22
9/2026in
s
tal
.
pc
z
.
pl
W
o
d
o
c
i
ąg
i
i
k
a
n
a
li
z
a
c
j
a
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a
t
e
r
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u
pp
l
y
a
n
d
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e
w
age
syst
em
s
N
u
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ri
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c
o
mpa
r
a
t
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v
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a
n
a
l
ys
i
s
of
t
h
e
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r
g
y c
onv
e
rs
i
on
p
r
o
c
e
ss
i
n
a
s
em
i
-
o
pe
n
a
n
d
c
l
o
s
ed
i
mpe
ll
e
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of
a
c
e
n
t
ri
fu
ga
l
p
u
mp
N
u
me
r
yc
z
n
a
a
n
a
li
z
a
p
o
r
ó
w
n
a
wc
z
a
p
r
z
eb
i
eg
u
k
on
w
e
r
s
ji
e
n
e
r
g
ii
w w
ir
n
i
k
u
p
ó
ł
o
tw
a
r
ty
m
i
z
am
k
n
i
ę
ty
m
p
o
mp
y
o
d
ś
r
o
d
k
o
w
e
j
KO
NRA
D
B
A
BU
L
,
AN
D
R
Z
E
J
KO
C
HM
AŃS
K
I
,
PALAC
K
S
O
N
E
V
O
N
G
XA
Y
ALAT
H,
T
OM
AS
Z
DĘ
B
S
K
I
D
O
I
:
10
.
17512/
I
NST
AL.
2026
.
09
.
01
n
The article pre
s
ent
s
a numerical c
o
mparative anal
y
s
i
s
o
f the energ
y
c
o
nver
s
i
o
n pr
o
ce
ss
in
s
emi-
o
pen and cl
o
s
ed
impeller
s
o
f a centrifugal pump,
w
h
o
s
e blade
s
y
s
tem
s
w
ere de
s
igned f
o
r identical
o
perating c
o
nditi
o
n
s
.
B
a
s
ed
o
n C
F
D
s
imulati
o
n
s
, the fl
ow
s
tructure, pre
ss
ure di
s
tributi
o
n, and vel
o
cit
y
field
s
w
ere anal
y
z
ed f
o
r b
o
th de
s
ign c
o
nfigurati
o
n
s
.
The re
s
ult
s
indicate that v
o
rtical regi
o
n
s
devel
o
p in the
s
emi-
o
pen impeller, leading t
o
s
ignificant energ
y
l
o
ss
e
s
, prima-
ril
y
due t
o
a
x
ial clearance
.
The de
s
ign
o
f the cl
o
s
ed impeller enable
s
higher
o
utlet vel
o
citie
s
, greater head, and impr
o
ved
efficienc
y
b
y
reducing h
y
draulic l
o
ss
e
s
and
s
tabili
z
ing fl
ow
c
o
nditi
o
n
s
.
A
t the n
o
minal fl
ow
rate (
Q
=
500 dm³/min),
the intr
o
ducti
o
n
o
f an a
x
ial clearance
o
f 0,5 mm re
s
ulted in an appr
o
x
imatel
y
11
%
reducti
o
n in head and
a decrea
s
e in h
y
draulic efficienc
y
o
f m
o
re than 6
%
.
F
urtherm
o
re, the
s
e difference
s
bec
o
me increa
s
ingl
y
pr
o
n
o
unced
a
s
the fl
ow
rate decrea
s
e
s
f
o
r the anal
y
z
ed impeller c
o
nfigurati
o
n
s
.
The
s
tud
y
c
o
nfirm
s
the u
s
efulne
ss
o
f numerical
meth
o
d
s
f
o
r anal
y
z
ing detailed fl
ow
phen
o
mena and dem
o
n
s
trate
s
the
s
ignificant impact
o
f impeller de
s
ign
o
n energ
y
c
o
nver
s
i
o
n efficienc
y
in centrifugal pump
s
.
