In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
Vo
l
.
1
0
, No
.
2
, Ju
n
e
20
1
9
, p
p
.
1
0
7
2
~
1
080
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
2.pp1072-1080
1072
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
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score
.
com
/
j
o
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s
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x
.
p
hp/IJ
PED
S
The com
putational fl
u
id dynam
ics performance analysis o
f
horizontal axis wind turbine
N
a
ji A
bdullah
M
ezaal
1
,
O
s
i
n
t
s
e
v
K
.
V
.
2
,
A
l
yu
ko
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.
V.
3
1
M
a
st
e
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i
n
Heat and
P
ow
e
r
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ngin
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g, S
o
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Ural St
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n
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v
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ty, Russian
F
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e
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Heat
and
P
ower En
g
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, So
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U
ral St
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U
n
i
versity
,
Ru
s
s
i
an F
ederati
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Art
i
cl
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fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
No
v
2
9
,
2
018
Re
vise
d Mar
1,
201
9
Ac
ce
p
t
ed
M
ar 1
2
,
2
019
Com
p
uta
t
io
na
l
fl
uid
d
y
n
a
mics
(
CF
D)
s
i
m
u
l
ations
w
ere
p
e
rf
o
r
m
e
d
i
n
th
e
pres
ent
st
ud
y
us
ing
A
N
S
Y
S
Flu
e
nt
1
8.
0
,
a
c
o
m
m
e
rcially
a
vai
l
ab
le
C
F
D
pack
ag
e,
t
o
ch
ara
c
t
e
rize
th
e
b
e
h
a
vi
ou
r
of
t
he
n
ew
HAWT.
S
tati
c
t
h
ree-
di
mensional
C
F
D
simulation
s
w
ere
con
d
u
c
ted.
T
he
s
tat
i
c
t
o
rqu
e
chara
c
t
e
ri
stics
o
f
t
he
t
urbin
e
a
nd
the
si
mpli
cit
y
o
f
desig
n
h
ig
hli
ght
its
sui
t
a
b
ili
ty
f
or
t
he
G
E
1
.
5x
le
t
u
r
bine
.
The
ma
j
o
r
fa
c
t
o
r
f
or
g
e
n
erat
in
g
th
e
po
wer
th
roug
h
th
e
H
A
W
T
i
s
t
h
e
velo
cit
y
o
f
air
a
n
d
t
h
e
positi
on
of
t
h
e
b
la
de
ang
l
e
in
t
he
HAW
T
bl
ade
assem
b
ly.
T
h
e
pap
e
r
p
r
e
s
ent
s
t
h
e
e
f
f
ect
o
f
T
h
e
bl
ade
is
4
3
.
2
m
length
a
nd
s
t
a
r
t
s
wi
th
a
c
ylind
r
i
cal
s
hape
a
t
t
h
e
r
oot
then
tran
siti
ons
t
o
t
h
e
airf
oils
S
818,
S
82
5
and
S
8
26
f
o
r
the
ro
ot,
b
od
y
and
t
i
p
resp
ectiv
ely
.
T
h
i
s
bl
ade
als
o
h
as
p
it
ch
t
o
v
a
ry
a
s
a
f
u
nct
i
on
o
f
radiu
s
,
g
i
ving
it
a
t
wis
t
a
n
d
t
h
e
p
i
t
ch
a
ng
le
a
t
t
h
e
bl
ade
t
i
p
i
s
4
d
egrees
.
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his
b
l
ad
e
was
created
t
o
be
s
i
m
ilar
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n
size
t
o
a
G
E
1.
5
x
l
e
t
urbin
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b
y
Cornel
l
U
nive
rs
ity
.
I
n
addition,
n
ote
that
t
o
represent
t
h
e
bl
ade
bei
ng
connect
ed
t
o
a
h
u
b
,
th
e
blad
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roo
t
i
s
offset
f
ro
m
th
e
axi
s
o
f
rotati
on
by
1
m
et
er.
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h
e
hu
b
i
s
not
i
n
c
lud
e
d
in
ou
r
m
odel.
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h
e
e
xp
eri
m
ent
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l
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ys
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o
f
GE
1
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5xle
t
u
rbin
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s
o
t
h
a
t
p
o
s
s
ib
le
th
e
result
of
C
FD
a
naly
sis
can
b
e
co
m
p
ared
w
it
h
th
eoret
i
cal
cal
culations.
CF
D
wo
rk
ben
c
h
of
A
NS
YS
i
s
us
e
d
t
o
carry
out
t
he
v
i
r
tu
e
sim
u
l
a
ti
on
a
nd
te
st
in
g.
T
he
s
o
f
twa
r
e
ge
ne
ra
ted
te
st
r
e
s
ul
ts
a
re
v
a
l
ida
t
e
d
t
h
r
o
ug
h
th
e
experiment
al
r
eadings.
T
h
rough
thi
s
obtainabl
e
resul
t
w
ill
be
i
n
the
m
eans
o
f
m
a
xim
u
m con
s
tant
po
w
er g
enerati
o
n
f
r
o
m
H
A
W
T.
K
eyw
ord
s
:
A
i
rfo
i
l
s
(S
818, S
825,
S
826)
CF
D
Ho
ri
z
ont
a
l
a
xi
s W
i
nd
Tu
r
b
i
n
e
Mo
de
l
l
i
n
g a
nd
S
i
m
u
lat
i
o
n
Power
coefficient (Cp)
W
T
_P
erf anal
ysis
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
N
a
ji A
b
d
u
lla
h
M
e
zaa
l,
Mas
t
er
i
n
H
e
a
t
a
nd
P
o
w
e
r
En
gi
nee
r
i
n
g
,
Al W
ihda, Baghda
d
,
10075,
Ir
aq.
Em
ail:
naj
i
.
a
l
l
a
m
ee@
gma
i
l.
co
m
1.
I
N
TR
OD
U
C
TI
O
N
The
foc
u
s
o
n
R
e
n
e
w
ab
le
E
n
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rgy
Re
sour
ce
s
has
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cre
a
se
d
s
i
g
n
i
f
i
c
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nt
l
y
i
n
the
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n
t
y
ea
rs
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n
t
h
e
w
a
ke
of
grow
i
ng e
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vi
r
onm
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ta
l
p
o
ll
ut
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r
isi
ng e
n
erg
y
de
m
a
nd a
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d
e
p
le
t
i
ng
f
o
s
si
l
fu
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l
re
s
ou
rce
s
. Di
f
f
e
re
nt
source
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o
f
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n
e
w
able
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ne
rg
y
i
n
cl
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bi
om
a
s
s,
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ol
ar
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geo
t
herm
al,
h
y
d
ro
ele
c
tr
ic,
an
d
w
i
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d
.
A
m
ong
t
hese
resour
ces,
the
w
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t
urne
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o
u
t
t
o
be
a
c
hea
p
e
r
a
lterna
t
i
v
e
e
n
er
g
y
r
e
s
our
ce
,
and,
t
her
e
fore
,
exte
nsi
v
e
re
sear
ch
efforts
were
m
ade
to
i
m
p
rove
t
he
t
e
c
hn
ol
og
y
o
f
e
l
ect
ri
city
g
e
n
e
ra
tio
n
b
y
w
in
d.
T
he
w
orld
h
a
s
e
nor
mous
po
te
nt
i
a
l
o
f
w
i
nd
e
n
ergy
tha
t
can
b
e
u
t
ilize
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f
or
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lec
t
r
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c
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t
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on.
C
u
r
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e
ntly,
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H
A
W
Ts
a
re
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lly
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tt
r
a
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the
y
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rgy
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tio
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ac
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w
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m
a
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i
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s
a
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p
l
a
ces
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re
l
a
r
ge
w
ind
farm
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ca
nn
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b
e
i
n
sta
lle
d
due
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vir
o
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m
e
n
t
a
l
c
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nce
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ns
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n
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l
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s
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e
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sed
gene
ra
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on
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n
i
t
s
are
pr
efe
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d.
