Environmental Engineering Reference
In-Depth Information
when considering optimum performance. Clifton-Smith [
3
] tested a number of
different tip loss methods and recommended the correction of de Vries [
4
] which
rewrites Eqs.
3.10
and
3.11
as
a
b
F 1
a
b
F
ð
Þ
rC
a
4 sin
2
/
¼
ð
5
:
3
Þ
Þ
2
ð
1
a
b
and
a
0
b
F 1
a
b
F
ð
Þ
rC
a
0
4 sin / cos /
1
a
b
Þ
¼
ð
5
:
4
Þ
1
þ
a
0
b
ð
where the top line on the left hand sides represents the momentum, from Eq.
5.3
,
and angular momentum, Eq.
5.4
, in the wake and so involves a
0
and a whereas the
denominators relate to the forces at the blade elements and so involve a
b
and a
0
b
.
Clifton-Smith [
3
] used the blade element version of the high thrust correction to
the momentum equation, Eq.
2.20
, so that (
3.13
) is replaced by
a
b
F 1
a
b
F
ð
Þ
a
b
a
c
f
a
¼
ð
5
:
5
Þ
a
c
F
2
þ
1
2a
c
F
ð
Þ
a
b
F
b
[ a
c
where the usual value for a
c
is 1/3. In other words, the high thrust correction begins
at the Betz-Joukowsky limit. Shen et al. [
1
] defined two intermediate functions, Y
1
and Y
2
(in the form to be used with Eqs.
5.3
and
5.4
):
Y
1
¼
4F sin
2
/
rC
a
ð
Þ
ð
5
:
6a
Þ
and
Y
2
¼
4F sin / cos /
=
rC
a
0
ð
Þ
ð
5
:
6b
Þ
which are used in the following expressions for the induction factors:
a
b
¼
2
þ
Y
1
p
4Y
1
1
F
ð
Þ
Y
1
ð
5
:
7a
Þ
21
þ
FY
1
ð
Þ
and
1
a
0
b
¼
ð
5
:
7b
Þ
ð
1
aF
Þ
Y
2
=
ð
1
a
Þ
1
5.2 Altering the Programs from
Chap. 3
The chord and twist distribution shown in the file
tcdist.m
from
Chap. 3
are fitted
curves to the tabulated data in Anderson et al. [
5
]. They measured the power and
thrust of a 3 m diameter turbine whose two blades had a NACA 4412 profile.
There are two important aspects of this turbine to be noted and remembered: firstly
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