Environmental Engineering Reference
In-Depth Information
P
=
2
π
n
M
=
P
η
(7.16)
Rot
Rot
Rot
,
th
The tangential force F T that ultimately creates the power is influenced by the
tangential component size of the drag force F D,t . Since, especially within the ef-
fective outer blade range, the angle γ usually amounts to values below 20°, almost
the entire drag force is consumed to reduce the tangential component (Fig. 7.5).
Hence, design and manufacture of wind power stations of favourable power
coefficients have to ensure that profile shape and surface roughness produce low
drag forces. Modern wind power stations are thus equipped with drop-shaped pro-
files that are optimised with regard to their L/D ratio ( ε ≈ tan ε = c d /c l = F D /F L ).
Lift/drag ratios ε of aerodynamically favourable profiles amount to 0.02 to 0.08.
For aerodynamically inferior profiles (e.g. ε = 0.1) the optimum tip speed ratios
and the maximum power coefficient are reduced by approximately 50 %.
The described lift principle almost reaches the Betz power coefficient. This is
why practically all commercially available wind energy converters operate ac-
cording to this principle.
Drag principle. For conversion of the wind energy according to the drag princi-
ple (Fig. 7.9) air hits a wind-blown surface S at velocity v Wi,Rot (i.e. projected wind
attack surface). The power received P Wi by the wind-blown surface is calculated
by means of the drag force F D and the velocity v S , at which the wind-blown sur-
face moves (Equation (7.17)). The values of the drag force F D and the reaction
force F R, that slows down the airflow, are equal (Fig. 7.9).
P =
F
v
(7.17)
Wi
D
S
The relative speed between wind velocity v Wi and the speed incident on the
wind-blown surface S ( v Wi - v S ), have a deciding effect on the air drag. By means
of the air drag coefficient c d, drag force F D is determined by Equation (7.18). F D
thus largely depends on the square of the effective approach/rotor tip velocity ( v Wi
- v S ).
ρ
(
) S
2
F
=
c
Wi
v
v
(7.18)
D
d
Wi
S
2
The power extracted from the wind P Wi,ext according to the drag principle is cal-
culated by Equation (7.19).
ρ
(
)
2
P
=
F
v
=
c
v
v
S
v
Wi
(7.19)
Wi
,
ext
D
S
d
Wi
S
S
2
 
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