Flapping Flight in Insects and Fish: 3-D Unsteady Computations

Introduction: Recent computational technology developments have enabled three-dimensional unsteady computations to be successfully completed for flapping wings and deforming shapes. The mathematical description of the performance of flying creatures has been limited, due to the previously insurmountable difficulties associated with flapping wings with changing shape. There are numerous operational advantages if we could successfully incorporate live creature performance characteristics into our vehicles and systems. Before we can proceed with such an undertaking we wish to understand, quantitatively, the fluid dynamics of the observed performance of those creatures. We describe below two recent computations carried out for the Drosophila (fruit fly),¹ and the Gomphosus varius (bird wrasse—a coral reef fish),² creatures, which might serve as biological inspiration for air and undersea vehicles, respectively.

Insect Wing Flapping: The three-dimensional wing strokes of the insects can be divided into two translational phases and two rotational phases. During the translational phases, upstroke and downstroke, the wings move through the air with high angles of attack; during the rotational phases, the wings rotate rapidly and reverse direction. Professor Michael Dickinson and his collaborators at the University of California Berkeley have studied the effects of the translational and rotational mechanisms of the wing in Drosophila.³

Our insect flapping wing computations were performed for the same conditions as in their experiments. The unsteady computation was carried out for five cycles of oscillation. Figure 6 compares thrust and drag forces, respectively, during one cycle of the wing beat. Professor Dickinson has suggested that the slight differences between our computed results and his experimental measurements may be due to a small asymmetry that was present in the experimental setup.

(a) Thrust	(b) Drag
FIGURE 6 Comparison of time history of thrust and drag forces (from Ref. 1).

To gain insight into the flow behavior associated with the wing flapping motion, a considerable amount of flow visualization was computed. Figure 7 is an example of a particular case of the flow about the wing during the downstroke.

Fish Pectoral Fin Flapping with Changing Shape: In the bird wrasse computations, we extended the development to the unsteady flow about a flapping 3-D surface whose shape is changing in time. In this pectoral fin investigation, we are continuing to focus our fish swimming work on oscillating control surface flows for nonundulating bodies that began on the swimming tuna several years ago. There is a more direct applicability of findings on the unsteady hydrodynamics of flapping fins on a nonundulating fish like the bird wrasse to the oscillating control surfaces on rigid naval vehicles.

FIGURE 7
Flow field about flapping Drosophila wing at t = 13.79 s at 50% of the downstroke (from Ref. 1).

The unsteady computations were carried out using a new mesh movement capability developed to accommodate the deforming fin surface. Unsteady simulations were carried out with the bird wrasse swimming at two body lengths per second. The computations were carried out for more than four cycles of fin oscillation. Figure 8 shows the instantaneous velocity field on the swimming wrasse. The time-varying 3-D lift and thrust forces, shown in Fig. 9, were computed by integrating the surface pressure over the wrasse body and fin at each time step throughout the simulation. These force time histories lead to horizontal and vertical accelerations that are in very good agreement with the experimentally obtained fish center of mass accelerations obtained by Prof. Westneat and Dr. Walker of the Field Museum of Natural History in Chicago.⁴ As in the Drosophila computations, we also carried out extensive visualization to gain insight into the flow dynamics associated with the time history of force generation. The particle traces plotted in Fig. 10 are indicative of the fluid motion past the pectoral fin at the middle of the down stroke.

FIGURE 8
Velocity vectors on the surface of the bird wrasse at one instant during the fin oscillation (from Ref. 2).

(a) Lift forces	(b) Thrust forces
FIGURE 9 Time variation of unsteady (from Ref. 2).

FIGURE 10
Instantaneous traces of particles released from a rake that is parallel to the fin leading edge throughout the stroke cycle. Color indicates the magnitude of the velocity (in cm/s) at each location along the trace.

Summary: We have computed the unsteady dynamics around the rigid wing of a flapping fruit fly and around the deforming pectoral fin of a swimming bird wrasse. The unsteady computations have been compared with experimental data and found to be in excellent agreement. The understanding gained from these computations is useful as we proceed to the design of high-performance air and undersea autonomous vehicles.

Acknowledgments: This work was supported by the Office of Naval Research through the NRL Undersea Warfare Focus Area Swimming Vehicles Project and the NRL Tactical Electronic Warfare Division Micro Air Vehicles Program. The authors thank Prof. M. Dickinson (now of California Institute of Technology), Mr. S. Sane, and Dr. J. Birch from University of California Berkeley for providing experimental Drosophila wing kinematics, force data for comparison, and many very useful discussions. We also thank Prof. M.W. Westneat of the Field Museum of Natural History and the University of Chicago and Prof. J. Walker (now of the University of Southern Maine) for experimental kinematics, measured data, close collaboration, and again, many useful discussions throughout the bird wrasse computations. We also thank Prof. R. Löhner and Dr. J. Cebral of the George Mason University for their support with grid generation and flow visualization throughout the course of this work. The computations carried out for this work were supported in part by a grant of HPC time from the DOD HPC centers, ARL MSRC SGI-O2K, and NRL SGI-O2K.

[Sponsored by ONR] References

¹ R. Ramamurti and W.C. Sandberg, "A 3-D Computational Study of Aerodynamic Mechanisms of Insect Flight," J. Exp. Biol. 205, 1507-1518 (2002).
² R. Ramamurti, W.C. Sandberg, R. Löhner, J.A. Walker, and M.W. Westneat, "Fluid Dynamics of Flapping Aquatic Flight in the Bird Wrasse: Three-Dimensional Unsteady Computations with Fin Deformation," J. Exp. Biol. 205(19) 2997-3008 (2002).
³ M.H. Dickinson, F.O. Lehmann, and S. Sane, "Wing Rotation and the Aerodynamic Basis of Insect Flights," Science 284, 1954-1960 (1999).
⁴ J.A. Walker and M.W. Weastneat, "Labriform Propulsion in Fishes: Kinematics of Flapping Aquatic Flight in the Bird Wrasse," Gomphosus Varius," J. Exp. Biol. 200, 1549-1568
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