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se
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ter
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n
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m
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rica
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o
rm
a
n
c
e
c
h
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c
teristics
o
f
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ro
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d
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v
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n
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l
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s
fro
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d
1
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fu
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sis
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ey
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s
:
B
-
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m
p
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p
r
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p
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b
lad
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Hy
d
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y
n
am
ic
c
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ar
ac
ter
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Op
en
wate
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f
icien
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y
T
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is i
s
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n
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u
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d
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e
CC B
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SA
li
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se
.
C
o
r
r
e
s
p
o
nd
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A
uth
o
r
:
Vijay
K
Sin
g
h
Natio
n
al
Pro
ject
I
m
p
lem
en
tati
o
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Un
it
-
Min
is
tr
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o
f
Hu
m
an
R
eso
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Dev
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m
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Ma
d
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Mo
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Ma
lav
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Un
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Go
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p
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Uttar
Pra
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I
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E
m
ail:
v
ijay
n
itr1
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co
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NT
RO
D
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O
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Sin
ce
1
9
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n
tu
r
y
,
s
cr
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p
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s
h
av
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s
ec
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ip
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d
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b
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p
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s
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esp
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e
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s
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ig
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er
ef
f
icien
cy
o
v
er
a
lo
n
g
p
e
r
io
d
o
f
tim
e.
W
ith
th
e
r
ap
id
ad
v
an
ce
m
e
n
ts
in
tech
n
o
l
o
g
y
,
th
e
d
eter
m
in
atio
n
o
f
p
r
in
cip
al
d
i
m
en
s
io
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lik
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s
h
ip
s
ize,
s
p
ee
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f
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d
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o
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m
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m
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-
b
ased
to
o
ls
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as
g
ain
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m
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ch
im
p
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tan
ce
.
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h
ese
n
u
m
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ap
p
lied
co
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p
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al
m
eth
o
d
s
h
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g
ain
ed
th
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clo
s
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r
m
o
f
s
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tio
n
s
with
an
aly
tical
o
r
ex
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tal
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T
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e
u
s
e
o
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W
ag
en
in
g
en
B
-
s
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ase
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m
ar
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v
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g
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m
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ch
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th
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b
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in
d
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m
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in
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wate
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T
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m
a
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tim
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d
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ca
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m
ad
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s
in
g
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Evaluation Warning : The document was created with Spire.PDF for Python.
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21
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p
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id
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b
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e
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f
t
h
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m
o
s
t
ef
f
ec
tiv
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t
ec
h
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iq
u
es
f
o
r
an
aly
s
is
o
f
f
lu
i
d
f
lo
w
p
ar
a
m
eter
s
.
T
h
e
d
e
s
ig
n
o
f
m
a
r
in
e
p
r
o
p
e
ller
was
d
o
n
e
[
1
]
,
s
y
s
tem
atic
p
r
o
p
eller
s
er
ies
an
d
im
p
le
m
en
ted
n
u
m
er
ical
r
elatio
n
s
in
th
e
d
esig
n
o
f
p
r
o
p
eller
b
lad
e
(
B
-
s
er
ies)
u
n
d
er
v
ar
io
u
s
lo
a
d
in
g
co
n
d
itio
n
s
.
A
th
r
ee
-
d
im
en
s
io
n
al
h
y
d
r
o
f
o
il
i
n
a
wate
r
tu
n
n
el
h
a
s
b
ee
n
in
v
esti
g
ated
with
r
esp
e
ct
to
its
’
f
lu
id
-
s
tr
u
ct
u
r
e
i
n
ter
a
ctio
n
(
FS
I
),
S
h
il
ian
g
H
u
et
a
l
.
[
2
]
u
s
in
g
th
e
f
in
ite
v
o
lu
m
e
m
eth
o
d
(
FVM)
an
d
f
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ite
elem
en
t
m
eth
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d
(
FEM
)
.
T
h
e
p
r
o
p
elle
r
ef
f
icien
cy
(
o
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en
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r
a
n
d
b
o
d
y
)
f
o
r
s
in
g
le
an
d
twin
-
s
cr
ew
s
h
ip
s
was
co
m
p
u
ted
[
3
]
,
u
s
in
g
s
ev
er
al
ad
v
a
n
ce
d
co
ef
f
icien
ts
d
ef
in
itio
n
s
.
T
h
e
c
o
m
p
r
eh
e
n
s
iv
e
d
escr
ip
tio
n
o
f
t
h
e
s
tate
o
f
ar
t
ca
n
b
e
f
o
u
n
d
[
4
]
,
wh
er
e
t
h
e
f
lo
w
ac
r
o
s
s
a
p
r
o
p
eller
e
x
am
in
ed
e
x
p
er
im
en
tally
in
o
p
e
n
wate
r
c
h
an
n
els k
ee
p
in
g
th
e
f
lo
w
co
n
d
itio
n
s
u
n
if
o
r
m
.
T
h
e
f
lo
w
f
ield
a
n
d
p
h
y
s
ical
p
ar
am
eter
s
s
u
b
jecte
d
to
a
p
r
o
p
eller
s
im
u
ltan
eo
u
s
ly
was
an
aly
s
ed
[
5
]
u
s
in
g
co
m
p
u
tatio
n
al
f
lu
id
d
y
n
am
ics
(
C
FD)
tech
n
o
lo
g
y
.
W
h
ile
d
ea
lin
g
with
th
e
tu
r
b
u
le
n
t
s
h
o
ck
wav
e
an
d
b
r
ea
k
wa
v
e
to
tak
e
ca
r
e
n
o
n
li
n
ea
r
ity
,
th
e
y
a
p
p
lied
th
e
Nav
i
er
s
to
k
es
eq
u
atio
n
h
as
b
ee
n
a
p
p
lied
to
th
e
s
o
lv
e
r
.
T
h
e
th
r
u
s
t
an
d
to
r
q
u
e
p
er
f
o
r
m
an
ce
o
f
th
e
m
ar
in
e
p
r
o
p
eller
b
lad
e
at
d
if
f
e
r
en
t
r
o
tatio
n
al
s
p
ee
d
h
as
b
e
e
n
esti
m
ated
u
s
in
g
C
FD
an
d
f
o
u
n
d
a
g
o
o
d
r
elev
an
c
e
with
th
e
ex
p
er
im
en
tal
r
esu
lts
r
ep
o
r
te
d
[6
]
,
[
7
]
.
