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Hydrodynamic Performance of Two-Dimensional Undulating Foils in Triangular Formation

Published online by Cambridge University Press:  16 June 2011

M.-H. Chung
M.-H. Chung*
Affiliation:
Institute of Ocean Engineering and Technology, National Kaohsiung Marine University, Kaohsiung City, Taiwan 81157, R.O.C.
*
*Assistant Professor, corresponding author
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Abstract

As inspired by studies of fish schooling in literature, this work investigates hydrodynamic performance of a two-dimensional undulating-foil triad in viscous flows via numerical simulation. The chord of foil oscillates in the form of a streamwise traveling wave. The triad is in triangular formation, i.e., two foils followed by one. A series of triad configuration are computed assuming the same wave speed, amplitude, and frequency of chord traveling wave for each foil. The results show that, to achieve highest thrust efficiency, the two leading foils should separate from each other by 0.4 chord length, perform antiphase undulating motion, and the leading edge of the trailing foil stay 0.2 chord length in front of the trailing edges of the leading foils. An underlining mechanism, vortex pair shedding from the leading foil interacting with boundary-layer vorticity field of the trailing foil, has been identified to explain the efficiency enhancement. This optimal triad configuration is different from that obtained in a previous potential flow analysiss.

Keywords

Undulating foilVortex pairEfficiencyNumerical simulation
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 2 , June 2011 , pp. 177 - 190
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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References

