Energy harvesting characteristics of flapping turbines using non-sinusoidal trajectories

This study constructs a flapping motion model with an elliptic equation based non-sinusoidal trajectory through numerical simulation, systematically investigating the influence mechanisms of heaving and pitching amplitudes, reduced frequency, and non-sinusoidal parameters on energy extraction performance. The results reveal that when the non-sinusoidal parameter S is set to 1.4, the pitching amplitude θ0 to 90°, the heaving amplitude h0 to 0.25, and the reduced frequency f∗ to 0.16, the energy extraction efficiency reaches 53.7%, representing a 17.6% improvement over the optimal sinusoidal trajectory and approaching the Betz theoretical limit. The study indicates that non-sinusoidal trajectories can overcome the operational constraints of heaving and pitching amplitudes through parametric optimization. Specifically, sawtooth-like trajectories are better suited for small-amplitude conditions (h0/c<1, θ0≥100°), while square-wave trajectories exhibit superior performance under large-amplitude conditions (h0/c>1, θ0<100°). Moreover, the reduced frequency maintains a high-efficiency regime (η>50%) within an extended range of 0.12 to 0.2. Through vortices dynamics analysis, four characteristic vorticity patterns are identified, revealing that the formation of a reverse Kármán vortex street is strongly correlated with high energy extraction efficiency. An evaluation criterion about the effective angle of attack αe is established, demonstrating that high-efficiency energy harvesting is achievable when |αe| ranges between 0.4 to 0.65 under t/T=0.1, with this principle exhibiting universal applicability across a reduced frequency range of 0.14−0.24. The findings provide a theoretical foundation for optimizing non-sinusoidal trajectory in flapping-foil energy harvesting systems, while also highlighting three-dimensional structural effects and intelligent algorithm-based predictions as key directions for future research.