Page 84 - Wind Energy Handbook

58 AERODYNAMICS OF HORIZONTAL-AXIS WIND TURBINES

0.01

0.005
Tangential flow induction factor -0.005 0

-0.01

-0.015
−1 −0.5 0 0.5 1
Axial distance
Figure 3.11 The Axial Variation of Tangential Velocity in the Vicinity of an Actuator Disc at
101 percent Radius, a ¼ 1=3, º ¼ 6

3.4.8 Radial flow field

Although the vortex cylinder theory has been simplified by not allowing the
cylinder to expand, nevertheless the theory predicts flow expansion. A radial
velocity distribution is predicted by the theory as shown in Figure 3.12 which
shows a longitudinal section of the flow field through the rotor disc.
The radial velocity, as calculated, is greatest as the flow passes through the rotor
disc and, although not shown in Figure 3.12, it is infinite at the edge of the disc. The
situation is very similar to the determination of the potential flow field around a
flat, solid, circular disc which is normal to the oncoming flow; an infinite radial

1.5

1

0.5
r
—
R 0
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
0.5

1

1.5
Figure 3.12 Flow Field Through an Actuator Disc for a ¼ 1=3