# Coupling Motion and Energy Harvesting of Two Side-by-Side Flexible Plates in a 3D Uniform Flow
## 3 Results and Discussion
### Flow around Two Flexible Plates in Side-by-Side Arrangement
#### 3.2.2 Force and Energy Conversion  
The plate's deformation is associated with the fluid force and energy harvesting performance. Figure 18 shows the relative force coefficient _versus_ transverse distance, including (a) the maximum lift coefficient and (b) the mean drag coefficient. As shown in Figure 18a, the trends of lift amplitude are similar to those of the flapping amplitude. This can be explained briefly by the fact that the plates' passive flapping is mainly dependent on the lift fore on the boundary. The higher lift force can induce a larger flapping amplitude. As shown in Figure 18b, the trends of the drag coefficient are similar to those of the flapping amplitude, as well, but for different reasons. This can be explained briefly as follows. The drag force on the plate's boundary is due to the resistance to the incoming flow. This resistance force is proportional to the up-wind area. Hence, the higher amplitude produces a higher projection area vertical to the streamwise, leading to the production of a higher drag force. Regarding the value, the phenomenon of drag reduction is observed when the plates' aspect ratio is less than 1.0 or the higher aspect ratio plates flap under a large transverse distance. Figure 17: Three typical vortical patterns in the wake of two side-by-side flexible plates (\(AR=1.5\)): (**a**) single-plate mode (\(G_{z}=0.1\)); (**b**) symmetrical flapping mode (\(G_{z}=3.0\)); (**c**) decoupled mode (\(G_{z}=4.0\)) (Supplementary Video S4 is available online). Figure 18: The relative force coefficient _versus_ transverse distance: (**a**) maximum lift coefficient; (**b**) mean drag coefficient. Here, we examine the relation between coupling modes and energy capture efficiency. Once the plate's flapping motion is induced by the incoming flow, the deformation is highly dependent on the bending energy captured from the fluid's kinetic energy. The bending energy \(E_{b}\left(t\right)\) is expressed as:  
\[E_{b}\left(t\right)=\frac{K_{B}}{2}\int\int\sum_{i,j=1}^{2}\gamma_{ij}\frac{ \partial^{2}\mathbf{X}}{\partial s_{i}^{2}}\cdot\frac{\partial^{2}\mathbf{X}} {\partial s_{j}^{2}}ds_{1}ds_{2} \tag{14}\]  
The conversion efficiency from the fluid kinetic energy to the plate's bending energy can be defined as [51]:  
\[\eta=\frac{E_{b,\max}}{E_{k}}=\frac{E_{b,\max}}{0.5\rho/\Omega_{0}^{3}Z_{B,out} WT_{out}} \tag{15}\]  
where \(E_{b,\max}\) is the maximum bending energy at the largest deformation status; \(E_{k}\) is the kinetic energy of the incoming fluid passing through the maximum up-wind area (\(Z_{B,out}W\)) during a bending phase; \(T_{out}\) is the time from when point \(B\) crosses the equilibrium position to when it reaches the peak position. The performance of energy harvesting is shown in Figure 19, including (a) the bending energy and (b) the efficiency of bending energy conversion. In Figure 19a, the red dashed line denotes the result of an isolated plate. It is shown that \(E_{b,\max}/E_{b0,\max}\) of the wider (\(AR=1.5\)) plate decreases monotonically as \(G_{z}\) increases, while the result of the slender (\(AR=0.5\)) plate increases monotonically. As \(G_{z}\) increases, both of the results tend to approach the value \(1.0\). Obviously, the wider plate in side-by-side configuration can capture more energy than in the isolated situation, while the slender plate captures less bending energy. For the purpose of harvesting more bending energy, the optimized selection is the higher aspect ratio plate flapping in the single-plate mode. In Figure 19b, the \(\eta\) for both of the plates under different \(AR\) is decreasing monotonically with \(G_{z}\). Compared to the isolated result, it is found that \(\eta\) is amplified when the plates are placed in the side-by-side configuration. In the present study, the maximum \(\eta\) is \(0.57\), which is about \(32\%\) higher than in the isolated situation. For the purpose of improving the efficiency of bending energy conversion, the plate in the side-by-side configuration is better than in the isolated situation.