How Does Energy Harvesting from a Fluttering Foil Influence Its Nonlinear Dynamics?

Dilip Thakur, Faisal Muhammad and Muhammad Saif Ullah Khalid ()
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Dilip Thakur: Nature-Inspired Engineering Research Lab (NIERL), Department of Mechanical & Mechatronics Engineering, Lakehead University, Thunder Bay, ON P7B 5E1, Canada
Faisal Muhammad: Nature-Inspired Engineering Research Lab (NIERL), Department of Mechanical & Mechatronics Engineering, Lakehead University, Thunder Bay, ON P7B 5E1, Canada
Muhammad Saif Ullah Khalid: Nature-Inspired Engineering Research Lab (NIERL), Department of Mechanical & Mechatronics Engineering, Lakehead University, Thunder Bay, ON P7B 5E1, Canada

Energies, 2025, vol. 18, issue 15, 1-26

Abstract: This study investigates the nonlinear aeroelastic behavior and energy harvesting performance of a two-degrees-of-freedom NACA 0012 airfoil under varying reduced velocities and electrical load resistances. The system exhibits a range of dynamic responses, including periodic and chaotic states, governed by strong fluid–structure interactions. Nonlinear oscillations first appear near the critical reduced velocity U r * = 6 , with large-amplitude limit-cycle oscillations emerging around U r * = 8 in the absence of the electrical loading. As the load resistance increases, this transition shifts to higher U r * , reflecting the damping effect of the electrical load. Fourier spectra reveal the presence of odd and even superharmonics in the lift coefficient, indicating nonlinearities induced by fluid–structure coupling, which diminishes at higher resistances. Phase portraits and Poincaré maps capture transitions across dynamical regimes, from periodic to chaotic behavior, particularly at a low resistance. The voltage output correlates with variations in the lift force, reaching its maximum at an intermediate resistance before declining due to a suppressing nonlinearity. Flow visualizations identify various vortex shedding patterns, including single (S), paired (P), triplet (T), multiple-pair (mP) and pair with single (P + S) that weaken at higher resistances and reduced velocities. The results demonstrate that nonlinearity plays a critical role in efficient voltage generation but remains effective only within specific parameter ranges.

Keywords: arbitrary Lagrangian–Eulerian method; non-linear dynamics; harmonics; energy harvesting; limit cycle oscillation; fluid structure–electrical interactions; fluttering foils; dynamic stall (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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