A
s
er
ies
o
f
m
ar
in
e
p
r
o
p
eller
h
a
v
e
test
ed
u
n
d
er
o
p
e
n
wate
r
ex
p
er
im
en
tatio
n
a
n
d
th
e
o
b
tai
n
ed
h
y
d
r
o
d
y
n
am
ic
ch
ar
ac
ter
is
tics
was c
o
m
p
ar
ed
with
th
at
o
f
th
e
n
u
m
er
ic
al
r
esu
lts
[
8
]
,
A
p
er
f
o
r
m
an
ce
test
wa
s
ca
r
r
ied
o
u
t [
9
]
f
o
r
7
9
p
r
o
p
eller
s
in
th
e
d
iam
eter
r
an
g
e
o
f
9
to
1
1
in
c
h
alo
n
g
with
th
e
m
ea
s
u
r
em
e
n
t
o
f
t
h
r
u
s
t
a
s
well
as
to
r
q
u
e
in
th
e
p
r
o
p
eller
s
p
ee
d
r
an
g
e
1
5
0
0
-
7
5
0
0
r
p
m
with
r
esp
ec
t
to
it
s
’
d
iam
eter
.
T
h
e
co
m
p
lem
en
t
at
io
n
o
f
co
m
b
i
n
ed
b
lad
e
–
m
o
m
en
tu
m
elem
en
t
-
t
h
eo
r
y
f
o
r
th
e
p
r
o
p
eller
s
wh
ich
ar
e
lig
h
t/m
o
d
er
ately
lo
ad
ed
was
illu
s
tr
ated
[
1
0
]
.
T
h
e
h
y
d
r
o
d
y
n
a
m
ic
ch
a
r
ac
ter
is
tics
f
o
r
th
e
p
r
o
p
eller
s
(
co
n
v
en
tio
n
al
m
etallic)
o
f
v
a
r
io
u
s
s
iz
es
was
d
eter
m
in
ed
[
1
1
]
,
[
1
2
]
u
s
in
g
ca
v
itatio
n
an
d
tu
n
n
el
test
.
Mo
s
t
o
f
t
h
ese
r
esear
ch
wo
r
k
h
ad
b
ee
n
ca
r
r
ied
o
u
t
eith
er
b
y
an
aly
tically
o
r
n
u
m
e
r
ically
i
n
v
is
cid
o
r
f
u
lly
v
is
co
u
s
/b
o
u
n
d
ar
y
lay
er
t
ec
h
n
iq
u
e
[
1
3
]
.
W
ith
th
e
ef
f
ec
t
s
o
f
tu
r
b
u
len
ce
f
lo
w
tak
in
g
in
t
o
co
n
s
id
er
atio
n
a
n
d
f
lo
w
f
ield
esti
m
atio
n
with
no
-
s
lip
b
o
u
n
d
ar
y
co
n
d
itio
n
s
ar
e
o
u
t
o
f
im
p
o
r
tan
t
R
ey
n
o
ld
s
a
v
er
ag
e
Nav
ier
s
to
k
es
eq
u
atio
n
(
R
ANS
)
with
ap
p
r
o
p
r
iate
tu
r
b
u
len
ce
m
o
d
el
is
u
s
ed
to
p
r
e
d
ict
th
e
f
lo
w
c
h
ar
ac
t
er
is
tics
o
f
p
r
o
p
eller
b
lad
e
ac
co
r
d
in
g
to
[
1
4
]
.
A
C
F
D
b
ased
liftin
g
lin
e
s
u
r
f
ac
e
th
eo
r
y
was
u
s
ed
[
15
]
,
[
16]
f
o
r
v
is
u
alizin
g
th
e
f
lo
w
p
atter
n
ar
o
u
n
d
th
e
m
er
c
h
an
t
’
s
s
h
ip
p
r
o
p
eller
.
T
h
e
v
is
co
u
s
eq
u
atio
n
s
o
lu
tio
n
f
o
r
th
e
f
lo
w
p
atter
n
was
im
p
lem
en
ted
[
1
7
]
.
A
s
h
ip
p
r
o
p
eller
d
esig
n
(
SPD
)
co
m
p
u
ter
co
d
e
d
ev
elo
p
ed
a
n
d
e
m
p
lo
y
ed
f
o
r
m
an
y
p
r
o
p
u
ls
o
r
s
(
p
r
o
p
eller
r
u
d
d
e
r
s
y
s
tem
an
d
co
n
tr
a
r
o
tatin
g
p
r
o
p
eller
[
1
8
]
-
[
22]
.
T
h
e
h
y
d
r
o
d
y
n
am
ic
an
aly
s
is
o
f
m
ar
in
e
p
r
o
p
eller
was
p
er
f
o
r
m
ed
u
s
in
g
t
h
is
SP
D
co
d
e
b
ased
o
n
b
o
u
n
d
ar
y
lay
er
th
eo
r
y
.
A
co
u
p
le
d
b
o
u
n
d
ar
y
e
lem
en
t
m
eth
o
d
alo
n
g
with
th
e
f
in
ite
elem
en
t
m
eth
o
d
was
a
p
p
lied
to
d
eter
m
in
e
t
h
e
n
u
m
er
ical
s
o
lu
tio
n
f
o
r
th
e
f
lex
ib
le
p
r
o
p
eller
s
(
co
m
p
o
s
ite
)
[
2
3
]
.
A
n
u
m
er
ical
an
aly
s
is
was
ca
r
r
ied
o
u
t
[
2
4
]
in
th
e
ca
s
e
o
f
p
r
o
p
eller
s
o
f
lar
g
e
-
s
ca
le
s
u
r
f
ac
e.
T
h
e
o
p
e
n
wate
r
c
h
ar
ac
ter
is
tics
was
co
m
p
u
ted
alo
n
g
with
th
e
a
n
aly
s
is
o
f
ca
v
itatio
n
p
r
o
b
lem
[
2
5
]
u
s
in
g
co
m
p
u
ter
co
d
e
(
s
o
lag
a
)
.
Sen
th
il
et
a
l
.
[
2
6
]
o
b
tain
ed
th
e
o
p
en
wate
r
ch
ar
ac
ter
is
tics
o
f
p
r
o
p
eller
(
B
-
s
er
ies)
u
s
in
g
C
F
D
s
im
u
latio
n
.
L
ater
on,
t
h
e
C
FD
an
aly
s
i
s
o
f
p
r
o
p
eller
(
c
o
n
tr
a
-
r
o
tatin
g
)
was
p
er
f
o
r
m
ed
b
y
Das
et
al
.
[
27
]
.
Das
an
d
J
ay
k
u
m
ar
[
2
8
]
p
r
ed
ic
ted
th
e
h
y
d
r
o
d
y
n
am
ic
ch
ar
ac
t
er
is
tics
o
f
a
co
n
tr
a
-
r
o
tatin
g
p
r
o
p
eller
b
y
v
alid
atin
g
th
e
co
m
p
u
ted
r
esu
lts
with
th
e
ex
p
e
r
im
en
tal
d
ata.
