12. Analysis of Turbulent Reacting Jets via Principal Component Analysis

The interpretation of high-dimensional data, like those obtained from Direct Numerical Simulations (DNS) of turbulent reacting flows, constitutes one of the biggest challenges in science and engineering. Although these simulations are a source of key information to advance the knowledge of turbulent combustion, as well as to develop and validate modeling approaches, the dimensionality of the data often limits the full opportunity to leverage the detailed and comprehensive information stored in datasets. The Principal Component Analysis (PCA) and its local formulation (LPCA) are widely used in many fields, including combustion. During the last 20 years, they have been used in combustion for the identification of low-dimensional manifolds, data analysis, and development of reduced-order models. Lower dimensional structures, either global or local, can provide better insights on the underlying physical phenomena, and lead to the formulation of high-fidelity models. This chapter aims to offer to the reader a comprehensive introduction of the PCA potential for data analysis, firstly introducing the main theoretical concepts, and then going through all the required computational steps by means of a MATLAB® code. Finally, the methodology is applied to data obtained from a DNS of a turbulent reacting non-premixed n-heptane jet in air. The latter can be regarded as an optimal case for data analysis because of the complex physics characterized by turbulence–chemistry interaction and soot formation.