Evaluation of reaction progress variable - mixture fraction statistics in partially premixed flames

Abstract

The mixture fraction and reaction progress variables are key for presumed probability density function (PDF) based flamelet models for partially premixed flames. The importance of the joint statistics of these two variables are evaluated using a joint composition-enthalpy transported PDF/Finite Volume method applied to established databases for inhomogeneous jet flames. The accuracy of the approach is first examined for three flames with different mixture fraction inlet profiles and departures from blow-off. The (joint-) statistics of mixture fraction and reaction progress variable are subsequently analysed with the covariance of the two variables used to evaluate the assumption of statistical independence. Results show that the current approach is able to reproduce the near-field features of both homogeneous and inhomogeneous jet flames. The latter leads to a stratified premixed flame that evolves to diffusion-dominated combustion as the influence of the pilot fades. In agreement with measured data, the mixture fraction variance is strongly affected by the near-field combustion mode and the misalignment with the reaction progress variable variance is obvious in the stratified premixed flame. It is shown that the covariance of the mixture fraction and reaction progress variable is influenced by turbulence-chemistry interactions and that, generally, the two parameters remain strongly correlated with the consequence that the assumption of statistical independence is implausible.