In a previous post I
introduced the concept of boundary layer separation and how aquatic animals
actively or passively morph their skins to delay this phenomenon. As a brief
recap, when flow over a surface encounters an adverse pressure gradient (i.e.
the fluid pressure increases in the flow direction) the fluid has to work
against this increasing pressure, which leads to momentum losses and
decelerations in flow. A classical example
where this occurs is after the point of maximum thickness in an aircraft wing
(Figure 1). The flow speed in the boundary layer close to the surface continues
to decrease in the direction of the adverse pressure gradient until at some
point the slowest moving fluid close to the wall will change direction. This is
called boundary layer separation and leads to a larger wake of vortices forming
behind the body. These vortices not only lead to greater pressure drag on
the body but also compromise the amount of upward lift the
aerofoil can produce, in effect reducing the efficiency of the wing.
Fig. 1. Boundary layer separation over aerofoil (1).
An aircraft is lifted up in the air by the net pressure difference
between the top and bottom surfaces of the wing. The bottom surface of the wing
is known as the pressure surface while the top is called
the suction surface. This is because the cambered shape of the
aerofoil and theangle of attack α with respect to the flight
direction redirects the flow such as to produce a higher fluid pressure on the
bottom than the top surface, resulting in a net upwards lift force L.
The amount of lift force an aerofoil produces is characterised by the lift coefficient CL,
Fig. 2. Lift Coefficient versus Angle of Attack (2).
Equation (1) shows that the lift that the aerofoil generates can be
increased by flying quicker (V), increasing the density of the fluid
(ρ – generally fixed by nature), the planform area of the wing (S –
generally fixed by construction) the lift coefficient CL. Now
during take-off and landing the velocity of the aircraft is limited by the
length of the runway. During take-off the aircraft can only achieve a certain
speed before reaching the end of the runway, while during landing the aircraft
must be able to break in the space available on the airfield. While moving at
the typical take-off and landing speeds of 300 km/hr a typical wing is not
capable of producing enough lift to keep the aircraft from falling out of the
sky. Luckily, the lift coefficient CL can be
enhanced by various parameters such as increasing the camber of the wing or
the angle of attack α. Various experiments
have shown that the lift coefficientCL increases
linearly with angle of attack α (Figure 2). The downside is
that the adverse pressure gradient over the aerofoil and profile drag on the
wing increase at the same time. At some critical angle of attack the boundary
layer starts separating towards the trailing edge of the aerofoil resulting in
a precipitous drop of the lift coefficient with any further
increases in α. This phenomenon is known as aerodynamic stall,
and αstall (around 14° for a typical plain aerofoil) corresponds
to the angle of attack at which the maximum lift coefficient CLmax is
achieved (around 1.4 for ordinary wing). Videos of an aircraft stalling during flight can be quite dramatic as the
pilot attempts to regain control of the spiralling aircraft and often end with
the deployment of the ejector seat.
As you might intuitively expect the maximum angle of attack also depends
on the velocity of the aircraft, as higher fluid flow will delay flow reversal.
This means that during cruise when the air velocity V is high
the aircraft flies with a low lift coefficient configuration
in order to decrease higher profile drag at large angles of attack.
During take-off and landing however the aircraft must increase the angle
of attack in order to compromise for the low flight velocity. The
issue is that for modern, heavy jumbo jets the typical CLmax of 1.4 is not enough to
lift the aircraft from the ground, and any further increases in angle
of attack would of course lead to the precipitous drop in CL of
aerodynamic stall.
Fig. 3. Leading-edge Slats
and trailing-edge Flaps deployed (2)
To avoid separation of the boundary layer engineers use high-lift
devices such as slats and flaps, which
you have probably seen deployed from the leading and trailing edges of the
wings respectively. Leading-edge slats are additional thin aerofoils deployed
at the front of the main aerofoil, which channel secondary airflow
from the bottom of the main airfoil through
a gap into to the primary airflow above (Figure 3). This
secondary flow injects additional high momentum fluid into the boundary layer
on the upper surface and consequently modifies the adverse pressure gradient
and delaying boundary layer separation. Similarly, trailing-edge flaps are
placed at points where the boundary layer would naturally start to separate
from the surface, and invigorate the “tired” boundary layer by the same
mechanism. In this manner the critical stalling angle astall is increased and the aerofoil yields
a higher value of CLmax often around 2.8 (double
the plain aerofoil).
Nature has provided the perfect laboratory for the evolution of
aerofoils and similar to many other engineering innovations leading-edge slats
and trailing-edge flaps are mimicked from bird flight. The sketches below show
that the pheasant uses the front Alula feather as a leading
edge slat, while the tail of the Falcon takes the form of a trailing edge flap
(Figure 6). Many research institutes are currently spending considerable
amounts of money into the development of other shape morphing mechanisms
exhibited by birds such as ruffling of feathers, increasing the camber of the
wing, lengthening the span or inducing a degree of surface roughness. However,
these technologies require materials that are compliant enough to rapidly
deform into the required shape, while stiff enough to resist the aerodynamic
loads. Unfortunately our current material systems do not facilitate such
capabilities.
Fig. 4. Different Wing configurations during flight (2).
Fig. 5 The position of
the leading edge slats on an airliner (Airbus A310-300). (Photo credit:
Wikipedia)
Fig. 6. Slats and Flaps as seen on birds in Nature (2).