## 3 Results and Discussions
### Adaptability under Multiple Kinetic Parameters  
Under the specified condition, the optimal configuration has been determined according to above analysis (\(D=11.0\%\) of c, \(X=0.5\%\) of c, \(Y=0\)). The implementation of this configuration results in a notable enhancement in energy harvesting efficiency up to \(19.26\%\) compared to the case without the cylindrical spoiler structure. To further investigate whether the cylindrical spoiler structure is equally effective in terms of performance improvement for a wide range of flutter motion parameters, relatively conservative cylinder parameters (\(D=3.0\%\) of c, \(X=0.5\%\) of c, \(Y=0\)) are chosen for this study instead of the optimal cylindrical spoiler structure parameters from the previous study. This approach allows for the further exploration of the adaptability of the trailing edge cylindrical structure under multiple kinetic parameters, and the purpose of not choosing the optimal trailing edge cylindrical structure is to minimize marginal effects and improve stability, while it can highlight the impact of different motion parameters on the energy harvesting performance. To begin with, the aerodynamic performance of the oscillating foil with a trailing edge cylindrical spoiler structure (\(D=3.0\%\) of c, \(X=0.5\%\) of c, and \(Y=0\)) is computed across a range of nondimensional reduced frequencies (\(f^{*}\)), from \(0.2\) to \(1.0\). Other parameters are kept constant to investigate the effectiveness of the new flow control method at various reduced frequencies. In Figure 15, the fluctuation of the energy harvesting efficiency is depicted as it varies with the nondimensional reduced frequency, both with and without the cylindrical spoiler structure. The energy harvesting efficiency of the oscillating foil increases with the reduced frequency up to a certain point before decreasing. Specifically, the optimal efficiency of the foil with the cylindrical structure is found to be \(8.17\%\) higher than the one without, under the same operating parameters. This optimal energy harvesting efficiency for both types of foils is achieved at a reduced frequency of \(0.6\). Notably, at a reduced frequency of \(0.2\), the cylindrical turbulence structure provides the greatest relative increase of \(22.39\%\) in efficiency, as the oscillating foils are in a relatively low-level energy harvesting performance state. It is worth mentioning that the energy harvesting efficiency of the oscillating foil equipped with the trailing edge cylindrical spoiler structure consistently surpasses that of the foil without for all the reduced frequencies examined in Figure 15. This suggests that the newly proposed flow control method, involving the use of cylindrical turbulence structures at the trailing edge of the oscillating foil, is effective over a broad range of reduced frequencies. Figure 14: Distribution of the pressure coefficient on the surface of the oscillating foil with/ without a cylindrical spoiler structure at the trailing edge for different cylinder longitudinal spacings. (**a**) \(t/T=0.25\); (**b**) \(t/T=0.75\). Subsequently, the aerodynamic performance of the oscillating foil with a trailing edge cylindrical spoiler structure (\(D\) = 3.0% of c, \(X\) = 0.5% of c, \(Y\) = 0) is computed across a wide range of relative heaving amplitudes (\(H/c\)), spanning from 0.2 to 1.4, as illustrated in Figure 16. The depicted trend in the figure reveals that the efficiency of the oscillating foil initially increases, followed by a subsequent decrease, with the rise in the relative heaving amplitude. Furthermore, it is observed that the performance of the oscillating foil equipped with a cylinder at the trailing edge consistently outperforms that of the one without, across all the relative heaving amplitudes. Notably, at a relative heaving amplitude of 0.4, the efficiency difference between the oscillating foil with and without the cylindrical spoiler structure is at its maximum.