[
2
9
]
Stu
d
ied
an
au
to
n
o
m
o
u
s
u
n
d
er
wate
r
v
e
h
icle
in
th
e
ca
s
e
o
f
h
u
ll
p
r
o
p
u
ls
o
r
in
ter
ac
tio
n
b
y
p
er
f
o
r
m
in
g
th
e
co
m
p
u
ta
tio
n
al
an
aly
s
is
an
d
ex
p
er
im
en
tal
v
alid
atio
n
.
Kr
is
h
n
a
et
a
l
.
[
3
0
]
p
r
esen
ted
th
e
ac
o
u
s
tic
ch
ar
ac
ter
izatio
n
o
f
a
B
en
ch
m
ar
k
Ma
r
in
e
p
r
o
p
eller
u
s
in
g
C
FD.
T
h
e
n
u
m
er
ical
p
r
ed
ictio
n
was
m
ad
e
[
31
]
f
o
r
t
h
e
f
o
r
ce
s
ac
tin
g
o
n
p
r
o
p
eller
s
(
p
o
d
d
e
d
an
d
o
p
en
),
wo
r
k
i
n
g
u
n
d
er
th
e
ab
n
o
r
m
al
f
lo
w
s
itu
atio
n
s
.
Su
b
r
am
an
ian
an
d
Sen
th
il [
3
2
]
im
p
lem
en
ted
a
s
ch
em
e
f
o
r
th
e
o
p
tim
izatio
n
o
f
th
e
p
r
o
p
eller
b
y
c
o
u
p
le
d
L
M
an
d
R
ANS
s
o
lv
er
m
eth
o
d
s
.
Ap
p
lica
tio
n
o
f
C
FD
f
o
r
th
e
p
r
ed
icti
on
o
f
p
er
f
o
r
m
a
n
ce
ch
a
r
ac
ter
is
tics
in
m
ar
in
e
p
r
o
p
elle
r
ca
n
b
e
f
o
u
n
d
in
Kim
u
r
a
et
a
l
.
[
3
3
]
,
T
ak
s
h
i
an
d
J
u
n
[
3
4
]
,
an
d
C
h
o
o
n
g
et
a
l
.
[
3
5
]
.
A
m
ec
h
an
ical
p
r
o
to
ty
p
e
o
f
o
s
cillatin
g
co
n
v
er
s
io
n
c
h
a
m
b
er
(
OW
C
)
d
ev
ice
was b
u
ilt
an
d
s
tu
d
ied
u
s
in
g
C
FD simu
lato
r
[
3
6
]
.
A
co
m
p
r
e
h
en
s
iv
e
s
tu
d
y
o
n
b
en
d
-
twis
t c
o
u
p
lin
g
o
f
c
o
m
p
o
s
ite
p
r
o
p
eller
b
lad
es in
o
r
d
er
to
im
p
r
o
v
e
t
h
e
h
y
d
r
o
d
y
n
a
m
ic
ef
f
ici
en
cy
was p
r
esen
ted
b
y
Das
an
d
Kap
u
r
ia
[
3
7
]
.
T
h
e
o
b
jectiv
e
o
f
t
h
e
p
r
esen
t
s
t
u
d
y
is
to
p
er
f
o
r
m
th
e
C
o
m
p
u
t
atio
n
al
f
lu
id
d
y
n
am
ics
s
im
u
lat
io
n
f
o
r
th
e
f
lo
w
ar
o
u
n
d
th
e
B
-
s
er
ies
W
ag
en
in
g
en
p
r
o
p
eller
u
s
in
g
an
u
n
s
tr
u
ctu
r
ed
m
esh
-
b
ased
R
ey
n
o
l
d
s
-
av
er
ag
ed
Na
v
ier
s
to
k
es
eq
u
atio
n
m
eth
o
d
.
T
h
e
co
m
p
u
ted
r
esu
lts
ar
e
v
alid
ated
with
th
e
s
tan
d
ar
d
B
-
s
er
ies
d
ata
in
o
r
d
e
r
to
tes
t
th
e
ef
f
icac
y
o
f
th
e
p
r
esen
t
m
e
th
o
d
.
A
m
o
v
in
g
r
ef
er
e
n
ce
f
r
a
m
e
ap
p
r
o
ac
h
is
s
elec
ted
u
s
in
g
th
e
K
-
ɛ
m
o
d
el
an
d
em
p
lo
y
ed
f
o
r
tu
r
b
u
len
ce
clo
s
u
r
e.
T
h
e
g
lo
b
al
q
u
an
titi
es
s
u
ch
as
th
r
u
s
t
an
d
to
r
q
u
e
co
e
f
f
icien
ts
alo
n
g
with
o
p
en
wate
r
ef
f
icien
cy
(
K
T,
K
Q,
a
n
d
o
)
ar
e
d
eter
m
in
e
d
in
ad
d
itio
n
to
p
r
ess
u
r
e
co
n
to
u
r
s
o
n
th
e
b
lad
e
s
u
r
f
ac
es.
T
h
e
d
ev
iatio
n
in
s
o
lu
tio
n
h
as
b
ee
n
f
o
u
n
d
f
r
o
m
5
to
1
5
%
in
th
e
c
ase
o
f
th
r
u
s
t
an
d
1
0
t
o
2
0
%
in
th
e
ca
s
e
o
f
to
r
q
u
e.
Pre
s
s
u
r
e
esti
m
atio
n
is
u
s
u
ally
q
u
ite
ac
cu
r
ate
with
5
to
8
%
v
a
r
iatio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
10
,
No
.
1
,
Ma
r
c
h
2
0
2
1
:
20
–
27
22
2.
M
AT
H
E
M
AT
I
CA
L
F
O
RM
UL
A
T
I
O
N
2
.
1
.
G
o
v
er
nin
g
equa
t
io
ns
Fo
r
th
e
p
r
ac
tical
d
esig
n
c
o
n
s
i
d
er
atio
n
an
d
p
er
f
o
r
m
a
n
ce
a
n
aly
s
is
p
o
in
t
o
f
v
iew
em
p
ir
ica
l
r
elatio
n
s
alo
n
g
with
d
iag
r
am
s
a
r
e
p
r
esen
ted
f
o
r
B
-
s
er
ies
p
r
o
p
eller
.
T
h
e
p
ar
a
m
eter
s
co
n
tain
e
d
f
o
r
d
esig
n
o
f
a
p
r
o
p
eller
b
lad
e
in
clu
d
e
th
e
p
o
wer
d
eliv
er
ed
(
PD)
,
th
e
n
u
m
b
er
o
f
b
la
d
es
b
lad
e
ar
ea
r
atio
,
ad
v
an
ce
d
s
p
ee
d
,
n
u
m
b
e
r
o
f
p
r
o
p
eller
r
ev
o
lu
tio
n
s
p
itch
r
a
tio
an
d
th
e
d
iam
ete
r
D,
b
y
s
y
s
tem
atica
lly
ch
an
g
in
g
th
e
ad
v
an
ce
d
s
p
ee
d
o
r
p
r
o
p
eller
r
e
v
o
lu
tio
n
s
th
e
p
er
f
o
r
m
an
ce
c
h
ar
ac
ter
is
tics
ar
e
in
v
esti
g
ated
am
o
n
g
p
r
o
b
ab
le
s
o
lu
tio
n
s
.
