Acta Mechanica

, Volume 145, Issue 1–4, pp 173–187 | Cite as

Aerodynamic forces and flow structures of an airfoil in some unsteady motions at small Reynolds number

  • H. Hamdani
  • M. Sun
Original Papers


The aerodynamic forces and flow structures of a NACA 0012 airfoil in some unsteady motions at small Reynolds number (Re=100) are studied by numerically solving the Navier-Stokes equations. These motions include airfoil acceleration and deceleration from one translational speed to another and rapidly pitching up in constant freestream (equivalent to pitching up during translational motion at constant speed). It is shown that at small Reynolds number (Re=100), when the airfoil is performing fast acceleration or deceleration from one speed to another, a large aerodynamic force can be generated during and for a time period after the acceleration or deceleration; a large aerodynamic force can also be generated when the airfoil is performing a fast pitching motion in a constant freestream. In these fast unsteady motions, an airfoil in low Re flow can produce a large aerodynamic force as effective as in large Re flow, or the effect of unsteady motion dominates the Reynolds number effect. During the fast unsteady motion of the airfoil, new layers of strong vorticity are formed near the upper and lower surfaces of the airfoil under the previously existing thick vorticity layers, and it is the generation and motion of the new vorticity layers that is mainly responsible for the generation of the large aerodynamic force; the large-scale structure and movement of the newly produced vorticity layers are similar to that of high Re flow.


Reynolds Number Vorticity Fluid Dynamics Flow Structure Translational Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Weis-Fogh, T.: Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Exp. Biology59, 169–230 (1973).Google Scholar
  2. [2]
    Ellington, C. P.: The aerodynamics of hovering flight. III. Kinematics. Phil. Trans. R. Soc. London305, 41–78 (1981).Google Scholar
  3. [3]
    Spedding, G. R., Maxworthy, T.: The generation of circulation and lift in a rigid two-dimensional fling. J. Fluid Mech.165, 247–272 (1986).Google Scholar
  4. [4]
    Lighthill, M. J.: On the Weis-Fogh mechanism of lift generation. J. Fluid Mech.60, 1–17 (1973).Google Scholar
  5. [5]
    Dickinson, M. H., Gotz, K. G.: Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Exp. Biology174, 45–64 (1993).Google Scholar
  6. [6]
    Dickinson, M. H.: The effects of wing rotation on unsteady aerodynamic performance at low Reynolds numbers. J. Exp. Biology192, 179–206 (1994).Google Scholar
  7. [7]
    Dickinson, M. H., Gotz, K. G.: The wake dynamics and flight forces of the fruit fly drosophila melanogaster. J. Exp. Biology199, 2085–2104 (1996).Google Scholar
  8. [8]
    Smith, M. J.: Simulating moth wing aerodynamics: towards the development of flappingwing technology. AIAA J.34, 1448–1455 (1996).Google Scholar
  9. [9]
    Liu, H., Ellington, C. P., Kawachi, K., Van Den Berg, C., Willmott, A. P.: A computational fluid dynamic study of hawkmoth hovering. J. Exp. Biology201, 461–477 (1988).Google Scholar
  10. [10]
    Dickinson, M. H., Lehmann, F. O., Gotz, K. G.: The active control of wing rotation by Drosophila. J. Exp. Biology182, 173–189 (1993).Google Scholar
  11. [11]
    Steger, J. L.: Implicit finite-difference simulation of flow about arbitrary two-dimensional geometries. AIAA J.16, 679–696 (1978).Google Scholar
  12. [12]
    Beam, R. M., Warming, R. F.: An implicit factored scheme for the compressible Navier-Stokes equations. AIAA J.16, 393–402 (1978).Google Scholar
  13. [13]
    Thomas, P. D.: Composite three-dimensional grids generated by elliptic systems. AIAA J.20, 1195–1202 (1982).Google Scholar
  14. [14]
    Liu, J. C., Sun, M., Wu, L. Y.: Navier-Stokes analysis of circulation control airfoil. Acta Mech. Sinica11, 137–143 (1995).Google Scholar
  15. [15]
    Schlichting, H.: Boundary layer theory, 2nd ed. New York: Pergamon Press 1955.Google Scholar
  16. [16]
    Wu, J. C.: Theory for aerodynamic force and moment in viscous flows. AIAA J.19, 432–441 (1981).Google Scholar

Copyright information

© Springer-Verlag 2000

Authors and Affiliations

  • H. Hamdani
    • 1
  • M. Sun
    • 1
  1. 1.Institute of Fluid MechanicsBeijing University of Aeronautics and AstronauticsBeijingP.R. China

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