Piezoelectric galloping energy harvesting enhanced by topological equivalent aerodynamic design

The topological equivalent aerodynamic method is introduced to design a funnel-shape galloping energy harvester with wide working wind-speed range and high normalized harvesting power. The funnel shape bluff body is designed from the square bluff body to avoid the vortex reattachment, enhance the structural non stream fluid flow and allow the pressure direction along the lift force. This design enlarges the aerodynamic force and thus improves the energy harvesting efficiency. To analyze the harvesting performance, the extended Hamilton principle and Gauss law are employed to derive the electro-mechanical coupled governing equations. The Galerkin procedure and equivalent structure method are then used to calculate the expressions of the onset galloping wind speed and harvested power density. Three energy harvesters of the square, triangular and funnel-shaped bluff bodies are tested in a closed direct-flow wind tunnel. The maximal experimental power densities for the funnel-shape, triangle and square bluff bodies are respectively 2.34 mW/cm(3), 1.56 mW/cm(3) and 0.207 mW/cm(3). The corresponding experimental onset galloping wind speeds are 7 m/s, 9 m/s and 13 m/s. The good agreement between the theoretical prediction and experimental result demonstrates the accuracy of the mathematical model. The parameter analysis using the analytical model indicates that the energy harvester with funnel-shape bluff body always maintains the smallest onset speed and the highest power density. Besides, compared with previous studies of energy harvesting from the wind, the proposed energy harvester has the largest normalized power density. To better understand the fluid dynamics, twodimensional unsteady numerical simulation is employed to show that the funnel shape has the largest lift coefficient compared to the other two cases. The velocity and pressure contours explain the physical cause that the flow pattern of the funnel shape can maintain the longest vortex region and highest vortex intensity.