## 3 Results and Discussions
### Effect of Cylinder Diameter on the Energy Harvesting Performance  
Under specific conditions (\(\theta_{0}=50^{\circ}\), \(\phi=90^{\circ}\), \(H_{o}/c=1\), \(f^{*}=0.14\), and \(Re=1100\)), the diameter (\(D\)) of the trailing edge cylinder is varied, ranging from 1.0% to 11.0% of the chord length, while maintaining constant transverse spacing (\(X=0.5\%\) of c) and longitudinal spacing (\(Y=0\)). The aerodynamic performance of the oscillating foil is assessed under identical conditions to analyze variations with and without cylinders of different diameters. In Figure 5(a), the curves depicting the mean power coefficient and efficiency of the oscillating foil across various cylindrical diameters are presented. The dashed lines represent the original foil without a cylinder, with mean power coefficient and efficiency values of 0.4042 and 17.60%, respectively. A noticeable enhancement in energy harvesting performance is observed with an increasing cylinder diameter. Specifically, at a cylinder diameter of 11.0% of c, the average total power coefficient reaches 0.4820, indicating a substantial 19.26% improvement compared to energy harvesting without a cylinder. An in-depth investigation into the instantaneous total power coefficient reveals fluctuation patterns for distinct cylinder diameters, as shown in Figure 5(b). Notably, the trend exhibits a diminishing steepness beyond a cylinder diameter of 7.0% of c, which is not depicted beyond this limit. The distinctions between curves for various cylindrical diameters are primarily evident in the range around peak and valley values. Overall, the energy capturing efficiencies of the oscillating foil with a cylinder surpass those of the foil without. There exists a direct correlation between the diameter of the trailing edge cylinder and the peak value, suggesting that a larger cylinder diameter leads to a higher peak value. This trend aligns with observations in the mean power coefficient, emphasizing the comparable nature of trends in mean power coefficient and energy capturing efficiency. Figure 5(c),d depict the variation of the instantaneous lift coefficient and the instantaneous heaving power coefficient of the oscillating foil, respectively. As the cylinder diameter increases, the peak values of the instantaneous lift coefficient and heaving power coefficient of the foil increase, while the valley values decrease. The maximum instantaneous heaving power coefficient occurs during the interval between the time of the instantaneous lift coefficient and the heaving speed reaching its maximum. Despite a synchronous difference existing between lift and heaving speed, the foil predominantly performs positive work in the direction of heaving throughout most of the cycle. Figure 5(e),f show the curves of the instantaneous torque coefficient and the instantaneous pitching power coefficient of the oscillating foil, respectively. The foil with a cylindrical spoiler structure has larger maximum values and smaller valley values for both coefficients than the foil without the spoiler structure. The instantaneous torque coefficients reach their maxima around \(t/T=0.2\) and 0.7, while the instantaneous pitching angular velocity has its minimum value at \(t/T=0.5\). The cylinder diameter does not change the timing of the maxima. The instantaneous pitching power coefficient, which is directly proportional to the product of the instantaneous torque coefficient and the pitching angular velocity, has its second peak between 0.4 and 0.5 cycles. In this interval, both the instantaneous torque coefficient and the pitching angular velocity are negative. However, the  
direction of the instantaneous torque does not match well with the direction of the pitching angular velocity over the entire cycle. The time difference between them is almost half of the cycle, which makes the instantaneous pitching power coefficient positive for most of the first half-cycle and negative for most of the second half-cycle.