T
h
e
v
ar
iab
le
p
ar
am
eter
s
r
ep
r
esen
tin
g
th
is
s
er
ies ar
e
th
e
p
r
o
p
eller
b
la
d
e
n
u
m
b
er
,
t
h
e
b
lad
e
a
r
ea
r
atio
,
an
d
th
e
p
itch
r
atio
.
=
∑
(
)
(
47
=
1
)
(
1
)
=
∑
(
)
(
39
=
1
)
(
2
)
T
h
e
d
im
en
s
io
n
less
ch
ar
ac
ter
is
tics
ar
e
ex
p
r
ess
ed
as
(
3
)
-
(
6
)
.
=
(
3
)
=
2
4
(
4
)
=
2
5
(
5
)
=
2
∗
(
6
)
T
h
e
W
ag
en
in
g
e
n
B
-
s
er
ies
b
ei
n
g
a
g
en
e
r
al
s
er
ies
ex
p
r
ess
ed
with
o
p
en
wate
r
d
iag
r
am
s
o
b
tain
ed
f
r
o
m
o
p
e
n
wate
r
o
r
m
o
d
el
test
s
wh
er
e
t
h
e
,
,
0
,
cu
r
v
es
ar
e
s
h
o
wed
with
c
o
n
s
tan
t
b
lad
e
n
u
m
b
er
,
b
lad
e
ar
ea
r
atio
an
d
p
itch
r
atio
s
.
2
.
2
.
F
lo
w
s
im
ula
t
io
n
T
h
e
ab
o
v
e
g
o
v
er
n
i
n
g
eq
u
atio
n
s
h
av
e
b
ee
n
co
n
v
er
te
d
to
th
e
alg
eb
r
aic
eq
u
atio
n
s
wh
ich
ca
n
b
e
s
o
lv
ed
n
u
m
er
ically
u
s
in
g
co
n
tr
o
l
v
o
l
u
m
e
tech
n
iq
u
e
o
f
Flu
en
t.
T
h
i
s
co
n
tr
o
l
v
o
lu
m
e
tech
n
i
q
u
e
c
o
n
s
is
ts
o
f
g
o
v
er
n
in
g
eq
u
atio
n
s
ab
o
u
t
ea
ch
co
n
tr
o
l
v
o
lu
m
e
y
ield
i
n
g
d
is
cr
ete
eq
u
a
tio
n
s
an
d
co
n
s
er
v
e
th
e
q
u
an
tit
ies
o
n
th
e
b
asis
o
f
co
n
tr
o
l
v
o
lu
m
e.
T
h
e
s
tan
d
ar
d
wall
f
u
n
ctio
n
s
u
s
ed
a
r
e
b
ase
d
o
n
t
h
e
p
r
o
p
o
s
al
o
f
L
au
n
d
er
an
d
s
p
an
g
lin
g
an
d
h
av
e
b
ee
n
f
o
u
n
d
q
u
ite
r
eliab
le
f
o
r
p
r
o
p
eller
f
lo
ws.
T
h
e
s
tan
d
ar
d
K
-
Ɛ
m
o
d
el
h
as b
e
en
u
s
ed
.
3.
NUM
E
RIC
AL
I
L
L
US
T
RA
T
I
O
N
T
h
e
co
m
p
u
tatio
n
al
d
o
m
ai
n
w
as
cr
ea
ted
f
o
r
th
e
s
ca
led
m
o
d
el
p
r
o
p
eller
with
a
h
u
b
s
u
r
r
o
u
n
d
ed
b
y
a
f
lu
id
d
o
m
ain
s
h
o
wn
in
Fig
u
r
e
1
(
a
)
an
d
1(
b
)
.
T
h
e
i
n
let
was
p
r
escr
ib
ed
at
3
D
u
p
s
tr
ea
m
e
x
it
at
4
D
d
o
wn
s
tr
ea
m
s
o
lid
s
u
r
f
ac
es
o
n
th
e
b
la
d
es
an
d
h
u
b
ce
n
tr
ed
at
th
e
o
r
ig
in
o
f
th
e
co
o
r
d
in
ate
s
y
s
tem
f
o
llo
w
ed
b
y
th
e
alig
n
m
en
t
with
u
n
if
o
r
m
in
f
lo
w.
A
h
y
b
r
id
m
esh
was
g
en
er
ated
in
s
id
e
th
e
d
o
m
ain
u
s
in
g
h
y
p
er
m
esh
1
1
.
0
s
h
o
wn
in
Fig
u
r
e
1
(
d
)
.
I
n
itially
th
e
b
lad
e
s
u
r
f
ac
es
wer
e
m
esh
ed
with
s
m
aller
tr
ian
g
u
lar
e
lem
en
t
wh
ile
th
e
in
n
er
r
eg
io
n
was
f
illed
ap
p
r
o
x
im
ately
with
g
r
o
win
g
tr
ia
n
g
u
lar
elem
e
n
t
an
d
f
in
ally
th
e
d
o
m
ain
r
eg
i
o
n
was
f
illed
with
tetr
ah
ed
r
al
elem
en
ts
.
T
h
e
n
u
m
b
er
o
f
ce
lls
u
s
ed
in
th
e
m
esh
is
ab
o
u
t
5
8
3
4
5
1
.
T
h
e
3
D
f
lo
w
(
v
is
co
u
s
an
d
in
co
m
p
r
ess
ib
le)
was
s
o
lv
ed
u
s
in
g
th
e
FLUE
NT
6
.
3
.
2
6
co
d
e.
T
h
e
f
lu
id
co
n
tin
u
u
m
was
ch
o
s
en
an
d
ass
ig
n
ed
with
th
e
p
r
o
p
er
ties
o
f
wate
r
.
A
m
o
v
in
g
r
ef
e
r
en
ce
f
r
a
m
e
is
ass
ig
n
ed
to
f
lu
id
wh
ich
h
as
th
e
s
am
e
r
o
tatio
n
al
v
elo
city
as
th
at
o
f
p
r
o
p
eller
.
T
h
e
wall
in
ter
f
ac
e
o
f
th
e
p
r
o
p
eller
b
lad
e
a
n
d
h
u
b
wer
e
ass
ig
n
ed
a
r
elativ
e
r
o
tatio
n
al
v
elo
city
o
f
ze
r
o
with
r
esp
ec
t
to
t
h
e
a
d
jace
n
t
ce
ll
zo
n
e
.
A
u
n
if
o
r
m
v
el
o
city
was
p
r
escr
ib
e
d
at
in
let.
