no notable influence on the values of S T ∕S L and A T ∕A L . Recently, Brearley et al (2020) investigated a similar stratified flame DNS database to that considered here, without any scalar or turbulence forcing mechanisms, and found that S T ∕S L and A T ∕A L remained comparable to each other, and the results presented in Fig. 16 under scalar forcing are consistent with the previous findings by Brearley et al (2020).…”

“…Recently, Brearley et al (2020) investigated a similar stratified flame DNS database to that considered here, without any scalar or turbulence forcing mechanisms, and found that S T ∕S L and A T ∕A L remained comparable to each other, and the results presented in Fig. 16 under scalar forcing are consistent with the previous findings by Brearley et al (2020).…”

“…Figure 8 (left) shows the PDF evolution of the initially bellshaped case D, and Fig. 8 (right) shows the corresponding plot for the initially roughly flat PDF distribution case E. It is worth noting that the distribution for case E is obtained if an initial bimodal distribution is allowed to evolve in the absence of forcing for passive scalar mixing before it eventually assumes a bell-shaped distribution (Hélie and Trouvé 1998;Brearley et al 2020). Figure 8 illustrates that the reaction analogy (Daniel et al 2018) method maintains both distributions of with reasonable accuracy during the course of the simulation until the quasi-steady condition is obtained.…”

A Priori Direct Numerical Simulation Analysis of the Closure of Cross-Scalar Dissipation Rate of Reaction Progress Variable and Mixture Fraction in Turbulent Stratified Flames

“…It has been shown elsewhere Chakraborty, 2010a, b, 2011a) that the laminar burning velocity variation with equivalence ratio is accurately captured using this thermo-chemistry. This simplification of chemical representation allows for a detailed parametric analysis in terms of u � ∕S b( =1) and ∕ (which was reported in detail by Brearley et al (2020)) with a reasonable amount of computational cost. The relative costs between simple and detailed chemistry DNS were discussed in detail by Keil et al (2021a).…”

“…To meet the objectives, a three-dimensional Direct Numerical Simulation (DNS) database of six statistically planar turbulent stratified flames has been considered (Brearley et al, 2020). This database consists of cases with a globally stochiometric mixture and an initially bimodal distribution of equivalence ratio in the unburned gas.…”