Ke
ywo
rd
s
:
centrifugal pump,
s
emi-
o
pen impeller, cl
o
s
ed impeller, numerical anal
y
s
i
s
, C
F
D
n
A
rt
yk
uł pr
z
ed
s
ta
w
ia numer
y
c
z
ną anali
z
ę p
o
r
ów
na
w
c
z
ą pr
o
ce
s
u
ko
n
w
er
s
ji energii
w
w
irni
k
u p
ó
ł
o
t
w
art
y
m i
z
am
k
nięt
y
m
p
o
mp
y
o
d
ś
r
o
d
kow
ej,
k
t
ó
r
y
ch u
k
ład
y
ł
o
pat
kow
e
z
o
s
tał
y
z
apr
o
je
k
t
ow
ane dla ident
y
c
z
n
y
ch
w
arun
ków
prac
y.
Na p
o
d
s
ta
w
ie
s
y
mulacji C
F
D
pr
z
eanali
z
ow
an
o
s
tru
k
turę pr
z
epł
yw
u, r
o
z
k
ład ci
ś
nienia
o
ra
z
p
o
la pręd
ko
ś
ci dla
o
bu
r
o
z
w
ią
z
ań
ko
n
s
tru
k
c
y
jn
y
ch
.
U
z
y
s
k
ane
wy
ni
k
i
w
s
k
a
z
ują,
ż
e
w
w
irni
k
u p
ó
ł
o
t
w
art
y
m p
ow
s
tają
o
b
s
z
ar
y
w
ir
ow
e,
k
t
ó
r
y
ch
s
k
ut
k
iem
s
ą
z
nac
z
ne
s
trat
y
energii,
wy
ni
k
ające gł
ów
nie
z
o
becn
o
ś
ci
s
z
c
z
elin
y
o
s
i
ow
ej
.
K
o
n
s
tru
k
cja
w
irni
k
a
z
am
k
nięteg
o
p
o
z
w
ala
o
s
iągnąć
wy
ż
s
z
e pręd
ko
ś
ci na
wy
l
o
cie,
w
ię
k
s
z
ą
wy
s
oko
ś
ć p
o
dn
o
s
z
enia
o
ra
z
wy
ż
s
z
ą
s
pra
w
n
o
ś
ć d
z
ię
k
i
o
granic
z
eniu
s
trat h
y
draulic
z
n
y
ch i bard
z
iej
s
tabiln
y
m
w
arun
ko
m pr
z
epł
yw
u
.
W efe
k
cie
w
pr
ow
ad
z
enia
s
z
c
z
elin
y
o
s
i
o
-
w
ej
o
w
art
o
ś
ci 0,5 mm, pr
z
y
n
o
minaln
y
m natę
ż
eniu pr
z
epł
yw
u (
Q
=
500 dm³/min), d
o
s
z
ł
o
d
o
ok.
11
%
s
pad
k
u
wy
s
oko
ś
ci p
o
dn
o
s
z
enia
o
ra
z
p
o
nad 6
%
s
pad
k
u
s
pra
w
n
o
ś
ci
.
Jedn
o
c
z
e
ś
nie
z
au
w
a
ż
o
n
o
,
ż
e im pr
z
epł
yw
je
s
t mniej
s
z
y
,
t
y
m te r
ó
ż
nice
s
ą
z
nac
z
nie
w
ię
k
s
z
e dla
o
bu t
y
p
ów
w
irni
ków.
Pr
z
epr
ow
ad
z
o
ne badania p
o
t
w
ierd
z
ają pr
z
y
datn
o
ś
ć
met
o
d numer
y
c
z
n
y
ch
w
anali
z
ie
s
z
c
z
eg
ó
ł
owy
ch
z
ja
w
i
s
k
pr
z
epł
ywowy
ch
o
ra
z
wyk
a
z
ują i
s
t
o
tn
y
w
pł
yw
ko
n
s
tru
k
cji
w
irni
k
a na efe
k
t
yw
n
o
ś
ć
ko
n
w
er
s
ji energii
w
p
o
mpach
o
d
ś
r
o
d
kowy
ch
.
