Environmental Engineering Reference
In-Depth Information
Lift
V 0
V
V r
Drag
S
FIGURE 6.2 Lift translator. Direction of motion, V, is perpendicular to the ground wind, V 0 . S is length of the
cross-sectional area of the blade or sail.
An example of a lift device is a sailboat, a lift translator (Figure 6.2), where the sails form an
airfoil. Notice that a sailboat moving downwind (a drag device) moves much slower than a sailboat
as it moves perpendicular to the wind (a lift device). Besides sailing ships, there have been propos-
als to use lift translators for generating power. The problems are the large speeds of the devices,
as lift devices can move faster than the wind, the proximity to the ground, and the necessity for
having a predominant wind direction. Some lift translators were actually built, but never operated
successfully.
The simple analysis for a lift device assumes streamline flow (irrotational, incompressible fluid)
and conservation of energy and momentum. The wind speed interacts with the disk (propeller, rotor,
screw, or whatever), and there is a pressure drop across the disk (Figure 6.3). The thrust (force) load-
ing, T , is uniform across the disk. Also, there is no friction or drag force. At large distances behind
the disk, the wind speed and pressure will have the same values as at a long distance in front of the
disk. As stated earlier, the pressure, p , is the force/area.
From conservation of momentum, momentum in momentum out. The mass low, Δ m t , across
any area is constant. Across the area of the disk, the mass flow is the product of air density ( l ), area
(A), and wind speed; so for the three regions
$
$
m
t
R
Av
R
Au
R
Av
00
2 2
V 0
P 0
V 2
V 0
P 0
u
P +
P -
FIGURE 6.3 Wind speeds and pressures at infinity, at the disk, and behind the disk.
 
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