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Computational analysis of fluid-structure interaction in case of fish swimming in the vortex street

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Abstract

The fluid-structure interaction (FSI) in case of fish swimming in the vortex street is investigated by numerical simulations. The vortex street is generated by a D-section cylinder. A 2-D fish model is placed on the downstream centerline of the bluff cylinder at a distance of 4 diameters away from the center of the cylinder. To simulate the fish body undulation and movement, the moving mesh is generated by a coupling approach based on the radial basis function and the overset grid technology. The Navier-Stokes equation in the arbitrary Lagrangian-Eulerian form is solved by coupling with the kinematics equation. Three cases are investigated: in a stationary position without deformation, a passive locomotion without deformation, and an active deformation based on the Kármán gait model. The results indicate that the fish body is acted by an alternating force and moment when it is located in the centerline of the vortex street. Furthermore, the fish could extract sufficient kinetic energy to overcome the drag under suitable conditions even when it keeps rigid and out of the suction zone. When the fish body undulates based on the Kármán gait model, the interaction is evidently shown between the fish body and the vortices. The theoretical analysis demonstrates that the lateral force and the moment acting on the fish body vary in a cosine formula, with the lateral translation and the body rotation as a result. This study focuses on the behavior of the fish body in the bluff cylinder wake and reproduces some phenomena observed in the experiments. Besides, the Kármán gait model is also theoretically analyzed, for the further exploration of the FSI mechanism in case of fish swimming.

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References

  1. Hemelrijk C. K., Reid D. A. P., Hildenbrandtet H. et al. The increased efficiency of fish swimming in a school [J]. Fish and Fisheries, 2015, 16(3): 511–521.

    Article  Google Scholar 

  2. Erik B., Christian T., Sebastiaan A. B. et al. Schooling reduces energy consumption in swimming male European eels, Anguilla anguilla L. [J]. Journal of Experimental Marine Biology and Ecology, 2013, 448: 66–71.

    Article  Google Scholar 

  3. Xiao Q., Sun K., Liu H. et al. Computational study on near wake interaction between undulation body and a D-section cylinder [J]. Ocean Engineering, 2011, 38(4): 673–683.

    Article  Google Scholar 

  4. Triantafyllou M. S., Triantafyllou G. S., Yue D. K. P. Hydrodynamics of fishlike swimming [J]. Annual Review of Fluid Mechanics, 2000, 32: 33–53.

    Article  MathSciNet  Google Scholar 

  5. Liao J. C. A review of fish swimming mechanics and behavior in altered flows [J]. Philosophical Transactions of the Royal Society B: Biological Science, 2007, 362(1487): 1973–1993.

    Article  Google Scholar 

  6. 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.

    Article  Google Scholar 

  7. Liao J. C., Beal D. N., Lauder G. V. et al. Fish exploiting vortices decrease muscle activity [J]. Science, 2003, 302(5650): 1566–1569.

    Article  Google Scholar 

  8. Liao J. C. Neuromuscular control of trout swimming in a vortex street: Implications for energy economy during the Karman gait [J]. Journal of Experimental Biology, 2004, 207(20): 3495–3506.

    Article  Google Scholar 

  9. 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.

    Article  Google Scholar 

  10. Taguchi M., Liao J. C. Rainbow trout consume less oxygen in turbulence: The energetics of swimming behaviors at different speeds [J]. Journal of Experimental Biology, 2011, 214(9): 1428–1436.

    Article  Google Scholar 

  11. Akanyeti O., Liao J. C. A kinematic model of Kármán gaiting in rainbow trout [J]. Journal of Experimental Biology, 2013, 216(24): 4666–4677.

    Google Scholar 

  12. Eldredge J. D., Pisani D. Passive locomotion of a simple articulated fish-like system in the wake of an obstacle [J]. Journal of Fluid Mechanics, 2008, 607: 279–288.

    Article  Google Scholar 

  13. 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.

    Article  Google Scholar 

  14. Li C., Yang W., Xu X. et al. Numerical investigation of fish exploiting vortices based on the Kármán gaiting model [J]. Ocean Engineering, 2017, 140: 7–18.

    Article  Google Scholar 

  15. Chang X., Zhang L., He X. Numerical study of the thunniform mode of fish swimming with different Reynolds number and caudal fin shape [J]. Computers and Fluids, 2012, 68: 54–70.