T
h
e
m
ag
n
itu
d
e
o
f
v
elo
city
was
ad
ju
s
ted
to
o
b
tain
ap
p
r
o
p
r
iate
ad
v
an
ce
d
co
ef
f
icien
ts
(
J
)
.
At
o
u
tlet
o
u
tf
lo
w
bou
n
d
ar
y
co
n
d
itio
n
was
s
et.
T
h
e
f
a
r
b
o
u
n
d
ar
y
(
f
ar
-
f
ield
)
wa
s
tak
en
as
in
v
is
cid
wall
an
d
ass
ig
n
ed
an
ab
s
o
lu
te
r
o
tatio
n
al
v
elo
city
o
f
ze
r
o
.
Flu
en
t
6
.
3
.
Has
b
ee
n
u
s
ed
f
o
r
th
e
co
m
p
u
tatio
n
o
f
Flo
w
th
r
o
u
g
h
p
r
o
p
eller
(B
-
s
er
ies).
T
h
e
s
im
u
latio
n
h
as
b
ee
n
ca
r
r
ied
o
u
t
to
d
eter
m
i
n
e
th
e
p
r
o
p
eller
’
s
o
p
en
wate
r
ch
ar
ac
ter
is
tics
with
d
if
f
er
en
t
v
ar
y
in
g
ad
v
an
ce
d
r
at
io
s
in
th
e
r
an
g
e
o
f
0
.
2
to
1
.
4
as
th
e
r
eq
u
ir
em
en
t
0
f
o
r
th
e
p
e
r
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
eller
in
th
is
o
p
er
atio
n
al
r
an
g
e.
T
h
e
d
is
cr
etize
d
f
lu
id
s
t
r
u
ctu
r
e
in
ter
ac
tio
n
ca
n
b
e
s
ee
n
in
th
e
Fig
u
r
e
2
wh
er
e
th
e
p
r
o
p
eller
b
lad
e
is
s
u
r
r
o
u
n
d
ed
b
y
th
e
tetr
a
h
ed
r
al
elem
en
t.
T
h
e
p
r
ess
u
r
e
d
is
tr
ib
u
tio
n
an
d
r
o
tatio
n
al
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Ap
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in
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h
)
23
s
p
ee
d
v
ar
ia
tio
n
ac
r
o
s
s
th
e
p
r
o
p
eller
b
lad
e
ca
n
b
e
o
b
s
er
v
e
d
in
th
e
Fig
u
r
e
3
an
d
Fig
u
r
e
4
r
esp
ec
tiv
ely
.
T
h
e
co
m
p
ar
is
o
n
o
f
p
r
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tly
c
o
m
p
u
ted
h
y
d
r
o
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te
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is
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en
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ef
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icien
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(
0
)
w
ith
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at
o
f
th
e
s
tan
d
ar
d
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-
s
er
ies
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ata
ar
e
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r
e
s
en
ted
in
th
e
Fig
u
r
e
5
.
I
t
ca
n
b
e
s
ee
n
th
at
t
h
e
p
r
esen
t
h
y
d
r
o
d
y
n
a
m
ic
ch
a
r
ac
ter
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tics
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o
n
s
es
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o
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t
h
e
s
am
e
tr
e
n
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i.e
.
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lin
ea
r
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ec
r
ea
s
in
g
as
in
th
e
s
ta
n
d
ar
d
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-
s
er
ies
d
ata
af
ter
r
ea
c
h
in
g
to
th
e
6
5
%
o
f
t
h
e
ad
v
an
ce
d
co
ef
f
icie
n
t
(
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.
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h
e
v
ar
iatio
n
in
th
e
o
p
e
n
wate
r
ch
ar
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ter
is
tic
ca
n
b
e
r
ea
lis
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with
r
esp
ec
t
to
th
e
ad
v
an
ce
d
co
ef
f
icien
t
(
J
)
i
n
th
e
Fig
u
r
e
6
.
T
h
e
s
p
ec
if
icatio
n
f
o
r
t
h
e
B
-
s
er
ies
p
r
o
p
eller
a
n
d
th
e
s
o
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er
s
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g
s
f
o
r
th
e
f
lo
w
s
im
u
latio
n
ar
e
p
r
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i
n
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e
T
ab
le
1
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d
T
ab
le
2
r
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T
ab
le
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p
r
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o
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tr
a
n
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ical
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en
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r
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h
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e
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v
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ef
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icien
t
(
J
)
wh
ic
h
was
d
if
f
icu
lt
to
r
ea
lis
e
in
th
e
Fig
u
r
e
5
.
T
h
e
v
ar
iatio
n
in
th
e
o
p
en
wate
r
c
h
a
r
ac
ter
is
tics
o
f
B
-
Ser
ies
p
r
o
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eller
with
th
e
v
ar
y
in
g
r
o
tatio
n
al
s
p
ee
d
an
d
th
e
ad
v
an
ce
d
v
elo
ci
ty
is
s
h
o
wn
in
t
h
e
T
ab
le
4
an
d
T
ab
le
5
r
esp
ec
tiv
ely
.
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t
is
o
b
s
er
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ed
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at
all
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ese
r
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o
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es
s
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o
w
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ig
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ican
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d
ec
r
em
en
t
with
a
m
ar
g
i
n
al
ch
an
g
e
in
th
e
r
o
tatio
n
al
s
p
ee
d
an
d
th
e
ad
v
a
n
ce
d
v
elo
city
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
.
Dif
f
e
r
en
t v
iews a
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iatio
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[1
]
S
e
rk
a
n
EKINCI
,
“
A
P
ra
c
ti
c
a
l
Ap
p
ro
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h
fo
r
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sig
n
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f
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a
rin
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ro
p
e
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rs
wi
th
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y
ste
m
a
ti
c
P
r
o
p
e
ll
e
r
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e
ries
,”
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d
o
g
ra
d
n
j
a
–
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h
i
p
b
u
il
d
in
g
,
Z
N
ANOS
T
/
S
CIENCE
,
v
o
l.
6
2
,
n
o
.
2
,
p
p
.
1
2
3
-
1
2
9
,
2
0
1
1
.
[2
]
S
h
il
ian
g
HU
,
C
h
u
a
n
j
in
g
LU
a
n
d
Yo
u
sh
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n
g
HE
,
“
F
lu
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-
str
u
c
tu
re
i
n
tera
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ti
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n
sim
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latio
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o
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flex
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y
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ro
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ter t
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e
l
,”
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p
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a
t
h
.
M
e
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h
.
-
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n
g
l
.
E
d
.
,
v
o
l.
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,
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o
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1
,
p
p
.
1
5
–
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6
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2
0
1
6
.
[3
]
Bu
rril
l,
L
.
C.
a
n
d
Ya
n
g
,
C.
