# Coupling Motion and Energy Harvesting of Two Side-by-Side Flexible Plates in a 3D Uniform Flow
## 4 Conclusions  
The fluid-structure interaction problems of finite aspect ratio flexible plates in a uniform flow have been numerically studied. In the framework of the simulations, the lattice Boltzmann method combined with the immersed boundary and finite element method was used to solve the flow field  
Figure 19: Performance of energy harvesting _versus_ transverse distance: (**a**) bending energy; (**b**) efficiency of bending energy conversion. and the plate's passive flapping. To compute the equations efficiently in the 3D flow field, the fluid domain was discretized by unifying Cartesian grids, while the structure domain was discretized by Lagrangian grids. To validate this coupled algorithm, the dynamics of flow past a square flexible plate were simulated at low Reynolds number. The results of the validation show good agreements with previous studies by CFD simulations, indicating the efficiency and accuracy of the present method. Then, numerical simulations based on various parameters were carried out, and the mechanisms governing the motions of flexible plates were analyzed systematically. The results related to the plates' passive flapping dynamics are briefly summarized as follows. Firstly, the effects of aspect ratio on the fluid-structure interaction dynamics of an isolated plate in a uniform flow have been studied. We have found that the flexible plate can flap periodically with a large amplitude. This passive flapping behavior contains transverse and spanwise deformation. The flexible plate with a larger aspect ratio induced a larger flapping amplitude and Strouhal number. Furthermore, the flexible plate with a larger aspect ratio was subjected to greater drag and lift force. Further, the vortex shed from the side-edge was merged with the one shed from the trailing-edge and formed a hairpin-like structure. The shedding of the side-edge vortex was the main cause for its spanwise deformation. Secondly, the effects of aspect ratio and transverse gap distance on the hydrodynamics interactions between two side-by-side flexible plates have been studied. With the transverse distance getting higher, we have found three distinct coupling modes of the plates' motion, including single-plate mode, symmetrical flapping mode and decoupled mode. In the single-plate mode, both of the two plates flapped synchronously, and there was a row of vortex shed from the plates' system, acting like the characteristic of a single plate in the same flow. In the symmetrical flapping mode, the two plates flapped out of phase, and there was a row of vortex shed form each plate, but with opposite directions. In the decoupled mode, each of the plates flapped synchronously, and there was a row of vortex with the same direction shed from each one, acting like two isolated plates flapping passively in the same flow field. Compared to the flow past an isolated plate, when the plates' motion was in the single-plate mode, those with a higher aspect ratio got larger flapping amplitudes. Further, the phenomenon of drag reduction was found when the plates' aspect ratios were less than 1.0 or the higher aspect ratio plates flap in the symmetrical flapping or decoupled mode. For the energy conversion performance, the wider plate in the side-by-side configuration can capture more bending energy than in the isolated situation, while the slender plate captures less bending energy than in the isolated situation. For the purpose of improving the bending energy conversion efficiency, the plate in the side-by-side configuration is better than in the isolated situation. More specifically, the optimized selection for higher bending energy conversion efficiency is the plate flapping in single-plate mode, especially the plate with a higher aspect ratio. This work has provided several physical insights into the understanding of aquatic animal swimming and is expected to inspire the development of bionic thrusters or renewable energy harvesters.