Sł
ow
a
k
luc
z
ow
e
:
p
o
mpa
o
d
ś
r
o
d
kow
a,
w
irni
k
p
ó
ł
o
t
w
art
y
,
w
irni
k
z
am
k
nięt
y
, anali
z
a numer
y
c
z
na, C
F
D
dr in
ż
.
K
o
nrad
B
abul
O
R
C
I
D:
0000-0003-2719-3247, Katedra
I
n
ż
y
nierii K
o
n
w
er
s
ji
E
nergii, W
y
d
z
iał
M
echanic
z
n
o
-
E
nerget
y
c
z
n
y
, P
o
litechni
k
a
Wr
o
cła
w
s
k
a, C
o
rre
s
p
o
nding auth
o
r
:
e-mail
:
ko
nrad
.
babul
@
p
w
r
.
edu
.
pl; mgr in
ż
.
A
ndr
z
ej K
o
chmań
s
k
i
O
R
C
I
D:
0009-0007-5352-2004,
A
b
s
o
l
w
ent P
o
litechni
k
i Wr
o
cła
w
s
k
iej,
I
n
s
pe
k
t
o
r ur
z
ąd
z
eń ci
ś
nieni
owy
ch
w
Ur
z
ęd
z
ie
Do
z
o
ru Technic
z
neg
o
(U
D
T),
D
epartament
E
nerget
yk
i Jądr
ow
ej U
D
T,
e-mail
:
andr
z
ej
.ko
chman
s
k
i
@
udt
.
g
o
v
.
pl; mgr in
ż
.
Palac
k
s
o
ne V
o
ng
x
a
y
alath
O
R
C
I
D:
0009-0002-3632-8836, W
y
d
z
iał
M
echanic
z
n
o
-
E
nerget
y
c
z
n
y
,
P
o
litechni
k
a Wr
o
cła
w
s
k
a, e-mail
:
270310
@
s
tudent
.
p
w
r
.
edu
.
pl; in
ż
.
T
o
ma
s
z
D
ęb
s
k
i
O
R
C
I
D:
0009-0001-8837-7149,
W
y
d
z
iał
M
echanic
z
n
o
-
E
nerget
y
c
z
n
y
, P
o
litechni
k
a Wr
o
cła
w
s
k
a, e-mail
:
t
o
me
k
d0
@o
2
.
pl
D
ata zgło
s
zenia: 13.05.2026.
D
ata p
r
z
y
jęcia: 26.08.2026.
D
ata publi
k
acji: 22.09.2026
I
n
t
r
o
d
u
ct
i
on
A
dvance
s
in material
s
engineering and
c
o
mputati
o
nal
s
o
ft
w
are enable de
s
ign and
o
perati
o
nal impr
o
vement
s
in ne
w
l
y
devel
o
-
ped machine
s
and equipment
.
A
dditi
o
nall
y
,
numerical fl
ow
s
imulati
o
n
s
s
ignificantl
y
reduce the time and c
o
s
t
s
a
ss
o
ciated
w
ith
the de
s
ign and implementati
o
n pha
s
e
s
o
f
a pr
o
duct
.
I
nput data f
o
r equipment de
s
ign
re
s
ult directl
y
fr
o
m the equipment’
s
o
pera-
ting c
o
nditi
o
n
s
and e
x
pected perf
o
rmance
characteri
s
tic
s
.
I
n pump engineering, al
o
ng
s
ide univer-
s
al
s
o
luti
o
n
s
, highl
y
applicati
o
n-
s
pecific
de
s
ign
s
are al
s
o
quite c
o
mm
o
n
.
Pumping
w
ater c
o
ntaining
s
o
lid particle
s
s
uch a
s
gra
ss
, algae,
o
r
s
and require
s
appr
o
priate-
l
y
de
s
igned h
y
draulic channel
s
in the pump
s
ecti
o
n t
o
en
s
ure ma
x
imum
o
perati
o
nal
reliabilit
y
o
f the entire unit
.