I
n
th
is
p
ap
e
r
,
th
e
bl
ad
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wa
s
c
r
e
a
t
ed
t
o
b
e
s
i
m
il
a
r
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n
si
ze
to
a G
E 1.
5x
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bi
ne
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ha
t
us
ed
t
o
va
l
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da
te t
he
C
F
D
resul
t
s
,
w
he
re th
e
e
x
p
e
r
im
enta
l da
t
a
of G
E
1.
5
x
l
e
t
u
rb
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ca
n
be
c
ompa
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w
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th
t
he
ore
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ic
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c
a
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a
t
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s
a
n
d
CF
D
a
n
a
l
ys
is
of
t
h
i
s
pape
r.
I
n
the
fol
l
o
w
i
ng
sec
t
i
ons
w
e
w
ill
sh
ow
t
he p
ur
p
o
se
of
t
h
is
p
a
p
er.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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P
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Elec
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:
2088-
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94
Th
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du
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a
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Me
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1
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Ele
m
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(BEM) de
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t
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te
c
om
pu
t
a
ti
o
n
al
d
om
ai
n
f
o
r
f
l
ow
f
ie
l
d
a
nal
y
s
i
s
an
d
ge
ner
a
t
e
hi
gh
q
ual
i
t
y
me
sh
.
d.
Cre
a
te
t
he
ca
v
ity
m
ode
l
for
t
h
e
c
a
vity
a
na
lys
i
s for
t
h
e
C
F
D a
n
a
l
y
s
i
s
an
d
si
m
u
la
ti
on.
e.
Ca
lcu
l
a
t
e
the
p
o
w
e
r
extrac
te
d
by
t
h
e
t
u
rb
i
n
e.
f.
C
o
mpa
r
is
on
o
f
t
he
s
of
tw
a
r
e
sim
u
lat
i
o
n
d
a
ta
a
nd
t
h
e
o
r
e
t
i
cal
calc
ul
a
t
i
ons
o
f
G
E
1
.
5xle
tur
b
i
n
e.
g.
V
a
lida
t
i
on
of
t
he
r
esul
t
w
i
l
l
b
e
done.
I
n
t
h
i
s
se
c
t
ion
of
t
he
s
t
u
dy,
t
he
b
lade
g
e
o
me
t
r
y
i
s
i
mp
or
t
e
d,
a
m
e
s
h
i
s
c
rea
t
e
d
a
rou
nd
t
h
e
b
l
ad
e
and
the
f
l
ue
n
t
s
o
l
v
e
r
is
t
he
n
use
d
t
o
f
i
n
d
t
he
a
e
r
od
yna
mics
l
oa
di
ng
o
n
the
b
l
ade
,
t
he
f
lu
id
s
tre
a
m
line
s
a
nd
t
h
e
tor
que
g
e
n
er
at
ed.
We
w
i
l
l
us
e
a
i
r
a
t
s
tan
d
a
r
d
c
o
n
d
i
t
i
on
s
(
15-
de
gr
e
e
C
e
l
s
i
us)
.
I
ts
d
e
n
sit
y
i
s
1.
22
5
k
g
/
m
3
a
n
d
it
s
v
i
sc
os
it
y
i
s
1
.
789
4e
-
0
5
k
g
/
(
m
*s)
.
U
sing
pe
r
i
o
d
i
c
i
ty,
w
e
w
i
ll
s
i
m
u
l
at
e
t
h
e
fl
o
w
a
r
o
un
d
on
e
bl
a
d
e
and
e
x
t
r
a
p
o
l
a
t
e
t
h
e
sol
u
ti
on
t
o
t
w
o
m
or
e
b
l
a
d
es
i
n
or
der
t
o
v
isu
a
l
i
ze
t
h
e
res
ults f
o
r
a 3
-b
lad
e
ro
t
o
r
.
A
n
a
l
y
s
i
s
o
f
t
h
e
b
l
a
d
e
i
n
t
h
e
a
n
a
l
y
t
i
c
a
l
m
o
d
e
g
i
v
e
s
u
s
e
f
u
l
r
e
s
u
l
t
s
o
f
th
e
first
p
a
ss
a
bo
ut
s
tresses
an
d
m
o
m
e
nts
tha
t
a
re
u
seful
in
d
eter
mi
ni
n
g
t
h
e
b
as
ic
r
eq
uir
e
me
nt
s
f
or
s
t
r
eng
t
h
a
n
d
m
a
t
e
r
i
a
l
s.
T
h
i
s
t
y
pe
o
f
a
n
al
y
t
i
c
al
a
n
a
ly
sis,
t
hou
gh
u
seful,
i
s
i
n
suf
f
icie
n
t
t
o
pr
o
p
erly
e
val
u
ate
the
fu
ll
w
i
nd
tu
r
b
in
e
bla
d
e
.
A
c
cor
d
i
n
gl
y,
w
e
so
ug
h
t
t
o
use
f
i
n
i
t
e
e
le
m
e
nt
a
na
l
y
s
i
s
to
m
or
e
a
cc
ur
atel
y
c
a
p
t
ure
the
loa
d
s
a
n
d
st
r
e
sses
ge
ner
a
t
e
d
o
n
t
he
bla
de
ge
o
m
e
tr
y
by
p
a
r
ti
c
u
la
r
l
o
a
d
i
n
g sce
n
a
r
ios
. This
co
m
put
a
tio
na
l me
t
h
o
d
a
ll
ows for
m
u
ch
gr
eater
f
le
x
i
b
i
l
i
t
y
i
n
tes
tin
g
ou
t
v
a
r
i
o
u
s
lo
a
d
s
a
n
d
b
l
a
d
e
geom
etr
i
es,
a
l
l
o
w
i
ng
for
an
i
ter
a
tive
a
ppr
oa
c
h
t
o
de
ve
l
o
p
i
ng
o
u
r
tur
b
ine
bla
d
e.
F
i
r
st,
w
e
b
ega
n
b
y
se
l
e
ct
i
ng
our
ai
rfoil
s
.
We
d
e
c
i
d
e
d
t
o
u
s
e
t
h
e
NR
E
L
S-s
e
ri
e
s
of
a
ir
f
o
il
as
de
s
cr
ibe
d
i
n
(
M
a
l
colm
a
n
d
H
a
n
s
e
n 2
0
0
6
)
.
The
s
e
a
ir
fo
i
l
s are
in
ge
n
era
l
s
ome
w
hat th
ick
e
r th
an t
he
ty
pes
t
y
p
i
ca
l
l
y
seen o
n
a
i
r
p
l
a
n
e
s
due
t
o str
u
c
t
ur
al
c
o
n
cer
ns,
a
nd
a
r
e lar
g
e
l
y
inse
ns
iti
ve to
r
o
u
g
h
n
ess.
A
s
suc
h
,
the
y
a
re
we
l
l
suite
d
for
tur
b
in
e
blade
s
.
F
i
g
u
r
e
1
shows tur
b
i
n
e
b
l
a
de
a
ir
f
o
il
s
(S
818,
S
825,
S
826)
.
F
i
gur
e
1.
T
ur
bine
b
la
de
a
i
r
f
o
ils
(
S
818,
S
82
5,
S
826)
Th
e
b
e
gi
nni
ng
o
f
t
h
e
b
l
a
d
e
i
s
t
h
e
c
i
r
c
ul
a
r
h
ub
s
e
c
t
i
on
.
