Skip to main content
Log in

Self-propulsion of flapping bodies in viscous fluids: Recent advances and perspectives

  • Review Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Flapping-powered propulsion is used by many animals to locomote through air or water. Here we review recent experimental and numerical studies on self-propelled mechanical systems powered by a flapping motion. These studies improve our understanding of the mutual interaction between actively flapping bodies and surrounding fluids. The results obtained in these works provide not only new insights into biolocomotion but also useful information for the biomimetic design of artificial flyers and swimmers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Knoller, R.: Die Gesetze des Luftwiderstandes. Flugund Motortchnik(Wien) 3, 1–7 (1909) (in German)

  2. Betz, A.: Ein Beitrag zur Erklarung des Segelfluges. Z. fur Flugtech. und Motorluftschiffahrt 3, 269–272 (1912) (in German)

  3. Katzmayr, R.: Effect of Periodic Changes of Angle of Attack on Behavior of Airfoils. NACA TM-147 (1922)

  4. von Kármán, T., Burgers, J.M.: Aerodynamic Theory, vol. 2. Springer, Berlin (1934)

    Google Scholar 

  5. Garrick, I.E.: Propulsion of a Flapping and Oscillating Airfoil. NACA 567 (1937)

  6. Tuncer, I.H., Platzer, M.F.: Thrust generation due to airfoil flapping. AIAA J. 34, 324–331 (1996)

    Article  MATH  Google Scholar 

  7. Jones, K.D., Platzer, M.F.: Numerical computation of flapping-wing propulsion and power extraction. In: 35th Aerospace Sciences Meeting & Exhibit, Reno, NV (1997)

  8. Isogai, K., Shinmoto, Y., Watanabe, Y.: Effects of dynamic stall on propulsive efficiency and thrust of flapping airfoil. AIAA J. 37, 1145–1151 (1999)

    Article  Google Scholar 

  9. Pederzani, J., Haj-Hariri, H.: Numerical analysis of heaving flexible airfoils in a viscous flow. AIAA J. 44, 2773–2779 (2006)

    Article  MATH  Google Scholar 

  10. Ramamurti, R., Sandberg, W.: Simulation of flow about flapping airfoils using finite element incompressible flow solver. AIAA J. 39, 253–260 (2001)

    Article  Google Scholar 

  11. Sarkar, S., Venkatraman, K.: Numerical simulation of incompressible viscous flow past a heaving airfoil. Int. J. Numer. Meth. Fluids 51, 1–29 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sarkar, S., Venkatraman, K.: Numerical simulation of thrust generating flow past a pitching airfoil. Comput. Fluids 35, 16–42 (2006)

    Article  MATH  Google Scholar 

  13. Tuncer, I.H., Platzer, M.F.: Computational study of flapping airfoil aerodynamics. AIAA J. Aircr. 37, 514–520 (2000)

    Article  Google Scholar 

  14. Tuncer, I.H., Platzer, M.F.: Thrust generation due to airfoil flapping. AIAA J. 34, 324–331 (1996)

    Article  MATH  Google Scholar 

  15. Young, J., Lai, J.C.S.: Oscillation frequency and amplitude effects on the wake of plunging airfoil. AIAA J. 42, 2042–2052 (2004)

    Article  Google Scholar 

  16. Young, J., Lai, J.C.S.: Mechanisms influencing the efficiency of oscillating airfoil propulsion. AIAA J. 45, 1695–1702 (2007)

    Article  Google Scholar 

  17. Anderson, J.M., Streitlien, K., Barrett, D.S., et al.: Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  18. Freymuth, P.: Propulsive vortical signature of plunging and pitching airfoils. AIAA J. 26, 881–883 (1988)

    Article  Google Scholar 

  19. Heathcote, S., Gursul, I.: Flexible flapping airfoil propulsion at low reynolds number. AIAA J. 45, 1066–1078 (2007)

    Article  Google Scholar 

  20. Jones, K.D., Dohring, C.M., Platzer, M.F.: Experimental and computational investigation of the Knoller–Betz Effect. AIAA J. 36, 1240–1246 (1998)

    Article  Google Scholar 

  21. Koochesfahani, M.M.: Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27, 1200–1205 (1989)

    Article  Google Scholar 

  22. Read, D.A., Hover, F.S., Triantafyllou, M.S.: Forces on oscillating foils for propulsion and maneuvering. J. Fluids Struct. 17, 163–183 (2003)

