Skip to main content
Log in

Dynamic performance and wake structure of flapping plates with different shapes

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

Abstract

The dynamic performance and wake structure of flapping plates with different shapes were studied using multi-block lattice Boltzman and immersed boundary method. Two typical regimes relevant to thrust behavior are identified. One is nonlinear relation between the thrust and the area moment of plate for lower area moment region and the other is linear relation for larger area moment region. The tendency of the power variation with the area moment is reasonably similar to the thrust behavior and the efficiency decreases gradually as the area moment increases. As the mechanism of the dynamic properties is associated with the evolution of vortical structures around the plate, the formation and evolution of vortical structures are investigated and the effects of the plate shape, plate area, Strouhal number and Reynolds number on the vortical structures are analyzed. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to flapping locomotion.

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.

Similar content being viewed by others

References

  1. Ellington, C.P.: The aerodynamics of hovering insect flight. II. Morphological parameters. Phil. Trans. R. Soc. Lond. B 305, 17–40 (1984)

    Article  Google Scholar 

  2. Webb, P.W.: Form and function in fish swimming. Sci. Amer. 251, 58–68 (1984)

    Article  Google Scholar 

  3. Videler, J.J.: Fish Swimming. Chapman and Hall, Cambridge (1993)

    Book  Google Scholar 

  4. Weis-Fogh, T.: Quick estimates of flight fitness in hovering animals, including novel mechanism for lift production. J. Exp. Biol. 59, 169–230 (1973)

    Google Scholar 

  5. Combes, S.A., Daniel, T.L.: Shape, flapping and flexion: wing and fin design for forward flight. J. Exp. Biol. 204, 2073–2085 (2001)

    Google Scholar 

  6. Luo, G., Sun, M.: The effects of corrugation and wing plan-form on the aerodynamic force production of sweeping model insect wings. Acta Mech. Sinica 21, 531–541 (2005)

    Article  MATH  Google Scholar 

  7. Wilga, C.D., Lauder, G.V.: Hydrodynamic function of the shark’s tail. Nature 430, 850–850 (2004)

    Article  Google Scholar 

  8. Green, A.M., Smits, A.J.: Effects of three-dimensionality on thrust production by pitching panel. J. Fluid Mech. 615, 211–220 (2008)

    Article  MATH  Google Scholar 

  9. Li, G.J., Lu, X.Y.: Force and power of flapping plates in a fluid. J. Fluid Mech. 712, 598–613 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  10. Li, G.J., Zhu, L., Lu, X.Y.: Numerical studies on locomotion performance of fishlike tail fins. J. Hydrodyn. B 24, 488–495 (2012)

    Article  Google Scholar 

  11. Von Ellenrieder, K.D., Parker, K., Soria, J.: Flow structures behind a heaving and pitching finite-span wing. J. Fluid Mech. 490, 129–138 (2003)

    Article  MATH  Google Scholar 

  12. Dong, H., Mittal, R., Najjar, F.M.: Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils. J. Fluid Mech. 566, 309–343 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Buchholz, J.H.J., Smits, A.J.: Gallery of fluid motion: the wake of a low aspect ratio pitching plate. Phys. Fluids 17, 091102 (2005)

    Article  Google Scholar 

  14. Buchholz, J.H.J., Smits, A.J.: The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J. Fluid Mech. 603, 331–365 (2008)

    Article  MATH  Google Scholar 

  15. Green, A.M., Smits, A.J.: Effects of three-dimensionality on thrust production by a pitching panel. J. FluidMech. 615, 211–220 (2008)

    Article  MATH  Google Scholar 

  16. Vogel, S.: Life in Moving Fluids. Princeton University Press, Princeton (1994)

    Google Scholar 

  17. Usherwood, J. R., Ellington, C. P.: The aerodynamics of revolving wings. II. Propeller force coefficients from mayfly to quail. J. Exp. Biol. 205, 1565–1576 (2002)

    Google Scholar 

  18. Dudley, R.: The Biomechanics of Insect Flight: Form, Function, Evolution. Princeton University Press, Princeton (2002)

    Google Scholar 

  19. Lu, X.Y., Yin, X.Z., Tong, B.G.: Studies of hydrodynamics in fishlike swimming propulsion. Bio-mechanisms of Swimming and Flying, Springer 12, 143–155 (2008)

    Article  Google Scholar 

  20. Weis-Fogh, T.: Energetics of hovring flight in hummingbirds and in drodophila. J. Exp. Biol. 56, 79–104 (1972)

    Google Scholar 

  21. Peskin, C.S.: The immersed boundary method. Acta Numer. 11, 479–517 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  22. Feng, Z.G., Michaelides, E. E.: The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems. J. Comput. Phys. 195, 602–628 (2004)

    Article  MATH  Google Scholar 

  23. Gao, T., Lu, X.Y.: Insect normal hovering flight in ground effect. Phys. Fluids 20, 087101 (2008)

    Article  Google Scholar 

  24. Guo, Z.L., Zheng, C.G., Shi, B.C.: Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 65, 046308 (2002)

    Article  Google Scholar 

  25. Goldstein, D., Handler, R., Sirovich, L.: Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 105, 354–366 (1993)

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  27. Triantafyllou, M.S., Triantafyllou, G. S., Gopalkrishnan, R.: Wake mechanics for thrust generation in oscillating foils. Phys. Fluids A 3, 2835–2837 (1991)

    Article  Google Scholar 

  28. Lewin, G.C., Haj-Hariri, H.: Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow. J. Fluid Mech. 492, 339–362 (2003)

    Article  MATH  Google Scholar 

  29. Taylor, G.K., Nudds, R.L., Thomas, A.L.R.: Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature 425, 707–711 (2003)

    Article  Google Scholar 

  30. Wu, J.Z., Lu, X.Y., Zhuang, L.X.: Integral force acting on a body due to local flow structures. J. Fluid Mech. 576, 265–286 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  31. Taira, K., Colonius, T.: Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers. J. Fluid Mech. 623, 187–207 (2009)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xi-Yun Lu.

Additional information

The project was supported by the National Natural Science Foundation of China (11372304 and 11132010) and the 111 Project (B07033).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, GJ., Liu, NS. & Lu, XY. Dynamic performance and wake structure of flapping plates with different shapes. Acta Mech Sin 30, 800–808 (2014). https://doi.org/10.1007/s10409-014-0112-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-014-0112-z

Keywords

Navigation