In turbulent premixed flames, much experimental evidence points to a strong influence of pre-mixture turbulence intensity on the turbulent burning velocity. The linear enhancement of turbulent burning velocity in low-intensity turbulence is predicted accurately by current models. In contrast, the deviation from linearity in high-intensity turbulence, known as the "bending effect," remains to be explained. The present work has employed Direct Numerical Simulation (DNS) to investigate the bending effect. An initially laminar methane-air premixed flame was subjected to increasing levels of turbulence across five different simulations which maintained all parameters except the turbulence intensity constant. The bending effect was captured within these simulations. Subsequently, plausible explanations were investigated using the framework of the Flame Surface Density (FSD) approach. From the ensuing analysis, it is evident that flame surface area reflects distinctly the variation of turbulent burning velocity with turbulence intensity. Local flame quenching does not appear to be the primary mechanism behind the bending effect. Instead, the observed bending effect results from a shift in balance, under high-intensity turbulence, towards mechanisms that favour destruction of flame surface area. These mechanisms tend to preserve the reaction layer and, thereby, ensure the validity of Damköhler's hypothesis and flamelet models in conditions that cause the bending effect that is observed here to occur.

The turbulent burning velocity of premixed flames is sensitive to the turbulence intensity of the unburned mixture. Premixed flame propagation models that incorporate these effects of turbulence rest on either of two hypotheses proposed by Damköhler. The first hypothesis applies to lowintensity turbulence which acts mainly to increase the turbulent burning velocity by increasing the flame surface area. The second hypothesis states that, at sufficiently high intensities of turbulence, the turbulent burning velocity is governed mainly by enhanced diffusivity. Most studies to date have examined the validity of the first hypothesis under increasingly high intensities of turbulence. In the present study, the validity of Damköhler's second hypothesis is investigated. A range of turbulence intensities is addressed by means of Direct Numerical Simulations spanning the "flamelet" and "broken reaction zones" regimes. The validity of Damköhler's second hypothesis is found to be strongly linked to the behaviour of turbulent transport within the flame.

A discrepancy between the enhancement in overall burning rate and the enhancement in flame surface area measured for high-intensity turbulence is addressed. In order to reconcile the two quantities, an additional contribution from the effective turbulent diffusivity is considered. This contribution is expected to arise in sufficiently intense turbulence from eddies smaller than the flamelet thickness. In the present work, the enhancement in diffusivity arising from these eddies is estimated based on a model energy spectrum; individual contributions from all turbulence length scales smaller the flamelet thickness are integrated over the corresponding portion of the spectrum. It is shown that diffusivity enhancement, estimated in this manner, is able to account for the measured discrepancy between the overall burning rate enhancement and flame surface area enhancement. The factor quantifying this discrepancy is formalized as a closed-form function of the Karlovitz number.

Probability density functions of the components of stretch rate are investigated using a previously-published Direct Numerical Simulation dataset spanning a range of turbulence intensities in the Thin Reaction Zones (TRZ) regime. The dataset was generated by varying the turbulence intensity across five different simulations while maintaining fixed the remaining physico-chemical input parameters such as integral length scale and laminar flame thickness and speed. Across the entire dataset, the joint probability density function of stretch rate and displacement speed displays a distinctive shape with two branches consistent with previous studies at low turbulence intensities. This joint probability density function is analysed further by extracting individual contributions of stretch rate components to determine their relative importance across the branches. The curvature dependence of displacement speed appears to play an important role in shaping these branches. Implications of this result with regard to evaluation of the components of stretch rate in the TRZ regime are discussed.

The topology of flame-flame interaction is analysed for single turbulent premixed flames with increasing turbulence intensity. Morse theory for critical points is used for identifying the flame-flame interaction and characterising the local topology. The interactions have been categorised into four different groups, namely reactant pocket, tunnel formation, tunnel closure and product pocket. A histogram showing the frequency of occurrence of each of these groups is presented for single flames representative of hydrocarbon-air combustion and is compared with the results of colliding hydrogen-air flames.It is observed that most interactions for a single flame occur toward the leading edge. Also, more interactions are observed for higher intensity turbulence.The cylindrical topology types are found to dominate over spherical topology types. The relative frequency of occurrence of each type of topology is observed to change with changes in turbulence intensity. With increasing turbulence intensity, the fraction of product pockets and tunnel formation events increases whereas the fraction of reactant pockets and tunnel closure