Reconstructing 3D Flow Around a Flexible Airfoil Using Limited Planar Data

This study introduces the Sectional Snapshot Optimization (SSO) technique, a method for reconstructing time resolved three-dimensional wake flow from limited two-dimensional, three-component (2D–3C) velocity measurements. The method is demonstrated for the wake of a highly flexible airfoil undergoing flow-induced vibration. SSO extends the conventional snapshot optimization approach, which assumes turbulence homogeneity along the span—an assumption that breaks down in the post-flutter regime of flexible wings. To overcome this limitation, the proposed SSO framework partitions the span into locally homogeneous sections. The optimal number and placement of observation planes (OPs), where measurements are required, are determined using K-means clustering of the initial plane (IP) vorticity f ield combined with the elbow method. The reconstruction algorithm is applied to a flexible NACA 0018 airfoil undergoing first bending-mode oscillations at a Reynolds number of 1,650 in a water tunnel, with time-resolved volumetric PTV measurements serving as the reference dataset. Quantitative validation using root-mean-square error (RMSE), probability density histograms, correlation coefficients, and snapshot proper orthogonal decomposition (SPOD) demonstrates that the SSO method accurately captures the dominant flow dynamics and vortex shedding characteristics with high fidelity. This work establishes a practical and robust framework for three-dimensional flow reconstruction in complex, spanwise-inhomogeneous wakes relevant to flexible aerodynamic systems.