  Experimental multi-scalar measurements in laboratory flames have provided
important databases for the validation of turbulent combustion closure models.
In this work, we present a framework for data-based closure in turbulent
combustion and establish an a priori validation of this framework. The approach
is based on the construction of joint probability density functions (PDFs) and
conditional statistics using experimental data based on the parameterization of
the composition space using principal component analysis (PCA). The PCA on the
data identifies key parameters, principal components (PCs), on which joint
scalar PDFs and conditional scalar means can be constructed. To enable a
generic implementation for the construction of joint scalar PDFs, we use the
multi-dimensional kernel density estimation (KDE) approach. An a priori
validation of the PCA-KDE approach is carried out using the Sandia piloted jet
turbulent flames D, E and F. The analysis of the results suggests that a few
PCs are adequate to reproduce the statistics, resulting in a low-dimensional
representation of the joint scalars PDFs and the scalars' conditional means. A
reconstruction of the scalars' means and RMS statistics are in agreement with
the corresponding statistics extracted directly from the experimental data. We
also propose one strategy to recover missing species and construct conditional
means for the reaction rates based on a variation of the pairwise-mixing
stirred reactor (PMSR) model. The model is demonstrated using numerical
simulations based on the one-dimensional turbulence (ODT) model for the same
flames.
