Nonlinear dynamics and vortex mechanics for energy harvesting from fluttering wings

Abstract

This research investigates the nonlinear aeroelastic dynamics and energy harvesting performance of a two-degrees-of-freedom NACA 0012 wing under varying reduced velocities and electrical load resistances. In the first part of this work related to two-dimensional computational simulations, nonlinear oscillations emerge near the critical reduced velocity U∗r=6, with large amplitude limit-cycle oscillations forming around U∗r=8 in the absence of an electrical loading. As the electrical resistance increases, this transition is delayed, indicating the damping effect of the energy extraction mechanism. Fourier spectral analysis reveals the presence of both odd and even superharmonics in the aerodynamic lift force, highlighting the strong nonlinear fluid-structure coupling, which becomes less prominent at higher resistances. Phase portraits and Poincare maps demonstrate clear transitions between periodic and chaotic states, particularly under low resistance conditions. The voltage output is strongly correlated with fluctuations in the lift force, reaching a maximum at intermediate resistance before declining due to nonlinear suppression. Flow visualizations uncover a range of vortex shedding patterns, including single, paired, and multi-pair vortex configurations that weaken at high resistances and lower U∗r . Building upon the insights gained from two-dimensional simulations, this study is extended to three-dimensional configurations by systematically increasing the wing's spanwise length to 0.3c, 0.6c, and 0.9c. The three-dimensional analysis focuses on the conditions that yielded optimal voltage output in the two-dimensional simulation results, particularly at U∗r=10 for different load resistances. The objective is to examine how variations in spanwise length influence fluid-structure interactions, alter vortex formation and organization, and impact the onset and intensity of nonlinear behaviors. Also, the comparative analysis of the 3D and 2D results highlight the influence of spanwise flow instabilities on the energy harvesting performance. These findings provide valuable insights for identifying optimal spanwise length and operational parameters that enhance power generation efficiency in flutter-based energy harvesting systems.