## 3 Results and Discussions
### Effect of Cylinder Diameter on the Energy Harvesting Performance
As a result, the mean pitching power coefficient over the entire cycle is relatively low, and it has little contribution to the overall average total power coefficient. This indicates that the foil mainly harvests energy through having motions. Figure 6: Comparison of \(C_{pn}\) & \(\eta\), \(C_{p}\), \(C_{Fy}\), \(C_{y}\), \(C_{M}\), and \(C_{p\theta}\) of the oscillating foil with/without cylindrical spoiler structure at the trailing edge for different diameters: (**a**) Average total power coefficient and efficiency; (**b**) instantaneous total power coefficient; (**c**) instantaneous lift coefficient; (**d**) instantaneous heaving power coefficients; (**e**) instantaneous torque coefficient; and (**f**) instantaneous pitching power coefficients. To comprehensively understand the aerodynamic flow field of oscillating foils and assess the influence of a cylindrical spoiler structure at the trailing edge on their energy harvesting performance, we employ pressure distribution and streamlines near the trailing edge for a further analysis, as illustrated in Figure 7. Specifically, we focus on two critical moments (\(t/T=0.25\) and \(0.75\)) during the entire motion cycle, representing opposite states in terms of pitching direction, having direction, and angle of attack. In the absence of a cylinder, the fluid flow near the trailing edge appears smooth. Taking \(t/T=0.2\) as an example, as the fluid traverses the foil's surface, an obstruction materializes on the upper surface, causing a reduction in fluid velocity and an increase in pressure. Consequently, a heightened pressure zone manifests on the upper surface at the forefront of the foil, while a low-pressure region emerges on the lower surface. With the introduction of the cylinder, a high-pressure zone forms on the cylinder surface. As depicted in the diagram, the increase in cylinder diameter not only amplifies the high-pressure zone but also extends its influence across a broader range of the flow field. This expansion is visually represented in the diagram, highlighting the larger area of high-pressure zone formation. Moreover, the initial parameter fixing the longitudinal spacing to 0, coupled with the symmetry of the cylinder about the median chord of the foil, leads to notable effects. Specifically, the presence of the cylinder enhances fluid backflow and accentuates pressure differentials near the trailing edge. The influence of the cylinder becomes more pronounced with an increasing diameter, intensifying the fluid reflow effect. This augmentation results in a heightened total pressure differential on the foil. Consequently, this intensified pressure distribution contributes to an elevation in the lift of the foil. Simultaneously, there is a corresponding increase in the instantaneous heaving power coefficient. These combined effects synergistically contribute to enhancing the overall energy harvesting efficiency of the system. Figure 8 shows the pressure coefficient distribution on the foil's surface for different cylinder diameters at \(t/Ts\) of 0.25 and 0.75, which are two critical moments in the motion  
Figure 7: Pressure coefficient cloud and streamline of the oscillating foil with/without cylindrical spoiler structure at the trailing edge for different diameters. (**a**) \(t/T=0.25\); (**b**) \(t/T=0.75\). cycle. The upper and lower curves correspond to the upper and lower surfaces of the foil, respectively, but they switch roles at a \(t/T\) of 0.75. The analysis of pressure coefficient distribution provides crucial insights into how the cylindrical spoiler structure influences the pressure dynamics on the foil's surface, further elucidating the mechanisms contributing to enhanced lift and energy harvesting efficiency. The flow characteristics and the cylinder effect are almost the same for both moments. For the original foil without the cylindrical spoiler structure, the pressure coefficient curves almost completely overlap at the trailing edge, signifying a negligible pressure disparity between the upper and lower surfaces.