Performance of Semi-Active Flapping Hydrofoil with Arc Trajectory
Abstract
:1. Introduction
2. Description and Definition of Flapping Foil Propulsion
2.1. Geometric Structure and Motion
2.2. Nondimensional Propulsive Indicators
3. Computational Method and Validation
3.1. Governing Equations
3.2. Mesh and Method
3.3. Validation
4. Results and Analysis
4.1. Propulsive Efficiency and the Thrust Coefficient
4.2. Angle of Attack Analysis
4.3. Analysis of Vortex Structure
5. Conclusions
- The influence of arm length and spring stiffness on the performance of the semi-active flapping foil is very clear. Increasing the length of the swing arm is beneficial to improving the peak efficiency of this semi-active flapping foil with circular-arc trajectory. At the same swing arm length, reducing the spring stiffness is also conducive to improving the peak efficiency of the flapping foil. The analysis of the maximum angle of attack shows that there is a definite corresponding relationship between the maximum angle of attack and the peak efficiency. For the flapping foil with the small aspect ratio NACA0012 airfoil structure, its peak efficiency is usually concentrated near , and it can maintain high efficiency within a certain range of .
- The influencing factors of the thrust coefficient of the semi-active flapping foil propulsion are complex. The length of the swinging arm, the spring stiffness, and the advance coefficient can all have a significant impact on the thrust coefficient of the flapping foil. On the whole, compared with the conventional semi-active foil, the elliptical trajectory system also has a large thrust coefficient at low advance coefficient. The curve of the thrust coefficient decreases monotonically with the increase in advance coefficient when the spring stiffness is small. Under the condition of high spring stiffness, there is a peak value and a valley value of the thrust coefficient. According to the analysis of the flow field, the reason for the thrust valley may be the combined effect of the swing angle and the angle of attack. At the valley point of the thrust coefficient, the angle of attack of the flapping foil is large, so the vortex separation of foil is significant and the lift value is low. At the same time, the swing angle is small, so the contribution of lift to the thrust is low, which leads to the appearance of the thrust valley. In addition, by comparing the thrust coefficient and the maximum angle of attack , it is found that too large or too small is unfavorable to the thrust under the working condition of the intermediate advance stage, and the peak thrust tends to appear in the range .
- The flow-field analysis of the low aspect ratio airfoil shows that the vortex rings are interlocked in the wake field of the flapping foil at a low advance speed. With the increase in advance coefficient, the vortex rings are gradually lengthened first, and then separated from each other. When the advance coefficient is further increased, the vortex ring is split into a tip vortex and separated vortex on the airfoil surface. From the reverse analysis, the vortex ring is the result of the tip vortex and the separated vortex on the airfoil surface sticking together, while the vortex ring interlocking is formed by the compression of the vortex ring in space.
Author Contributions
Funding
Conflicts of Interest
References
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Symbol | Units | Definition |
---|---|---|
VA | m/s | speed of the hull |
T | s | period of the flapping hydrofoil |
L/c | m | arm length |
c | m | chord length of the flapping hydrofoil |
H | m | spanwise of the flapping hydrofoil |
R | m | radius of round corners designed at both ends of the span direction of the flapping hydrofoil |
β | radian | swing angle of the swing arm |
f | Hz | swing frequency of the swing arm |
θ | radian | pitching angle of the flapping hydrofoil |
Vrel,0 | m/s | pitching center speed of the foil relative to the hull |
Vx0,Vy0 | m/s | velocity components of Vrel,0 |
Fx0,Fy0 | m | X-direction force, Y-direction force exerted by the swing arm on the pitching center of flapping foil, respectively |
Mz0 | N m | torque exerted by the swing arm on the pitching center of flapping foil |
Mz | N m | fluid moment imposed on foil |
K | Nm/rad | torsion spring stiffness |
I | Kg m2 | rotational inertia about the axis of the flapping hydrofoil considering the attached water |
N | average thrust in the forward direction | |
α (AoA) | radian | angle of attack of flapping hydrofoil |
St | St number of flapping hydrofoil | |
J | advance coefficient | |
KT | thrust coefficient | |
η | propulsive efficiency of flapping hydrofoil |
Direction | Hydrofoil Surface Region | Refinement Area |
---|---|---|
spanwise/Z | ||
chordwise/X | ||
normal direction/Y |
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Zhou, J.; Yan, W.; Mei, L.; Shi, W. Performance of Semi-Active Flapping Hydrofoil with Arc Trajectory. Water 2023, 15, 269. https://doi.org/10.3390/w15020269
Zhou J, Yan W, Mei L, Shi W. Performance of Semi-Active Flapping Hydrofoil with Arc Trajectory. Water. 2023; 15(2):269. https://doi.org/10.3390/w15020269
Chicago/Turabian StyleZhou, Junwei, Wenhui Yan, Lei Mei, and Weichao Shi. 2023. "Performance of Semi-Active Flapping Hydrofoil with Arc Trajectory" Water 15, no. 2: 269. https://doi.org/10.3390/w15020269