Th
is
c
i
r
c
u
l
a
r
r
oot
t
r
a
ns
it
io
ns
i
nt
o
t
h
e
S
8
1
8
a
i
r
f
o
i
l
,
w
hic
h
t
hen
tr
a
n
si
t
i
o
n
s
t
o
t
he
S
82
5
a
i
r
f
oi
l
,
w
h
i
ch
t
h
e
n
t
r
a
ns
it
ion
s
i
nto
t
h
e
S
8
26
a
ir
f
o
i
l
u
se
d
a
t
t
he
t
i
p
.
A
ll
ge
o
m
e
t
r
y
o
f
t
h
e
bl
a
d
e,
i
ncl
u
din
g
t
he
l
eng
t
h
of
t
he
t
w
i
st,
s
pan
a
n
d
ch
or
d,
w
as
d
eter
m
i
ne
d
usi
n
g
th
e
WT
_Per
f a
n
aly
s
i
s
a
n
d
c
an
b
e se
en be
l
o
w
i
n Ta
b
l
e
2
[1-2].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
107
2 –
1
0
80
1
074
Tab
l
e
1. Tur
bine
bla
de
ge
o
m
e
try
Re
lm
(
%
s
pa
n)
S
pa
n
(
m
)
T
w
i
s
t
(d
e
g
)
C
hord
(%
s
pa
n)
C
hord
(
m
)
A
i
rf
oil
0.
075
3
.
0937
5
42
0
.
0614
0
2
.
5328
S818
0.
125
5
.
1562
5
32
0
.
0682
6
2
.
8157
0.
175
7
.
2187
5
23
0
.
0745
2
3
.
0740
0.
225
9
.
2812
5
15
0
.
0778
2
3
.
2101
0.
275
11.
343
75
11.
5
0.
0754
3
3
.
1115
0.
325
13.
406
25
8
.
2
0
.
0718
8
2
.
9651
0.
375
15.
468
75
7
0
.
0683
2
2
.
8182
0.
425
17.
531
25
6
0
.
0647
9
2
.
6726
0.
475
19.
593
75
5
0
.
0612
6
2
.
5270
S825
0.
525
21.
656
25
4
0
.
0577
1
2
.
3805
0.
575
23.
718
75
4
.
1
5
0.
0541
5
2
.
2337
0.
625
25.
781
25
3
.
8
5
0.
0506
2
2
.
0881
0.
675
27.
843
75
3
.
2
5
0.
0470
7
1
.
9416
0.
725
29.
906
25
2
.
7
5
0.
0436
0
1
.
7985
0.
775
31.
968
75
1
.
2
5
0.
0402
4
1
.
6599
0.
825
34.
031
25
0
.
7
5
0.
0370
4
1
.
5279
0.
875
36.
093
75
0
.
5
5
0.
0338
5
1
.
3963
S826
0.
925
38.
156
25
0
.
8
5
0.
0306
6
1
.
2647
0.
975
40.
218
75
0
.
0
5
0.
0274
7
1
.
1331
1
41.
25
0
0
.
0242
4
1
Wit
h
t
he
g
iv
en
ge
o
me
try of
t
h
e
b
lade
, w
e st
a
r
te the
proc
e
ss of
cre
a
t
i
n
g t
h
e
bl
a
d
e for our
F
EA
m
odel
.
A
ltho
u
gh
w
e
c
an
s
imu
l
a
t
e
an
d
ana
l
yz
e
t
h
e
ful
l
w
in
g
us
i
ng
A
N
S
Y
S
,
s
o
w
e
d
e
c
i
d
e
d
t
o
m
o
d
e
l
t
h
e
b
l
a
d
e
u
s
i
n
g
the
So
li
d
W
or
k
s
C
AD
packa
g
e
i
n
st
e
a
d
.
B
e
c
a
use
we
c
a
n
i
m
p
ort
ge
o
m
e
try
direc
t
l
y
f
r
o
m
S
o
l
i
d
W
or
ks
t
o
ANSYS, this
s
eem
ed
t
o be
t
h
e
m
ost
effec
t
i
v
e
way
t
o
m
a
n
age
the
c
re
at
i
o
n
of t
he
b
lade
[
1-2]
.
2.
MATHE
M
A
T
ICAL MODEL
Th
e
tu
rb
ul
e
n
t
wi
nd
f
lo
ws
t
oward
s
t
h
e
n
ega
t
i
v
e
z
-
d
i
re
ct
ion
at
1
2
m
/s,
w
h
ic
h
is
a
t
y
p
i
c
a
l
r
ate
d
w
i
n
d
sp
e
e
d
fo
r
a
tu
rb
in
e
th
i
s
s
i
z
e
.
T
hi
s
i
n
c
o
ming
f
lo
w
assu
me
d
to
m
a
ke
t
he
b
la
de
r
ota
t
e
a
t
a
n
a
ngu
la
r
ve
loc
i
ty
o
f
-
2.22
r
a
d
/
s
a
b
o
ut
t
he
z
-
a
xis (t
he
b
la
de
i
s
t
h
u
s
s
p
i
nn
i
ng
c
l
o
c
kw
i
se
w
he
n
lo
ok
ing
a
t
i
t
fro
m
t
he
f
ro
nt,
l
i
k
e
m
o
st
r
e
a
l
w
i
n
d
t
u
r
b
i
n
e
s
)
.
T
h
e
t
i
p
s
p
e
e
d
r
a
t
i
o
(
T
S
R
)
(
t
h
e
r
a
t
i
o
o
f
t
h
e
bl
ade
ti
p
ve
loc
i
ty
t
o
the
i
n
c
o
m
i
ng
w
i
n
d
v
e
l
o
c
i
t
y
)
i
s
t
h
e
r
e
f
o
r
e
e
q
u
a
l
t
o
8
w
h
i
c
h
i
s
a
r
e
a
s
o
n
a
b
l
e
v
a
l
u
e
f
or
a
l
a
r
ge
w
i
n
d
t
u
rb
in
e.
N
ote
tha
t
t
o
re
prese
n
t
t
h
e
bl
ad
e
b
e
in
g
co
nn
e
c
t
e
d
t
o
a
hub
, t
h
e
b
l
ad
e
roo
t
i
s
offset
f
r
o
m
t
h
e
a
x
i
s
of
r
ot
at
io
n
by
1
m
e
t
e
r
.
Th
e
hu
b
i
s
no
t i
n
cl
u
d
e
d
in
our
m
odel.
2.1.
Go
ve
rn
in
g eq
u
a
t
i
on
s
The
g
over
n
i
n
g
eq
ua
ti
o
n
s
are
t
h
e
c
o
nt
i
n
u
i
t
y
a
nd
N
a
v
i
er-
S
toke
s
e
q
ua
tio
ns.
The
s
e
e
q
u
a
tio
ns
a
re
w
r
itte
n
i
n
a
f
ra
me
o
f
re
fere
nce
rotat
i
ng
w
i
t
h
t
he
b
l
a
de.
T
h
i
s
h
as
t
he
a
dva
nt
a
g
e
of
m
ak
in
g
o
u
r
simu
lat
i
on
n
o
t
requ
ire
a
m
o
v
i
n
g
m
esh
t
o
a
c
c
ou
n
t
f
or
t
he
r
ota
t
i
o
n
o
f
t
h
e
b
la
de
[
5
].
T
h
e
e
qu
a
t
ion
s
t
h
a
t
we
w
ill
u
se
l
ook
as
f
ol
lows:
Conse
r
vat
i
on o
f
m
a
s
s:
0
(
1
)
Conse
r
vat
i
on o
f
M
om
en
t
u
m
(N
a
v
ier-S
toke
s):
2
₸
(
2
)
W
h
ere;
v
r
i
s
t
he
r
elat
ive
ve
l
o
c
i
t
y
(
the ve
loc
i
t
y
v
i
e
w
e
d from
the
movi
n
g
f
ram
e
) and
ϖ
i
s
t
he a
n
gula
r
ve
l
oc
i
t
y
[5].
