Roles of displacement speed on evolution of flame surface density for different turbulent intensities and Lewis numbers in turbulent premixed combustion

Direct numerical simulations (DNS) are conducted in 3D to investigate the evolution of flame surface density (FSD) in turbulent premixed combustion. A parametric study is performed with respect to turbulent intensity and Lewis number to investigate all component terms in the FSD transport equation. A higher turbulent intensity leads to a higher turbulent burning velocity due to increased flame area, while the mean consumption speed remains close to the laminar flame speed. A lower Lewis number leads to a higher turbulent burning velocity, with increases in both total flame area and mean consumption speed. There are two source terms to govern FSD: tangential strain and propagation term, given as a product of displacement speed and curvature. The mean strain rate varies linearly with the turbulent intensity, but shows no noticeable dependence on the Lewis number. The correlation between curvature and displacement speed does not depend on the turbulent intensity, but shows significant influence of the Lewis number. The propagation term decreases with increasing turbulent intensity to become a larger negative sink in the rear of flame brush with flame elements of smaller radii of curvature and higher displacement speeds. A lower Lewis number leads to a larger positive propagation term in the front due to an increased displacement speed to produce more flame area through diffusive thermal instability.