Publishers version - DTU Orbit

The power law profile is defined as:
u = uhub
z
zhub
α
, (159)
where u is the wind speed at height z, zhub the hub height, uhub the wind speed at that
height and α the shear exponent. Both profiles are shown in Figure 83.
The model used was HAWC2Aero. The modeled turbine was a Siemens 3.6 MW with a
rotor diameter of 107 m and a hub height of 80 m.The wind speed is assumed horizontally
homogeneous (i.e. the wind speed is the same everywhere on each horizontal plane). In order
to emphasize the effect of wind speed shear, the simulations were carried out with laminar
inflow, the tower shadow was turned off and the tilt angle of the rotor was set to 0 ◦ .
heightm
140
120
100
80
60
40
wind speedms
4 6 8 10
Figure 83: Wind profiles used as input for the wind speed shear aerodynamic investigation.
Black curve: no shear; grey curve: power law profile with shear exponent of 0.5. Both profiles
have the same wind speed at hub height
Figure 84 shows the free wind speed (i.e. the absolute wind speed in absence of a turbine)
seen by a point at a radius of 30 m from the rotor centre, rotating at the same speed as
the rotor as a function of time for the 2 inflow cases. Whereas in a uniform flow the blade is
subjected to a constant wind speed, in a sheared flow, the point is exposed to large variations
of wind speed even though the inflow is laminar. The variation of the wind speed seen by this
rotating point in time is only due to the fact that it is rotating within a non uniform flow
(wind speed varying with height).
Figure 85 shows the variations of the free wind speed seen by the same rotating point as
function of the azimuth position (0 ◦ = downwards). The point experiences the hub height
wind speed (same as uniform inflow) when it is horizontal (±90 ◦ ), lower wind speed when it
is downward (0 ◦ ) and higher wind speed when it is upward (180 ◦ ).
A rotating blade does not experience the free wind speed because of the induction from the
drag of the rotor. In reality, a rotating blade is directly subjected to the relative wind speed w
(i.e. the speed of the wind passing over the airfoil relative to the rotating blade) and the angle
of attack φ (i.e. the angle between the blade chord line and the relative wind speed) with the
effects of the induced speed included. The variations of these two parameters as function of θ
are shown in Figure 86. As these two parameters directly depend on the free wind speed, they
vary with the azimuth angle in a sheared inflow, whereas they remain constant in a uniform
inflow.
The relative speed and the angle of attack are derived from the rotor speed and the induced
velocity. Therefore, they depend on the way that the induction is modeled and it is difficult
144 DTU Wind Energy-E-Report-0029(EN)