    Article  MathSciNet  Google Scholar 

  16. Yan L., Chang X., Tian R. et al. A numerical simulation method for bionic fish self-propelled swimming under control based on deep reinforcement learning [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2020, 234(17): 3397–3415.

    Google Scholar 

  17. von Kármán T., Sears W. R. Airfoil theory for nonuniform motion [J]. Journal of the Aeronautical Sciences, 1938, 5(10): 379–390.

    Article  Google Scholar 

  18. Sears W. R. Some aspects of non-stationary airfoil theory and its practical application [J]. Journal of the Aeronautical Sciences, 1941, 8(3): 104–108.

    Article  MathSciNet  Google Scholar 

  19. Lighthill M. J. Aquatic animal propulsion of high hydromechanical efficiency [J]. Journal of Fluid Mechanics, 1970, 44(2): 265–301.

    Article  Google Scholar 

  20. Wu T. Y. Extraction of flow energy by a wing oscillating in waves [J]. Journal of Ship Research, 1972, 16(1): 66–77.

    Article  Google Scholar 

  21. Cheng J. Y., Zhuang L. X., Tong B. G. Analysis of swimming three-dimensional waving plates [J]. Journal of Fluid Mechanics, 1991, 232: 341–355.

    Article  MathSciNet  Google Scholar 

  22. Streitlien K., Triantafyllou M. S. Force and moment on a Joukowski profile in the presence of point vortices [J]. AIAA Journal, 1995, 33(4): 603–610.

    Article  Google Scholar 

  23. Chang X. H., Ma R., Wang N. H. et al. A parallel implicit hole-cutting method based on background mesh for unstructured Chimera grid [J]. Computers and Fluids, 2020, 198: 104403.

    Article  MathSciNet  Google Scholar 

  24. Zhang L. P., Wang Z. J. A block LU-SGS implicit dual time-stepping algorithm for hybrid dynamic meshes [J]. Computers and Fluids, 2004, 33(7): 891–916.

    Article  Google Scholar 

  25. Zhang L. P., Chang X. H., Duan X. P. et al. A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations [J]. Computers and Fluids, 2009, 38(2): 290–308.

    Article  Google Scholar 

  26. Zdravkovich M. M. Flow around circular cylinders: A comprehensive guide through flow phenomena, experiments, applications, mathematical models, and computer simulations [M]. Oxford, UK: Oxford University Press, 1997.

    Google Scholar 

  27. Verma S., Novati G., Koumoutsakos P. Efficient collective swimming by harnessing vortices through deep reinforcement learning [J]. Proceedings of the National Academy of Sciences, 2018, 115(23): 5849–5854.

    Article  Google Scholar 

  28. Gerrard J. H. Formation region of vortices behind bluff bodies [J]. Journal of Fluid Mechanics, 1966, 25: 401–413.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, China

    Lang Yan & Wei Liu

  2. Unmanned Systems Research Center, National Innovation Institute of Defense Technology, Beijing, 100071, China

    Xing-hua Chang & Lai-ping Zhang

  3. China Aerodynamics Research and Development Center, State Key Laboratory of Aerodynamics, Mianyang, 621000, China

    Nian-hua Wang

  4. Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang, 621000, China

    Run-yu Tian

Authors
  1. Lang Yan
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  2. Xing-hua Chang
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  3. Nian-hua Wang
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  4. Run-yu Tian
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  5. Lai-ping Zhang
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  6. Wei Liu
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Corresponding author

Correspondence to Lai-ping Zhang.

Additional information

Project supported by the National Key Research and Development Program of China (Grant No. 2016YFB0200701), the National Natural Science Foundation of China (Grant Nos. 11532016, 11672324) and the National Key Project (Grant No. GJXM92579).

Biography: Lang Yan (1995-), Male, Ph. D. Candidate

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Yan, L., Chang, Xh., Wang, Nh. et al. Computational analysis of fluid-structure interaction in case of fish swimming in the vortex street. J Hydrodyn 33, 747–762 (2021). https://doi.org/10.1007/s42241-021-0070-4

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  • DOI: https://doi.org/10.1007/s42241-021-0070-4

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