N
o
t
e
t
he
a
d
d
iti
ona
l
term
s
for
the
Cor
i
o
l
is
f
o
r
ce
(
2ϖ
×
v
r
)
a
n
d
t
h
e
c
e
n
t
r
i
p
e
t
a
l
a
c
c
e
l
e
r
a
t
i
o
n
(
ϖ
×
ϖ
×
r
)
i
n
the N
a
v
i
er-
S
to
kes e
q
uat
i
o
n
s.
In F
l
uen
t
, w
e'l
l
turn o
n t
h
e ad
di
t
io
na
l t
e
rm
s for a movin
g
f
r
a
m
e
of
reference and
in
put
ϖ
=-2.2
2
r
ad/sec
.
Im
portant
:
We
u
se
t
h
e
R
ey
n
o
l
d
s
A
v
e
r
age
d
f
o
r
m
o
f
c
o
n
t
i
n
u
i
t
y
a
n
d
m
o
m
e
n
t
u
m
a
n
d
u
s
e
the S
S
T
k-om
e
g
a
tur
b
u
l
e
n
ce
mode
l t
o
c
lose
t
he e
q
u
a
t
i
o
n
set [6]-
[
7
]
.
2.2.
B
o
un
da
ry
c
o
n
di
ti
o
n
s
We
m
ode
l
o
n
l
y
1/
3 o
f
t
he
ful
l dom
ai
n us
i
n
g
per
i
odic
i
ty a
ssum
p
t
i
on
s:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Th
e co
mp
ut
atio
nal
f
l
u
i
d
dyna
m
i
cs p
e
rfo
r
m
a
n
c
e a
nal
y
s
i
s
o
f
h
o
r
i
z
ont
al
a
x
is w
i
n
d
…
(
N
aj
i Ab
du
ll
a
h
Me
za
al
)
1
075
F
i
g
u
r
e
2
sho
ws p
er
i
o
d
i
city
assu
mp
tio
n
s.
F
i
gur
e
2.
P
er
io
di
c
i
t
y
a
ss
ump
t
i
ons
This
t
her
e
for
e
p
r
oves
that
t
he
v
e
l
ocit
y
distr
i
but
ion
at
t
he
ta
o
f
0
a
nd
12
0
de
gr
ee
s
a
r
e
the
sam
e
.
I
f
w
e
de
not
e
theta
_1
to
r
epr
e
sent
one
o
f
the
per
i
odic
boundar
i
es
f
or
the
1/
3
dom
ain
a
nd
theta-
2
be
i
ng
the
ot
he
r
bounda
r
y
,
t
h
e
n
,
,
Th
e bo
und
a
r
y
c
o
ndi
ti
o
n
s o
n
th
e
fl
ui
d
do
ma
in
a
re a
s
f
o
ll
o
w
:
Inle
t: Ve
loc
i
t
y
o
f
12
m/s
wit
h
t
urb
u
l
en
t
in
te
ns
ity
o
f
5
%
a
nd
tu
r
b
u
l
e
n
t
vi
sc
os
ity
r
ati
o
o
f
1
0
,
Out
l
et
: P
r
essure
of
1 a
t
m
,
B
la
de: No-
s
l
i
p
,
Si
de
B
ou
n
d
ar
ies
:
P
er
io
di
c [3
].
2.
3.
Nu
meri
ca
l solu
tio
n pro
ced
u
r
e
i
n
ANSY
S
F
L
U
E
N
T
c
on
ve
r
t
s
t
h
ese
d
i
f
f
er
ent
i
a
l
e
qu
a
tio
ns
i
n
t
o
a
se
t
of
a
l
g
e
b
r
a
i
c
eq
u
a
ti
on
s
.
I
nvert
i
n
g
th
e
s
e
a
l
ge
br
aic
e
qua
tio
ns
g
ive
s
t
he
v
al
ue
o
f
(
u,
v,
w
,
p,
k
,
and
om
ega
)
a
t
t
he
c
e
l
l
cen
te
rs.
Every
t
h
i
ng
e
lse
is
d
e
r
ive
d
f
r
o
m
t
h
e
c
e
l
l
centr
e
s
v
a
l
ues
(
pos
t
-
pr
oce
s
si
ng)
.
I
n
our
m
esh,
w
e
'
l
l
h
a
ve
a
ro
und
1
0000
,0
00
c
ell
s
.
Th
e
t
o
t
a
l
num
ber
of
u
nk
now
ns
a
nd
he
n
ce
algebr
a
i
c
e
q
uat
i
ons
i
s:
10,00
0
,
0
0
0
6
6
0
Th
is
h
u
g
e
se
t
of
a
l
g
e
b
r
a
i
c
e
qua
t
i
o
n
s
i
s
i
nve
r
t
ed
t
hr
ou
g
h
a
n
ite
r
a
tive
pr
oc
ess.
T
he
m
atr
i
x
to
b
e
inv
e
r
t
e
d
is hu
ge
b
u
t
s
p
a
rse. In
F
L
UENT, we
will
u
se th
e
p
res
s
u
r
e-
ba
se
d
sol
v
er
.
2.
4.
Han
d
-
c
alcu
lat
i
on
s
of
e
xp
ec
ted
re
su
lt
s
A
c
cor
d
i
n
g to
t
he
s
pec
i
f
i
c
a
t
i
on
shee
t
o
f
the
t
ur
b
i
ne
G
E 1.
5 xle
w
i
n
d
,
one
s
imple
han
d
-
c
al
cula
t
i
o
n
t
ha
t
w
e
c
a
n
do
n
o
w
be
f
o
r
e
e
ve
n
star
t
i
n
g
o
ur
s
im
u
l
a
tio
n
i
s
t
o
f
i
n
d
t
he
or
e
tic
a
l
w
i
n
d
ve
loc
i
t
y
a
t
t
h
e
ti
p.
W
e
ca
n
t
h
en
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
107
2 –
1
0
80
1
076
later
c
o
m
p
ar
e
our
a
nsw
e
r
w
i
th
w
ha
t
we
g
et
from
our
s
i
m
u
lation
t
o
ver
i
fy
t
ha
t
the
y
a
gree
. The
v
e
l
oc
ity
(
v),
on
the b
l
a
d
e
sh
ou
l
d
fo
l
low t
h
e
fo
rm
ula:
∙
⍵
(
3
)
Pl
u
ggi
ng
i
n
ou
r
a
n
g
u
l
a
r
v
e
lo
cit
y
o
f
2
.
22
r
a
d
/s
a
nd
u
si
ng
th
e
bl
a
d
e
len
g
t
h
o
f
4
3
.2
m
eters
p
l
us
1
m
eter
t
o
ac
cou
n
t
for
th
e
dis
tance
from
the r
o
ot
t
o
t
h
e hu
b,
w
e
get 44.
2
m.
v=
2
.
22
ꞏ 4
4
.
2
=
98.
12 m
/
s
A
d
d
i
t
i
ona
l
l
y
,
by
usin
g
t
h
e
sim
p
l
e
o
ne-di
m
ensi
ona
l
mo
m
e
ntum
t
he
o
r
y
,
we
c
a
n
e
sti
m
ate
t
h
e
p
o
w
e
r
c
o
eff
i
ci
ent
wh
ich
i
s
t
h
e
f
ra
ct
io
n
of
h
a
r
n
e
ss
e
d
p
o
w
e
r
t
o
tot
a
l
p
o
w
e
r
i
n
t
h
e
w
i
n
d
f
o
r
t
h
e
g
i
v
e
n
t
u
r
b
i
n
e
s
w
e
p
t
are
a
. This a
n
a
l
ysis use
s
t
h
e fo
l
l
ow
i
n
g a
s
sum
p
t
i
on
s:
a.
