Page 122 - Wind Energy Handbook

96 AERODYNAMICS OF HORIZONTAL-AXIS WIND TURBINES

1.5
20
Axial force coefficient 0.5 1 Axial force (kN) 10 5
15

0
0 0 5 10 15 20 25 30
0 5 10 15 Wind speed (m/s)
Tip speed ratio

Figure 3.45 Axial Force Coefficient and the Variation of the Actual Force with Wind Speed
remembered that the actual thrust force increases with wind speed as is demon-
strated in Figure 3.45.

3.10 The Aerodynamics of a Wind Turbine in Steady
Yaw

The rotor axis of a wind turbine rotor is usually not aligned with the wind because
the wind is continuously changing direction; the rotor is not capable of following
this variability and so spends most of its time in a yawed condition. The yawed
rotor is less efficient than the non-yawed rotor and so it is vital to assess the
efficiency for purposes of energy production estimation.
In the yawed condition, even in a steady wind, the angle of attack on each blade
is continuously changing as it rotates and so the loads on the rotor blades are
fluctuating, causing fatigue damage. The changes in angle of attack mean that the
blade forces cause not only a thrust in the axial direction but also moments about
the yaw (z) axis and the tilt axis.
Even if the rotor is operating with a uniform induced velocity over the rotor disc
when aligned with a steady wind, once the rotor is misaligned the induced velocity
varies both azimuthally and radially which makes its determination much more
difficult (Figure 3.46).

3.10.1 Momentum theory for a turbine rotor in steady yaw

The application of the momentum theory to an actuator disc representing a yawed
rotor is somewhat problematical. The momentum theory is only capable of deter-
mining an average induced velocity for the whole rotor disc but, although in the
non-yawed case the restriction was relaxed to allow some radial variation, it would
not be appropriate to do this in the yawed case because the blade circulation is also
changing with azimuth position. If it is assumed that the force on the rotor disc,