## 3 Results
### Motion Way Effects on Hydrofoil Hydrodynamic Characteristics
When the trailing edge vortex was shed, the wingtip destroyed the integrity of the trailing edge vortex along the oblique direction, resulting in part of the trailing edge vortex being retained on the surface of the hydrofoil, which dissipated and generated additional drag during the reversed oscillations, consuming a large amount of the central vortex strength of the trailing edge vortex, and led to the rapid dissipation of the subsequently reversed Karman vortex street. Comparing the vortex nephograms at the oscillation amplitude position, it was found that the flexible hydrofoil deformed due to inertial force at this position, exacerbating the negative angle-of-attack phenomenon, while the rigid wing just avoided the extra energy loss due to deformation. This phenomenon was more helpful in explaining the hydrodynamic difference between the rigid hydrofoil  
Figure 15: Comparison of the vortex nephograms of the flow field under different oscillation modes: (**a**) Inward oscillation mode. (**b**) Outward oscillation mode. (**c**) Pitch-only oscillation mode. and flexible hydrofoil in the outer oscillation and pitch-only oscillation modes as they appeared in Figure 14, which will be further analyzed in conjunction with the thrust curves and vortex nephogram later. Figure 17 illustrates the vortex structures of the rigid and flexible hydrofoils in response to inward oscillation motion over the course of a single oscillation cycle. The analysis of the vortex structures indicated that the inward oscillation motion can result in the elongation of the shedding trailing edge vortex in a direction perpendicular to the incoming flow velocity. This resulted in the strengthening of the central vortex of the trailing edge vortex, an enhancement of the kinetic energy along the direction of the incoming flow velocity at the time of shedding, and a significant reduction in the dissipation speed of the vortex volume. In the case of the flexible hydrofoil, the chord-wise deformation of the hydrofoil reduced the surface resistance between the shedding vortex and the airfoil surface, increased the effective angle of attack of the hydrofoil, and was conducive to the enhancement of the trailing edge vortex strength. Conversely, the rigid hydrofoil was devoid of deformation at the wingtip, thereby retaining surface drag. This resulted in a reduction in hydrodynamic performance relative to the flexible hydrofoil. Figure 16: Comparison of the vortex structures on the surface of the rigid hydrofoil and the flexible hydrofoil under outward oscillating motion: (**a**) Rigid hydrofoil. (**b**) Flexible hydrofoil. Figure 17: Comparison of the vortex structures on the surface between the rigid hydrofoil and the flexible hydrofoil under inward oscillating motion: (**a**) Rigid hydrofoil. (**b**) Flexible hydrofoil. A more intuitive understanding of the force change of the hydrofoil during motion can be gained by linking the vortex structure change with the instantaneous thrust change. To illustrate, the flexible hydrofoil under consideration in this study exhibited distinct thrust curves in a single stable cycle across three distinct motion modes, as depicted in Figure 18. The results demonstrated that the flexible hydrofoil generated a heightened peak thrust under the outward oscillation motion, which can be attributed to the phenomenon of shed vortex stacking and squeezing. Near the wingtip, the outward oscillation motion gave rise to the accumulation of vortices at the trailing edge and the splitting of vortices at the wingtip, due to the deformation of the wingtip. This resulted in the consumption of additional kinetic energy during the reverse oscillation, which increased the instantaneous thrust of the hydrofoil, reduced the stability of the thrust curve, and consequently resulted in a significant efficiency loss. The pitch-only oscillation motion lacked the additional kinetic energy derived from the heaving motion.