1. Wolfgang, M., Anderson, J. M., Grosenbaugh, M. A., Yue, D. K. P. and Triantafyllou, M. S., “Nearbody Flow Dynamics in Swimming Fish,” Journal of Experimental Biology, 202, pp. 2303–2327 (1999).CrossRefGoogle ScholarPubMed
2. Barrett, D. S., Triantafyllou, M. S., Yue, D. K. P., Grosenbaugh MA, M. A. and Wolfgang, M., “Drag Reduction in Fish-Like Locomotion,” Journal of Fluid Mechanics, 392, pp. 183–212 (1999).CrossRefGoogle Scholar
3. Stamhuis, E. and Videler, J., “Quantitative Flow Analysis Around Aquatic Animals Using Laser Sheet Particle Image Velocimetry,” Journal of Experimental Biology, 198, pp. 283–294 (1995).CrossRefGoogle ScholarPubMed
4. Drucker, E. and Lauder, G., “Locomotor Forces on a Swimming Fish: Three Dimensional Vortex Wake Dynamics Quantified Using Digital Particle Image Velocimetry,” Journal of Experimental Biology, 202, pp. 2393–2412 (1999).CrossRefGoogle ScholarPubMed
5. Wilga, C. D. and Lauder, G. V., “Hydrodynamic Function of the Shark's Tail,” Nature (London), 430, pp. 850–850 (2004).CrossRefGoogle ScholarPubMed
6. Triantafyllou, M. S., Triantafyllou, G. S. and Yue, D. K. P., “Hydrodynamics of Fishlike Swimming,” Annual Review of Fluid Mechanics, 32, pp. 33–53 (2000).CrossRefGoogle Scholar
7. Lighthill, M. J., “Note on the Swimming of Slender Fish,” Journal of Fluid Mechanics, 9, pp. 305–317 (1960).CrossRefGoogle Scholar
8. Wu, T. Y., “Swimming of a Waving Plate,” Journal of Fluid Mechanics, 10, pp. 321–344 (1961).CrossRefGoogle Scholar
9. Chopra, M. G. and Kambe, T., “Hydromechanics of Lunate-Tail Swimming Propulsion,” Journal of Fluid Mechanics, 79, pp. 375–392 (1977).Google Scholar
10. Cheng, J. Y., Zhuang, L. X. and Tong, B. G., “Analysis of Swimming of Three-Dimensional Waving Plates,” Journal of Fluid Mechanics, 232, pp. 341–351 (1991).CrossRefGoogle Scholar
11. Zhu, Q., Wolfgang, M. J., Yue, D. K. P. and Triantafyllou, M. S., “Three Dimensional Flow Structures and Vorticity Control in Fish-Like Swimming,” Journal of Fluid Mechanics, 468, pp. 1–28 (2002).CrossRefGoogle Scholar
12. Fauci, L. J., “A Computational Model of the Fluid Dynamics of Undulatory and Flagellar Swimming,” American Zoologist, 36, pp. 599–607 (1996).CrossRefGoogle Scholar
13. Liu, H., Wassenberg, R. and Kawachi, K., “A Computational Fluid Dynamics Study of Tadpole Swimming,” Journal of Experimental Biology, 199, pp. 1245–1260 (1996).CrossRefGoogle ScholarPubMed
14. Liu, H., Wassenberg, R. and Kawachi, K., “The Three-Dimensional Hydrodynamics of Tadpole Swimming,” Journal of Experimental Biology, 200, pp. 2807–2819 (1997). 15.CrossRefGoogle Scholar
Carling, J., Williams, T. L. and Bowtell, G., “Self-Propelled Anguilliform Swimming: Simultaneous Solution of the Two-Dimensional NavierStokes Equations and Newton's Laws of Motion,” Journal of Experimental Biology, 201, pp. 3143–3166 (1998).CrossRefGoogle ScholarPubMed
16. Shen, L., Zhang, X., Yue, D. K. P. and Triantafyllou, M. S., “Turbulent Flow Over a Flexible Wall Undergoing a Streamwise Travelling Wave Motion,” Journal of Fluid Mechanics, 484, pp. 197–221 (2003).CrossRefGoogle Scholar
17. Dong, G. J. and Lu, X. Y., “Numerical Analysis on the Propulsive Performance and Vortex Shedding of Fish-Like Travelling Wavy Plate,” International Journal for Numerical Methods in Fluids, 48, pp. 1351–1373 (2005).CrossRefGoogle Scholar
18. Wu, J. Z., Pan, Z. L. and Lu, X. Y., “Unsteady Fluid-Dynamic Force Solely in Terms of Control Surface Integral,” Physics of Fluids, 17, 098102 (2005).CrossRefGoogle Scholar
19. Liao, J. C., Beal, D. N., Lauder, G. V. and Triantafyllou, M. S., “The Kármán Gait: Novel Body Kinematics of Rainbow Trout Swimming in a Vortex Street,” Journal of Experimental Biology, 206, pp. 1059–1073 (2003).CrossRefGoogle Scholar
20. Liao, J. C., Beal, D. N., Lauder, G. V. and Triantafyllou, M. S., “Fish Exploiting Vortices Decrease Muscle Activity,” Science, 302, pp. 1566–1569 (2003).CrossRefGoogle ScholarPubMed
21. Beal, D. N., Hower, F. S., Triantafyllou, M. S., Liao, J. C. and Lauder, G. V., “Passive Propulsion in Vortex Wakes,” Journal of Fluid Mechanics, 549, pp. 385–402 (2006).CrossRefGoogle Scholar
22. Gopalkrishnan, R., Triantafyllou, M. S., Triantafyllou, G. S. and Barrett, D., “Active Vorticity Control in a Shear Flow Using a Flapping Foil,” Journal of Fluid Mechanics, 274, pp. 1–21 (1994).CrossRefGoogle Scholar
23. Streitlien, K., Triantafyllou, G. S. and Triantafyllou, M. S., “Efficient Foil Propulsion Through Vortex Control,” American Institute of Aeronautics and Astronautics, 34, pp. 2315–2319 (1996).CrossRefGoogle Scholar
24. Parrish, J. K. and Keshet, L. E., “Complexity, Pattern and Evolutionary Trade-Offs in Animal Aggregation,” Science, 284, pp. 99–101 (1999).CrossRefGoogle ScholarPubMed
25. Stöker, S., “Models for Tuna School Formation,” Mathematical Bioscience, 156, pp. 167–190 (1999).CrossRefGoogle Scholar
26. Weihs, D., “Hydromechanics of Fish Schooling,” Nature (London), 241, pp. 290–291 (1973).CrossRefGoogle Scholar
27. Weihs, D., “Some Hydrodynamical Aspects of Fish Schooling,” Swimming Flying Nature, 2, pp. 703–718 (1975).CrossRefGoogle Scholar
28. Partridge, B. L. and Pitcher, T. J., “Evidence Against a Hydrodynamic Function for Fish Schools,” Nature (London), 279, pp. 418–419 (1979).CrossRefGoogle ScholarPubMed
29. Keenleyside, M. H. A., “Some Aspects of the Schooling Behaviour of Fish,” Behaviour, 8, pp. 183–247 (1955).CrossRefGoogle Scholar
30. Jian, D., Shao, X.-M. and Ren, A.-L., “Numerical Study on Propulsive Performance of Fish-Like Swimming Foils,” Journal of Hydrodynamics, 18, pp. 681–247 (2006).Google Scholar
31. Dong, G. J. and Lu, X. Y., “Characteristics of Flow Over Traveling-Wavy Foils in a Side-By-Side Arrangement,” Physics of Fluids, 19, 057107 (2007).CrossRefGoogle Scholar
32. Kelly, S. D. and Xiong, H. L., “Controlled Hydrodynamic Interactions in Schooling Aquatic Locomotion,” Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain, December 12–15, pp. 3904–3910 (2005).Google Scholar
33. Eldredge, J., Hector, D. and Kelly, S., “Computations of Wake Dynamics in a Simple Model for Fish Schooling,” SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah (2007).Google Scholar
34. Breder, C. M., “Fish Schools as Operational Structures,” Fishery Bulletin of the Fish and Wildlife Service, 74, pp. 471–502 (1976).Google Scholar
35. Chung, M-H., “On Burst-And-Coast Swimming Performance in Fish-Like Locomotion,” Bioinspiration and Biomimetics, 4, 036001 (2009).CrossRefGoogle ScholarPubMed
36. Chung, M-H., “Cartesian Cut Cell Approach for Simulating Incompressible Flows with Rigid Bodies of Arbitrary Shape,” Computers and Fluids, 35, pp. 607–623 (2006).CrossRefGoogle Scholar
37. Chung, M-H., “Numerical Study of Rowing Hydrofoil Performance at Low Reynolds Numbers,” Journal of Fluids and Structures, 24, pp. 313–335 (2008).CrossRefGoogle Scholar
38. Bohl, D. G. and Koochesfahani, M. M., “MTV Measurements of the Vortical Field in the Wake of an Airfoil Oscillating at High Reduced Frequency,” Journal of Fluid Mechanics, 620, pp. 63–88 (2009).CrossRefGoogle Scholar
39. Milne-Thompson, L. M., “Theoretical Aerodynamics,” Macmillan, New York (1966).Google Scholar