Structural Dynamic Behavior of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 615

Induced (Retardation) Wind Speeds

In an unducted rotor, extraction of power reduces the speed of the wind at the rotor
blades compared to the free-stream wind speed, as discussed in Chapter 5. This reduction
is termed the induced wind speed and its magnitude is usually given as a fraction of the
free-stream wind speed by a parameter called the axial induction factor (see Figs. 2-14 and
5-11). Calculation of axial induction factors is routinely performed using aerodynamic perfor-
mance models, balancing the rate of change of the momentum in the wind stream with the ro-
tor thrust. Because thrust is not normally uniform across the swept area of the rotor, advanced
performance codes determine radial and circumferential distributions of the induction
factors.
Some dynamic-load computer models also include the calculation of induced wind
speeds. Whatever their source ( i.e. , external or internal to the load model), provision must
be made for induced wind speeds, because they can have a significant effect on airfoil
angles of attack and on aerodynamic loading. In our wind model this is done as follows:

(11-13)

V i ( r , y) = a ( r , y) U H

where

V i = induced wind speed (m/s)
a ( r ,y) = prescribed spatial distribution of axial induction factors

Combined Wind Effects

The net wind speed at a point in the plane of rotation is the sum of free-stream, wind
shear, tower shadow, turbulence, and induction components. These are usually combined
in a linear fashion, neglecting minor interaction terms. To help avoid ill-conditioned
simultaneous equations later, wind speeds are then normalized by the tip speed of the rotor.
The net wind velocity vector is specified in the X-Y-Z coordinate system and is composed
of steady and turbulence terms, as follows:

é
ê ë V r + d V r

é
ê ë

0 d u

d v
d w

V w ( X-Y-Z ) = R W + R W (11-14a)

0

V r = V H [1 - a ( r , y)]
R W

(11-14b)

d V r = V H [ W S ( r , y) - W T ( r , y)]
R W

(11-14c)

(11-14d)

d u = d u ( r ,y)/ R W

d v = d v ( r , y) / R W (11-14e)

d w = d w ( r , y) / R W

(11-14f)

where

Vw ( r , i) = net wind speed at the plane of rotation (m/s)
R = rotor tip radius (m)
W = rotor rotational speed (rad/s)