The three-dimensional flows in the Weis-Fogh mechanism are studied by flow visualization and numerical simulation by a discrete vortex method. In this mechanism, two wings open, touching their trailing edges (fling), and rotate in opposite directions in the horizontal plane. At the “fling” stage, the flow separates at the leading edge and the tip of each wing. Then they rotate, and the flow separates also at the trailing edges. The structure of the vortex systems shed from the wings is very complicated and their effect on the forces on the wings have not yet been clarified. Discrete vortex method, especially the vortex stick method, is employed to investigate the vortex structure in the wake of the two wings. The wings are represented by lattice vortices, and the shed vortices are expressed by discrete three-dimensional vortex sticks. In this calculation, the GRAPE3A hardware is used to calculate at high speed the induced velocity of the vortex sticks and the viscous diffusion of fluid is represented by the random walk method. The vortex distributions and the velocity field are calculated. The pressure is estimated by the Bernoulli equation, and the lift and moment on the wing are also obtained. However, the simulations, especially those for various Reynolds numbers, should be treated with caution, because there is no measurement to compare them with and the discrete vortex method is approximate due to rudimentary modeling of viscosity.

1.
Beale
J. T.
, and
Majda
A.
,
1982
, “
Vortex Methods. I: Convergence in Three Dimensions
,”
Mathematics of Computation
, Vol.
39
, pp.
1
27
.
2.
Chorin
A. J.
,
1973
, “
Numerical Study of Slightly Viscous Flow
,”
Journal of Fluid Mechanics
, Vol.
57
, pp.
785
796
.
3.
Kamemoto
K.
,
1993
, “
Ranryu Moderu Toshiteno Uzuhouno Hattensei
,”
Japan Society of Computational Fluid Dynamics
, Vol.
2
, No.
1
, pp.
20
29
. (in Japanese)
4.
Leonard
A.
,
1980
, “
Vortex Method for Flow Simulation
,”
Journal of Computational Physics
, Vol.
37
, pp.
289
335
.
5.
Lighthill
M. J.
,
1973
, “
On the Weis-Fogh Mechanism of Lift Generation
,”
Journal of Fluid Mechanics
, Vol.
60
, pp.
1
17
.
6.
Maxworthy
T.
,
1979
, “
Experiments on the Weis-Fogh Mechanism of Lift Generation by Insects in Hovering Flight
,”
Journal of Fluid Mechanics
, Vol.
93
, pp.
47
63
.
7.
Ogami
Y.
, and
Akamatsu
T.
,
1991
, “
Viscous Flow Simulation Using the Discrete Vortex Method—The Diffusion Velocity Method
,”
Computers and Fluids
, Vol.
19
, Pt. 3, pp.
433
441
.
8.
Okumura, S. K., Makino, J., Ito, T., Fukushige, T., Sugimoto, D., Hashmoto, E., Tomita, K., and Miyakawa, N., 1992, “GRAPE-3: Highly parallelized Special Purpose Computer for Gravitational Many-Body Simulations,” Proceedings of the Twenty-Fifth Hawaii International Conference on System Sciences, Vol. 1, pp. 151–160.
9.
Sarpkaya
T.
,
1989
, “
Computational Methods with Vortices
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
111
, March, pp.
5
52
.
10.
Shirayama, S., et. al., 1985, “A Three-dimensional Vortex Method,” AIAA Paper, 85-1488, pp. 14–24.
11.
Spedding
G. R.
, and
Maxworthy
T.
,
1986
, “
The Generation of Circulation and Lift in a Rigid Two-Dimensional Fling
,”
Journal of Fluid Mechanics
, Vol.
165
, pp.
247
272
.
12.
Sugimoto, D., 1994, “Senyo Kesanki Niyoru Simulation,” Asakura Shoten (in Japanese).
13.
Weis-Fogh
T.
,
1973
, “
Quick Estimates of Flight Fitness in Hovering Animals, Including Novel Mechanism for Lift Production
,”
Journal of Experimental Biology
, Vol.
59
, pp.
169
231
.
This content is only available via PDF.