On the Wing

By Sutthiphong Srigrarom, Associate Professor, Aerospace Systems, University of Glasgow Singapore, Singapore

Butterfly wings generate far more lift than can be accounted for by steady-state, non-transitory aerodynamics.

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On the Wing

The wing structures of monarch and swallowtail butterflies are a marvel of aerospace design.

Butterfly

The delicate butterfly is well known for its ability to fly great distances. The wing structures of monarch and swallowtail butterflies are a marvel of aerospace design, allowing for a wide range of mechanisms to generate force: wake capture, two different types of leading-edge vortex, and active and inactive upstrokes. Aerospace engineers at the University of Glasgow became fascinated with this and saw a perfect opportunity to capture workings of this natural design in their ongoing development of a butterfly-like ornithopter (flapping wing) micro-aerial vehicle (MAV).

Engineers selected the butterfly species based on the requirements for an MAV: agility and in-flight stability. Monarch butterflies have the ability to turn on a dime while evading predators, while the swallowtail’s hind wings sport unique streamers that appear to act as stabilizers. Both wing types generate far more lift than can be accounted for by steady-state, non-transitory aerodynamics, so Glasgow engineers decided to focus on transient analysis to discover precisely what flow interactions enable butterfly wings to perform so effectively.

The work used ANSYS Fluent to study the fluid flow. Engineers conducted a fully 3-D unsteady direct numerical simulation (DNS) of Navier–Stokes equations to completely capture all the structures of the flow generated by the wing motion. The computer chosen to run the simulations was a 64-bit Intel® Core i7-2600 CPU at 3.4 GHz with eight processors and 16 GB of RAM.

Swallowtail butterfly
Swallowtail butterfly
Monarch butterfly
Monarch butterfly

The team treated the butterfly models as rigid structures. For fluid-flow studies, engineers made the simplifying assumption that the butterflies’ bodies and wings exhibited no deformation during flight. A half-model of each butterfly was used to reduce problem size, and the fluid domain around each model was extended to 20 to 40 times the butterflies’ bodies in all directions. The mesh was unstructured, with approximately 10 million elements clustered around the wings. Engineers used observations of real natural flight to model the flapping-wing motion during translation (forward motion) and hovering. The effective Reynolds number ranges of the flow for both flight modes based on body length, maximum wingtip speeds and free stream velocity were about 500.

During CFD analyses, the flight behavior of the monarch butterfly served as the standard for comparison with that of the swallowtail butterfly because the differences in the flow patterns allowed researchers to isolate stabilization effects of the tail streamers. Both butterflies have a high flight velocity, with a high-amplitude, low-frequency wing stroke. Engineers observed from real flight that the wing strokes were roughly perpendicular to the body axis. This allowed the butterfly fluid model to be solved in a frame that rotated about the body axis. The midpoint of the power stroke (down stroke) at φ = 0 degrees was taken as the start-point for the simulations, which captured a wing beat range from –80 degrees to +80 degrees at a frequency of 1 Hz.

Both wing types generate far more lift than can be accounted for by steady-state, non-transitory aerodynamics.

The CFD analyses showed that wing beats during the hovering motion created an intensive, stable leading-edge vortex along the leading edges of both fore- and hind-wings. This vertical vortex rotates counterclockwise toward the inside back of the wing. Simultaneously, airflow that passes directly through the gap between the wings at the beginning of the power stroke moves along the axis of the vertical vortex ring and begins to drive it backward. There is a horizontal stopping vortex downstream of the butterfly caused by deceleration of the wings at the bottom of the previous stroke. During flight, both vortices merge into a new attached horizontal vortex ring generated by the continued flapping of the wing. The overall mechanism is similar to wake-capturing and is responsible for the unprecedented lift generated by the down-stroke of the butterfly’s wings.

Results from forward flight motion were discovered to be quite similar, with the main difference being that the leading-edge vortex ring was tilted. Researchers observed that the subsequent vortex formation pattern differed as well. For forward flight, the vertical vortex ring moves quickly backward because of convection caused by forward motion. At the bottom of the stroke, the wings shed a horizontal vortex ring downward and backward. Unlike in hovering flight, in which the horizontal ring merges with the vertical one and is attached near the edges of the hind wings, in migration flight, deceleration of the wings at the bottom of the stroke is accompanied by vortex ring shedding. Leaving the wings, the horizontal vortex ring moves downward and backward.

Comparison of streamlines of both butterflies side-by-side: isometric view, front
Comparison of streamlines of both butterflies side-by-side: isometric view, front
Comparison of streamlines of both butterflies side-by-side: 3-D view, top
Comparison of streamlines of both butterflies side-by-side: 3-D view, top
 

The unconventional aerodynamics of butterfly wings will greatly assist in ongoing refinement of Glasgow’s MAV.

Force and moment generated by both butterflies
Comparison of vortex structures of both butterflies side-by-side: isometric view, below
Comparison of vortex structures of both butterflies side-by-side: isometric view, below
Comparison of vortex structures of both butterflies sideby- side: isometric view, front
Comparison of vortex structures of both butterflies side-by-side: isometric view, front

The aerodynamics of the swallowtail butterfly were similar to that of the monarch in both flight conditions. Dominant leading-edge vortices again emanated along the wings’ leading edges. Airflow passes through the gap between the flapping wings to move along the axis of the vertical vortex ring. The most interesting finding of the study was the large impact of the streamers on the flow structures produced during flight. Streamers at the lower and outer corner of the swallowtail’s hind-wings introduce additional horseshoe-like vortices around the edge of the streamer. Wake vortices become aligned behind the wings by these additional horseshoe vortices, making the swallowtail butterfly flight more stable.

Engineers also found that the leading-edge vortices that are generated by the swallowtail’s wings are enlarged by the stabilization, creating a more effective wing. The forces and moments of swallowtail wings are approximately 20 percent greater than those generated by monarch wings, even though the area difference between the two wings is only 5 percent. Since there were few other differences between the two models, researchers concluded that the significant increase in forces and moments must result solely from the streamers.

Both CFD studies gave engineers increased insight into the flow patterns required for a light, powerful wing design beneficial to the continued development of MAV technology. The unconventional aerodynamics employed by butterfly wings revealed by this study will greatly assist in the ongoing refinement of Glasgow’s MAV.

Support for this project has been provided by ANSYS channel partner CAD-IT Consultants (Asia) Pte Ltd.

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