Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T22:47:20.721Z Has data issue: false hasContentIssue false
  • English
  • Français

Self-organization of multiple self-propelling flapping foils: energy saving and increased speed

Published online by Cambridge University Press:  05 December 2019

Xingjian Lin ,
Jie Wu Open the ORCID record for Jie Wu [Opens in a new window] ,
Tongwei Zhang  and
Liming Yang
Xingjian Lin
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China Key Laboratory of Unsteady Aerodynamics and Flow Control, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China
Jie Wu*
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China Key Laboratory of Unsteady Aerodynamics and Flow Control, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China
Tongwei Zhang
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China Key Laboratory of Unsteady Aerodynamics and Flow Control, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, Jiangsu 210016, China
Liming Yang
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The collective hydrodynamics in fish schools and bird flocks, which includes self-organization of multiple dynamic bodies, is complex and lacks sufficient exploration. In this paper, we study the performance of multiple self-propelled foils in tandem formation, whose flapping motions are asynchronous with a phase difference. It is shown that a compact formation, in which all of the foils perform like a complete anguilliform swimmer, can be spontaneously formed by multiple foils via hydrodynamic interactions. Both velocity enhancement and energy saving can be achieved by multiple foils in anguilliform-like swimming. Furthermore, such anguilliform-like swimming behaviour can be observed over a wide range of parameters, including the number of foils, the phase difference, the initial distance, the heaving amplitude and the pitching amplitude. The results obtained here may provide some light on understanding the self-organization behaviour of biological collectives.