F
o
r c
o
ntaminated
liquid
s
, vari
o
u
s
s
emi-
o
pen impeller de
s
ign
s
are m
o
s
t c
o
mm
o
nl
y
u
s
ed,
w
ith their
s
tructure
directl
y
determined b
y
the pr
o
pertie
s
o
f the
pumped medium
.
The meth
o
d
o
l
o
g
y
f
o
r
s
ha-
ping the fl
ow
channel in the meridi
o
nal
cr
o
ss
-
s
ecti
o
n i
s
de
s
cribed in c
o
n
s
iderable
detail in the literature
.
A
lth
o
ugh m
o
s
t
s
tudie
s
date bac
k
t
o
the 1960
s
and 1970
s
[
1-4
]
,
the c
o
mputati
o
nal alg
o
rithm ha
s
n
o
t been
updated and c
o
ntinue
s
t
o
be
s
ucce
ss
full
y
u
s
ed in impeller de
s
ign
.
Than
k
s
t
o
the
w
ide-
s
pread availabilit
y
o
f c
o
mputati
o
nal
s
o
ft
w
a-
re
–
either unavailable
o
r limited at the time
w
hen m
o
s
t te
x
tb
ook
s
o
n centrifugal pump
de
s
ign
w
ere
w
ritten
–
it ha
s
bec
o
me p
o
ss
i-
ble t
o
aut
o
mate the
s
e alg
o
rithm
s
t
o
increa
s
e
efficienc
y
in the devel
o
pment
o
f engineering
de
s
ign
s
.
23
in
s
tal
.
pc
z
.
pl
9/2026
W
o
d
o
c
i
ąg
i
i
k
a
n
a
li
z
a
c
j
a
The available literature lac
k
s
detailed
alg
o
rithm
s
f
o
r calculating
s
emi-
o
pen impel-
ler
s
that acc
o
unt f
o
r all their de
s
ign feature
s
,
s
uch a
s
the a
x
ial clearance bet
w
een
the impeller and the ca
s
ing fr
o
nt
w
all
.
Neverthele
ss
, current
s
cientific re
s
earch,
ba
s
ed in part
o
n numerical fl
ow
s
imulati
o
n
s
,
aim
s
t
o
e
x
plain the de
s
ign relati
o
n
s
hip
s
bet
w
een the impeller and the pump perf
o
r-
mance parameter
s
achieved
[
5-8
].
I
n the available literature
o
n centrifugal
pump de
s
ign,
s
tudie
s
f
o
cu
s
ing
o
n
s
emi--
o
pen and cl
o
s
ed impeller
s
are t
y
picall
y
c
o
nducted
s
eparatel
y
,
w
ith empha
s
i
s
pla-
ced
o
n their individual h
y
draulic perf
o
rman-
ce, fl
ow
s
tructure
s
,
o
r applicati
o
n-
s
pecific
advantage
s
.
D
irect c
o
mparative anal
y
s
e
s
o
f
the
s
e t
wo
impeller c
o
nfigurati
o
n
s
under
identical
o
perating and ge
o
metric c
o
ndi-
ti
o
n
s
remain relativel
y
s
carce
.
M
o
s
t publi-
s
hed
wo
r
k
s
addre
ss
s
elected a
s
pect
s
,
s
uch
a
s
the influence
o
f clearance, blade ge
o
me-
tr
y
,
o
r multipha
s
e fl
ow
behavi
o
r, rather than
pr
o
viding a c
o
mprehen
s
ive evaluati
o
n
o
f
the energ
y
c
o
nver
s
i
o
n pr
o
ce
ss
in b
o
th de
s
i-
gn
s
.
