Introduction to Modern Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 75

(1) Specify a free-stream wind speed, U ; assume a trial value of a = a' , calculate
C T by Equation (2-15), calculate a by Equation (2-16), iterate until a = a', and
inally, calculate P R ; or
(2) Specify an axial airspeed at the rotor, V X , calculate P R and C T , calculate a from
Equation (2-16), and inally, calculate U from Equation (2-11b).

Airfoil Angle of Attack and Twist

As illustrated in Figure 2-13, the angle of attack is measured counter-clockwise from the
geometric chordline of the airfoil section to the relative airspeed vector and is calculated as
follows:

a = f - s (2-18a)

f = arctan( V X / V Y )

(2-18b)

(2-18c)

s = b + q

where
s= section setting angle; measured counter-clockwise from the plane of rota-
tion to the local chordline (deg)
b = section pre-twist angle; built-in rotation of local chordline; measured coun-
ter-clockwise from an arbitrary datum (deg)
q = blade pitch angle; rotation of blade pitch axis and all chordlines; measured
counter-clockwise from pre-twist datum; applied during blade installation
and/or by active pitch control system (deg)

As discussed further in Chapter 5 (see Table 5-3), the blade pre-twist angle (or simply
twist angle), b, is smallest at the tip and largest at the root, in order to keep the angle of attack,
a, in an optimum range for maximum energy capture. Near the root, the forward speed of
an airfoil section, V Y , becomes small, so the relative inlow angle, φ , becomes large in accor-
dance with Equation (2-18b). As φ increases from tip to root, b must increase accordingly if
the angle of attack is to remain in the preferred design range.

Models of Airfoil Lift and Drag Coeficients

Mathematical models of the lift and drag coeficients in Equation (2-11f) and (2-11g),
as functions of the local angle of attack, are required before rotor power and turbine perfor-
mance can be estimated. As discussed in more detail in Chapter 6 and illustrated in Figure
6-2(a), airfoil behavior can be characterized by three low regimes: the attached regime , for
angles of attack from about -15 to +15 deg; the high-lift/stall-development regime, for angles
of attack between about +15 and +30 deg; and the deep-stall regime , with angles of attack
from +30 to more than +90 deg. In the attached regime, lift and drag coeficients are strongly
airfoil-dependent, while in the deep-stall regime most airfoils exhibit similar lift and drag
behavior.
In addition to its angle of attack, an airfoil's lift and drag behavior depend strongly on
its aspect ratio , which is a measure of its slenderness. For a wind turbine rotor, blade aspect
ratio is deined as the ratio of twice the active span length of a blade to its mean chord . For
example, consider the typical blade planform shape shown in Figure 2-15 [Grifin 2001].