Effects of Leading-Edge Tubercles on Three-Dimensional Flapping Foils
Abstract
:1. Introduction
2. Materials and Methods
2.1. Description of Flapping Foils
2.2. Kinematics Equations
2.2.1. Rigid Motion
2.2.2. Spanwise Motion for Flexibility
2.2.3. Dimensionless Parameters
2.3. Approach
2.4. Validation and Verification
3. Results
3.1. Effect of Tubercle Size
3.2. Effect of Strouhal Number
3.3. Effect of Maximum Angle of Attack
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Mesh No. | Mesh Densities | Cell Numbers (×106) | Time Steps | Mean Thrust Coefficient | Relative Error/% | /% | /% |
---|---|---|---|---|---|---|---|
3 | Coarse | 3.23 | T/250 | 0.2235 | −0.75 | 1.06 | 0.13 |
2 | Medium | 6.58 | T/250 | 0.2247 | −0.20 | ||
T/500 | 0.2252 | 0.00 | |||||
T/1000 | 0.2238 | −0.62 | |||||
1 | Fine | 10.04 | T/250 | 0.2271 | 0.86 |
No. | Foil Name | A/c | λ/c | St | αmax (°) | Re |
---|---|---|---|---|---|---|
1 | L025A0025 | 0.025 | 0.25 | [0.2, 0.5], interval 0.1 | 20 | 50,000 |
0.3 | [15, 40], interval 5 | 50,000 | ||||
2 | L025A005 | 0.05 | 0.25 | 0.3 | 20 | 50,000 |
3 | L025A0075 | 0.075 | 0.25 | 0.3 | 20 | 50,000 |
4 | L025A01 | 0.1 | 0.25 | 0.3 | 20 | 50,000 |
5 | L05A0025 | 0.025 | 0.5 | 0.3 | 20 | 50,000 |
6 | L05A005 | 0.05 | 0.5 | 0.3 | 20 | 50,000 |
7 | L05A0075 | 0.075 | 0.5 | 0.3 | 20 | 50,000 |
8 | L05A01 | 0.1 | 0.5 | 0.3 | 20 | 50,000 |
9 | Baseline | 0 | 0 | [0.2, 0.5], interval 0.1 | 20 | 50,000 |
0.3 | [15, 40], interval 5 | 50,000 |
St | αmax (°) | ω (Rad/s) | (s) | CFL | θ0 (°) | φ0 (°) | B (mm) |
---|---|---|---|---|---|---|---|
0.2 | 20 | 2.09 | 0.0060 | 1.07 | 12.33 | 27.28 | 22.5 |
0.3 | 15 | 3.14 | 0.0040 | 0.71 | 30.08 | 27.28 | 22.5 |
0.3 | 20 | 3.14 | 0.0040 | 0.71 | 24.13 | 27.28 | 22.5 |
0.3 | 25 | 3.14 | 0.0040 | 0.71 | 18.74 | 27.28 | 22.5 |
0.3 | 30 | 3.14 | 0.0040 | 0.71 | 13.57 | 27.28 | 22.5 |
0.3 | 35 | 3.14 | 0.0040 | 0.71 | 8.47 | 27.28 | 22.5 |
0.3 | 40 | 3.14 | 0.0040 | 0.71 | 3.40 | 27.28 | 22.5 |
0.4 | 20 | 4.19 | 0.0030 | 0.54 | 34.87 | 27.28 | 22.5 |
0.5 | 20 | 5.24 | 0.0024 | 0.43 | 46.17 | 27.28 | 22.5 |
Foil Name | CTmax | Relative Error/% | CPmax | Relative Error/% |
---|---|---|---|---|
L025A0025 | 0.6088 | −1.66 | 1.0385 | 0.80 |
L025A005 | 0.5946 | −3.95 | 1.0535 | 2.26 |
L025A0075 | 0.5715 | −7.68 | 1.0755 | 4.39 |
L025A01 | 0.5505 | −11.08 | 1.0841 | 5.23 |
L05A0025 | 0.6149 | −0.68 | 1.0438 | 1.31 |
L05A005 | 0.6085 | −1.71 | 1.0702 | 3.88 |
L05A0075 | 0.6004 | −3.03 | 1.0947 | 6.26 |
L05A01 | 0.5873 | −5.13 | 1.1066 | 7.41 |
baseline | 0.6191 | 0.00 | 1.0302 | 0.00 |
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He, R.; Wang, X.; Li, J.; Liu, X.; Song, B. Effects of Leading-Edge Tubercles on Three-Dimensional Flapping Foils. J. Mar. Sci. Eng. 2023, 11, 1882. https://doi.org/10.3390/jmse11101882
He R, Wang X, Li J, Liu X, Song B. Effects of Leading-Edge Tubercles on Three-Dimensional Flapping Foils. Journal of Marine Science and Engineering. 2023; 11(10):1882. https://doi.org/10.3390/jmse11101882
Chicago/Turabian StyleHe, Ruixuan, Xinjing Wang, Jian Li, Xiaodong Liu, and Baowei Song. 2023. "Effects of Leading-Edge Tubercles on Three-Dimensional Flapping Foils" Journal of Marine Science and Engineering 11, no. 10: 1882. https://doi.org/10.3390/jmse11101882
APA StyleHe, R., Wang, X., Li, J., Liu, X., & Song, B. (2023). Effects of Leading-Edge Tubercles on Three-Dimensional Flapping Foils. Journal of Marine Science and Engineering, 11(10), 1882. https://doi.org/10.3390/jmse11101882