Environmental Engineering Reference
In-Depth Information
Actuator Disk Theory for Horizontal-Axis Wind Turbines
The simplest aerodynamic model of a HAWT is the
actuator disk model
, in which the ro-
tor becomes a homogeneous disk that removes energy from the wind. Originated by Rankine
[1895], the actuator disk concept was motivated by the development of the marine propeller.
The actuator disk provides a rational basis for illustrating that the flow velocity at the rotor
is different from the free-stream velocity. However well the actuator disk theory provides
an understanding of the flow field, this theory fails to provide a link between rotor geometry
and rotor performance.
Rankine-Froude Theory
The
axial momentum theory
[Rankine 1865, W. Froude 1878, R. Froude 1889] idealizes
flow through the rotor of a wind turbine as shown in Figure 5-7. The free-stream wind speed
is
U
, which is slowed by the wind device. Applying requirements for
continuity
, momentum,
and energy to the flow, we may determine the
thrust
and
power
if the flow is assumed to be
entirely
axial
, with no rotational motion. Two expressions for thrust may be obtained. First,
from the momentum theorem, the thrust is
T
=
M
a
(
U
-
V
1
) =
r
AV
(
U
-
V
1
)
(5-9)
where
T
= thrust force on the disk (N)
M
ยท
a
= air mass flow rate through the disk (kg/s)
V
= wind velocity at the disk (m/s)
V
1
= wind velocity in the far wake (m/s)
Second, from consideration of the pressure drop caused by the wind machine,
T
=
A
(
p
u
-
p
d
)
(5-10)
where
p
u
,
p
d
= pressures upwind and downwind of the disk, respectively (N/m
2
)
Figure 5-7. Idealized flow through a wind turbine represented by a non-rotating,
actuator disk.
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