Conditional space evaluation of progress variable definitions for Cambridge/Sandia swirl flames

Data from all spatial locations of nine turbulent flames in the Cambridge/Sandia swirl database are combined to study how the choice of scalar variables in conditional moment closure (CMC) type approaches affect the conditional spatial fluctuations of reactive scalars. In order to investigate the influence of swirl and stratification, two additional data-sets have been constructed. Principal component analysis (PCA) is applied to help identify the number of scalar variables and the most appropriate choices to describe the composition space. Two PCA scaling methods have been adopted, namely Pareto and Auto-scaling. Regardless of the data-set investigated and the scaling method used, the results suggest that a single principal component correlated with temperature accounted for the largest variance. For the first moment hypothesis, four progress variable, c, definitions identified by PCA are selected as conditioning variables to investigate the conditional fluctuations and normalised RMS of various species and temperature from all three databases at all axial locations. The results indicate that two control variables based on mixture fraction, Z, and progress variable significantly reduce the conditional fluctuations of scalars compared to a single variable. The selection of progress variables had minimal effects on the RMS of conditional fluctuations for all tested conditions, although a slight reduction of conditional fluctuations was found for the temperature-based progress variable, which can potentially help the further extension of CMC-based models in different flame configurations. The present study also shows that using Z and c (regardless of its definition) as two conditioning scalars enables the detachment of the thermo-chemical state from space, swirl and stratification effects. This suggests that adopting a doubly conditioned source term estimation (DCSE) approach might successfully predict the considered set of flames, assuming that ensembles are divided along the axial direction.