A
s
a re
s
ult, there i
s
a n
o
ticeable gap in
the literature
o
n
s
y
s
tematic inve
s
tigati
o
n
s
that
wo
uld enable a clear and c
o
n
s
i
s
tent
a
ss
e
ss
ment
o
f difference
s
in energ
y
-tran
s
fer
mechani
s
m
s
and a
ss
o
ciated h
y
draulic
l
o
ss
e
s
bet
w
een
s
emi-
o
pen and cl
o
s
ed
impeller
s
.
A
lth
o
ugh limited in number,
s
everal
s
tu-
die
s
have attempted t
o
addre
ss
s
elected
a
s
pect
s
o
f the c
o
mpari
s
o
n bet
w
een
s
emi--
o
pen and cl
o
s
ed impeller
s
.
F
o
r in
s
tance,
Ay
ad et al
.
[
9
]
dem
o
n
s
trated that increa
s
ing
a
x
ial clearance in
s
emi-
o
pen impeller
s
inten
s
ifie
s
lea
k
age fl
ow
s
, re
s
ulting in a n
o
ti-
ceable reducti
o
n in head and
o
verall effi-
cienc
y
, thereb
y
highlighting the direct rela-
ti
o
n
s
hip bet
w
een ge
o
metric feature
s
and
h
y
draulic l
o
ss
e
s
.
Several
s
tudie
s
referenced
in
[
9
]
pr
o
vided a c
o
mparative C
F
D
-ba
s
ed
evaluati
o
n
o
f different impeller t
y
pe
s
, indi-
cating that cl
o
s
ed impeller
s
generall
y
achieve higher efficienc
y.
A
t the
s
ame time,
s
emi-
o
pen c
o
nfigurati
o
n
s
e
x
hibit greater
r
o
bu
s
tne
ss
under challenging
o
perating
c
o
nditi
o
n
s
, particularl
y
in multipha
s
e fl
ow
s
.
A
dditi
o
nall
y
,
s
tudie
s
s
uch a
s
th
o
s
e rep
o
rted
in
[
10
]
empha
s
i
z
e difference
s
in internal
fl
ow
s
tructure
s
, including turbulence inten
s
i-
t
y
and
s
ec
o
ndar
y
fl
ow
devel
o
pment,
w
hich
further influence perf
o
rmance characteri-
s
tic
s
.
R
ecent
s
tudie
s
c
o
nfirm that re
s
earch
o
n
centrifugal pump impeller
s
remain
s
an acti-
ve and ev
o
lving field, particularl
y
regarding
s
emi-
o
pen impeller c
o
nfigurati
o
n
s
.
Current
inve
s
tigati
o
n
s
increa
s
ingl
y
c
o
mbine advan-
ced C
F
D
technique
s
w
ith e
x
perimental vali-
dati
o
n t
o
anal
y
z
e the effect
s
o
f blade ge
o
-
metr
y
, tip clearance, er
o
s
i
o
n mechani
s
m
s
,
and c
o
mple
x
fl
ow
s
tructure
s
.
M
an
s
o
ur and
Thévenin
[
11
]
e
x
perimentall
y
and numeri-
call
y
inve
s
tigated the influence
o
f blade t
w
i-
s
ting and tip clearance
o
n the perf
o
rmance
o
f a centrifugal pump
o
perating under
air
–
w
ater t
wo
-pha
s
e fl
ow
c
o
nditi
o
n
s
, pr
o
-
viding valuable validati
o
n data f
o
r numeri-
cal m
o
del
s
.
Wang et al
.
[
12
]
c
o
nduct C
F
D
s
imulati
o
n
s
t
o
inve
s
tigate the influence
o
f
particle
s
i
z
e
o
n v
o
rte
x
f
o
rmati
o
n and er
o
-
s
i
o
n behavi
o
r in a
s
emi-
o
pen centrifugal
pump
.
I
n a
s
ub
s
equent
s
tud
y
[
13
]
, the
auth
o
r
s
e
x
tended thi
s
wo
r
k
b
y
anal
y
z
ing the
effect
o
f the particle
o
n v
o
rte
x
–
w
all interac-
ti
o
n
s
and er
o
s
i
o
n mechani
s
m
s
.
