Evolution of Displacement Speed Statistics During Head-On Flame-Wall Interaction within Turbulent Boundary Layers

The statistical behaviours of the density-weighted displacement speed and its curvature and strain rate dependence during head-on interaction of statistically planar premixed flames have been analysed based on Direct Numerical Simulations. The analysis has been conducted within turbulent boundary layers featuring inert walls, under both isothermal and adiabatic wall boundary conditions. The flame quenches due to heat loss when it reaches close to the wall in the case of isothermal wall boundary condition. By contrast, the flame can propagate all the way to the wall before extinguishing due to the consumption of reactants in the case of adiabatic wall boundary conditions. Thus, the effects of thermal expansion, quantified by dilatation rate, and flame normal acceleration during flame-wall interaction in the case of the isothermal wall are weaker than that in the case of the adiabatic wall case due to flame quenching. This gives rise to significant differences in the curvature and strain rate dependences of the reactive scalar gradient magnitude, which affects the statistical behaviours of the reaction and normal diffusion components of density-weighted displacement speed including their mean values, widths of their probability density functions, and their local strain rate and curvature dependences. It has been found that the interaction of near-wall vortical structures with flame surface increases the range of curvature variation during head-on interaction, which acts to widen the probability density function of the density-weighted displacement speed. This trend is relatively stronger for the isothermal wall boundary condition because of the larger variation of the reaction rate component of the density-weighted displacement speed due to local flame quenching, which also acts to widen the range of the density-weighted displacement speed variation in comparison to that in the case of adiabatic wall boundary conditions. Although the qualitative nature of curvature, strain rate, and stretch rate dependences of the density-weighted displacement speed remain unaffected by the wall boundary condition, the strength of the correlation changes with the progress of head-on interaction. It has been found that the negative correlation between the density-weighted displacement speed and flame curvature weakens with the progress of head-on interaction, which gives rise to a reduction in the strength of the correlation between the density-weighted displacement speed and flame stretch rate. Similarly, the correlation between the tangential strain rate and the density-weighted displacement speed weakens with the progress of head-on interaction. Detailed physical explanations are provided for these behaviours, and their modeling implications are indicated.