Wind turbine blades, wind turbines, and wind farms having increased power output
A wind turbine blade having a geometry that decreases the distance downstream at which freestream momentum is recovered is disclosed. The blade design increases the loading on the inboard portion of the blade and unloads the tip portion relative to a conventional blade designed to maximize power coefficient. A wind farm having a reduced inter-turbine distance and including one or more wind turbines having the new blade designs is also disclosed.
1. A turbine blade, comprising:
an inboard region; and
an outboard region;
wherein the inboard region has an induction factor of between ⅓ and ½ at a tip speed ratio of 9; and
wherein the tangential induction factor is calculated by
a
′
(
λ
,
r
R
)
=
[
λ
2
k
2
(
r
R
)
2
+
2
λ
k
r
R
-
4
ak
[
λ
r
R
-
k
(
1
-
a
)
]
+
1
]
0.5
-
(
λ
k
r
R
+
1
)
2
λ
k
r
R
(
1
)
and wherein the blade geometry parameter is calculated by
Λ
(
λ
,
r
R
)
=
8
π
a
(
1
-
a
)
B
λ
(
1
+
a
′
)
(
1
-
a
)
2
+
λ
2
(
r
R
)
2
(
1
+
a
′
)
2
F
[
1
+
(
1
-
a
)
k
λ
r
R
(
1
+
a
′
)
]
,
(
2
)
and wherein the normalized chord is calculated by
c
R
=
Λ
(
λ
,
r
R
)
C
l
(
r
R
)
,
(
3
)
and wherein the blade twist is calculated by
β
=
arc
sin
(
1
-
a
(
1
-
a
)
2
+
λ
2
(
r
R
)
2
(
1
+
a
′
)
2
)
-
α
(
4
)
and wherein parameters are defined as found in this disclosure.
2. The turbine blade of claim 1 , wherein the outboard region has an average induction value of no less than 0 and no greater than ⅓.
3. The turbine blade of claim 1 , wherein the inboard region has an induction factor of between 0.35 and 0.45.
4. The turbine blade of claim 1 , further comprising:
a base at a first end of the inboard region;
a tip at a first end of the outboard region; and
a length extending from the base at the first end of the inboard region to the tip at the first end of the outboard region;
wherein the outboard region is between 3% and 40% of the length.
5. The turbine blade of claim 4 , wherein the outboard region is between 15% and 25% of the length.
6. The turbine of claim 4 , wherein the inboard region is between 60% and 97% of the length.
7. The turbine blade of claim 1 , wherein the outboard region comprises at least one region using a NACA 63 6 -618 airfoil.
8. A wind turbine, comprising:
at least one turbine blade, comprising:
an inboard region; and
an outboard region;
wherein the inboard region has an induction factor of between ⅓ and ½ at a tip speed ratio of 9; and
wherein the tangential induction factor is calculated by
a
′
(
λ
,
r
R
)
=
[
λ
2
k
2
(
r
R
)
2
+
2
λ
k
r
R
-
4
ak
[
λ
r
R
-
k
(
1
-
a
)
]
+
1
]
0.5
-
(
λ
k
r
R
+
1
)
2
λ
k
r
R
.
(
1
)
and wherein the blade geometry parameter is calculated by
Λ
(
λ
,
r
R
)
=
8
π
a
(
1
-
a
)
B
λ
(
1
+
a
′
)
(
1
-
a
)
2
+
λ
2
(
r
R
)
2
(
1
+
a
′
)
2
F
[
1
+
(
1
-
a
)
k
λ
r
R
(
1
+
a
′
)
]
,
(
2
)
and wherein the normalized chord is calculated by
c
R
=
Λ
(
λ
,
r
R
)
C
l
(
r
R
)
,
(
3
)
and wherein the blade twist is calculated by
β
=
arc
sin
(
1
-
a
(
1
-
a
)
2
+
λ
2
(
r
R
)
2
(
1
+
a
′
)
2
)
-
α
(
4
)
and wherein parameters are defined as found in this disclosure.
9. The turbine blade of claim 8 , wherein the outboard region has an average induction value of no less than 0 and no greater than ⅓.
10. The turbine blade of claim 8 , wherein the inboard region has an induction factor of between 0.35 and 0.45.
11. The turbine blade of claim 8 , further comprising:
a base at a first end of the inboard region;
a tip at a first end of the outboard region; and
a length extending from the base at the first end of the inboard region to the tip at the first end of the outboard region;
wherein the outboard region is between 3% and 40% of the length.
12. The turbine blade of claim 11 , wherein the outboard region is between 15% and 25% of the length.
13. The turbine of claim 11 , wherein the inboard region is between 60% and 97% of the length.
14. The turbine blade of claim 8 , wherein the outboard region comprises at least one region using a NACA 63 6 -618 airfoil.
15. A wind farm, comprising:
two or more wind turbines of claim 8 .