Empirical low-dimensional manifolds in composition space

To reduce the computational cost of turbulent combustion simulations with a detailed chemical mechanism, it is useful to find a low-dimensional manifold in composition space. Most previous low-dimensional manifolds in turbulent combustion are based on the governing conservation equations or thermochemistry and their application involves certain assumptions. On the other hand, empirical low-dimensional manifolds (ELDMs) are constructed based on samples of the compositions observed in experiments or in direct numerical simulation (DNS). Plane and curved ELDMs can be obtained using principal component analysis (PCA) and multivariate adaptive spline regression (MARS), respectively. The framework for ELDMs based on the represented compositions and principal components is considered in this study, where the represented compositions are selected from the PCA results. Both PCA and MARS are applied to the DNS databases of a nonpremixed CO/H2 temporally evolving jet flame and of an ethylene lifted jet flame. It is more accurate to represent the species mass fractions by curved MARS ELDMs than by plane PCA ELDMs. To achieve a overall departure less than a given level, more dimensions are required for the ethylene case (which involves 22 species) than for the CO/H2 case (which involves 11 species). For MARS to achieve less than the 5% departure level, seven dimensions are required for the ethylene case, and just two dimensions are required for the CO/H2 case. However, it is much more challenging to obtain the ELDMs with high accuracy for the chemical source terms using a small 1 number of dimensions. In addition, the effects on the departure from ELDMs of the scaling method in PCA, local extinction, and the Reynolds number are discussed. Two different approximations for the chemical source term are compared with discussions for further a posteriori simulations.