## 3 Results
### Hardness Effects on Hydrofoil Hydrodynamic Characteristics
The researchers observed that the fluid separation resulted in the formation of a small reflux region in the vicinity of the wingtip, which exerted a significant influence on the generation and evolution of the vortices in this region. Similarly, the flow field around the flexible hydrofoil was investigated in this study. The results demonstrated that the distribution of the vortices and the characteristics of the flow field had a significant impact on the performance of the hydrofoil. As illustrated in Figure 12, the  
Figure 11: Transient thrust of hydrofoils at a single oscillation cycle of motion with five materials. Figure 10: Hydrofoil chord-wise strain for five materials in a single kinematic cycle. generation of chord-wise deformation by the hydrofoil resulted in the partial absorption of the trailing edge vortex during the process of shedding, due to the hydrofoil shear force. The appropriate chord-wise deformation had the effect of reducing the viscous drag. The process of vortex shedding was accompanied by a rise in the drag coefficient, which was a consequence of the strengthening of the central vortex of the trailing edge vortex following its shedding. This, in turn, led to an increase in the drag experienced by the hydrofoil during its motion, resulting in a rise in the peak instantaneous thrust. To better assess the effect of hydrofoil hardness on the pumping efficiency, a comparative analysis of the hydrodynamic performance of hydrofoils with different Shore hardness D is also presented in this section. The analyses included drag-to-lift ratio, pumping efficiency, and propulsion efficiency as shown in Figure 13. The drag-to-lift ratio reflected the hydrodynamic performance of the hydrofoil during motion. A higher drag-to-lift ratio indicates that the hydrofoil can produce the same lift with less drag, which means less energy loss and higher efficiency. The results showed that the hydrodynamic performance of the hydrofoil was best when the Shore hardness was D50. When the Shore hardness exceeded D50, the drag-to-lift ratio, pumping efficiency, and propulsion efficiency of the hydrofoil gradually decreased as the hydrofoil hardness increased, resulting in a decrease in hydrodynamic performance. Conversely, when the Shore value was less than D50, the decrease in hydrofoil hardness resulted in a significant decrease in the drag-to-lift ratio and propulsion performance. Figure 12: Trailing edge vortex shedding process. Figure 13: Comparison of hydrodynamic performance of hydrofoils of different stiffnesses under a single oscillation cycle. Analysis of the results showed that the hydrofoil was capable of moderate deformation while maintaining a high degree of shape stability when its Shore hardness was D50. This increased the effective angle of attack and improved propulsion efficiency. A hydrofoil with excessive hardness was unable to adapt effectively to changes in hydrodynamic load, resulting in a reduction in the lift resistance ratio and a consequent deterioration in pumping and propulsion efficiency. Hydrofoils with insufficient hardness exhibited excessive deformation during oscillation, which resulted in partial energy loss and exacerbated tail vortex dissipation, thereby reducing the hydrodynamic performance of the hydrofoil. Furthermore, Figure 13 shows that the hardness of the hydrofoil had a pronounced effect on the propulsive efficiency, but a less pronounced effect on the pumping efficiency. This was mainly since the pumping efficiency is mainly dependent on the pressure difference between the inlet and outlet of the runner. Consequently, the deformation caused by the blade movement had relatively little effect on this.