An a priori analysis on principal component analysis based conditional source-term estimation model for Sandia jet flames

Abstract

Data from all spatial locations and two turbulent flames in the Sandia/TUD database are used to explore the feasibility of adopting principal components (PC) as conditional variables in the conditional source-term estimation (CSE) model. Principal component analysis (PCA) is applied to both Flame C and F to generate the new set of controlling variables, PC-scores. Two PCA scaling methods have been adopted, namely Pareto and Auto-scaling (AS). Regardless of the scaling option selected and the flame investigated, it was found that a single principal component score (PC1-score) correlated with temperature accounts for the largest amount of variance. As such, the conditional space fluctuations and normalized RMS of both flames’ reactive scalars around PC1-Pareto and PC1-AS are examined and compared against the ones obtained with the mixture fraction, Z. The results indicate that both PC1-scores are not able to accurately quantify the thermo-chemical state-space of Flame C compared to mixture fraction, in particular for the fuel and all the intermediate species. Interestingly, using a single principal component score for Flame F significantly improved the conditional fluctuations, suggesting that a single PC-score well correlated with temperature can more effectively reduce the spatial gradient and Reynolds numbers effects than mixture fraction. The results are further depicted by comparing the trends obtained for Flame F with two-condition conditional averages around Z and four different progress variable definitions, c. While doubly conditioning enabled to detach the conditional averages of all the scalars from the physical domain, the results obtained with PC1-Pareto and PC1-AS were found to not deviate by much (excluding the mass fractions of CH4). This leads to believe that a conditional moment closure-based model such as CSE, coupled with PCA, can perhaps recover with satisfactory levels of approximation the thermo-chemical state-space of Flame F and separate the conditional manifold from the real domain.