Extended cluster-based network modeling for coherent structures in turbulent flows

This study introduces the Extended Cluster-based Network Modeling (eCNM), a methodology to analyze complex fluid flows. The eCNM focuses on characterizing dynamics within specific subspaces or subsets of variables, providing valuable insights into complex flow phenomena. The effectiveness of the eCNM is demonstrated on a swirl flame in unforced conditions, characterized by a precessing vortex core (PVC), using synchronized data from PIV measurements, UV-images filtered around the OH* chemiluminescence wavelength, featuring the heat release rate distribution, and pressure signals from jet inlet probes. The analysis starts with choosing the distance metric for the coarse-graining process and the number of clusters of the model. This has been pursued by designing a filtered distance metric based on the filtered correlation matrix and minimizing the Bayesian information criterion (BIC) score, balancing the goodness of the fit of a model with its complexity. The standard cluster-based network model on the velocity fluctuations allowed for determining the characteristic frequency of the PVC. The construction of extended cluster centroids of the heat release rate reveals a rotating flame pattern, predominantly localized within regions influenced by PVC's vortices roll-up. Spatial subdomain analysis is carried out, demonstrating the benefits of focusing on specific regions of interest within the fluid system and providing significant computational savings. Furthermore, eCNM allows for the handling of different sampling frequencies among datasets. Leveraging high-resolution pressure measurements as a reference dataset and velocity components as undersampled data, extended cluster centroids for velocity are successfully estimated, even when the velocity sampling frequency is artificially reduced. This study showcases the adaptability and robustness of eCNM as a valuable tool for comprehending and analyzing coherent structures in complex fluid flows.