Effects of turbulent length scale on the bending effect of turbulent burning velocity in premixed turbulent combustion

Abstract The effects of turbulent integral length scale to flame thickness ratio on the bending effect of turbulent burning velocity variation have been analysed based on a three-dimensional Direct Numerical Simulation database of statistically planar turbulent premixed flames with a characteristic Lewis number of unity propagating into forced unburned gas turbulence. It has been demonstrated that Damkohler's first hypothesis remains valid for the cases considered here and this has been utilised to explain the bending effect by analysing the terms in the generalised Flame Surface Density (FSD) transport equation. Under steady-state, the flame surface area generation by the FSD tangential strain rate term remains in equilibrium with the flame surface destruction by the FSD curvature term. It has been found that the length scale ratio influences the relative contributions of the dilatation and normal strain rate to the flame surface area generation due to tangential strain rate. Similarly, relative contributions of the flame surface area destruction due to the curvature terms arising from the combined reaction and normal diffusion component of displacement speed, and the tangential diffusion component of displacement speed are affected by the length scale ratio. The propensity of the flame area generation due to the normal strain rate term and the dominance of the flame area destruction arising from the tangential diffusion component of displacement speed are strengthened with decreasing length scale ratio. The flame surface area destruction due to the FSD curvature term arising from tangential diffusion component of displacement speed strengthens with increasing turbulence intensity and it becomes the major contributor to the destruction of flame surface area for large turbulence intensities. However, the inner cut-off scale, which also limits maximum possible flame area generation by the FSD strain rate term under statistically stationary state, determines the maximum possible destruction of flame surface area for a given length scale ratio and this is manifested in the bending effects of turbulent burning velocity and flame surface area. At high turbulence intensities, the turbulent burning velocity levels off at a smaller value for the smaller length scale ratio, which is consistent with Damkohler's second hypothesis and has been explained based on scaling arguments utilising the leading order balance between the strain rate and curvature contributions to the flame surface area evolution for large turbulence intensities characterised by large Karlovitz number and small Damkohler number values.