Joint statistics of mixture fraction and progress variable in piloted partially-premixed jet flames

Mixture fraction and progress variable are central terms in many modeling approaches for partially-premixed combustion, and their variances and covariance appear in model closures. In the present work, the Bilger mixture fraction, ξ, and a progress variable based on oxygen, c_O, are calculated from the mass fractions of seven measured species (CH₄, O₂, N₂, CO₂, H₂O, CO, and H₂). We examine the joint statistics of ξ and c_O in two turbulent piloted methane-air jet flames that exhibit different levels of compositional inhomogeneity at the inlet and hence different modes of combustion near the flame base. The Favre covariance, ξ"c_O", and correlation coefficient, R_ξ,c, behave very differently in the near field of these two flames, with the magnitude of both being much lower in the stratified-premixed reaction zone of the flame with an inhomogeneous exit profile of mixture fraction. Farther downstream in each flame, the joint pdfs and correlation statistics in both flames are influenced by the degree of local extinction.