# Study on the Propulsion Characteristics of a Flapping Flat-Plate Pumping Device
## 4 Results
### Effect of Flow Channel Structure on the Water Body
#### 4.2.1 Effect of Flow Channel Structure on the Flow Field  
To investigate the influence of the outlet angle at the end of the flow channel on the hydrodynamic performance of the flapping hydrofoil device, seven sets of numerical simulations were conducted with a flapping frequency of 1 Hz. The channel outlet angle was varied from \(-30^{\circ}\) to \(30^{\circ}\) in \(10^{\circ}\) increments. The results are shown in Figure 15.  
Variation in the outlet angle of the flow channel does not significantly alter the number of vortices but does affect their spatial distribution. Negative outlet angles enhance flow separation at the channel exit, leading to more concentrated vortex structures near the outlet. In contrast, positive outlet angles cause the fluid to stretch along the outlet direction due to wall shear effects, forming elongated vortex structures and gradually disrupting the regularity of the wake. Figure 14: Vorticity contour maps at the channel outlet over one cycle. Figure 15: Vorticity contour maps for different outlet angles. When the outlet angle is \(\alpha=-10^{\circ}\), the wake of the flapping flat-plate hydrofoil maintains a stable alternating shedding pattern. No significant flow separation occurs at the channel outlet, and the flow field remains well organized. At \(\alpha=-20^{\circ}\), the trailing vortices at the outlet become slightly larger compared to \(\alpha=-10^{\circ}\), and the shear layer becomes more pronounced. However, at \(\alpha=-30^{\circ}\), changes in the shear layer at the outlet result in the formation of large vortices near the exit. Vorticity retention appears above the flapping flat-plate hydrofoil, increasing flow field non-uniformity and causing the wake to lose its reverse Karman symmetry and shift upward as a whole. Under positive outlet angle conditions, the trailing vortices exhibit relatively regular alternating shedding, and the reverse Karman vortex street structure remains largely unchanged. However, as the outlet angle increases, shear forces acting on the fluid as it leaves the channel wall cause the flow to stretch. As a result, the flow no longer rolls up into localized vortices but instead extends along the streamwise direction, forming elongated regions of high vorticity that gradually intensify. In addition, at outlet angles of \(\alpha=\pm 20^{\circ}\) and \(\alpha=\pm 30^{\circ}\), inward-converging vorticity regions can be observed along the upper and lower boundary layers outside the channel outlet. Due to the variation in outlet angle, a pressure difference arises between the upper and lower boundary layers, inducing an inward entrainment of fluid along the boundary layers. This causes the vorticity structures in the upper and lower boundary layers to converge toward the center region. This entrainment effect leads to a more concentrated overall wake structure, although it does not significantly alter the alternating shedding pattern of the wake. Figure 16 presents the velocity contour maps for different outlet angles. When the outlet angles are \(\alpha=-20^{\circ}\), \(-10^{\circ}\), \(0^{\circ}\), and \(10^{\circ}\), the flow velocity distribution in the wake region is uniform, with high-speed fluid concentrated at the center of the channel outlet, and no significant deflection of the wake is observed. Figure 16: Velocity contour maps at different outlet angles. When the outlet angle is positive (\(\alpha=10^{\circ},20^{\circ},30^{\circ}\)), a distinct elongated low-velocity region forms near the channel outlet, and as the angle increases, this low-velocity region becomes more pronounced and gradually extends in the flow direction. This is due to the positive outlet angle of the channel, which causes the fluid to experience stronger shear forces as it leaves the channel wall, leading to localized flow separation. This effect gradually intensifies with increasing angle, causing the low-velocity region to extend more noticeably downstream.