Cluster-Based Reduced-Order Modeling of Flow Around a High-Aspect-Ratio Wing

The post-flutter response of high-aspect-ratio flexible wings involves complex, nonlinear interactions between structural deformation and unsteady flow dynamics. Understanding these fluid–structure interaction (FSI) mechanisms is critical for ensuring flight safety and enabling active control, yet characterizing the high-dimensional flow field remains a challenge. In this study, simultaneous time-resolved particle image velocimetry (TR-PIV) and digital image correlation (DIC) measurements are conducted to capture the coupled flow evolution and structural response of a flexible wing. A cluster-based reduced-order modeling (CROM) method is applied specifically to the flow field data to autonomously analyze the evolution of the flow and extract the dominant features. We investigate two distinct post-critical regimes: a periodic limit cycle oscillation (LCO) dominated by the second bending mode, and a more complex multi-frequency response involving coupled bending and edgewise motions. By partitioning the flow data into optimal clusters, the method constructs a probabilistic state transition network that maps the cyclic evolution of the flow. The results indicate that the complexity of the structural response directly informs the dimensionality of the flow model; while five clusters are sufficient to resolve the single-mode dynamics, the multi-frequency case requires six clusters to fully capture the periodic cycle. Furthermore, the cluster centroids reveal distinct topological features, including a massive leading-edge separation induced by edgewise motion, which mimics the effect of a transverse gust. Ultimately, this framework demonstrates that CROM can objectively extract coherent structures and transition pathways without prior knowledge, providing a robust, low-dimensional basis for future state-aware control strategies.