The
fl
ow
is ste
a
dy, hom
o
g
e
n
ous a
nd i
n
c
o
m
p
ressi
ble
.
b.
There
is no
fric
ti
o
n
al dr
a
g.
c.
There
is a
n in
fi
ni
t
e
n
um
ber
of bla
de
s.
d.
There
is un
i
for
m
thrust
ove
r the
di
sc or
rotor
are
a
.
e.
The
w
a
ke
i
s no
n-rota
ti
n
g
.
f.
The
s
t
a
tic
p
r
e
ssure
f
ar
u
p
s
trea
m
and
d
o
w
n
s
t
rea
m
o
f
the
ro
tor
is
e
qu
a
l
t
o
th
e
und
is
tur
b
ed
am
bien
t pre
ssu
r
e
.
A
c
cordi
n
g
to
t
hi
s
b
l
a
d
e
is
m
ea
nt
t
o
rese
mb
le
G
E
1.5
xl
e
w
i
n
d
t
u
rb
i
n
e
b
l
ade
[8].
T
he
s
peci
fica
t
i
on
shee
t
of
t
h
i
s
tu
rbi
n
e
s
t
at
es
t
he
r
a
t
ed
p
ower
o
f
t
h
is
t
ur
b
i
ne
t
o
b
e
1.
5
M
W,
t
he
r
ate
d
w
in
d
spe
e
d
t
o
be
1
1
.
5
m
/
s
and
the
rot
o
r
dia
m
e
t
er
t
o
be
8
2
.
5 m
.
A
pow
e a
nd pow
er
c
oe
ffic
i
e
nt
[
9
]
i
s
th
en
d
ef
i
n
ed
a
s
:
∙
(
4
)
.
(
5
)
,
.
∙
.
∙
.
∙
.
=0
.3
The
r
e
su
lti
ng
p
o
w
e
r
coe
f
fic
i
e
n
t
of
0
.3
i
t
i
s
v
e
r
y
rea
s
ona
ble.
W
e
w
i
l
l
c
o
m
p
a
r
e
i
t
t
o
p
o
w
e
r
c
o
e
f
f
i
c
i
e
n
t
ob
ta
ine
d
from
the s
i
m
u
l
a
tio
n
i
n
t
he
V
e
r
ifi
cat
io
n a
n
d C
o
n
c
l
u
si
on
section.
2.5.
B
e
tz
e
quation
a
nd
criteri
on
The
Be
tz
E
qua
ti
o
n
d
e
a
ls
w
it
h
the
w
i
nd
spe
e
d
upstre
a
m
a
nd
the
d
o
w
n
s
t
rea
m
w
ind
spee
d
of
t
h
e
tur
b
ine
.
T
he
v
alue
o
f
the
Be
tz
l
imit
s
u
g
g
es
ts
t
ha
t
a
w
i
nd
tur
b
i
n
e
c
an
b
e
e
x
t
r
ac
t
e
d
a
t
m
o
s
t
59
.3
p
erc
e
n
t
o
f
ene
r
g
y
in a
n
u
nd
ist
u
rbe
d
w
i
n
d spee
d strea
m
[
11],
it c
a
n be
def
i
ne
d a
s
:
B
e
tz coeffi
c
i
ent=
=
=0
.5
925
93=
5
9
.
3%
Lanc
hester
–B
e
t
z–
Jo
u
kow
s
k
y
lim
it
[
1
0]
s
h
o
w
s
t
h
a
t
t
h
e
ac
t
u
al
t
urb
i
n
e
c
a
n
no
t
e
x
trac
t
mo
re
t
ha
n
5
9
.3%
of
t
he
pow
er
in an
u
n
d
ist
u
rbe
d
t
u
b
e of a
ir
o
f
the
sam
e
a
s show
n
in
F
ig
ure
3
[4-
1
1].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Th
e co
mp
ut
atio
nal
f
l
u
i
d
dyna
m
i
cs p
e
rfo
r
m
a
n
c
e a
nal
y
s
i
s
o
f
h
o
r
i
z
ont
al
a
x
is w
i
n
d
…
(
N
aj
i Ab
du
ll
a
h
Me
za
al
)
1
077
F
i
gur
e
3.
C
o
n
tr
ol
v
o
l
um
e
f
o
r
t
h
e
idea
l
i
ze
d
ac
t
u
a
t
or
-dis
k ana
l
y
s
is
2.
6.
Po
we
r c
o
eff
i
c
i
ent
The
p
o
w
e
r
ge
ner
a
te
d
by
t
he
k
ine
tic
e
ner
g
y
of
a
f
r
e
e
f
l
o
w
in
g
w
i
n
d
s
t
r
e
am
i
s
s
how
n
i
n
t
he
F
ig
ur
e
3,
whe
r
e
is
d
e
f
in
ed
a
s
t
h
e
ra
tio
o
f
the
p
o
we
r
extrac
ted
by
t
he
w
in
d
t
u
r
b
in
e
r
e
la
ti
ve
t
o
th
e
e
n
e
r
g
y
a
vai
l
a
b
l
e
i
n
t
h
e
wind
s
tr
eam.
P
o
wer
co
efficien
t
(C
p)
,
r
e
pr
e
s
ente
d as
e
x
t
r
a
c
t
e
d
p
ow
e
r
o
ve
r
the
to
ta
l
p
o
w
e
r
,
it
ca
n
be
e
xp
r
e
ssed
by
the
i
n
d
u
c
t
io
n
fa
ct
or
(
a)
a
s:
4
1
(
6
)
Wher
e
(
a
)
i
s
I
n
duc
t
i
on
fa
c
t
or
,
t
he
f
r
a
c
t
i
ona
l
d
ecr
ease
in
w
i
n
d
ve
l
o
c
ity
b
e
t
w
e
e
n
t
he
f
r
e
e s
t
r
e
am
a
n
d
r
ot
o
r
p
la
ne
c
a
n
be
e
xpr
ess
e
d
i
n
t
er
m
s
o
f
an
a
xia
l
i
n
duc
t
i
o
n
f
a
c
t
or
,
a:
(
7
)
Where,
V
is th
e
veloc
i
ty
a
t th
e
disk
a
nd
it
i
s
d
efi
n
ed
b
y
:
(
8
)
a
nd
a
r
e
f
r
e
e
s
t
r
e
a
m
a
n
d
d
o
w
n
s
t
r
e
a
m
v
e
l
o
c
i
t
i
e
s
r
e
s
p
e
c
t
i
v
e
l
y
.
T
h
e
a
m
ou
nt
o
f
a
x
ia
l
in
d
u
c
t
i
on
fa
ct
o
r
de
t
e
r
m
ine
s
t
he
a
m
ount
o
f
pow
e
r
e
xtr
a
c
t
e
d
b
y
tur
b
ine
[
4
]
.
3.
RESEARCH METHOD
3.
1.
Geo
m
etry
a
nd
mesh
g
e
nera
tio
n
I
n
t
he
f
ollow
i
ng
section,
w
e
w
i
ll
cr
e
a
te
our
g
e
o
me
t
r
y
and
th
e
b
lade
volume
fr
om
t
he
f
luid
g
e
o
me
tr
y
as
shown
i
n
F
igure
4.
A
s
we
m
e
n
tioned
in
boundar
y
c
ondition
pa
rt
a
s
show
ed
i
n
F
i
gur
e
2
pe
r
i
odi
c
i
t
y
a
ssumptions.
G
r
id
g
e
n
er
a
t
ion
is
o
f
t
e
n
c
onsider
ed
a
s
the
m
o
st
t
i
m
e
consuming
par
t
o
f
C
F
D
sim
u
l
a
t
i
on.
