# Study on the Propulsion Characteristics of a Flapping Flat-Plate Pumping Device
## 5 Conclusions  
This study, based on numerical simulation methods, investigates the effects of different flapping modes and channel outlet angles on the water-pushing performance and flow field characteristics of a flapping flat-plate hydrofoil pumping device, providing theoretical support and reference for the engineering design and practical application of bionic water-pumping systems. The main conclusions are as follows:  
* Both simple harmonic and quasi-harmonic motions generate reverse Karman vortex streets, but differences exist in wake structure and thrust characteristics. The wake generated by simple harmonic motion exhibits good symmetry, while the wake in quasi-harmonic motion deflects downward, with the degree of deflection increasing as the flapping frequency rises.
* Simple harmonic motion maintains a relatively high pumping efficiency overall, reaching a maximum of 21.5% at a flapping frequency of 0.7 Hz. In contrast, the pumping efficiency of quasi-harmonic motion fluctuates more significantly across frequencies, with a peak of 17.8% at 0.6 Hz. At this frequency, the pumping efficiency of simple harmonic motion is still 20.2% higher than the peak value of quasi-harmonic motion.
* Variation in the channel outlet angle does not significantly change the number of vortices but does affect their spatial distribution. Negative outlet angles enhance flow  
Figure 19: Comparison between simulated and experimental flow velocities.  
separation at the channel exit, resulting in more concentrated vortices near the outlet. However, at \(\alpha=-30^{\circ}\), a distinct recirculation region appears above the outlet, causing the wake to deflect upward and compromising the directionality of water propulsion. In contrast, positive outlet angles cause the fluid to stretch along the outlet direction under wall shear effects, forming elongated vortex structures. As the angle increases, the boundary layer entrainment effect becomes more pronounced, altering the wake expansion pattern and leading to reduced water-pushing performance. With variation in the channel outlet angle, pumping efficiency and propulsion efficiency exhibit a strong positive correlation. Both reach their peak values at \(\alpha=-10^{\circ}\), with pumping efficiency at 22.9% and propulsion efficiency at 25.9%. Compared to \(\alpha=0^{\circ}\), pumping efficiency increases by 8.5% and propulsion efficiency by 10.2%. A moderate negative angle helps enhance fluid propulsion performance.  
While the present study includes experimental validation based on outlet flow velocity measurements, further experimental work is planned to enhance the verification of the numerical model. Specifically, future studies will incorporate thrust measurements and flow visualization techniques such as particle image velocimetry (PIV) to capture unsteady flow characteristics and vortex evolution in greater detail. These efforts will provide more comprehensive validation of the CFD model's predictive capabilities.  
[PERSON] articulated the main research directions on the Influence of the Flapping Mode of the Device and the Outlet Angle of the Flow Channel on the Hydrodynamic Performance of the Device; [PERSON] was involved in the full writing of the manuscript as well as in data processing; [PERSON] participated in the construction of the model and the design details of the device; [PERSON] provided the writing ideas. [PERSON] reviewed the manuscript. All authors have read and agreed to the published version of the manuscript. This research was funded by the Zhejiang Provincial Key Research and Development Project (Grant No. 2021C03019). Not applicable. Not applicable. Not applicable.  
**Data Availability Statement:** All data, models, and code generated or used during the study appear in the submitted article. The authors gratefully thank the Zhejiang Provincial Key Research and Development Project for their financial support.  
The authors declare no conflicts of interest.