    Article  Google Scholar 

  23. Lauder, G.V., Anderson, E.J., Tangorra, J., et al.: Fish biorobotics: kinematics and hydrodynamics of self-propulsion. J. Exp. Biol. 210, 2767–2780 (2007)

    Article  Google Scholar 

  24. Vandenberghe, N., Zhang, J., Childress, S.: Symmetry breaking leads to forward flapping flight. J. Fluid Mech. 506, 147–155 (2004)

    Article  MATH  Google Scholar 

  25. Vandenberghe, N., Childress, S., Zhang, J.: On unidirectional flight of a free flapping wing. Phys. Fluids 18, 99–124 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  26. Alben, S., Shelley, M.J.: Coherent locomotion as an attracting state for a free flapping body. Proc. Natl. Acad. Sci. USA 102, 11163–11166 (2005)

    Article  Google Scholar 

  27. Lu, X.Y., Liao, Q.: Dynamic responses of a two-dimensional flapping foil motion. Phys. Fluids 18, 4173–4180 (2006)

    Google Scholar 

  28. Zhang, X., Ni, S.Z., Wang, S.Z., et al.: Effects of geometric shape on the hydrodynamics of a self-propelled flapping foil. Phys. Fluids 21, 593–598 (2009)

    MATH  Google Scholar 

  29. Deng, J., Caulfield, C.P.: Dependence on aspect ratio of symmetry breaking for oscillating foils: implications for flapping flight. J. Fluid Mech. 787, 16–49 (2015)

    Article  MathSciNet  Google Scholar 

  30. Hu, J., Xiao, Q.: Three-dimensional effects on the translational locomotion of a passive heaving wing. J. Fluids Struct. 46, 77–88 (2014)

    Article  Google Scholar 

  31. Spagnolie, S.E., Moret, L., Shelley, M.J., et al.: Surprising behaviors in flapping locomotion with passive pitching. Phys. Fluids 22, 041903 (2009)

    Article  MATH  Google Scholar 

  32. Zhang, J., Liu, N.S., Lu, X.Y.: Locomotion of a passively flapping flat plate. J. Fluid Mech. 659, 43–68 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  33. Arora, N., Gupta, A., Hikaru, A., et al.: Propulsion of a plunging flexible airfoil using a torsion spring model. In: AIAA Aviation, 33rd AIAA Applied Aerodynamics Conference, Dallas (2015)

  34. Xiao, Q., Hu, J., Liu, H.: Effect of torsional stiffness and inertia on the dynamics of low aspect ratio flapping wings. Bioinspir. Biomim. 9, 016008 (2014)

    Article  Google Scholar 

  35. Thiria, B., Godoy-Diana, R.: How wing compliance drives the efficiency of self-propelled flapping flyers. Phys. Rev. E 82, 015303 (2010)

    Article  Google Scholar 

  36. Ramananarivo, S., Godoy-Diana, R., Thiria, B.: Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance. Proc. Natl. Acad. Sci. USA 108, 5964–5969 (2011)

    Article  Google Scholar 

  37. Alben, S., Charles, W., Baker, T.V., et al.: Dynamics of freely swimming flexible foils. Phys. Fluids 24, 051901 (2012)

    Article  MATH  Google Scholar 

  38. Lee, J., Lee, S.: Fluid-structure interaction for the propulsive velocity of a flapping flexible plate at low reynolds number. Comput. Fluids 71, 348–374 (2013)

    Article  MathSciNet  Google Scholar 

  39. Hua, R.N., Zhu, L.D., Lu, X.Y.: Locomotion of a flapping flexible plate. Phys. Fluids 25, 121901 (2013)

    Article  Google Scholar 

  40. Zhu, X.J., He, G.W., Zhang, X.: Numerical study on hydrodynamic effect of flexibility in a self-propelled plunging foil. Comput. Fluids 97, 1–20 (2014)

    Article  MathSciNet  Google Scholar 

  41. Yeh, P.D., Alexeev, A.: Free swimming of an elastic plate plunging at low Reynolds number. Phys. Fluids 26, 053604 (2014)

    Article  Google Scholar 

  42. Yeh, P.D., Alexeev, A.: Effect of aspect ratio in free-swimming plunging flexible plates. Comput. Fluids 124, 220–225 (2015)