W
e
star
t
of
f
by
na
ming
var
i
ous
f
ac
es
o
f
our
g
eom
e
tr
y
for
later
use
in
F
L
U
E
N
T
a
nd
to
m
ake
sur
f
a
c
e
body
r
e
fer
e
ncing
m
u
ch
e
asier
w
h
e
n
c
r
eating
our
m
esh
as
s
how
n
in
F
igur
e
5.
A
f
t
e
r
seve
ral
a
t
te
mpts to
m
e
sh
t
he
g
eom
e
try
we
ha
ve
b
ee
n
obtained
on
t
h
is
good
num
ber
of
m
esh,
our
g
eom
e
tr
y
ha
s
a
hi
gh
quali
ty
m
esh
ar
ound
10884336
e
l
e
m
e
n
ts
a
s
show
n
i
n
F
igur
e
6,
t
his
is
c
onsi
d
e
r
ing
a
ver
y
f
ine
enough
to
obta
i
n
a
suf
f
iciently
a
c
c
ur
a
t
e
soluti
on.
W
e
ar
e
applyi
ng
spe
c
ifying
some
g
lob
a
l
me
sh
s
e
t
t
i
ngs
which
m
e
a
n
s
tha
t
t
he
se
s
etti
ngs
w
ill
be
a
ppl
ie
d
to
t
he
w
hol
e
m
e
sh
a
lt
oge
t
h
e
r
.
A
f
ter
applyin
g
c
ontr
o
l
s
t
o
t
h
e
w
hole
me
sh,
w
e
now
a
pply
m
e
sh
s
ett
i
ngs
to
s
pe
cific
ar
e
a
s
of
our
g
eom
e
tr
y.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
1
0
72
–
1
080
1
078
F
i
gur
e
4.
Wi
nd
t
ur
b
i
ne
b
la
de
G
e
o
me
tr
y
F
i
gur
e
5
.
F
i
na
l
F
l
uid
d
o
m
a
i
n
w
it
h
va
r
i
ous
f
a
ces
of
g
e
o
m
e
tr
y
F
i
gur
e
6.
M
esh
ge
ome
t
r
y
g
e
n
e
r
ati
on
w
i
th
n
u
m
ber
of
m
esh
elem
en
ts
in
A
N
SY
S F
l
u
en
t
4.
RESU
L
T
S
A
ND ANALY
S
IS
4.
1.
B
l
ad
e
vel
o
c
i
t
y
In
C
F
D
-P
ost
for
t
h
e
nume
r
ic
al
r
e
s
u
l
ts.
We
w
il
l
e
n
ab
le
t
he
v
isua
l
i
za
ti
o
n
o
f
a
f
u
ll
3-b
l
a
d
e
ro
tor
as
show
n
in
F
i
g
ur
e
7.
F
ir
st
,
a
ha
nd-
c
a
l
cu
la
ti
o
n
i
s
di
d
ba
se
d
o
n
th
e
c
l
a
s
si
c
a
l
a
er
odyna
mic
t
h
eor
y
i
n
or
de
r
to
f
i
n
d
the
the
o
re
tic
a
l
w
i
n
d
ve
l
o
ci
t
y
a
t
t
h
e
t
i
p.
T
hi
s
da
ta
i
s
c
o
mp
a
r
in
g
w
i
t
h
t
he
v
a
l
u
e
o
f
t
h
e
vel
o
c
i
t
y
o
b
t
a
i
n
e
d
by
A
N
S
Y
S
.
F
i
gur
e 7
a
n
d
i
l
l
us
tr
a
t
e
tha
t
t
he
l
oca
l
w
i
n
d
t
u
r
b
i
n
e
bl
a
d
e
ve
loc
i
ty
i
ncr
e
ases w
ith
r
adi
u
s be
ca
use
of
t
he
r
o
t
a
t
i
o
n
o
f
t
h
e
bla
d
es.
The
ve
loc
i
t
y
o
f
t
h
e
t
i
p
,
w
h
ich
is
t
he
h
ig
he
st
v
el
o
c
it
y
,
i
t
i
s
a
roun
d
9
8
.
14
/
,
the
same
va
lue
a
s
e
qua
t
i
on.
F
i
gur
e
7.
B
la
d
e
v
eloc
i
t
y
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Th
e
c
o
mp
ut
ati
o
nal
f
l
ui
d
dy
nami
c
s
p
e
rf
o
r
m
a
n
c
e
a
nal
y
s
i
s
o
f
h
o
r
i
z
o
n
t
a
l
a
x
i
s
w
i
n
d
…
(N
aj
i Ab
du
lla
h
Me
za
al
)
1
079
4.2.
V
e
loc
i
ty
s
t
rea
m
line
s
Win
d
v
e
l
oc
i
t
y
stre
am
l
i
ne
s
h
o
w
s
t
he
v
e
l
oci
t
y
o
f
t
he
f
l
u
id
d
oma
i
n
a
ro
un
d
the
thre
e
w
i
nd
t
ur
b
i
n
e
bla
d
es,
see
F
i
gure
8
show
s
v
i
sua
l
ize
t
h
e
flo
w
a
round t
h
e
tur
b
i
n
e
us
i
ng v
e
loc
i
ty s
trea
mline
s
:
F
i
gur
e 8.
Bla
d
e
v
eloc
i
t
y
s
trea
mline
s
N
o
te
t
ha
t
the
l
e
ge
n
d
b
a
r
i
n
the
a
b
ove
p
i
c
tu
r
e
p
r
e
sents
a
col
o
r
gr
ad
uat
i
o
n
from
bl
ue,
w
h
ic
h
is
t
he
low
e
s
t
v
e
l
oc
ity
,
unt
i
l
r
e
d
.
Inle
t
sec
t
i
o
n
(
)
ha
s
ye
l
l
ow
c
olor
s
o
it
is
12
/
,
as
it
w
a
s
m
e
ntione
d
e
a
rlier
.
T
he
col
o
r
bl
ue
i
n
the
stre
am
li
ne
s
me
ans
that
w
he
n
the
airflo
w
p
a
s
se
s
the
blade
s
(
)
so
i
t
is
10
m
/
s,
it
su
ffer
s
a
slow
i
ng
dow
n
a
nd
th
e
ve
loc
i
t
y
d
e
c
re
ases.
C
l
ear
l
y
,
a
n
a
cc
el
era
t
i
on
of
t
he
f
l
o
w
a
r
o
u
n
d
t
he
w
ake
is
r
epr
e
sente
d
by re
d c
o
l
o
r
. A
l
l
t
he
se
fea
t
u
re
s
ma
tch the
m
a
ss conse
r
va
t
i
o
n
an
d
mom
e
nt
u
m
theory.
5.
VERIFI
CA
T
I
ON
F
r
om
t
he
F
ig
u
r
e
8
and
b
y
a
p
p
l
y
in
g
(6)
to
(
8)
f
or
o
b
t
a
i
ni
n
g
t
he
ef
fi
ci
ency
(
C
p
)
of
t
h
e
t
u
r
bi
n
e
s
i
s
t
h
e
implem
e
n
ta
t
i
o
n
o
f
the
A
c
tu
ator
D
isk
The
o
r
y
.
Fre
e
s
tre
a
m
veloc
i
t
y
a
nd
d
o
w
n
s
t
r
e
a
m
v
eloci
t
y
,
ar
e
ob
ta
ine
d
from
CFD
a
nd (6)
to (
8) w
ill a
g
a
i
n re
sul
t
the
p
ow
e
r
c
o
e
ffic
i
e
n
t
(Cp)
is 0.
2
9
8.
