## 3 Results and Discussions
### Effect of Cylinder Transverse Spacing on the Energy Harvesting Performance  
Retaining the same cylindrical diameter (\(D\) = 3.0% of c) and longitudinal spacing (\(Y\) = 0), the cylindrical transverse spacing \(X\) is varied at discrete intervals, from 0.5% of c to 65.5% of c. Subsequently, we evaluate the foils' aerodynamic traits under identical conditions to investigate the impact of cylinders with varying transverse spacing \(X\) on the efficacy of energy extraction. Figure 9a illustrates the mean total power coefficient during one cycle and the efficiency of the oscillating foil with varying \(X\) of the cylinders. The transverse spacing ranging from 0.5% of c to 2.5% of c yields a higher energy harvesting efficiency than the foil without cylinders. At \(X\) = 0.5% of c, the average total power coefficient is 0.4543, with an energy harvesting efficiency of 19.78%, showing a 12.39% improvement compared to the configuration without cylinders. Conversely, the transverse spacing in the range of 3.5% of c to 65.5% of c results in a lower energy harvesting efficiency. When \(X\) = 9.5% of c, the energy harvesting efficiency is 2.10% lower than that of the original foil without cylinders, representing the minimum efficiency in the evaluated operating range. Beyond \(X\) = 9.5% of c, the efficacy of energy harvesting decreases, becoming equivalent to the foil  
Figure 8: Distribution of the pressure coefficient on the surface of the oscillating foil with/without a cylindrical spoiler structure at the trailing edge for different diameters. (**a**) \(t/T\) = 0.25; (**b**) \(t/T\) = 0.75.  
without a cylindrical spoiler structure at \(X=65.5\%\) of c. Practical applications should avoid unfavorable transverse spacing to enhance energy harvesting efficiency. Figure 9: Comparison of \(C_{Pm}\)\(\mathcal{S}\)\(\eta\), \(C_{P}\), \(C_{Fy}\), \(C_{Py}\), \(C_{M}\), and \(C_{P\theta}\) of the oscillating foil with/without a cylindrical spoiler structure at the trailing edge for different cylinder transverse spacings: (**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. Figure 9b presents curves depicting the fluctuation of the instantaneous total power coefficient for the oscillating foil with different cylindrical transverse spacings. For \(X\) equal to or less than 9.5% of c, the instantaneous total power coefficient near both the peak and the valley decreases as \(X\) increases, with smaller transverse spacing exhibiting the best energy harvesting performance. When the spacing is greater than 9.5% of c, the instantaneous total power coefficient near the peak slightly increases, and the change near the valley is not obvious, resulting in a slight improvement in energy harvesting performance until \(X=65.5\%\) of c.  
Figure 9c,d show the variations in instantaneous lift coefficients and heaving power coefficients. For transverse spacing less than or equal to 9.5% of c, the instantaneous lift coefficient decreases near the peak and increases near the valley as the transverse spacing increases. Simultaneously, the instantaneous heaving power coefficient declines near the peak and rises near the valley. Figure 9e,f illustrate the variation of the instantaneous torque coefficient and the instantaneous pitching power coefficient. The maximum instantaneous torque coefficient occurs around \(t/T=0.2\) and 0.7, while the instantaneous pitching angular velocity achieves its minimum value at \(t/T=0.5\). The transient pitching power coefficient exhibits asymmetry between the front and rear half-cycles in one cycle, resulting in a small average pitching power coefficient, contributing little to the overall average total power coefficient.