Abstract
The vortex structure and the hydrodynamic performance of a tadpole undulating in the wake of a D-section cylinder are studied by solving the Navier-Stokes equations for the unsteady incompressible viscous flow. A dynamic mesh fitting the tadpole’s deforming body surface is used in the simulation. It is found that three main factors can contribute to the thrust of the tadpole behind a D-cylinder: the backward jet in the wake, the local reverse flows on the tadpole surface and the suction force caused by the passing vortices. The tadpole’s relative undulating frequency and the distance between the D-cylinder and the tadpole have a great influence on both the vortex structure and the hydrodynamic performance. At some undulating frequency, a tadpole may break or dodge vortices from the D-cylinder. When the vortices are broken, the tadpole can gain a great thrust but will consume much energy to maintain its undulation. When the vortices are dodged, the tadpole is subject to a small thrust or even a drag. However, it is an effective way to save much energy in the undulating swimming, as the Kármán gait does. As the tadpole is located behind the D-cylinder at different distances, three typical kinds of wake are observed. When an incomplete Kármán vortex street forms between the D-cylinder and the tadpole, the tadpole is subject to the highest thrust.
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References
Marras S., Killen S. S., Lindström J. et al. Fish swimming in schools save energy regardless of their spatial position [J]. Behavioral Ecology and Sociobiology, 2015, 69 (2): 219–226.
Hemelrij C. K., Reid D. A. P., Hildenbrandt H. et al. The increased efficiency of fish swimming in a school [J]. Fish and Fisheries, 2015, 16 (3): 511–521.
Dong G. J., Lu X. Y. Characteristics of flow over traveling wavy foils in a side-by-side arrangement [J]. Physics of Fluids, 2007, 19(5): 057107.
Gopalkrishnan R., Triantafyllou M. S., Triantafyllou G. S. et al. Active vorticity control in a shear flow using a flapping foil [J]. Journal of Fluid Mechanics, 1994, 274: 1–21.
Shao X. M., Pan D. Y. Hydrodynamics of a flapping foil in the wake of a d-section cylinder [J]. Journal of Hydrodynamics, 2011, 23 (4): 422–430.
Beal D. N., Hover F. S., Triantafyllou M. S. et al. Passive propulsion in vortex wakes [J]. Journal of Fluid Mechanics, 2006, 549: 385–402.
Fish F. E., Lauder G. V. Passive and active flow control by swimming fishes and mammals [J]. Annual Review of Fluid Mechanics, 2006, 38: 193–224.
Liao J. C. A review of fish swimming mechanics and behaviour in altered flows [J]. Philosophical Transactions of the Royal Society B: Biological Sciences, 2007, 362 (1487): 1973–1993.
Liao J. C., Beal D. N., Lauder G. V. et al. Fish exploiting vortices decrease muscle activity [J]. Science, 2003, 302 (5650): 1566–1569.
Liao J. C., Beal D. N., Lauder G. V. et al. The Kármán gait: Novel body kinematics of rainbow trout swimming in a vortex street [J]. Journal of Experimental Biology, 2003, 206 (6): 1059–1073.
Dong G. J., Lu X. Y. Numerical analysis on the propulsive performance and vortex shedding of fish-like travelling wavy plate [J]. International Journal for Numerical Methods in Fluids, 2005, 48 (12): 1351–1373.
Deng J., Shao X. M., Yu Z. S. Hydrodynamic studies on two traveling wavy foils in tandem arrangement [J]. Physics of Fluids, 2007, 19(11): 113104.
Deng J., Shao X. M. Hydrodynamics in a diamond-shaped fish school [J]. Journal of Hydrodynamics, 2006, 18 (3): 438–442.
Shao X. M., Pan D., Deng J. et al. Hydrodynamic performance of a fishlike undulating foil in the wake of a cylinder [J]. Physics of Fluids, 2010, 22(11): 111903.
Wu J., Shu C. Numerical study of flow characteristics behind a stationary circular cylinder with a flapping plate [J]. Physics of Fluids, 2011, 23(7): 073601.
Wu J., Shu C., Zhao N. Investigation of flow characteristics around a stationary circular cylinder with an undulatory plate [J]. European Journal of Mechanics-B/Fluids, 2014, 48 (1): 27–39.
Wu J., Shu C., Zhao N. Numerical study of flow control via the interaction between a circular cylinder and a flexible plate [J]. Journal of Fluids and Structures, 2014, 49 (8): 594–613.
Hoff K. V. S., Wassersug R. J. Tadpole locomotion: Axial movement and tail functions in a largely vertebraeless vertebrate [J]. American Zoologist, 2000, 40 (1): 62–76.
Azizia E., Landbergb T., Wassersug R. J. Vertebral function during tadpole locomotion [J]. Zoology, 2007, 110 (4): 290–297.
Wassersug R. J. Locomotion in amphibian larvae (or “Why aren’t tadpoles built like fishes?”) [J]. American Zoologist, 1989, 29 (1): 65–84.
Liu H., Wassersug R., Kawachi K. The three-dimensional hydrodynamics of tadpole locomotion [J]. The Journal of Experimental Biology, 1997, 200 (22): 2807–2819.
Köhler G., Lehr E., Mccranie J. R. The tadpole of the central american toad bufo luetkenii boulenger [J]. Journal of Herpetology, 2000, 34 (2): 303–306.
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Project supported by the National Natural Science Foundation of China (Grant No. 11472173).
Biography: Hao-tian Yuan (1991-), Male, Master
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Yuan, Ht., Hu, Wr. A numerical study of tadpole swimming in the wake of a D-section cylinder. J Hydrodyn 29, 1044–1053 (2017). https://doi.org/10.1016/S1001-6058(16)60818-1
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DOI: https://doi.org/10.1016/S1001-6058(16)60818-1