Environmental Engineering Reference
In-Depth Information
power output by means of an ideal wind energy converter (using the example of a
rotor).
7.1.1
Idealised wind energy converter
The considerations outlined throughout this section with regard to assessing the
theoretical total capacity extractable by means of wind energy converters (such as
a rotor) are based on the following ideal conditions and assumptions:
−
frictionless, stationary wind flow,
−
constant, shear-free wind flow (i.e. wind speed is the same at every point of the
energy extracting surface (e.g. circular rotor surface
S
Rot
) and flows into shaft
direction),
−
rotation-free flow (i.e. no wind deviation into circumferential direction),
−
incompressible flow (
ρ
Wi
≈ const. = 1.22 kg/m
3
) and
−
free wind flow around the wind energy converter (no external impacts on wind
flow).
On the basis of the above conditions the maximum physically achievable wind
conversion can be derived by a theoretical model that is independent from the
technical construction of a wind power station.
For this purpose an imaginary wind driven air package with air particles is as-
sumed whose flow filaments are bordered by a fictitious stream-tube. The stream-
tube is examined at three characteristic cross-sections (
S
1
- way before the wind
converter rotor,
S
Rot
- at the circular rotor surface,
S
2
- way behind the wind con-
verter rotor). Investigations result in the stream-tube illustrated in Fig. 7.1.
According to the mass conservation law, air throughput (i.e. mass flow
m
.
Wi
)
has to be the same for every cross-section
i
of the stream-tube (whereby
i =
1 far
before the rotor,
i = Rot
within the rotor plane and
i =
2 far behind the rotor). This
also applies to the surfaces
S
1
, S
Rot
and
S
2
. Under these circumstances the continu-
ity Equation (7.1) may be applied.
&
m
= ρ
S
v
=
const
.
(7.1)
Wi
Wi
i
Wi
,
i
According to Bernoulli´s law, the power contained in every point
i
of the air
flow
P
Wi,i
consists of kinetic capacity (1/2 (
m
.
Wi,i
v
Wi,i
2
)), pressure capacity ((
m
.
Wi,i
p
Wi,i
)/
ρ
Wi
) and potential capacity which is in this case negligible by approximation.
With regard to continuity the wind capacity balance at any location
i
far before
(e.g.
S
1
) and far behind the rotor (e.g.
S
2
) reads as expressed in Equation (7.2).
P
Rot,th
describes the theoretical power at the rotor shaft of the wind turbine.
&
&
m
p
m
p
1
1
2
Wi
Wi
,
2
Wi
Wi
,
2
P
=
const
.
=
m
&
v
+
=
m
&
v
+
+
P
(7.2)
Wi
,
i
Wi
Wi
,
Wi
Wi
,
2
Rot
,
th
2
ρ
2
ρ
Wi
Wi
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