The
va
lue
o
f
t
he
v
e
l
o
c
ity
obt
a
i
ne
d
b
y
A
N
S
Y
S
F
igure
7
illu
strate
t
h
a
t
t
h
e
l
o
c
a
l
wi
n
d
t
u
rb
i
n
e
bl
ad
e
vel
o
c
i
t
y
i
nc
rea
s
e
s
w
i
t
h
ra
diu
s
b
ec
ause
o
f
t
h
e
r
o
t
a
tio
n
o
f
t
he
b
la
des.
T
h
e
v
el
oci
t
y
of
t
he
tip,
w
h
i
c
h
i
s
t
he
hi
ghe
s
t
v
el
oc
it
y,
it
is
a
r
oun
d
98.1
4
/
,
the
sam
e
v
alue
a
s
(3).
T
he
T
orque
i
s
a
forc
e
t
h
at
t
urns
o
r
ro
ta
te
s
t
h
e
w
i
n
d
t
ur
bine
a
nd
i
t
is
e
q
u
a
l
t
o
the
forc
e
m
u
lti
pl
ie
d
b
y
d
is
ta
nc
e.
T
h
i
s
m
eans
t
h
at
s
o
lo
n
g
er
b
l
a
des
a
r
e,
m
o
r
e
t
o
rq
u
e
can
g
enera
t
e.
T
h
e
v
alue
t
h
a
t
we
h
a
v
e
b
e
en
obt
ai
n
e
d
f
r
o
m
our
C
F
D
a
na
l
y
sis
for
one
b
la
de
i
s
421
9
1
0
n.m
.
a
nd
b
y
a
pp
l
y
in
g
(4)
w
e
h
a
v
e
p
o
w
e
r
i
s
9
3
6
.
6
4
kW.
N
o
w
w
e
c
a
n
c
o
m
p
a
r
e
t
h
e
C
F
D
r
e
s
u
l
t
s
a
n
d
ma
them
at
i
c
al c
alcu
la
t
i
o
n
s wit
h
the
e
x
p
erim
e
n
ta
l da
ta of
G
E
1
.
5
xle
turbine
i
n
the T
a
ble 2.
Tab
l
e
2.
C
om
p
a
riso
n of Re
s
u
l
t
s
Pa
r
a
m
e
te
r
T
h
e
o
r
e
ti
ca
l
cal
c
u
l
a
t
i
o
n
s
GE
1.
5
xl
e
tur
b
i
n
e
C
F
D
a
n
a
l
ysi
s
Ve
loc
i
t
y
(
v) m
/s
98.
12
9
7
98.14
P
o
w
e
r c
o
e
f
fi
c
i
e
n
t
(
)
0.
59
0
.
265
0
.
2
98
6.
CONCL
U
S
ION
I
n
t
he
p
re
se
n
t
i
n
v
es
t
i
ga
t
i
o
n
,
t
h
e
ae
ro
d
ynam
i
c
effi
c
i
e
n
cy
o
f
the
h
or
i
z
on
t
a
l
ax
is
w
ind
t
u
rbi
n
e
us
ing
com
p
u
t
a
t
i
o
na
l
m
e
tho
d
s
o
f
f
lu
i
d
dyna
mic
s
i
s
st
ud
ie
d.
T
he
o
bta
i
ne
d
CF
D
results
a
re
c
om
par
e
d
w
i
t
h
t
he
ma
them
at
i
c
al
c
alcu
la
t
i
o
n
a
n
d
e
x
p
erim
en
tal
da
t
a
o
f
the
GE1.
5
x
l
e
t
urb
i
ne.
This
s
tud
y
ha
s
dem
o
nst
r
ated
t
h
a
t
t
h
e
CFD
me
t
h
o
d
s
c
on
fi
rm
t
he
e
xp
e
r
i
m
e
n
ta
l
re
su
lt
s
a
n
d
c
a
n
b
e
u
se
d
to
o
p
t
i
m
i
z
e
and
con
f
i
r
ma
t
i
o
n
t
h
e
sh
ape
S
p
e
c
ifica
t
i
o
ns
o
f
the
t
u
rb
i
n
e
.
A
cc
ordi
ng
t
o
the
re
sul
t
s
of
t
hi
s
r
es
ea
rc
h
,
i
t
c
a
n
b
e
c
on
clud
ed
t
h
a
t
t
h
e
po
wer
coe
f
fic
i
e
n
t of t
he
t
ur
bine
is a
c
t
ua
l
l
y
ma
tc
hes
t
o
t
he
t
heore
t
i
c
al r
esults a
s dem
ons
trated.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
107
2 –
1
0
80
1
080
REFE
RENCES
[1]
C.
P
h
e
lps,
J
.
Si
ngl
e
t
o
n
,
"
W
in
d
T
u
rb
ine
Blade
Desi
gn
.
Co
rnell
Un
iversity,"
Sib
l
ey
Scho
ol
of
En
gi
neering
,
p
p
. 2-1
4
, 2
01
3.
[2]
Tukesh
S
inhg
Thakur,
Brij
esh
P
a
t
e
l,
"
S
t
ructur
al
A
naly
si
s
o
f
a
C
om
po
s
i
te
W
i
n
d
Turb
in
e
Bl
ad
e
to
o
p
t
i
m
i
ze
its
Con
s
tru
c
ti
on
al
P
aram
et
e
r
s
u
s
i
n
g
a
F
E
A
S
o
ftware,
"
IJ
S
R
D-In
te
rn
at
io
na
l J
o
urna
l
for
Scientif
i
c
Research &
Devel
opm
ent
.
Vol
. 3
.
No.
4
pp.
5
7
2
-5
76
,
No
v
.
2016.
[3]
Ack
e
r,
T
.
,
H
a
nd,
M
.
,
"
A
e
rod
yna
m
i
c
P
e
rf
orm
a
nce
of
t
he
N
REL
Un
st
e
ady
Aero
d
y
nam
i
cs
E
x
p
erim
e
n
t
(P
hase
I
V)
Twisted
Rotor
,
"
Pr
e
p
ar
ed
f
o
r the 37
th AIAA
Aer
o
s
pace
Sc
ie
nc
es Me
e
t
ing
an
d Ex
h
i
b
i
t
,
Re
n
o
,
10pp
.
2
11-2
2
1
,
Jan.
19
99
.
[4]
Arme
n
Sa
rg
sy
a
n
,
"
S
imu
l
a
t
io
n
a
n
d
mo
de
l
i
n
g
o
f
flow
f
ie
ld
a
ro
un
d
a
h
ori
z
ontal
axi
s
w
ind
turbine
(HAWT
)
u
sing
RAN
S
m
e
t
ho
d,
"
Fl
ori
d
a A
t
l
a
nti
c
U
n
i
v
e
rsity,
8
p
p
.
7-1
5
,
20
10
[5]
Flue
n
t
,
ANS
Y
S
FLU
E
NT 12
.
0
Th
e
o
ry
Gu
i
de
,
ANSYS
I
nc
.,
A
p
r
il 20
09
,
Se
c
tion
s
1
8.1.1
a
n
d
18
.1
.
2
.
[6]
F
l
u
e
nt,
AN
SYS F
L
UENT
1
2
.
0,
T
ut
or
i
a
l
9
-
11
-12
-
2
3
-2
8-2
9
,
T
urbulen
c
e
and
Di
scret
e
P
has
e
M
odelin
g.
[7]
Ba
rd
in
a
,
J
.
E.,
H
ua
ng
,
P.
G
.
a
n
d
Coa
k
le
y
,
T
.J.,
"
T
urb
u
le
nc
e
Mo
d
elin
g vali
datio
n,
t
estin
g,
a
nd
D
ev
elo
p
m
e
nt,
"
NASA
T
echn
i
cal
M
e
m
o
r
a
n
dum
11
04
46,
A
pril
1
997
.
[8]
GE
E
nergy
1
.
