Experimental Mechanics

, Volume 50, Issue 9, pp 1361–1366 | Cite as

A Unified Introduction to Fluid Mechanics of Flying and Swimming at High Reynolds Number

Article

Abstract

Modeling the flow around a deformable and moving surface is required to calculate the forces exerted by a swimming or flying animal on the surrounding fluid. Assuming that viscosity plays a minor role, linear potential models can be used. These models derived from unsteady airfoil theory are usually divided in two categories depending on the aspect ratio of the moving surface: for small aspect ratios, slender-body theory applies while for large aspect ratios two-dimensional or lifting-line theory is used. This paper aims at presenting these models with a unified approach. These potential models being analytical, they allow fast computations and can therefore be used for optimization or control.

Keywords

Potential flow Unsteady airfoil theory Slender-body theory Lifting-line theory Lifting-surface integral Asymptotic methods 

Notes

Acknowledgement

This work was sponsored by the French ANR under the project ANR-06-JCJC-0087.

References

  1. 1.
    Childress S (1981) Mechanics of swimming and flying. Cambridge University Press, CambridgeMATHCrossRefGoogle Scholar
  2. 2.
    Dowell EH, Hall KC (2001) Modeling of fluid-structure interaction. Ann Rev Fluid Mech 33:445–490CrossRefGoogle Scholar
  3. 3.
    Lighthill J (1987) Mathematical biofluiddynamics. SIAM, PhiladelphiaGoogle Scholar
  4. 4.
    Taylor GI (1952) Analysis of the swimming of long and narrow animals. Proc R Soc Lond Ser A 214(1117):158–183MATHCrossRefGoogle Scholar
  5. 5.
    Wu TY (2001) Mathematical biofluiddynamics and mechanophysiology of fish locomotion. Math Methods Appl Sci 24:1541–1464MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Wu TY (2002) On theoretical modeling of aquatic and aerial animal locomotion. In: van der Giessen E, Wu TY (eds) Advances in applied mechanics, vol 38. Elsevier, Amsterdam, pp 291–353Google Scholar
  7. 7.
    Cheng JY, Pedley TJ, Altringham JD (1998) A continuous dynamic beam model for swiming fish. Philos Trans R Soc Lond B 353:981–997CrossRefGoogle Scholar
  8. 8.
    Lighthill MJ (1960) Note on the swimming of slender fish. J Fluid Mech 9:305–317CrossRefMathSciNetGoogle Scholar
  9. 9.
    Lighthill MJ (1971) Large-amplitude elongated-body theory of fish locomotion. Proc R Soc Lond B 179:125–138CrossRefGoogle Scholar
  10. 10.
    Guermond JL, Sellier A (1991) A unified unsteady lifting-line theory. J Fluid Mech 229:427–451MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Wu TYT (1961) Swimming of a waving plate. J Fluid Mech 10:321–344MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Morse PM, Feshbach H (1953) Methods of theoretical physics. McGraw-Hill, New YorkMATHGoogle Scholar
  13. 13.
    Hadamard J (1932) Lectures on Cauchy’s problem in linear differential equation. Dover, New YorkGoogle Scholar
  14. 14.
    Mangler KW (1951) Improprer integrals in theoretical aerodynamics. Tech. Rep. Aero 2424, British Aeronautical Research CouncilGoogle Scholar
  15. 15.
    Van Dyke M (1975) Perturbation methods in fluid mechanics. Parabolic, StanfordMATHGoogle Scholar
  16. 16.
    Van Dyke M (1964) Lifting-line theory as a singular perturbation problem. Appl Math Mech 28:90–101MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Watkins CE, Runyan HL, Woolston DS (1955) On the kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow. Tech. Rep. TR-1234, NACAGoogle Scholar
  18. 18.
    Katz J, Plotkin A (2001) Low-speed aerodynamics, 2nd edn. Cambridge University Press, CambridgeMATHGoogle Scholar
  19. 19.
    Tuck EO (1993) Some accurate solutions of the lifting surface integral-equation. J Aust Math Soc Ser B 35:127–144MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Albano E, Rodden WP (1969) A doublet-lattice method for calculating lift distributions on oscillating surfaces in subsonic flows. AIAA J 7(2):279–285MATHCrossRefGoogle Scholar
  21. 21.
    Rodden WP, Taylor PF, McIntosh SC (1998) Further refinement of the subsonic doublet-lattice method. J Aircr 35(5):720–727CrossRefGoogle Scholar
  22. 22.
    Cheng JY, Zhuang LX, Tong BG (1991) Analysis of swimming three-dimensional waving plates. J Fluid Mech 232:341–355MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Bisplinghoff RL, Ashley H, Halfman RL (1983) Aeroelasticity. Dover, New YorkGoogle Scholar
  24. 24.
    Theodorsen T (1935) General theory of aerodynamic instability and the mechanism of flutter. Tech. Rep. TR-496, NACAGoogle Scholar
  25. 25.
    Eloy C, Lagrange R, Souilliez C, Schouveiler L (2008) Aeroelastic instability of cantilevered flexible plates in uniform flow. J Fluid Mech 611:97–106MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Eloy C, Souilliez C, Schouveiler L (2007) Flutter of a rectangular plate. J Fluids Struct 23:904–919CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2009

Authors and Affiliations

  • C. Eloy
    • 1
  • O. Doaré
    • 2
  • L. Duchemin
    • 1
  • L. Schouveiler
    • 1
  1. 1.IRPHECNRS & Aix-Marseille UniversitéMarseilleFrance
  2. 2.UME, ENSTAPalaiseauFrance

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