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 (S-d(2D)), curvature (kappa(2D)), and tangential strain rate (a(t)(2D)) 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 20 kHz. 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 S-d(2D) and a(t)(2D) indicate that S-d(2D) tends to decrease as the magnitude of a(t)(2D) increases. JPDFs and CM profiles of S-d(2D) and kappa(2D) exhibit a strong negative correlation and demonstrate that density weighted values of S-d(2D) (S-d*(2D) = rho(F) S-d(2D)/rho(0), where rho(0) and rho(F) 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 (S-L(0)) when kappa(2D) <<0. Global averages of S-d*(2D) extracted near the bases of flames were 20%-30% less than S-L(0); yet, such values increased with axial distance (y). 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 (0 <= tau* <= 1) 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 tau* less than or similar to 0.8, kappa(2D) slowly decreases as tau* increases and S-d*(2D) approximate to 0.7 S-L(0); and (2) when tau* greater than or similar to 0.8, S-d*(2D) sharply increases to values exceeding 2S(L)(0) and there is a marked rise in the decay rate of kappa(2D). These trends are consistent with recent DNS studies and support implementing a kappa-based S-d-model capable of predicting its extreme characteristics as flame-edge-points approach annihilation.