Skip to main content
Log in

Numerical analysis on transitions and symmetry-breaking in the wake of a flapping foil

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

Abstract

Flying and marine animals often use flapping wings or tails to generate thrust. In this paper, we will use the simplest flapping model with a sinusoidal pitching motion over a range of frequency and amplitude to investigate the mechanism of thrust generation. Previous work focuses on the Karman vortex street and the reversed Karman vortex street but the transition between two states remains unknown. The present numerical simulation provides a complete scenario of flow patterns from the Karman vortex street to reversed Karman vortex street via aligned vortices and the ultimate state is the deflected Karman vortex street, as the parameters of flapping motions change. The results are in agreement with the previous experiment. We make further discussion on the relationship of the observed states with drag and thrust coefficients and explore the mechanism of enhanced thrust generation using flapping motions.

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. Anderson, J.M., Streitlien, K., Barrett, D.S., et al.: Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 4–72 (1998)

    Article  MathSciNet  Google Scholar 

  2. Buchholz, J.H.J., Smits, A.J.: On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J. Fluid Mech. 546, 43–443 (2006)

    Google Scholar 

  3. 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 

  4. Couder, Y., Basdevant, C.: Experimental and numerical study of vortex couples in two dimensional flows. J. Fluid Mech. 173, 225–251 (1986)

    Article  Google Scholar 

  5. 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 

  6. von Ellenrieder, K.D., Pothos, S.: PIV measurements of the asymmetric wake of a two dimensional heaving hydrofoil. Exp. Fluids 44, 733–745 (2008)

    Article  Google Scholar 

  7. Knoller, R.: Die Gesetze des Luftwiderstandes. Flug- und Motor-technik (Wien). 3, 1–7 (1909)

    Google Scholar 

  8. Betz, A.: Ein Beitrag zur Erklärung des Segelfluges. Zeitschrift fur Flugtechnik und Motorluftschiffahrt 3, 269–272 (1912)

    Google Scholar 

  9. von Karman, T., Burgers, J.M.: General Aerodynamic Theory Perfect Fluids, Aerodynamic Theory. Durand, W. F. edn. Division E 2, Julius-Springer, Berlin (1943)

    Google Scholar 

  10. Bohl, D.G., Koochesfahani, M.M.: MTV measurements of the vertical field in the wake of an airfoil oscillating at high reduced frequency. J. Fluid Mech. 620, 63–88 (2009)

    Article  MATH  Google Scholar 

  11. von Ellenrieder, K.D., Parker, K., Soria, J.: Fluid mechanics of flapping wings. Experimental Thermal and Fluid Science 32, 1578–1589 (2008)

    Article  Google Scholar 

  12. Wolfgang, M.J., Anderson, J.M., Grosenbaugh, M.A., et al.: Near-body flow dynamics in swimming fish. J. Exp. Biol. J. Exp. Biol. 202, 2303–2307 (1999)

    Google Scholar 

  13. Drucker, E.G., Lauder, G.V.: Locomotor function of the dorsal fin in teleost fishes: Experimental analysis of wake forces in sunfish. J. Exp. Biol. 204, 2943–2958 (2001)

    Google Scholar 

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

    Article  Google Scholar 

  15. Gopalkrishnan, R., Triantafyllou, M.S., Triantafyllou, G.S., et al.: Active vorticity control in a shear-flow using a flapping foil. J. Fluid Mech. 274, 1–21 (1994)

    Article  Google Scholar 

  16. Jones, K.D., Dohring, C.M., Platzer, M.F.: An experimental and computational investigation of the Knoller-Betz effect. AIAA J. 36, 1240–1246 (1998)

    Article  Google Scholar 

  17. Molina, J., Zhang, X., Angland, D.: On the unsteady motion and stability of a heaving airfoil in ground effect. Acta Mech. Sin. 27, 164–178 (2011)

    Article  Google Scholar 

  18. Shyy, W., Liang, Y., Tang, J., et al.: Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings. Acta Mech. Sin. 24, 351–373 (2008)

    Article  Google Scholar 

  19. Dong, G.J., Lu, X.Y.: Numerical analysis on the propulsive performance and vortex shedding of fish-like traveling wavy plate. Int. J. Numer. Meth. Fluids 49, 1351–1373 (2005)

    Article  Google Scholar 

  20. Sun, M., Wang, J.K., Xiong, Y.: Dynamic flight stability of hovering insects. Acta Mech. Sin. 23, 231–246 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Wu, J.H., Sun, M.: Unsteady aerodynamic forces of a flapping wing. J. Exp. Biol. 207, 1137–1150 (2004)

    Article  Google Scholar 

  22. Godoy-Diana, R., Aider, J.L., Wesfreid, J.E.: Transitions in the wake of a flapping foil. Physical Review E 77 (2008)

  23. Mittal, R., Iaccarino, G.: Immersed boundary methods. Annual Review of Fluid Mechanics 37, 239–261 (2005)

    Article  MathSciNet  Google Scholar 

  24. Kim, J., Kim, D., Choi, H.: An immersed-boundary finitevolume method for simulations of flow in complex geometries. J. Comp. Phys. 171, 132–150 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  25. Su, S.W., Lai, M.C., Lin, C.A.: An immersed boundary technique for simulating complex flows with rigid boundary. Computers and Fluids 36, 313–324 (2007)

    Article  MATH  Google Scholar 

  26. Yang, X.L., He, G.W., Zhang, X.: Large-eddy simulation of flows past a flapping airfoil using immersed boundary method. Science China Physics, Mechanics and Astronomy 53, 1101–1108 (2010)

    Article  Google Scholar 

  27. Yang, X.L., Zhang, X., Li, Z.L., et al.: A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. Journal of Computational Physics 228, 7821–7836 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. Ravoux, J.F., Nadim, A., Haj-Hariri H.: An embedding method for bluff body flows: Interactions of two side-by-side cylinder wakes. Theoret. Comput. Fluid Dynamics 16, 433–466 (2003)

    Article  MATH  Google Scholar 

  29. Dutsch, H., Durst, F., Becker, S., et al.: Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers. J. Fluid Mech. 360, 249–271 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xing Zhang.

Additional information

The project was supported by the Natural Science Foundation of Jiangxi Province (2010GZC0162).

Rights and permissions

Reprints and permissions

About this article

Cite this article

He, GY., Wang, Q., Zhang, X. et al. Numerical analysis on transitions and symmetry-breaking in the wake of a flapping foil. Acta Mech Sin 28, 1551–1556 (2012). https://doi.org/10.1007/s10409-012-0158-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-012-0158-8

Keywords

Navigation