Data-Efficient Estimation of Unsteady 3D Flow from Limited Planar Data Using Sectional Snapshot Optimization

Reconstructing unsteady three-dimensional (3D) flow fields remains a significant challenge in fluid mechanics, especially in experimental settings where volumetric measurements are costly and limited. This study presents a time-resolved reconstruction framework that uses limited two-dimensional, three-component velocity field data to approximate 3D wake dynamics. We experimentally evaluated the Snapshot Optimization (SO) method, previously applied only to stationary bluff body wakes, on time-resolved vortex-induced vibration (VIV) of a flexibly mounted cylinder. Results show that SO captures key flow features when spanwise variations are moderate. However, in highly three-dimensional flows, such as those around a flexible wing undergoing dynamic deformation, the global turbulence homogeneity assumption underlying SO breaks down, leading to discontinuities and reduced accuracy. To address this, we introduce Sectional Snapshot Optimization (SSO), a novel extension that partitions the spanwise domain into locally homogeneous regions. Optimal measurement planes are selected via unsupervised K-means clustering and the elbow method. Using volumetric Particle Tracking Velocimetry (PTV) as reference, we demonstrate that SSO substantially improves spatial coherence and continuity of reconstructed flow field.