JFM classification

Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex dynamics Wakes/Jets: Vortex streets
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , R1
Copyright
© 2019 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akhtar, I., Mittal, R., Lauder, G. V. & Drucker, E. 2004 Hydrodynamics of biologically inspired tandem flapping foil configuration. Theor. Comput. Fluid Dyn. 21, 155–170.CrossRefGoogle Scholar
Ashraf, I., Bradshaw, H., Ha, T. T., Halloy, J., Godoy-Diana, R. & Thiria, B. 2017 Simple phalanx pattern leads to energy saving in cohesive fish schooling. Proc. Natl Acad. Sci. USA 114, 9599–9604.CrossRefGoogle ScholarPubMed
Ashraf, I., Godoy-Diana, R., Halloy, J., Collignon, B. & Thiria, B. 2016 Synchronization and collective swimming patterns in fish (Hemigrammus bleheri). J. R. Soc. Interface 13, 20160734.CrossRefGoogle Scholar
Becker, A. D., Masoud, H., Newbolt, J. W., Shelley, M. & Ristroph, L. 2015 Hydrodynamic schooling of flapping swimmers. Nat. Commun. 6, 8514.CrossRefGoogle ScholarPubMed
Boschitsch, B. M., Dewey, P. A. & Smits, A. J. 2014 Propulsive performance of unsteady tandem hydrofoils in an in-line configuration. Phys. Fluids 26, 051901.CrossRefGoogle Scholar
Broering, T. M., Lian, Y. S. & Henshaw, W. 2012 Numerical investigation of energy extraction in a tandem flapping wing configuration. AIAA J. 50, 2295–2307.CrossRefGoogle Scholar
Couzin, I. D. 2009 Collective cognition in animal groups. Trends Cognit. Sci. 13, 36–43.CrossRefGoogle ScholarPubMed
Deng, J. & Caulfield, C. P. 2018 Horizontal locomotion of a vertically flapping oblate spheroid. J. Fluid Mech. 840, 688–708.CrossRefGoogle Scholar
Dong, G.-J. & Lu, X.-Y. 2007 Characteristics of flow over traveling wavy foils in a side-by-side arrangement. Phys. Fluids 19, 057107.CrossRefGoogle Scholar
Filella, A., Nadal, F., Sire, C., Kanso, E. & Eloy, C. 2018 Model of collective fish behavior with hydrodynamic interactions. Phys. Rev. Lett. 120, 198101.CrossRefGoogle ScholarPubMed
Gao, A. & Triantafyllou, M. S. 2018 Independent caudal fin actuation enables high energy extraction and control in two-dimensional fish-like group swimming. J. Fluid Mech. 850, 304–335.CrossRefGoogle Scholar
Guazzelli, E. & Hinch, J. 2011 Fluctuations and instability in sedimentation. Annu. Rev. Fluid Mech. 43, 97–116.CrossRefGoogle Scholar
Hemelrijk, C. K. & Hildenbrandt, H. 2012 Schools of fish and flocks of birds: their shape and internal structure by self-organization. Interface Focus 2, 726–737.CrossRefGoogle ScholarPubMed
Kim, S., Huang, W.-X. & Sung, H. J. 2010 Constructive and destructive interaction modes between two tandem flexible flags in viscous flow. J. Fluid Mech. 661, 511–521.CrossRefGoogle Scholar
Kinsey, T. & Dumas, G. 2008 Parametric study of an oscillating airfoil in a power extraction regime. AIAA J. 46, 1318–1330.CrossRefGoogle Scholar
Koch, D. L. & Subramanian, G. 2011 Collective hydrodynamics of swimming microorganisms: living fluids. Annu. Rev. Fluid Mech. 43, 637–659.CrossRefGoogle Scholar
Kurt, M. & Moored, K. W. 2018 Flow interactions of two- and three-dimensional networked bio-inspired control elements in an in-line arrangement. Bioinspir. Biomim. 13, 045002.CrossRefGoogle Scholar
Liao, J. C. 2002 Swimming in needlefish (Belonidae): anguilliform locomotion with fins. J. Exp. Biol. 205, 2875–2884.Google ScholarPubMed
Lin, X., Wu, J. & Zhang, T. 2019a Performance investigation of a self-propelled foil with combined oscillating motion in stationary fluid. Ocean Engng 175, 33–49.CrossRefGoogle Scholar
Lin, X., Wu, J., Zhang, T. & Yang, L. 2019b Phase difference effect on collective locomotion of two tandem autopropelled flapping foils. Phys. Rev. Fluids 4, 054101.CrossRefGoogle Scholar
Liu, H. & Curet, O. 2018 Swimming performance of a bio-inspired robotic vessel with undulating fin propulsion. Bioinspir. Biomim. 13, 056006.CrossRefGoogle ScholarPubMed
Maertens, A. P., Gao, A. & Triantafyllou, M. S. 2017 Optimal undulatory swimming for a single fish-like body and for a pair of interacting swimmers. J. Fluid Mech. 813, 301–345.CrossRefGoogle Scholar
Marras, S., Killen, S. S., Lindstrom, J., McKenzie, D. J., Steffensen, J. F. & Domenici, P. 2015 Fish swimming in schools save energy regardless of their spatial position. Behav. Ecol. Sociobiol. 69, 219–226.CrossRefGoogle ScholarPubMed
Muscutt, L. E., Weymouth, G. D. & Ganapathisubramani, B. 2017 Performance augmentation mechanism of in-line tandem flapping foils. J. Fluid Mech. 827, 484–505.CrossRefGoogle Scholar
Newbolt, J. W., Zhang, J. & Ristroph, L. 2019 Flow interactions between uncoordinated flapping swimmers give rise to group cohesion. Proc. Natl Acad. Sci. USA 116, 2419–2424.CrossRefGoogle ScholarPubMed
Partridge, B. L. & Pitcher, T. J. 1979 Evidence against a hydrodynamic function for fish schools. Nature 279, 418–419.CrossRefGoogle ScholarPubMed
Peng, Z.-R., Huang, H. & Lu, X.-Y. 2018a Collective locomotion of two closely spaced self-propelled flapping plates. J. Fluid Mech. 849, 1068–1095.CrossRefGoogle Scholar
Peng, Z.-R., Huang, H. & Lu, X.-Y. 2018b Hydrodynamic schooling of multiple self-propelled flapping plates. J. Fluid Mech. 853, 587–600.CrossRefGoogle Scholar
Portugal, S. J., Hubel, T. Y., Fritz, J., Heese, S., Trobe, D., Voelkl, B., Hailes, S., Wilson, A. M. & Usherwood, J. R. 2014 Upwash exploitation and downwash avoidance by flap phasing in ibis formation flight. Nature 505, 399–402.CrossRefGoogle ScholarPubMed
Ramananarivo, S., Fang., F., Oza, A., Zhang, J. & Ristroph, L. 2016 Flow interactions lead to orderly formations of flapping wings in forward flight. Phys. Rev. Fluids 1, 071201.CrossRefGoogle Scholar
Rival, D., Hass, G. & Tropea, C. 2011 Recovery of energy from leading- and trailing-edge vortices in tandem-airfoil configurations. J. Aircraft 48, 203–211.CrossRefGoogle Scholar
Shoele, K. & Zhu, Q. 2015 Performance of synchronized fins in biomimetic propulsion. Bioinspir. Biomim. 10, 026008.CrossRefGoogle ScholarPubMed
Sumpter, D. J. 2006 The principles of collective animal behavior. Phil. Trans. R. Soc. Lond. B 361, 5–22.CrossRefGoogle Scholar
Uddin, E., Huang, W.-X. & Sung, H. J. 2015 Actively flapping tandem flexible flags in a viscous flow. J. Fluid Mech. 780, 120–142.CrossRefGoogle Scholar
Usherwood, J. R., Stavrou, M., Lowe, J. C., Roskilly, K. & Wilson, A. M. 2011 Flying in a flock comes at a cost in pigeons. Nature 474, 494–497.CrossRefGoogle Scholar
Weihs, D. 1973 Hydromechanics of fish schooling. Nature 241, 290–291.CrossRefGoogle Scholar
Wu, J. & Shu, C. 2009 Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications. J. Comput. Phys. 228, 1963–1979.CrossRefGoogle Scholar
Yang, L. M., Shu, C., Yang, W. M. & Wang, Y. 2017a A simplified circular function-based gas kinetic scheme for simulation of incompressible flows. Intl J. Numer. Meth. Fluids 85, 583–598.CrossRefGoogle Scholar
Yang, L. M., Shu, C., Yang, W. M., Wang, Y. & Wu, J. 2017b An immersed boundary-simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible flows. Phys. Fluids 29, 083605.CrossRefGoogle Scholar
Zhu, X., He, G. & Zhang, X. 2014 Flow-mediated interactions between two self-propelled flapping filaments in tandem configuration. Phys. Rev. Lett. 113, 238105.CrossRefGoogle ScholarPubMed

Lin et al. supplementary movie 1

Anguilliform-like swimming of five flapping foils.

Download Lin et al. supplementary movie 1(Video)
Video 2.6 MB

Lin et al. supplementary movie 2

Anguilliform-like swimming of ten flapping foils.

Download Lin et al. supplementary movie 2(Video)
Video 3.4 MB

Lin et al. supplementary movie 3

Anguilliform-like swimming of fifteen flapping foils.

Download Lin et al. supplementary movie 3(Video)
Video 3.5 MB