Optimizing progress variable definition in flamelet-based dimension reduction in combustion

An automated method to optimize the definition of the progress variables in the flamelet-based dimension reduction is proposed. The performance of these optimized progress variables in coupling the flamelets and flow solver is presented. In the proposed method, the progress variables are defined according to the first two principal components （PCs） from the principal component analysis （PCA） or kernel-density-weighted PCA （KEDPCA） of a set of flamelets. These flamelets can then be mapped to these new progress variables instead of the mixture fraction/conventional progress variables. Thus, a new chemistry look-up table is constructed. A priori validation of these optimized progress variables and the new chemistry table is implemented in a CH4/N2/air lift-off flame. The reconstruction of the lift-off flame shows that the optimized progress variables perform better than the conventional ones, especially in the high temperature area. The coefficient determinations （R2 statistics） show that the KEDPCA performs slightly better than the PCA except for some minor species. The main advantage of the KEDPCA is that it is less sensitive to the database. Meanwhile, the criteria for the optimization are proposed and discussed. The constraint that the progress variables should monotonically evolve from fresh gas to burnt gas is analyzed in detail.