Dimensionality reduction and unsupervised classification for high-fidelity reacting flow simulations

The development of reduced-order combustion models able to accurately reproduce the physics of reactive systems has been a highly challenging aspect of numerical combustion research in the recent past. The complexity of the problem can be reduced by identifying and using low-dimensional manifolds able to account for turbulence-chemistry interactions. Recently, Principal Components Analysis (PCA) has shown its potential in reducing the dimensionality of a chemically reactive system while minimizing the reconstruction error. The present work demonstrates the application of the Manifold Generated by Local PCA (MG-L-PCA) approach in direct numerical simulation (DNS) of turbulent flames. The approach is enhanced with an unsupervised clustering based on Vector Quantization PCA (VQPCA) and an on-the-flyPCA-based classification technique. The reduced model is then applied on a three-dimensional (3D) turbulent premixed NH3/air flame by transporting only a subset of the original state-space variables on the computational grid and using the PCA basis to reconstruct the non-transported variables. Results are compared with both a detailed reaction mechanism and a Computational Singular Perturbation (CSP) reduced skeletal mechanism. A comparison between training the reduced model using one-dimensional (1D) and 3D data sets is also included. Overall, the MG-L-PCA allows not only for a reduction in the number of transport equations, but also a significant reduction in the stiffness of the system, while providing highly accurate results.