Publishers version - DTU Orbit

uyms
9.0
8.5
8.0
7.5
7.0
120 140 160 180 200 times
Figure 84: Time series of free wind speed seen from a rotating point, positioned at a radius
of 30 m, rotating at rotor rotational speed (no induced velocity). Black curve: no shear; grey
curve: power law profile with shear exponent of 0.5
uyms
9.0
8.5
8.0
7.5
7.0
150 100 50 50 100 150
Figure 85: Free wind speed seen from a rotatingpoint, positionedat a radius of30m, rotating
atrotorrotationalspeed,asfunctionoftheazimuthangleθ.Blackcurve:noshear;greycurve:
power law profile with shear exponent of 0.5
to evaluate their variations due to a non uniform flow in a simple way. However, some basic
considerations (ignoring the induction) can give a basic insight to the variation of the relative
speed and the angle of attack as the blade rotates. In case of uniform inflow, the free wind
speed is the same at any point of the swept rotor area. Therefore, the angle of attack and
the relative speed are the same at any azimuthal position (see Figure 87).
In case of sheared inflow, the free wind speed depends on the position of the blade. When
the blade is horizontal, the free wind speed is the speed at hub height and the speed triangle
is the same as in Figure 87. Below hub height, the wind speed is lower than the hub height
speed, see Figure 88 (left). Consequently w and φ are lower than those at hub height. Above
hub height, the wind speed is higher than the hub height wind speed. Consequently w and φ
are higher than those at hub height, see Figure 88 (right). The variations in φ and w cause a
variation of the local lift and drag as the blade rotates, which finally results in the variation of
the local tangential force contributing to the wind turbine power (see Figure 89). For a given
φ, local lift dFL and local drag dFD, the local tangential force dFT is given by (Manwell
DTU Wind Energy-E-Report-0029(EN) 145
Θ