The
s
e
s
tudie
s
dem
o
n
s
trate that numerical m
o
deling,
s
up-
p
o
rted b
y
e
x
perimental inve
s
tigati
o
n
s
, ha
s
bec
o
me an indi
s
pen
s
able t
oo
l f
o
r anal
y
z
ing
c
o
mple
x
fl
ow
phen
o
mena in centrifugal
pump
s
.
A
t the
s
ame time, the
y
c
o
nfirm that
s
tudie
s
directl
y
c
o
mparing the h
y
draulic
perf
o
rmance and energ
y
c
o
nver
s
i
o
n
mechani
s
m
s
o
f cl
o
s
ed and
s
emi-
o
pen
impeller
s
under identical
o
perating c
o
ndi-
ti
o
n
s
remain relativel
y
limited
.
D
e
s
pite the
s
e c
o
ntributi
o
n
s
, the literature
s
till lac
k
s
a detailed,
s
y
s
tematic anal
y
s
i
s
that
e
x
plicitl
y
f
o
cu
s
e
s
o
n the mechani
s
m
s
o
f
energ
y
c
o
nver
s
i
o
n in b
o
th impeller t
y
pe
s
.
I
n
particular, there i
s
a
s
h
o
rtage
o
f
s
tudie
s
that
s
imultane
o
u
s
l
y
evaluate pre
ss
ure ri
s
e, ener-
g
y
tran
s
fer pr
o
ce
ss
e
s
, and h
y
draulic l
o
ss
e
s
under full
y
c
o
mparable c
o
nditi
o
n
s
.
Theref
o
re, the pre
s
ent
wo
r
k
aim
s
t
o
addre
ss
thi
s
gap b
y
c
o
nducting a numerical c
o
mpa-
rative anal
y
s
i
s
u
s
ing an identical ba
s
eline
ge
o
metr
y
,
w
ith
o
nl
y
the impeller t
y
pe (
s
emi--
o
pen ver
s
u
s
cl
o
s
ed) varied, enabling
a c
o
n
s
i
s
tent and ph
y
s
icall
y
meaningful
a
ss
e
ss
ment
o
f difference
s
in energ
y
c
o
nver-
s
i
o
n mechani
s
m
s
.
A
k
e
y
a
s
pect
o
f the pr
o
-
p
o
s
ed appr
o
ach i
s
en
s
uring c
o
mparabilit
y
and
s
tabilit
y
o
f
o
perating parameter
s
acr
o
ss
b
o
th impeller
s
in numerical
s
imulati
o
n
s
,
w
hich i
s
o
ften difficult t
o
achieve in e
x
peri-
mental inve
s
tigati
o
n
s
due t
o
mea
s
urement
limitati
o
n
s
and
s
en
s
itivit
y
t
o
o
perating c
o
n-
diti
o
n
s
.
F
urtherm
o
re, C
F
D
-ba
s
ed anal
y
s
e
s
enable detailed e
x
aminati
o
n
o
f l
o
cal fl
ow
phen
o
mena, including v
o
rte
x
s
tructure
s
,
s
ec
o
ndar
y
fl
ow
s
, and
o
ther l
o
cali
z
ed di
s
tur-
bance
s
that ma
y
o
ccur
w
ithin fl
ow
channel
s
.
M
e
t
ho
d
o
l
o
g
y
of
nu
me
ri
c
a
l
CF
D
a
n
a
l
ys
i
s
D
e
s
i
g
n
a
n
d
o
pe
r
a
t
i
n
g
pa
r
ame
t
e
rs
n
n
D
e
s
ign calculati
o
n
s
ba
s
ed
o
n the alg
o
-
rithm pre
s
ented in
[
2
]
, f
o
r the a
ss
umed
o
pe-
rating parameter
s
c
o
rre
s
p
o
nding t
o
a pump
capacit
y
o
f
Q
=
500 dm³/min and a head
o
f H
=
26 m,
w
ere perf
o
rmed u
s
ing PTC
M
athcad and
M
S
Ex
cel
.
