Assessment of optimal reaction progress variable characteristics for partially premixed flames

The reaction progress variable is a crucial concept in the advanced flamelet combustion models. As a controlling variable, a well-defined progress variable must consider the essential features of the combustion process. It is usually a heuristically defined linear combination of some major chemical species mass fractions. However, such a simple definition could lead to inaccurate results for the fuel-rich reactive mixtures or complicated fuels, due to the vast number of chemical species in the combustion process. In this paper, a new method for generating a reaction progress variable is proposed through solving a constrained optimisation problem. The proposed method uses a genetic algorithm with new constraints. The major new constraint is the minimisation of the inverse of a progress variable-based Damköhler number in addition to the minimisation of the gradients of a collection of chemical species concentrations, as used in the previous methods. Hence, this scheme increases the Damköhler number defined based on the progress variable. The applicability and performance of the current optimised progress variable are evaluated for ethanol–air partially premixed flames in an axisymmetric two-dimensional counterflow burner and a two-dimensional plugged flow triple-flame burner. The effects of the number of chemical species included in the progress variable and the flow field strain rate on a partially premixed ethanol–air flame prediction are investigated. Results indicate that including the progress variable Damköhler number in the determination of the progress variable has a considerable effect on the accuracy of Flamelet Generated Manifold (FGM) model prediction of fuel-rich and lean reactive mixtures, especially at higher strain rates. Also, it is shown that the inclusion of the critical chemical species for ignition and fuel decomposition processes, such as CH3O2, CH3CHO, sC2H4OH, HO2, H and H2O2, in the definition of progress variable has a significant effect on the accuracy of the ethanol–air flame predictions.