S
,
“
Th
e
Eff
e
c
t
o
f
Ra
d
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P
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h
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t
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rm
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a
M
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ra
n
sa
c
ti
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In
stit
u
ti
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v
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l
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ts,
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l.
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,
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p
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1
1
9
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[4
]
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e
ll
i
M
.
,
Ca
m
u
ss
i
R.
,
Di
F
e
li
c
e
F
,
“
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c
h
a
n
ism
s
o
f
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u
ti
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th
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ler
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n
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tran
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a
n
d
fa
re
ld
s
,”
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o
u
rn
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l
o
f
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u
id
M
e
c
h
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n
ics
,
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o
l
.
5
,
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o
.
2
,
p
p
.
6
8
2
-
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9
5
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1
.
[5
]
M
ih
a
e
la,
A
,
“
De
v
e
lo
p
m
e
n
ts
i
n
t
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sig
n
o
f
sh
ip
p
ro
p
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r
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n
sa
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ti
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n
ics
,
Un
ive
rs
it
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o
f
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la
ti
,
2
0
0
5
.
[6
]
M
iy
a
ta
H
,
“
Ti
m
e
-
m
a
rc
h
in
g
CF
D
sim
u
latio
n
f
o
r
m
o
v
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n
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b
o
u
n
d
a
r
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p
r
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b
lem
s
,”
21
st
S
y
mp
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siu
m
o
n
N
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v
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l
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d
ro
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y
n
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mic
s
,
Tro
n
d
h
e
im,
No
r
wa
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,
1
9
9
6
.
[7
]
S
u
b
h
a
s
S
.
,
S
a
ji
V.F
.
,
Ra
m
a
k
rish
n
a
S
.
,
Da
s
H.N
,
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D
a
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l
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sis
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f
p
ro
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ter
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ti
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l
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n
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l
.
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,
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,
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p
.
26
-
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,
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0
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.
[8
]
M
a
rti
n
e
z
,
J.,
Ba
lb
o
n
a
Ca
lv
o
,
L
.
,
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o
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z
a
lez
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é
r
e
z
,
J.,
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c
o
M
a
rig
o
rta
E
,
“
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Op
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n
Wate
r
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m
e
rica
l
M
o
d
e
l
fo
r
A
M
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rin
e
P
ro
p
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ll
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r:
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Co
m
p
a
riso
n
with
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x
p
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rime
n
tal
Da
ta
,”
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u
i
d
s
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g
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n
e
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rin
g
S
u
mm
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r
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n
fer
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e
,
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o
n
trea
l,
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n
a
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,
2
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0
2
.
[9
]
Bra
n
d
t
J.B
.
,
S
e
li
g
M
.
S
,
“
P
ro
p
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r
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rfo
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Da
ta
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t
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Re
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n
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ld
s
N
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m
b
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rs
,”
49
th
AI
AA
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o
sp
a
c
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c
ien
c
e
s
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e
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ti
n
g
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,
1
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1
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2
5
5
,
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n
d
o
,
F
L,
U
S
A
,
2
0
1
1
.
[1
0
]
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n
in
i
E
,
“
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ig
n
ifi
c
a
n
c
e
o
f
b
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t
th
e
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n
c
e
p
re
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n
o
f
m
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rin
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p
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p
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ll
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,”
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e
a
n
En
g
i
n
e
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rin
g
,
v
o
l.
31
,
n
o
.
9
,
p
p
.
9
5
7
–
9
7
4
,
2
0
0
4
.
[1
1
]
Weic
k
F
.
E
,
“
F
u
ll
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c
a
le
Wi
n
d
Tu
n
n
e
l
Tes
ts
with
a
S
e
ries
o
f
P
ro
p
e
ll
e
rs
o
f
Diffe
re
n
t
Dia
m
e
ters
o
n
a
S
in
g
le
F
u
se
lag
e
,”
NACA
Re
p
.
v
ol
.
8
,
n
o
.
4
,
p
p
.
3
3
9
-
3
5
1
,
1
9
3
0
.
[1
2
]
Weic
k
F
.
E
,
“
F
u
ll
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c
a
le
Wi
n
d
T
u
n
n
e
l
Tes
ts
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n
S
e
v
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ra
l
M
e
tal
P
r
o
p
e
ll
e
rs
Ha
v
i
n
g
Diffe
re
n
t
Blad
e
F
o
rm
s
,”
NACA
Rep
.
,
v
ol
.
13
,
n
o
.
7
,
p
p
.
3
3
9
-
3
5
1
,
1
9
3
0
.
[1
3
]
Ju
stin
,
E
,
“
M
a
ri
n
e
p
ro
p
e
ll
e
rs
,”
An
n
u
a
l
Rev
iew
o
f
Fl
u
id
M
e
c
h
a
n
ics
,
v
o
l.
18
,
n
o
.
6
,
p
p
.
3
6
7
-
4
0
3
,
1
9
8
6
.
[1
4
]
Va
len
ti
n
e
D.T
,
“
Re
y
n
o
ld
s
-
a
v
e
r
a
g
e
d
Na
v
ier
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sto
k
e
s
c
o
d
e
s
a
n
d
m
a
rin
e
p
ro
p
u
lso
r
a
n
a
l
y
sis
,”
Hy
d
ro
d
y
n
a
mic
s
Dire
c
to
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te
Res
e
a
rc
h
a
n
d
De
v
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lo
p
me
n
t
Rep
o
rt
,
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rd
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ro
c
k
Div
is
io
n
,
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v
a
l
S
u
rfa
c
e
Warfa
c
e
Ce
n
tre,
Be
th
e
sd
a
,
M
D.,
USA
1
9
9
3
.
[1
5
]
Ke
rwin
J.E
.
a
n
d
Lee
C.
S
,
“
P
re
d
ictio
n
o
f
S
tea
d
y
a
n
d
Un
ste
a
d
y
M
a
ri
n
e
P
ro
p
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ll
e
r
P
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rm
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n
c
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b
y
Nu
m
e
rica
l
Li
fti
n
g
-
S
u
rfa
c
e
Th
e
o
r
y
,”
T
ra
n
sa
c
ti
o
n
S
N
AM
E
,
v
o
l.
86
,
n
o
.
4
,
p
p
.
2
1
8
–
2
5
3
,
1
9
7
8
.
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27
[1
6
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S
trec
k
wa
ll
H
,
“
A
M
e
th
o
d
to
P
r
e
d
ict
th
e
Ex
te
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t
o
f
Ca
v
it
a
ti
o
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a
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ll
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rs
b
y
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ft
in
g
-
su
rfa
c
e
-
th
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ry
,”
In
ter
n
a
t
io
n
a
l
S
y
mp
o
si
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m o
n
C
a
v
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ti
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n
,
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e
n
d
a
i
,
J
a
p
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n
,
1
9
8
6
.
[1
7
]
Kim
H.