The main impeller
dimen
s
i
o
n
s
w
ere determined, including the
hub diameter, number
o
f blade
s
and their
thic
k
ne
ss
, the
w
idth
s
o
f the fl
ow
channel
s
at
the inlet and
o
utlet, and the impeller inlet
and
o
utlet diameter
s
.
I
n the ne
x
t
s
tage, the ge
o
metr
y
o
f the
fl
ow
channel in the meridi
o
nal plane
w
a
s
defined, f
o
ll
ow
ed b
y
determining the impel-
ler blade pr
o
file
w
ith
s
ingle curvature u
s
ing
the p
o
int-b
y
-p
o
int meth
o
d
.
B
a
s
ed
o
n the
de
s
ign characteri
s
tic
s
o
btained, a parame-
tric C
AD
m
o
del
o
f the impeller ge
o
metr
y
w
a
s
devel
o
ped
.
F
ig
.
1 pre
s
ent
s
an
o
vervie
w
o
f a
w
ell-prepared m
o
del
o
f a five-bladed
s
emi-
o
pen impeller bel
ow.
F
ig
.
1
.
M
o
del
o
f a
s
emi-
o
pen centrifugal impeller
w
ith
five blade
s
Ry
s
.
1
.
M
o
del p
ó
ł
o
t
w
arteg
o
w
irni
k
a
o
d
ś
r
o
d
kow
eg
o
z
pięci
o
ma ł
o
pat
k
ami
N
u
me
r
i
c
a
l
CF
D
m
o
de
l
B
ecau
s
e a centrifugal impeller can be
divided int
o
1/
z
ge
o
metricall
y
s
imilar
s
ec-
ti
o
n
s
w
ith peri
o
dic fl
ow
pattern
s
, the
A
n
s
y
s
B
lade
G
en 2020
R
2 pr
o
gram
w
a
s
s
elected
t
o
generate the impeller
s
urface m
o
del
.
R
educing the anal
y
z
ed impeller d
o
main t
o
1/
z
o
f it
s
full ge
o
metr
y
y
ield
s
a den
s
er fini-
te-v
o
lume me
s
h and reduce
s
c
o
mputati
o
nal
time c
o
mpared t
o
s
imulati
o
n
s
o
n the full
impeller
.
F
ig
.
2a pre
s
ent
s
the
s
urface m
o
del
o
f a five-bladed
s
emi-
o
pen impeller,
w
hile
F
ig
.
2b
s
h
ow
s
the c
o
rre
s
p
o
nding
s
ect
o
r
o
f
the impeller that i
s
u
s
ed f
o
r the numerical
calculati
o
n
s
.
T
o
perf
o
rm
s
imulati
o
n
s
u
s
ing the finite
v
o
lume meth
o
d, the ne
x
t
s
tep i
s
t
o
di
s
creti
z
e
the fluid d
o
main
w
ithin the impeller, a
s
s
h
ow
n in
F
ig
.
3
.
24
9/2026in
s
tal
.
pc
z
.
pl
W
The c
o
mputati
o
nal me
s
h
w
a
s
created
u
s
ing
A
NS
Y
S Turb
o
G
rid 2020
R
2, a dedi-
cated me
s
hing t
oo
l f
o
r turb
o
machiner
y
applicati
o
n
s
, including centrifugal pump
s
.
M
e
s
h generati
o
n parameter
s
w
ere
s
elec-
ted t
o
o
btain a high-qualit
y
s
tructured
c
o
mputati
o
nal me
s
h
.
F
o
r greater clarit
y
,
o
nl
y
the
s
urface
o
f the me
s
h that pa
ss
e
s
thr
o
ugh the center
o
f the impeller fl
ow
channel al
o
ng the mid
s
tream line i
s
s
h
ow
n
.
