  Dragonfly beats its wings independently, resulting in its superior
maneuverability. Depending on the magnitude of phase difference between the
fore- and hind-wings of dragonfly, the vortical structures and their
interaction with wings become significantly changed, and so does the
aerodynamic performance. In this study, we consider hovering flights of
modelled dragonfly with three different phase differences (phi=-90, 90, 180
degrees). The three-dimensional wing shape is based on that of Aeschna juncea
(Norberg, 1972), and the Reynolds number is 1,000 based on the maximum
translational velocity and mean chord length. The numerical method is based on
an immersed boundary method (Kim et al., 2001). In counter-stroke (phi=180
degree), the wing-tip vortices from both wings are connected in the wake,
generating an entangled wing-tip vortex (e-WTV). A strong downward motion
induced by this vortex decreases the lift force in the following downstroke
(Kweon and Choi, 2008). When the fore-wing leads the hind-wing (phi=90 degree),
the hind-wing is submerged in the vortices generated by the fore-wing and
suffers from their induced downwash flow throughout the downstroke, resulting
in a significant reduction of lift force. On the other hand, when the hind-wing
leads the fore-wing (phi=-90 degree), the e-WTV is found only near the start of
hind-wing upstroke. In the following downstroke of hind-wing, most of the e-WTV
disappears and the hind-wing is little affected by this vortex, which produces
relatively large lift force.
