Direct and indirect measurements of flame surface density, orientation, and curvature for premixed turbulent combustion modeling in a cruciform burner

This paper analyzes experimentally the Bray-Moss-Libby (BML) model and the flame surface density (Σ) transport equation using premixed flames propagating through isotropic turbulence in a new cruciform burner and, thus, makes the analogy in both cases for the first time. The burner consists of a long vertical vessel that provides a downward propagating, lean premixed C₃H₈/air flame and a horizontal vessel. The latter is equipped with a pair of counter-rotating fans and perforated plates at each end to generate nearisotropic turbulence between two perforated plates. Visualization of turbulent flame fronts is obtained from high-speed laser sheet imaging. Several hundred runs at the same experimental conditions are carried out to obtain sufficient images in the central uniform region that are then processed to extract flame wrinkling length (L_y), flamelet crossing angle (h), Σ, flame front normal vector, curvature, etcetera. It is found that L_y is much smaller than the integral length scale in the unreacted turbulence, suggesting that the BML model needs a precise closure for L_y. The overall mean cosine value of θ(=σ_y) is 0.62, very close to 0.65 measured in liquid flames (Shy et al. 1996), revealing that σ_y is not influenced by thermal expansion. Symmetric distributions of Σ in the c¯ space are observed for both analyses of the BML model (indirect) and the Σ equation (direct), in which both values of Σ are comparable. Concerning the Σ equation, the propagation term is negligible and the curvature term has three different modes: (1) mainly negative, (2) positive/negative, production at the reactant side and destruction at the product side, and (3) mainly positive. Unlike liquid flames (the first two modes are equally important, each ∼45%), mode 2 is the major mode (∼70%) for present gaseous premixed turbulent flames. These results suggest that the curvature term is strongly influenced by thermal expansion.