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To investigate the hydrodynamic performance of manta rays swimming in staggered arranged group, a morphological and kinematic model of manta rays is developed based on biological observations, and then a numerical calculation method is established for group swimming of manta rays based on the Immersed Boundary Method and the Sphere function-based Gas Kinetic Scheme (IB-SGKS). The group swimming of two manta rays with a fixed vertical spacing of 0.1 times the body thickness, and a flow direction spacing of 0—1.5 times the body length is systematically investigated. The average thrust/efficiency of the group system and each individual in the group are analyzed by combining the global three-dimensional (3D) vortex structure and the characteristic cross-section two-dimensional (2D) vortex structure. The numerical results are shown below. When the streamwise spacing between individuals is small, the propulsive performance decreases sharply compared with swimming alone; as the streamwise spacing increases, the propulsive performance of the leader manta ray is consistently better than that of swimming alone, with the maximum thrust enhanced up to 11.24% when Dx = 0.4BL, and the maximum efficiency is enhanced up to 3.58% when Dx = 0.3BL; with the increase of the streamwise spacing, in the thrust/efficiency curves of the follower manta ray appears volatility, with the maximum thrust enhanced to 48.14% when Dx = 0.4BL and the maximum efficiency reached to 12.39% when Dx = 0.5BL; the system average thrust and efficiency enhancement both reach their corresponding maximum values, specifically, 29.69% and 6.77%, when Dx = 0.4BL, which is because the tail vortex of the leading manta ray just passes through the front edge of the follower manta ray and directly acts on the tip vortex that initially falls off from the follower manta rays, thus substantially increasing their vortex energy.
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Keywords:
- manta rays /
- group swimming /
- staggered arrangement /
- hydrodynamic performance /
- vortex structure
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图 1 真实蝠鲼集群游动
Figure 1. Real manta rays group swimming.
图 3 蝠鲼运动模型图
Figure 3. Manta ray motion model view.
图 4 交错队形示意图
Figure 4. Staggered formation schematic.
图 5 金枪鱼计算域设置及网格细节图
Figure 5. Tuna computational domain setup and mesh details.
图 6 流向力系数曲线
Figure 6. Streamwise force coefficient curve.
图 7 网格细节图
Figure 7. Mesh detail view.
图 8 不同网格下推力系数曲线
Figure 8. Thrust coefficient curves for different meshes.
图 9 不同时间步长下推力系数曲线
Figure 9. Thrust coefficient curves for different time steps.
图 10 不同流向间距下水动力性能表现 (a) 推力系数; (b) 推进效率
Figure 10. Hydrodynamic performance at different streamwise spacings: (a) Thrust coefficient; (b) propulsion efficiency.
图 11 蝠鲼单体游动状态流场结构及特征截面定义
Figure 11. Wake structure and the definition of characteristic cross sections for the single swimming state of manta rays.
图 12 蝠鲼交错排布集群游动时流场结构(Dx = 0.4BL)
Figure 12. Wake structures of manta rays during swimming in staggered arranged group (Dx = 0.4BL).
图 13 蝠鲼交错排布集群游动时流场结构(Dx = 0.8BL)
Figure 13. Wake structures of manta rays during swimming in staggered arranged group (Dx = 0.8BL).
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[1] Walker J A, Westneat M W 1997 J. Exp. Biol. 200 1549
Google Scholar
[2] Borazjani I, Sotiropoulos F, Tytell E D, Lauder G V 2012 J. Exp. Biol. 215 671
Google Scholar
[3] Wöhl S, Schuster S 2007 J. Exp. Biol. 210 311
Google Scholar
[4] Li L, Ravi S, Xie G, Couzin I D 2021 Proc. R. Soc. A-Math. Phys. Eng. Sci. 477 20200810
Google Scholar
[5] Weihs D 1973 Nature 241 290
Google Scholar
[6] Chen S Y, Fei Y H J, Chen Y C, Chi K J, Yang J T 2016 Ocean Eng. 122 22
Google Scholar
[7] Wei C, Hu Q, Li S J, Shi X D 2023 Ocean Eng. 267 113258
Google Scholar
[8] Tian F B, Luo H, Zhu L, Liao J C, Lu X Y 2011 J. Comput. Phys. 230 7266
Google Scholar
[9] Tian F B, Wang W, Wu J, Sui Y 2016 Comput. Fluids 124 1
Google Scholar
[10] Li Y F, Chang J T, Kong C, Bao W 2022 Chin. J. Aeronaut. 35 14
Google Scholar
[11] 王亮 2007 博士学位论文 (南京: 河海大学)
Wang L 2007 Ph. D. Dissertation (Nanjing: Hehai University
[12] Jian D, Shao X M 2006 J. Hydrodyn. 18 438
Google Scholar
[13] Chung M H 2011 J. Mech. 27 177
Google Scholar
[14] Dai L Z, He G W, Zhang X, Zhang X 2018 J. R. Soc. Interface 15 20180490
Google Scholar
[15] Chao L M, Zhang D, Cao Y H, Pan G 2018 Mod. Phys. Lett. B 32 1850034
Google Scholar
[16] Chao L M, Pan G, Zhang D, Yan G X 2019 Ocean Eng. 183 167
Google Scholar
[17] Li X H, Gu J Y, Su Z, Yao Z Q 2021 Phys. Fluids 33 121905
Google Scholar
[18] 高鹏骋, 刘冠杉, 黄桥高, 潘光, 马云龙 2023 力学学报 55 62
Google Scholar
Gao P C, Liu G S, Huang Q G, Pan G, Ma Y L 2023 Chin. J. Theor. Appl. Mech. 55 62
Google Scholar
[19] 高鹏骋, 黄桥高, 宋东, 潘光, 马云龙 2023 西北工业大学学报 41 595
Google Scholar
Gao P C, Huang Q G, Song D, Pan G, Ma Y L 2023 Journal of Northwestern Polytechnical University 41 595
Google Scholar
[20] Gao P C, Huang Q G, Pan G, Ma Y L, Song D 2022 Phys. Fluids 34 111908
Google Scholar
[21] Gao P C, Huang Q G, Pan G, Cao Y, Luo Y 2023 Ocean Eng. 278 114389
Google Scholar
[22] Gao P C, Huang Q G, Pan G, Song D, Cao Y 2023 Phys. Fluids 35 061909
Google Scholar
[23] 张栋 2020 博士学位论文 (西安: 西北工业大学)
Zhang D 2020 Ph. D. Dissertation (Xi’an: Northwestern Polytechnical University
[24] Zhang D, Huang Q G, Pan G, Yang L M, Huang W X 2022 J. Fluid Mech. 930 A28
Google Scholar
[25] Zhang D, Huang W X 2023 J. Fluid Mech. 963 A16
Google Scholar
[26] Taira K, Colonius T 2007 J. Comput. Phys. 225 2118
Google Scholar
[27] Yang L M, Shu C, Wu J 2015 J. Comput. Phys. 295 322
Google Scholar
[28] Yang L M, Shu C, Wang Y, Sun Y 2016 J. Comput. Phys. 319 129
Google Scholar
[29] Yang L M, Shu C, Yang W M, Wang Y, Wu J 2017 Phys. Fluids 29 083605
Google Scholar
[30] Zhang J D, Sung H J, Huang W X 2020 Phys. Fluids 32 111902
Google Scholar
[31] Han P, Pan Y, Liu G, Dong H B 2022 J. Fluids Struct. 108 103422
Google Scholar
[32] Gao P C, Tian X S, Huang Q G, Pan G 2024 Phys. Fluids 36 0180621
Google Scholar
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