Biomedical Engineering Reference
In-Depth Information
In such a case, the forces generated can be quite
different than in the steady case. Several research-
ers have observed that at the Reynolds numbers
typical of bird and insect flight, steady aerody-
namic forces are insufficient to sustain flight of
the animal. Under steady conditions, the maxi-
mum lift coefficient of an airfoil is around 1.5 at
these Reynolds numbers. For example, measure-
ments on a gliding jackdaw yielded an estimate
of 2.1
[29]
for the lift coefficient.
Norberg
[30]
measured the wing-flapping kin-
ematics of a hovering dragonfly and, using
steady-state aerodynamics, calculated that the
wings produce only 40% of the lift required to
sustain the weight. Steady-state aerodynamics
predicted lift coefficients between 3.1 and 6.4 for
a hovering long-eared bat
[31]
. Weis-Fogh
[32]
studied the hovering flight of several species of
insects and concluded that lift coefficients calcu-
lated from flight were far in excess of values pre-
dicted by steady-state aerodynamics. Therefore,
he proposed several novel unsteady mechanisms
for lift production, including significant elastic
deformation of the wings, such as the clap-fling
mechanism and the flip mechanism. In the clap-
fling mechanism, the wings of the insect are
clapped together at the end of the upstroke and
are subsequently peeled apart during the begin-
ning of the downstroke, as shown in
Figure 5.9
.
The air rushing in to fill the space between the
wings results in a large area of vorticity. This
results in a significant transient increase in the lift
on the insect. The flip mechanism occurs when
the stroke reverses and the wing is rotated, cap-
turing additional vorticity.
Ellington
et al
.
[33]
visualized the flow field
around a scaled-up mechanical model of a flap-
ping hawkmoth wing and discovered the pres-
ence of a three-dimensional leading-edge vortex
stabilized by spanwise flow along the wing.
This leading-edge vortex is believed to be
responsible for the high lift measured on the
hawkmoth wing, which cannot be explained by
steady-state aerodynamics. Dickinson
et al
.
[34]
performed experiments on a scaled robotic flap-
ping model of fruit-fly wings and described
three unsteady mechanisms responsible for lift
production in excess of steady-state values. One
of these mechanisms, delayed stall, relies on the
production of a leading-edge vortex similar to
that observed during dynamic stall, while the
wing is translating at a large angle of attack. In
dynamic stall, a vortex is shed from the leading
edge of the airfoil, which results in a transient
lift significantly in excess of the maximum static
lift. This vortex is subsequently convected
downstream, causing a decrease in lift. The
overall result of the dynamic stall phenomenon
is to cause a hysteresis in the lift vs. angle of
attack curve, accompanied by a large increase
in the maximum lift in comparison to the static
lift case. A detailed description of the dynamic
stall phenomenon with experimental data for a
NACA 0012 airfoil was given by Carr
et al
.
[35]
.
FIGURE 5.9
Clap-fling mechanism of lift production in hovering insects
[32]
. Adapted with permission from T. Weis-Fogh,
Journal of Experimental Biology, 1973, 59(1), 169-230.
