Wind Turbine Aerodynamics Part A: Basic Principles - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 300

Figure 5-10 is altered somewhat, to that shown in Figure 5-13. The wind velocity normal to
the blade reference plane, V n , is equal to the free-stream wind velocity reduced by the axial
induction factor, a , and the cosine of the coning angle , q. The cosine of the coning angle also
appears in the tangential velocity, v , because the local radial distance to the axis, r , is equal to
s cosq. In addition, a drag force , D , is now included.

Figure 5-13. Flow velocity diagram at an annulus in a coned HAWT rotor disk.

Annulus Flow Equations

Momentum and moment of momentum relations are used to obtain equations with which
to determine the induced axial and tangential (rotational) velocities. The thrust coefficient in
Equation (5-30) can be written for an individual streamtube as follows:

dT
0.5 r U 2 ( 2 p r dr )

(5-31a)

C t =

R

T = dT

0

where C t = local value of the thrust coefficient, at radial coordinate r

dT = increment of axial thrust on the blade area within the streamtube (N)

Referring to Figure 5-13, the thrust increment, dT , for a rotor with B blades of chord c is

dT = 0.5 r V r B c ( C L cos f + C D sin f) dr

(5-31b)

Combining Equations (5-3la) and (5-31b),

2

B
2 p

c
r

V r
U

C t = ( C L cos f + C D sin f)

From Figure 5-13, we can express the velocity ratio in terms of the wind angle, f, and the
axial induction factor, a , and obtain