Acta Mechanica Sinica

, Volume 19, Issue 2, pp 103–117

# Flows around two airfoils performing fling and subsequent translation and translation and subsequent clap

• Sun Mao
• Yu Xin
Article

## Abstract

The aerodynamic forces and flow structures of two airfoils performing “fling and subsequent translation” and “translation and subsequent clap” are studied by numerically solving the Navier-Stokes equations in moving overset grids. These motions are relevant to the flight of very small insects. The Reynolds number, based on the airfoil chord lengthc and the translation velocityU, is 17. It is shown that: (1) For two airfoils performing fling and subsequent translation, a large lift is generated both in the fling phase and in the early part of the translation phase. During the fling phase, a pair of leading edge vortices of large strength is generated; the generation of the vortex pair in a short period results in a large time rate of change of fluid impulse, which explains the large lift in this period. During the early part of the translation, the two leading edge vortices move with the airfoils; the relative movement of the vortices also results in a large time rate of change of fluid impulse, which explains the large lift in this part of motion. (In the later part of the translation, the vorticity in the vortices is diffused and convected into the wake.) The time averaged lift coefficient is approximately 2.4 times as large as that of a single airfoil performing a similar motion. (2) For two airfoils performing translation and subsequent clap, a large lift is generated in the clap phase. During the clap, a pair of trailing edge vortices of large strength are generated; again, the generation of the vortex pair in a short period (which results in a large time rate of change of fluid impulse) is responsible for the large lift in this period. The time averaged lift coefficient is approximately 1.6 times as large as that of a single airfoil performing a similar motion. (3) When the initial distance between the airfoils (in the case of clap, the final distance between the airfoils) varies from 0.1 to 0.2c, the lift on an airfoil decreases only slightly but the torque decreases greatly. When the distance is about 1c, the interference effects between the two airfoils become very small.

## Key Words

two airfoils fling translation clap Navier-Stokes simulation

## References

1. 1.
Ellington CP. The aerodynamics of hovering insect flight, I: The quasi-steady analysis.Phl Trans R Soc Lond B, 1984, 305: 1–15Google Scholar
2. 2.
Spedding GR. The aerodynamics of flight. In: Alexander RMcN ed. Advances in Comparative and Environmental Physiology, vol. II, Mechanics of Animal Locomotion. London: Springer-Verlag, 1992. 51–111Google Scholar
3. 3.
Weis-Fogh T. Quick estimates of flight fitness in hovering animals, including novel mechanism for lift production.J Exp Biol, 1973, 59: 169–230Google Scholar
4. 4.
Lighthill MJ. On the Weis-Fogh mechanism of lift generation.J Fluid Mech, 1973, 60: 1–17
5. 5.
Maxworthy T. Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight. Part 1: Dynamics of the ‘fling’.J Fluid Mech, 1979, 93: 47–63
6. 6.
Edwards RH, Cheng HK. The separation vortex in the Weis-Fogh circulation-generation mechanism.J Fluid Mech, 1982, 120: 463–473
7. 7.
Wu JC, Hu-Chen H. Unsteady aerodynamics of articulate lifting bodies. AIAA Paper, No. 84-2184, 1984Google Scholar
8. 8.
Spedding GR, Maxworthy T. The generation of circulation and lift in a rigid two-dimensional fling.J Fluid Mech, 1986, 165: 247–272
9. 9.
Rogers SE, Kwak D. Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations.AIAA Journal, 1990, 28: 253–262
10. 10.
Rogers SE, Kwak D, Kiris C. Steady and unsteady solutions of the incompressible Navier-Stokes equations.AIAA Journal, 1991, 33: 2066–2072Google Scholar
11. 11.
Rogers SE. On the use of implicit line-relaxation and multi-zonal computations. AIAA Paper, No. 91-1611, 1991Google Scholar
12. 12.
Rogers SE, Pulliam TH. Accuracy enhancements for overset grids using a defect correction approach. AIAA Paper, No. 94-0523, 1994Google Scholar
13. 13.
Meakin RL. On the spatial and temporal accuracy of overset grid methods for moving body problems. AIAA Paper, No. 94-1925, 1994Google Scholar
14. 14.
Hilgenstock A. A fast method for the elliptic generation of three dimensional grids with full boundary control. In: Sengupta S, Hauser J, Eiseman PR, Thompson JF eds. Num Grid Generation in CFM'88. Swansea UK: Pineridge Press Ld., 1988. 137–146Google Scholar
15. 15.
Lan SL, Sun M. Aerodynamic properties of a wing performing unsteady rotational motions at low Reynolds numbers.Acta Mech, 2001, 149: 135–147
16. 16.
Wu JC. Theory for aerodynamic force and moment in viscous flows.AIAA Journal, 1981, 19: 432–441

© Chinese Society of Theoretical and Applied Mechanics 2003

## Authors and Affiliations

• Sun Mao
• 1
• Yu Xin
• 1
1. 1.Institute of Fluid MechanicsBeijing University of Aeronautics & AstronauticsBeijingChina