T.
a
n
d
S
tern
F
,
“
Visc
o
u
s
f
lo
w
a
ro
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n
d
a
p
r
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e
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sh
a
ft
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o
n
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ig
u
ra
ti
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n
fin
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e
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p
it
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h
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c
tan
g
u
lar
b
lad
e
s
,”
J
o
u
rn
a
l
o
f
Pro
p
u
lsi
o
n
,
v
o
l.
13
,
n
o
.
6
,
p
p
.
4
3
4
–
4
4
3
,
1
9
9
0
.
[1
8
]
G
h
a
ss
e
m
i
H.
a
n
d
G
h
a
d
imi
P
,
“
Co
m
p
u
tati
o
n
a
l
h
y
d
r
o
d
y
n
a
m
ic
a
n
a
ly
sis
o
f
th
e
p
ro
p
e
ll
e
r
–
r
u
d
d
e
r
a
n
d
t
h
e
AZIP
OD
sy
ste
m
s
,”
Oc
e
a
n
En
g
i
n
e
e
rin
g
,
v
o
l.
34
,
n
o
.
6
,
p
p
.
1
1
7
–
1
3
0
,
2
0
0
7
.
[1
9
]
G
h
a
ss
e
m
i
H
,
“
Th
e
e
ffe
c
t
o
f
wa
k
e
flo
w
a
n
d
s
k
e
w
a
n
g
le
o
n
t
h
e
sh
ip
p
r
o
p
e
ll
e
r
p
e
rfo
rm
a
n
c
e
,”
S
c
ien
t
ia
Ira
n
ica
,
v
o
l.
16
,
n
o
.
2
,
p
p
.
1
4
9
–
1
5
8
,
2
0
0
9
.
[2
0
]
G
h
a
ss
e
m
i
H
,
“
Hy
d
ro
d
y
n
a
m
ic
p
e
rfo
rm
a
n
c
e
o
f
c
o
a
x
ial
c
o
n
tra
-
r
o
ta
ti
n
g
p
r
o
p
e
ll
e
r
[CCRP
]
fo
r
larg
e
sh
ip
s
,”
P
o
li
s
h
M
a
riti
me
Res
e
a
rc
h
,
v
o
l.
16
,
n
o
.
5
9
,
p
p
.
2
2
–
2
8
,
2
0
0
9
.
[2
1
]
G
h
a
ss
e
m
i
H
,
“
Hy
d
ro
d
y
n
a
m
ic
c
h
a
ra
c
teristics
o
f
th
e
su
rfa
c
e
-
p
ierc
i
n
g
p
r
o
p
e
ll
e
rs
fo
r
t
h
e
p
lan
n
i
n
g
c
r
a
ft
,”
J
o
u
rn
a
l
o
f
M
a
rin
e
S
c
ien
c
e
a
n
d
Ap
p
li
c
a
ti
o
n
,
v
o
l.
11
,
n
o
.
7
,
p
p
.
1
4
7
–
1
5
6
,
2
0
0
8
.
[2
2
]
G
h
a
ss
e
m
i
H,
G
h
a
s
sa
b
z
a
d
e
h
M
,
a
n
d
S
a
r
y
a
z
d
i
M
G
,
“
Eff
e
c
t
o
f
m
a
teria
l
o
n
h
y
d
r
o
-
e
las
ti
c
b
e
h
a
v
io
u
r
o
f
m
a
rin
e
p
ro
p
e
ll
e
r
b
y
u
si
n
g
B
EM
-
F
E
M
h
y
b
rid
s
o
ftwa
re
,”
Po
li
s
h
M
a
riti
me
R
e
se
a
rc
h
,
v
o
l
.
20
,
n
o
.
9
,
p
p
.
62
-
70
,
2
0
1
3
.
[2
3
]
Yo
u
n
g
Y.L
.
F
lu
i
d
-
stru
c
t
u
re
in
ter
a
c
ti
o
n
a
n
a
ly
sis
o
f
fle
x
ib
le
c
o
m
p
o
site
m
a
rin
e
p
ro
p
e
ll
e
rs
,”
J
o
u
r
n
a
l
o
f
Fl
u
i
d
s
a
n
d
S
tru
c
tu
re
s
,
v
o
l
.
24
,
n
o
.
1
3
,
p
p
.
799
-
8
1
8
,
2
0
0
8
,
[2
4
]
Yo
u
n
g
,
Y
.
L.
An
d
S
a
v
a
n
d
e
r
BR
,
“
Nu
m
e
rica
l
a
n
a
ly
sis
o
f
la
rg
e
-
sc
a
le
su
rfa
c
e
-
p
ierc
in
g
p
r
o
p
e
ll
e
rs
,”
Oc
e
a
n
En
g
i
n
e
e
rin
g
,
v
o
l.
38
,
n
o
.
1
3
,
p
p
.
1
3
6
8
–
1
3
8
1
,
2
0
1
1
.
[2
5
]
Dy
m
a
rsk
i
P
,
“
Co
m
p
u
tati
o
n
s
o
f
t
h
e
p
r
o
p
e
ll
e
r
o
p
e
n
wa
ter
c
h
a
ra
c
t
e
risti
c
s
u
sin
g
th
e
S
OLAG
A
c
o
m
p
u
ter
p
r
o
g
ra
m
,
P
re
d
ictio
n
s o
f
th
e
c
a
v
it
a
ti
o
n
p
h
e
n
o
m
e
n
o
n
,
Arc
h
ive
s o
f
Civil
a
n
d
M
e
c
h
a
n
i
c
a
l
En
g
i
n
e
e
rin
g
,
v
o
l.
8
,
n
o
.
1
1
,
2
0
0
8
.
[2
6
]
P
ra
k
a
sh
S
.
a
n
d
S
u
b
ra
m
a
n
ian
VA
,
“
S
imu
lati
o
n
o
f
p
r
o
p
e
ll
e
r
-
h
u
ll
i
n
tera
c
ti
o
n
u
si
n
g
RAN
S
E
so
lv
e
r
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Oc
e
a
n
a
n
d
Cli
m
a
te S
y
ste
ms
,
v
o
l.
1
,
n
o
.
3
,
p
p
.
1
8
9
-
2
0
3
,
2
0
0
9
.
[2
7
]
Da
s
H.N
,
“
CF
D
An
a
ly
sis
f
o
r
c
a
v
it
a
ti
o
n
o
f
a
M
a
ri
n
e
P
r
o
p
e
ll
e
r
,”
8
th
sy
mp
o
si
u
m
o
n
Hi
g
h
sp
e
e
d
M
a
rin
e
Veh
icle
s
,
Na
p
les
,
Italy
,
2
0
0
8
.
[2
8
]
Da
s
H.N.,
Ja
y
a
k
u
m
a
r
L
.
C.
