# A Framework for Data-Based Turbulent Combustion Closure: A Priori Validation

## TL;DR

This paper introduces a data-driven framework for turbulent combustion closure validation using PCA and KDE on experimental data, demonstrating effective low-dimensional representations and reconstruction of scalar statistics in turbulent flames.

## Contribution

It presents a novel PCA-KDE based approach for a priori validation of turbulent combustion models using experimental data, enabling low-dimensional scalar PDF construction and missing species estimation.

## Key findings

- Few principal components suffice to accurately reproduce scalar statistics.
- Reconstructed scalar means and RMS match experimental data.
- The approach effectively estimates missing species and reaction rates.

## Abstract

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.

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Source: https://tomesphere.com/paper/1905.08319