    Article  MathSciNet  Google Scholar 

  43. Zhu, X.J., He, G.W., Zhang, X.: How flexibility affects the wake symmetry properties of a self-propelled plunging foil. J. Fluid Mech. 751, 164–183 (2014)

    Article  MathSciNet  Google Scholar 

  44. Michelin, S., Smith, S.G.L.: Resonance and propulsion performance of a heaving flexible wing. Phys. Fluids 21, 071902 (2009)

    Article  MATH  Google Scholar 

  45. Triantafyllou, G.S.: Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluids Struct. 7, 205–224 (1993)

    Article  Google Scholar 

  46. Moored, K.W., Dewey, P.A., Smits, A.J., et al.: Hydrodynamic wake resonance as an underlying principle of efficient unsteady propulsion. J. Fluid Mech. 708, 329–348 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  47. Moored, K.W., Dewey, P.A., Boschitsch, B.M., et al.: Linear instability mechanisms leading to optimally efficient locomotion with flexible propulsors. Phys. Fluids 26, 041905 (2014)

    Article  Google Scholar 

  48. Zhu, X.J., He, G.W., Zhang, X.: Underlying principle of efficient propulsion in flexible plunging foils. Acta Mech. Sin. 30, 839–845 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  49. Ramananarivo, S., Godoy-Diana, R., Thiria, B.: Passive elastic mechanism to mimic fish-muscle action in anguilliform swimming. J. R. Soc. Interface 10, 20130667 (2013)

    Article  Google Scholar 

  50. Ramananarivo, S., Godoy-Diana, R., Thiria, B.: Propagating waves in bounded elastic media: transition from standing waves to anguilliform kinematics. Europhys. Lett. 105, 54003 (2014)

    Article  Google Scholar 

  51. Borazjani, I., Sotiropoulos, F.: Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J. Exp. Biol. 211, 1541–1558 (2008)

    Article  Google Scholar 

  52. Borazjani, I., Sotiropoulos, F.: Numerical investigation of the hydrodynamics of anguilliform swimming in the transitional and inertial flow regimes. J. Exp. Biol. 212, 576–592 (2009)

    Article  Google Scholar 

  53. Bale, R., Shirgaonkar, A.A., Neveln, I.D., et al.: Separability of drag and thrust in undulatory animals and machines. Sci. Rep. 4, 7329 (2014)

    Article  Google Scholar 

  54. Maertens, A.P., Triantafyllou, M.S., Yue, D.K.: Efficiency of fish propulsion. Bioinspir. Biomim. 10, 046013 (2015)

    Article  Google Scholar 

  55. Bale, R., Hao, M., Bhalla, A.P., et al.: Gray’s paradox: a fluid mechanical perspective. Sci. Rep. 4, 5904 (2014)

    Google Scholar 

  56. Schultz, W.W., Webb, P.W.: Power requirements of swimming: do new methods resolve old questions? Integr. Comp. Biol. 42, 1018–1025 (2002)

    Article  Google Scholar 

  57. Kern, S., Koumoutsakos, P.: Simulations of optimized anguilliform swimming. J. Exp. Biol. 209, 4841–4857 (2006)

    Article  Google Scholar 

  58. Liu, G., Yu, Y.L., Tong, B.G.: Optimal energy-utilization ratio for long-distance cruising of a model fish. Phys. Rev. E 86, 016308 (2012)

    Article  Google Scholar 

  59. Eloy, C.: On the best design for undulatory swimming. J. Fluid Mech. 717, 48–89 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  60. Tokic, G., Yue, D.K.: Optimal shape and motion of undulatory swimming organisms. Proc. R. Soc. B 279, 3065–3074 (2012)

    Article  Google Scholar 

  61. Weihs, D.: Hydromechanics of fish schooling. Nautre 241, 290–291 (1973)

    Article  Google Scholar 

  62. Zdravkovich, M.M.: Review of flow interference between two circular cylinders in various arrangements. J. Fluids Eng. 99, 618–633 (1977)

    Article  Google Scholar 

  63. Ristroph, L., Zhang, J.: Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Letts. 101, 6797–6800 (2008)

    Article  Google Scholar 

  64. Alben, S.: Wake-mediated synchronization and drafting in coupled flags. J Fluid Mech. 641, 489–496 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  65. Zhu, L.D.: Interaction of two tandem deformable bodies in a viscous incompressible flow. J. Fluid Mech. 635, 455–475 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  66. Kim, S., Huang, W.X., Sung, H.J.: Constructive and destructive interaction modes between two tandem flexible flags in viscous flow. J. Fluid Mech. 661, 511–521 (2010)