P
,
“
C
o
m
p
u
tati
o
n
a
l
p
re
d
ictio
n
a
n
d
E
x
p
e
rime
n
tal
v
a
li
d
a
ti
o
n
o
f
th
e
Ch
a
r
a
c
teristics
o
f
a
c
o
n
tra ro
tatin
g
p
r
o
p
e
ll
e
r
,”
NR
B
se
min
a
r
o
n
M
a
r
i
n
e
Hy
d
ro
d
y
n
a
mic
s
,
Visa
k
h
a
p
a
t
n
a
m
,
In
d
ia,
2
0
0
2
.
[2
9
]
Ba
n
e
rjee
CN,
Da
s
HN
a
n
d
S
ris
u
d
h
a
B
,
“
Co
m
p
u
tati
o
n
a
l
a
n
a
ly
si
s
a
n
d
e
x
p
e
rime
n
tal
v
a
li
d
a
ti
o
n
o
f
h
u
l
l
p
ro
p
u
lso
r
in
tera
c
ti
o
n
fo
r
a
n
a
u
t
o
n
o
m
o
u
s
u
n
d
e
rwa
ter v
e
h
icle
(AU
V)
,”
7
th
Asi
a
n
CFD
C
o
n
fer
e
n
c
e
,
Ba
n
g
a
lo
re
,
I
n
d
ia
,
2
0
0
7
.
[3
0
]
Krish
n
a
G
V,
S
a
ji
VF,
Da
s
HN
,
a
n
d
P
a
n
i
g
ra
h
i
P
K
,
“
Ac
o
u
stic
C
h
a
ra
c
teriz
a
ti
o
n
o
f
a
Be
n
c
h
m
a
rk
M
a
rin
e
p
ro
p
e
ll
e
r
u
sin
g
CF
D
,”
Na
v
a
l
S
y
mp
o
si
u
m o
n
Aco
u
stics
(NS
A),
Visa
k
h
a
p
a
t
n
a
m
,
In
d
ia,
2
0
0
8
.
[3
1
]
Kra
sin
ik
o
v
V,
Z
h
a
n
g
Z
a
n
d
H
o
n
g
F
.
A
n
a
ly
sis
o
f
Un
ste
a
d
y
P
r
o
p
e
l
ler
Blad
e
F
o
rc
e
s
b
y
RAN
S
,”
1
st
In
ter
n
a
ti
o
n
a
l
sy
mp
o
siu
m o
n
M
a
ri
n
e
Pro
p
u
ls
o
rs
,
Tro
n
d
h
e
im,
No
rwa
y
,
2
0
0
9
.
[3
2
]
S
u
b
ra
m
a
n
ian
VA
a
n
d
S
e
n
t
h
il
P
M
N
,
“
Bo
d
y
f
o
rc
e
-
b
a
se
d
sim
u
lati
o
n
o
f
p
ro
p
e
l
ler
h
u
ll
i
n
tera
c
ti
o
n
,”
3
rd
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
in
Oc
e
a
n
\
E
n
g
i
n
e
e
rin
g
,
IIT
M
a
d
ra
s,
Ch
e
n
n
a
i,
In
d
ia
,
2
0
0
9
.
[3
3
]
Kim
u
ra
K,
Ka
wa
m
u
ra
T,
Hu
a
n
g
Z,
F
u
ji
A
a
n
d
Tak
e
tan
i
T
,
“
S
t
u
d
y
o
n
u
n
ste
a
d
y
c
a
v
it
a
t
in
g
flo
w
si
m
u
latio
n
a
r
o
u
n
d
m
a
rin
e
p
ro
p
e
ll
e
r
u
sin
g
a
RAN
S
C
F
D co
d
e
,”
7
th
In
ter
n
a
ti
o
n
a
l
S
y
mp
o
siu
m
o
n
C
a
v
it
a
t
io
n
,
An
n
Ar
b
o
r,
M
I
,
2
0
0
9
.
[3
4
]
Tak
a
sh
i.
K.,
J
u
n
A
,
“
Nu
m
e
rica
l
a
n
a
ly
sis
o
f
ste
a
d
y
a
n
d
u
n
ste
a
d
y
sh
e
e
t
c
a
v
it
a
ti
o
n
o
n
a
m
a
rin
e
p
r
o
p
e
ll
e
r
u
si
n
g
a
sim
p
le
su
rfa
c
e
p
a
n
e
l
m
e
th
o
d
S
Q
CM
,”
1
st
In
ter
n
a
ti
o
n
a
l
sy
mp
o
si
u
m
o
n
M
a
ri
n
e
p
ro
p
u
lsi
o
n
s,
Tro
n
d
h
e
im,
No
rwa
y
,
2
0
0
9
.
[3
5
]
Ch
o
o
n
g
W.
H.,
Ye
o
K.B
.
,
Tam
iri
F
.
a
n
d
Te
o
K.T
.
K
,
“
Ou
t
b
o
a
r
d
m
a
rin
e
p
ro
p
e
ll
e
r
p
e
rfo
rm
a
n
c
e
a
n
a
ly
s
is t
h
ro
u
g
h
CF
D
m
o
d
e
li
n
g
,”
15
th
I
n
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
C
o
mp
u
ter
M
o
d
e
ll
i
n
g
a
n
d
S
im
u
la
ti
o
n
,
Ca
m
b
ri
d
g
e
,
U
.
K.
2
0
1
3
[3
6
]
M
a
d
a
c
i
M
.
a
n
d
Ke
rd
o
u
n
D
,
“
A
CF
D
S
tu
d
y
wit
h
F
u
z
z
y
Lo
g
ic
P
i
tch
An
g
le
T
u
rb
i
n
e
Co
n
tro
l
Im
p
l
e
m
e
n
tatio
n
fo
r
OWC
Ge
n
e
ra
ti
o
n
S
y
ste
m
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
A
d
v
a
n
c
e
s
in
Ap
p
li
e
d
S
c
ien
c
e
s
(IJ
AA
S
)
,
v
o
l.
6
,
n
o
.
2
,
p
p
.
1
7
5
-
184
,
2
0
1
7
.
[
3
7
]
Da
s
H.N.
a
n
d
Ka
p
u
r
ia
S
,
“
On
th
e
u
se
o
f
b
e
n
d
–
twist
c
o
u
p
li
n
g
in
fu
l
l
-
sc
a
le
c
o
m
p
o
site
m
a
rin
e
p
r
o
p
e
ll
e
rs
f
o
r
imp
ro
v
i
n
g
h
y
d
r
o
d
y
n
a
m
ic p
e
rfo
r
m
a
n
c
e
,”
J
o
u
rn
a
l
o
f
F
lu
i
d
s a
n
d
S
t
ru
c
tu
re
s
,
v
o
l.
11
,
n
o
.
6
,
p
p
.
1
1
3
2
–
1
5
3
,
2
0
1
1
.
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