On local displacement speeds, their correlations with flame-front quantities, and their temporal evolution measured in turbulent premixed flames

This study reports measurements of two-dimensional (2D) local displacement speeds ( ▪ ), curvature ( ▪ ), and tangential strain rate ( ▪ ) extracted from premixed flames subjected to turbulent Karlovitz and Reynolds numbers ranging from 2.1–23 and 1500–3500, respectively. Such measurements were facilitated through joint implementation of OH PLIF and stereoscopic PIV at 20kHz. Deriving these quantities from OH-PLIF-based flame edges permitted, to our knowledge, the first experimental assessment of their statistical correlations. Namely, joint PDFs (JPDFs) and conditional mean (CM) profiles of ▪ and ▪ indicate that ▪ tends to decrease as the magnitude of ▪ increases. JPDFs and CM profiles of ▪ and ▪ exhibit a strong negative correlation and demonstrate that density weighted values of ▪ ( ▪ , where and represent the density within the reactants and at the iso-contours selected to define the flame front, respectively) exceed three times the un-stretched laminar flame speed () when ▪0. Global averages of ▪ extracted near the bases of flames were 20%–30% less than ; yet, such values increased with axial distance (). These findings are all consistent with prior direct numerical simulation (DNS) studies, particularly those of burner-stabilized flames. Beyond enabling correlations of the aforementioned quantities, the employed diagnostics, coupled with a unique flame-edge-point tracking algorithm, enabled statistical assessment of their temporal evolution. Specifically, deriving a normalized time (01) based on when two flame-edge-points merged allowed assessment of quantities conditioned on the flame-edge-points proceeding that merger. Such analysis revealed that, on average, the lives of flame-edge-points fall into two epochs: (1) for 0.8, ▪ slowly decreases as increases and ▪; and (2) when 0.8, ▪ sharply increases to values exceeding and there is a marked rise in the decay rate of ▪ . These trends are consistent with recent DNS studies and support implementing a -based -model capable of predicting its extreme characteristics as flame-edge-points approach annihilation.