On defining progress variable for Raman/Rayleigh experiments in partially-premixed methane flames

Abstract

Progress variable is a central concept in the theory and modeling of partially-premixed flames. However, there has been no consensus in the literature on its definition, particularly in the context of experiments. Several possible definitions of progress variable are considered, based on mass fractions of the seven major species that can be measured by combined Raman/Rayleigh scattering methods applied to turbulent methane flames. The behavior of three candidate progress variables is evaluated using laminar opposed-flow flame calculations. The effects of normalizing by the fully-burnt state rather than the more commonly used equilibrium state are considered. A progress variable, cO, defined as the mass of oxygen bound in the products CO2, CO and H2O, divided by that which would be bound if the sample were taken to its fully-burnt state, is argued to offer some advantages over the other definitions considered. It is shown that inclusion of a larger number of species in calculating cO (18 versus 7) makes little difference, such that the seven major species accessible to Raman/Rayleigh laser diagnostics are sufficient to quantify reaction progress in partially-premixed methane flames at atmospheric pressure. The measured joint statistics of mixture fraction, Z, and progress variable, cO, are presented for two turbulent piloted partially-premixed methane–air jet flames that have significantly different mixture fraction profiles at the jet exit. Favre average radial profiles of first and second moments, as well as the correlation coefficient, RZ, c, highlight differences in near-field scalar structure between the two flames. Examples of joint Z, cO histograms, sampled from 0.3-mm segments centered at the radial location where Z˜ = 0.065 in each profile, are presented. This mixture fraction value corresponds roughly to the location of peak heat release rate on the fuel-rich side in the laminar flame calculations. A clear conclusion is that the common modeling assumption of statistical independence of mixture fraction and progress variable is contradicted by the turbulent flame measurements. The proposed progress variable can be easily calculated from simulations as a post-processing step, independent of the modeling approach, allowing for consistent comparison of measured and modeled turbulent flame results.