Numerical Study on the Energy-Harvesting Performance of a Flapping Foil Under Vortical-Gust Encounters

Coherent vortices alter flapping-foil energy harvesting, but wake-generated vortex properties and timing are coupled to upstream-body kinematics. We use two-dimensional immersed boundary–lattice Boltzmann simulations of a prescribed heaving–pitching NACA0015 foil at Re=1100. An independently prescribed Taylor vortex allows nominal encounter phase, body-fixed offset, diameter, and intensity to be varied at fixed kinematics. Production-grid C¯P is within 0.10% of the fine-grid result; the fine-grid diffusion test gives a maximum full-field velocity L2 error of 0.0690% against the analytical solution over 0≤t*≤4. For the reference vortex with a pivot-centered nominal target (D/c=vθm/U∞=1), nominal-encounter-aligned mean power coefficients of 0.747, 0.862, and 0.987 occur at ψe=0.10, 0.40, and 0.60, respectively, compared with 0.832 without gusts. These define the power-reducing (PR), near-baseline (NB), and power-enhancing (PE) cases. Within the sampled ranges, diameter is associated mainly with disturbance reach and duration, intensity with loading magnitude, and offset with spatial overlap and interaction timing. Power variations are consistent with the timing of vortex-modified loading relative to prescribed foil motion. In three same-sign, once-per-cycle sequences, the PR–NB–PE ordering persists despite residual-wake interactions, with sustained mean power coefficients of 0.763, 0.916, and 0.965, respectively. Nominal encounter phase and foil placement should be considered jointly for repeatable or predictable vortex passages.