Coupled fluid-structure dynamics and multi-fidelity modeling of interacting inverted foils

Cantilevered elastic foils in the inverted configuration undergo self-induced, large-amplitude flapping in a flowing fluid, generating structural strain energy that can be harvested for electricity. In arrays, wake- and proximity-induced hydrodynamic interactions modify this response through coupled fluid-structure dynamics. Exploring the parameter space of stiffness, mass ratio, and spacing with high-fidelity simulation alone is prohibitively expensive. This thesis investigates the coupled dynamics using high-fidelity fluid-structure interaction (FSI) simulations and a physics-informed data-driven surrogate. The influence of external wake forcing is first examined for a flexible inverted foil downstream of a stationary cylinder over a range of bending rigidities and mass ratios. Relative to the isolated foil, interaction with the imposed vortex shedding produces small- and moderate-amplitude flapping regimes. Their transitions are governed by competition between elastic restoring forces and flow-induced inertial loading. An effective stiffness parameter based on this balance collapses the response across mass ratios and bending rigidities, providing a reduced-order characterization of wake-induced transitions. Building on these wake-forced dynamics, interacting foil arrays are then investigated using rigid foils mounted on torsional springs to isolate fluid-mediated interactions from distributed structural deformation. In side-by-side configurations, cross-gap shear-layer interactions accelerate the gap flow, amplify oscillations, and broaden sustained synchronized flapping. In tandem configurations, the upstream foil largely follows isolated-foil dynamics, while the downstream foil is governed by the convected upstream wake. This interaction suppresses its peak oscillation amplitude while extending sustained oscillations over a broader stiffness range. Spacing-dependent corrections to the effective stiffness collapse the collective response onto the isolated-foil scaling, revealing the distinct roles of proximity and wake interactions. To enable efficient prediction across parameter ranges, a hypergraph neural network surrogate (φ-GNN) is developed on a node-element hypergraph constructed from the finite element mesh. It reproduces tip displacement within 1.1%, force coefficients within 1.5%, and energy-transfer effectiveness within 2.2% across all mass ratios at two orders of magnitude lower computational cost than the full-order solver. Node-level Shapley-value attribution further shows that its predictions depend on physical regions, including the leading-edge vortex, surface shear layers, and stagnation region. Together, the interaction scaling and surrogate model enable efficient characterization and prediction of foil dynamics.