Wind Turbine Aerodynamics Part A: Basic Principles - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 335

The torque of a VAWT rotor varies with blade azimuthal position (the so-called torque
ripple ), so rotor power is defined as the average power over one revolution, as follows:

H / 2

2 p

P = B W
2 p

( dQ KJ + dQ D ) d y

(5-53)

- H / 2

0

where H = height of the area swept by the airfoils (m)

Airfoil Data for VAWT Blades

When using streamtube analysis, the determination of aerodynamic forces is accom-
plished using available static lift and drag data. Despite the amount of airfoil section proper-
ties compiled by the NACA and more recent work by NASA, extensive gaps remain in our
knowledge of wind turbine airfoils. Aircraft airfoils are designed to operate below stall, and
so the data base is concentrated in the below-stall region. A VAWT blade, however, operates
at angles of attack considerably beyond stall, particularly when it is producing peak power.
Another variance between VAWT and aircraft airfoils is that a VAWT blade follows a circu-
lar path with significant cyclic variations in relative velocity and angle of attack.
The applicability of steady-state airfoil data to the unsteady operating conditions of a
VAWT may be questioned. Below stall, however, the use of static lift data appears to be val-
id. Shown in Figure 5-36 is the variation in lift coefficient during a typical rotor revolution,
calculated for a section on a VAWT blade. The VAWT lift curve remains approximately
parallel to the theoretical static lift curve for chord-to-radius ratios of 0.10. Typical ratios for
current VAWTs are less than 0.08.
A third factor affecting airfoil data is the pitch rate of a VAWT blade, which is equal to
the rotor speed W. In Figure 5-36, the offset angle between the static and dynamic lift curves,
a p , is caused by pitching circulation. A first-order analysis of the effect of pitching on drag
coefficient of a pitching NACA 0015 airfoil below stall indicates that the offset angle for drag
is 40percent to 50percent less than that for lift [Wilson and Neff 1985].

Figure 5-36. Calculated lift coefficient vs . angle of attack at a VAWT blade section dur-
ing one rotor revolution. Tip-speed ratio is 3.5 and the chord-to-radius ratio is 0.2. [Wilson
et al. 1983]