## 3 Results and Discussions
### Effect of Cylinder Longitudinal Spacing on the Energy Harvesting Performance
The opposite patterns emerge at \(t/T\)s of 0.4 and 0.9. Since the instantaneous pitching angular velocity is maximal at \(t/T\)s of 0 and 1 and minimal at a \(t/T\) of 0.5, it influences the timing of the peak and trough values in both coefficients, resulting in multiple peaks and troughs in the pitching power coefficient curve. The first peak of this curve slightly precedes that of the moment coefficient curve, reflecting the impact of adding cylinders or changing their longitudinal spacing in both coefficients. The second peak of the pitching power coefficient curve occurs between \(t/T\)s of 0.4 and 0.5, aligning with the first trough of the moment coefficient curve. The second trough of the pitching power coefficient curve precedes a \(t/T\) of 0.7, displaying an opposite pattern to the second peak of the torque coefficient curve due to the reversal of the pitching angular velocity at this point. The third trough of the pitching power coefficient curve mirrors the second trough of the torque coefficient curve. In summary, there is a lack of synchronization between the direction of the transient torque and the direction of the foil pitching motion during one cycle; that is, they differ for almost half of each cycle, resulting in a near-zero average transient pitching power coefficient for the foil over each cycle, weakly affecting its total energy harvesting performance. Figure 13 presents a comprehensive analysis of the pressure coefficient distribution and streamlines, offering detailed insights into the intricate fluid dynamics around the oscillating foil with varying longitudinal spacings of the cylinder. At \(Y=0\%\) of c, the presence of the cylinder enhances fluid backflow on both surfaces of the foil's trailing edge, leading to increased pressure coefficients on both surfaces near the trailing edge. This augmentation results in increased pressure coefficients on both the upper and lower surfaces near the trailing edge. The localized pressure increase plays a pivotal role in generating a lifting effect on the trailing edge during both downward and upward heaving  
motions. This lifting effect contributes to an overall augmentation of the lift coefficient and energy harvesting performance in the oscillating foil. As the longitudinal spacing of the cylinder increases, more nuanced examination reveals how the localized high-pressure area at the forefront of the cylinder interacts differently during downward and upward heaving due to deviation from the foil mid-chord. This discrepancy becomes notably evident in the pressure coefficient distribution when \(t/T=0.75\). Specifically, at \(Y=0.5\%\) of c, the high-pressure area at the forefront of the cylinder positively influences the trailing edge of the flutter. However, a significant shift occurs when the longitudinal spacing of the cylinder exceeds or equals 2.0% of c. The altered flow conditions result in the cylinder exhibiting completely opposite effects during the initial and latter half-cycles of the foil. This observed trend indicates a gradual weakening of the enhancement effect on the energy harvesting performance and further underscores the intricate interplay between flow dynamics, vortices, and energy harvesting efficiency. The distribution curves of the surface pressure coefficient of the foil for different longitudinal spacings of the cylinder are presented in Figure 14. At \(Y=0\%\) of c, the corresponding curve exhibits the smallest range of the pressure coefficient distribution envelope, resulting in the foil experiencing the least lift value. Conversely, when the \(t/T\) is 0.25 and \(Y=2.0\%\) of c, the curve shows the broadest span of the pressure coefficient distribution envelope, accompanied by the most significant pressure differential between the upper and lower surfaces. At a \(t/T\) of 0.75, the pressure coefficient distribution curve range is the largest for \(Y=0\%\) of c, leading to the foil experiencing the greatest lift value.