    Article  MATH  Google Scholar 

  67. Uddin, E., Huang, W.X., Sung, H.J.: Interaction modes of multiple flexible flags in a uniform flow. J. Fluid Mech. 729, 563–583 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  68. Wang, Z., Russell, D.: Effect of forewing and hindwing interactions on aerodynamic forces and power in hovering dragonfly flight. Phys. Rev. Letts. 99, 12243–12254 (2007)

    Google Scholar 

  69. Deng, J., Shao, X.M., Yu, Z.S.: Hydrodynamic studies on two traveling wavy foils in tandem arrangement. Phys. Fluids 19, 113104 (2007)

    Article  MATH  Google Scholar 

  70. Uddin, E., Huang, W.X., Sung, H.J.: Actively flapping tandem flexible flags in a viscous flow. J. Fluid Mech. 780, 120–142 (2015)

    Article  MathSciNet  Google Scholar 

  71. Tian, F.B., Wang, W.Q., Wu, J., et al.: Swimming performance and vorticity structures of a mother-calf pair of fish. Comput. Fluids 124, 1–11 (2016)

    Article  MathSciNet  Google Scholar 

  72. Zhu, X.J., He, G.W., Zhang, X.: Flow-mediated interactions between two self-propelled flapping filaments in tandem configuration. Phys. Rev. Letts. 113, 238105 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  74. Becker, A.D., Masoud, H., Newbolt, J.W., et al.: Hydrodynamic schooling of flapping swimmers. Nat. Commun. 6, 8514 (2015)

    Article  Google Scholar 

  75. De Rosis, A.: Fluid forces enhance the performance of an aspirant leader in self-organized living groups. PLoS One 9, e114687 (2014)

    Article  Google Scholar 

  76. Raspa, V., Godoy-Diana, R., Thiria, B.: Topology-induced effect in biomimetic propulsive wakes. J. Fluid Mech. 729, 377–387 (2013)

    Article  MATH  Google Scholar 

  77. Webb, P.W.: The effect of solid and porous channel walls on steady swimming of steelhead trout Oncorhynchus mykiss. J. Exp. Biol. 178, 97–108 (1993)

  78. Webb, P.W.: Kinematics of plaice, Pleuronectes platessa, and cod, Gadus morhua, swimming near the bottom. J. Exp. Biol. 205, 2125–2134 (2002)

    Google Scholar 

  79. Quinn, D.B., Moored, K.W., Dewey, P.A., et al.: Unsteady propulsion near a solid boundary. J. Fluid Mech. 742, 152–170 (2014)

    Article  Google Scholar 

  80. Quinn, D.B., Lauder, G.V., Smits, A.J.: Flexible propulsors in ground effect. Bioinspir. Biomim. 9, 036008 (2014)

    Article  Google Scholar 

  81. Fernandez-Prats, R., Raspa, V., Thiria, B., et al.: Large-amplitude undulatory swimming near a wall. Bioinspir. Biomim. 10, 016003 (2015)

    Article  Google Scholar 

  82. Blevins, E.L., Lauder, G.V.: Swimming near the substrate: a simple robotic model of stingray locomotion. Bioinspir. Biomim. 8, 016005 (2013)

    Article  Google Scholar 

  83. Bottom II, R.G., Borazjani, I., Blevins, E.L., et al.: Hydrodynamics of swimming in stingrays: numerical simulations and the role of the leading-edge vortex. J. Fluid Mech. 788, 407–443 (2016)

    Article  MathSciNet  Google Scholar 

  84. Zhu, L.L., Guan, H., Wu, C.J.: A study of a three-dimensional self-propelled flying bird with flapping wings. Sci. China Ser. G 58, 1–16 (2015)

    MathSciNet  Google Scholar 

Download references

Acknowledgments

The project was supported by the Chinese Academy of Sciences (Grants KJCX-SW-L08, KJCX3-SYW-S01) and the National Natural Science Foundation of China (Grants 11021262, 11023001, 11232011, 11372331).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xing Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, S., He, G. & Zhang, X. Self-propulsion of flapping bodies in viscous fluids: Recent advances and perspectives. Acta Mech. Sin. 32, 980–990 (2016). https://doi.org/10.1007/s10409-016-0578-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-016-0578-y

Keywords

Navigation