Environmental Engineering Reference
In-Depth Information
Designing lift-type wind energy conversion systems depends on a knowledge of the
properties of airfoils. There is extensive experience in airfoil technology, derived primarily
from airplane wing design. It is normally assumed that the properties of airfoils that are
desirable for wings will also be desirable for wind turbines. This assumption is only
superficially valid, for reasons described later. It must be noted that fixed-pitch wind
turbine airfoils generally operate over angles of attack ranging from 0 deg to 90 deg, and
thus their
stall
and
post-stall behavior
are important. This situation does not apply for
aircraft wings, which seldom require operation at angles in excess of 30 deg.
An excellent review of wind turbine airfoils and their properties is given by Miley
[1980]. Included here are many of the airfoils that wind turbine designers have borrowed
from the aircraft industry. More recently, Tangler and Somers [1995] have described the
development of several families of airfoils designed specifically for HAWTs.
Airfoils are designed to generate lift; that is, to create a force normal to the incident
flow when immersed in this flow at a small angle to the airfoil's
chord line.
The geometry
of this flow and the forces created are shown in Figure 6-1. The angle from the
relative
velocity
vector,
V
r
,
to the chord line is the
angle of attack
,
a
.
The lift force is normal to
V
r
.
Generally this lift is produced simultaneously with a streamwise force at right angles
to itself, called the drag. These forces are normalized by dividing the force per unit span
by the
dynamic pressure
and the chord length to obtain
lift
and
drag coefficients
,
C
L
and
C
D
,
in accordance with Equations (5-3).
Characteristic Behavior of Airfoils
Reynolds Number
The most significant flow factor influencing the behavior of low-speed airfoils is that
of
viscosity
,
which indirectly causes lift and directly causes drag and
flow separation.
This
influence is characterized by the
Reynolds number
of the airfoil/fluid combination. For the
airfoil in Figure 6-1, Reynolds number can be calculated as follows:
N
R
=
V
r
c
r
W
30
m
/
s
c
0.5
m
´ 10
6
»
r
W
110
mph
c
1.0
f t
´ 10
6
n
»
(6-1)
where
v
= kinematic viscosity of air (m
2
/s)
V
r
= relative velocity (m/s)
r
W
= local tangential velocity (m/s or mph)
c
= chord length (m or ft)
Airfoils in use on modern turbines range in representative chord size (typically at 3/4 span)
from about 0.3 m (1 ft) on a small-scale turbine to over 2 m (7 ft) on a megawatt-scale
rotor. Tip speeds typically range from approximately 45 to 90 m/s (100 to 200 mph), so
tangential velocities at the 3/4-span of a HAWT blade can be estimated to range from about
34 to 68 m/s (75 to 150 mph). For turbine airfoils, then, Reynolds numbers range from
about 10 million down to 0.7 million. This implies that turbine airfoils generally operate
beyond the sensitive, low Reynolds number range (often taken to be below 0.5 million) in
which extreme and unusual behavior is caused by anomalous
transition, separation
,
and
bubble formation
phenomena. In this sensitive range, very large changes in airfoil behavior
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