5xle
-
M
a
n
u
f
actu
r
ers
and
tu
rbi
n
es
-
O
nlin
e
acc
es
s
-
T
h
e
W
i
n
d
P
o
w
e
r
,
R
M
T
,
I
n
c
.
|
N
o
r
t
h
C
o
a
s
t
W
i
n
d
& Pow
e
r
LL
C
.
[9]
Burt
on
T,
S
h
a
rp
e
D,
J
enk
i
ns
N
,
Bos
s
an
yi
E
,
"
Win
d
E
n
e
rgy
H
a
nd
boo
k
,"
J
o
hn
Wil
e
y
&
So
ns
,Ch
i
chester,
UK
,
p
p
.4
5-
47
,
2
001
.
[10]
Ku
ik
,
G.
A.
M
.
,
"
T
he
L
anch
ester-Bet
z
-Jo
uko
ws
ky
Li
mit,
Wi
nd
Energy
,
"
10p
p.
2
8
9
-29
1
,
10
,
20
07
.
[11]
M
a
gd
i
Ragh
eb
a
n
d
A
dam
M.
R
a
g
heb.
"
W
i
nd
T
urbi
nes
Theo
ry-The
B
et
z
E
qu
ati
o
n
and
Optim
a
l
R
ot
or
T
i
p
S
p
eed
Rati
o,"
INT
E
CH op
en s
c
ien
ces
,
21p
p
,
2
-22
,
J
u
l
y
5,
2
011
.
[12]
Yu
qi
a
o
Z
hen
,
R
on
g
Zh
en
Z
hao,
H
o
n
g
Liu
"
M
o
de
A
n
a
lys
i
s
o
f
H
ori
z
on
tal
Axi
s
W
i
n
d
Turbine
Bl
a
d
es,"
T
E
LKOM
NIKA In
do
nesi
an
Jou
r
nal
o
f
El
ectrical
En
gi
neer
ing,
Vol
.
12
,
p
p
.
1
2
12
~
12
16
,
Fe
br
ua
ry
20
1
4
.
[13]
S
h
u
a
ngw
en
S
h
e
n
g
,
Ry
an
O
’Conn
or
“
Reli
abili
t
y
of
W
i
nd
T
u
rb
in
es,
”
Wi
nd
En
ergy E
n
g
i
n
e
er
in
g
,
20
17
,
DOI
10
.
1
0
1
6
/
B97
8
-0-12
-
809
45
1-8
.
00
01
5-1
[14]
Di
n
i
ar
M
ungil
Ku
rni
a
wati
,
D
o
m
i
nicu
s
D
a
nardo
n
o
Dwi
P
rija
T
jah
j
an
a,
B
ud
i
S
a
nt
os
o
“E
xp
eriment
a
l
i
n
v
e
sti
g
atio
n
on
p
erf
o
rm
ance
o
f
c
ro
ssflow
w
i
nd
t
u
rb
ine
as
e
ff
ect
o
f
b
l
ad
es
n
u
mb
e
r
,”
T
h
e
1st
Inter
natio
nal Con
f
er
ence
An
d
Exh
i
biti
on
o
n
Powd
er T
ech
nol
o
g
y Ind
o
n
e
si
a
(
I
CeP
T
i) 2
0
1
7
, AIP
Conferen
ce Pr
oceed
ing
s
1931(1
)
:0
30
045
,
DOI
10
.
1
0
6
3
/
1.
50
24
1
0
4
[15]
Ilham
Sat
r
io
U
tomo,
Dom
i
n
i
cus
Da
nard
on
o
Dwi
P
rija
T
jahjana,
S
y
a
ms
u
l
H
ad
i
“Exp
erim
en
t
a
l
stud
ies
of
S
av
on
iu
s
wi
nd
t
urbines
w
i
th
v
ar
iations
s
iz
e
s
a
n
d
f
i
n
n
u
m
b
e
r
s
t
o
w
a
r
d
s
p
e
r
form
ance,”
T
h
e
1
s
t
Inter
n
a
t
io
nal Con
f
er
ence
An
d
Exh
i
biti
on
o
n
Powd
er T
ech
nol
o
g
y Ind
o
n
e
si
a
(
I
CeP
T
i) 2
0
1
7
, AIP
Conferen
ce Pr
oceed
ing
s
1931(1
)
:0
30
041
,
DOI
10
.
1
0
6
3
/
1.
50
24
1
0
0
[16]
Y
o
g
a
A
r
o
b
W
i
c
a
k
s
o
n
o
,
D
o
m
i
n
i
c
u
s
D
a
n
a
r
d
o
n
o
D
w
i
P
r
i
j
a
T
j
a
h
j
a
n
a
,
S
y
am
s
u
l
H
a
di
“
In
fl
uence
o
f
o
m
n
i-d
i
recti
onal
g
u
ide
va
n
e
o
n
t
h
e
pe
rforma
n
c
e
o
f
c
ro
ss-flo
w
r
ot
or
f
or
u
rb
a
n
w
in
d
energ
y
,”
T
h
e
1
s
t
Inter
natio
nal Con
f
er
ence And
Exh
i
biti
on
o
n
Powd
er T
ech
nol
o
g
y Ind
o
n
e
si
a
(
I
CeP
T
i) 2
0
1
7
, AIP
Conferen
ce Pr
oceed
ing
s
1931(1
)
:0
30
040
,
DOI
10
.
1
0
6
3
/
1.
50
24
0
9
9
[17]
Do
mini
cus
D
a
na
rd
on
o
Dw
i
P
r
ij
a
T
j
ah
jana,
A
r
nold
T
h
am
rin
Ha
lom
o
an
,
And
r
eas
W
i
bowo,
D
w
i
A
ries
H
im
aw
anto,
Yo
ga
A
ro
b
Wicaks
ono
“
Win
d
p
oten
ti
al
a
ss
es
s
m
ent
i
n
u
rb
an
a
rea
of
S
u
r
a
k
a
r
t
a
c
i
t
y
,
”
The 1st
Interna
t
iona
l
Conference And E
x
hi
b
ition on
P
o
wder
Technol
o
gy Indone
s
i
a
(
I
CeP
T
i)
2017
,
AI
P
Conf
erence Pr
oceedi
n
gs
1
9
3
1
(1
):03
00
70
,
DOI
10
.10
6
3
/
1
.
50
24
12
9
[18]
P
a
tri
c
k
A.B.
J
a
m
es,
Ab
uBak
r
S
Bah
a
j
“S
m
a
l
l
-S
cale
W
i
nd
Tu
rbi
n
es,
”
W
i
nd E
n
er
gy
E
ngin
eerin
g
,
20
17
,
D
O
I
10
.
1
0
1
6
/
B97
8
-0-12
-
809
45
1-8
.
00
01
9-9
[19]
Ad
am
M
.
Rag
h
eb
,
M
i
chael
S
S
elig
“
M
u
lti
ele
m
ent
A
i
rf
oil
s
f
o
r
W
in
d
T
urbi
nes,
”
Wi
nd E
n
er
gy En
gi
neer
ing
,
2
0
1
7
,
DO
I
10.
10
16
/B9
7
8-0
-
12
-809
45
1-8
.
00
01
1-4
[20]
Lo
iy
A
l-G
hussain,
O
n
u
r
T
ayl
a
n,
M
urat
F
ah
rio
g
l
u
“
S
i
z
i
ng
o
f
a
P
h
o
t
ovo
lt
aic-Wi
nd-Oil
S
h
al
e
H
y
b
r
id
S
y
s
t
e
m:
C
ase
An
alysis
i
n
J
o
rda
n
,
”
2
01
8,
Jo
ur
n
a
l of S
o
l
a
r En
er
g
y
En
gin
eer
i
n
g
.
Vol. 1
40
,
n
o
1
.
0
11
0
0
2
,
D
OI 1
0
.
1
1
1
5
/1.4
03
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0
4
8
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