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

The relation between turbulent burning velocity and flame surface area for turbulent stratified flames has been analyzed 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 and low turbulence intensity), although this trend weakens in fast mixing cases (low scalar integral length scale and high turbulence intensity). In slow mixing cases, the increase in the burning rate occurs at a smaller proportion than the increase in the 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 behavior reverses for small scalar length scale cases. These findings suggest that increases in the burning rate and flame surface area do not take place in the same proportions for turbulent stratified combustion.