The finite v
o
lume
s
u
s
ed f
o
r di
s
creti
z
ati
o
n
are he
x
ahedral
.
The
y
are refined in regi
o
n
s
o
f high vel
o
cit
y
and pre
ss
ure gradient
s
w
ithin the impeller, namel
y
o
n the blade
s
urface and in the vicinit
y
o
f the blade tra-
iling edge (
F
ig
.
4)
.
The c
o
n
s
idered di
s
crete fluid m
o
del
w
a
s
divided int
o
s
ubd
o
main
s
:
the inlet
regi
o
n, the regi
o
n
o
f fl
ow
driven b
y
the
impeller blade
s
, and the
o
utlet regi
o
n
.
D
ue
t
o
the di
s
tinctl
y
different fl
ow
characteri
s
tic
s
in the
s
e area
s
, the
y
w
ere c
o
n
s
tructed a
s
s
eparate fluid d
o
main
s
w
ith identical ph
y
-
s
ical pr
o
pertie
s
and then c
o
upled u
s
ing
an interface-t
y
pe b
o
undar
y
, a
s
s
h
ow
n in
F
ig
.
5
.
The inlet regi
o
n
w
a
s
defined a
s
a
s
tati
o
nar
y
fluid d
o
main
.
I
n c
o
ntra
s
t, the
impeller regi
o
n
w
a
s
defined a
s
a r
o
tating
fluid d
o
main u
s
ing the
M
ultiple
R
eference
F
rame m
o
del
.
D
ue t
o
the c
y
clic peri
o
dicit
y
o
f the fl
ow
w
ithin the pump impeller, peri
o
-
dic b
o
undar
y
c
o
nditi
o
n
s
w
ere applied t
o
the anal
y
z
ed 1/
z
s
ect
o
r
o
f the impeller
.
Since the primar
y
o
bjective
o
f the ana-
l
y
s
i
s
w
a
s
t
o
c
o
mpare the
o
perating charac-
teri
s
tic
s
o
f the cl
o
s
ed and
s
emi-
o
pen impel-
ler
s
, the f
o
ll
ow
ing
s
implif
y
ing a
ss
umpti
o
n
s
w
ere ad
o
pted
:
–
c
o
n
s
tant
w
ater den
s
it
y
o
f 998,2
k
g/m
3
,
–
c
o
n
s
tant d
y
namic vi
s
c
o
s
it
y
o
f
0,001003
k
g/(m·
s
),
–
the energ
y
equati
o
n
w
a
s
n
o
t
s
o
lved;
theref
o
re, the effect
s
o
f
w
ater temperatu-
re variati
o
n
s
w
ere neglected
.
B
a
s
ed
o
n the
s
implif
y
ing a
ss
umpti
o
n
s
pre
s
ented ab
o
ve, vi
s
c
o
u
s
di
ss
ipati
o
n
w
a
s
neglected becau
s
e the
o
bjective
o
f the
s
tud
y
w
a
s
t
o
c
o
mpare the h
y
draulic perf
o
rmance
o
f the cl
o
s
ed and
s
emi-
o
pen impeller
s
in
term
s
o
f m
o
mentum tran
s
fer and turbulence
effect
s
.
F
ig
.
2
.
Surface m
o
del
o
f the fr
o
nt
ge
o
metr
y
o
f a five-bladed
s
emi-
o
pen
impeller prepared f
o
r
:
a) the full impeller,
b) a 1/
z
s
ect
o
r
o
f the impeller
Ry
s
.
2
.
M
o
del p
ow
ier
z
chni
owy
pr
z
ednieg
o
z
ar
y
s
u pięci
o
ł
o
pat
kow
eg
o
w
irni
k
a p
ó
ł
o
t
w
arteg
o
wyko
nan
y
dla
:
a
)
pełneg
o
w
irni
k
a, b
)
1/
z
c
z
ę
ś
ci
w
irni
k
a
F
ig
.
3
.
Surface m
o
del
o
f the impeller
blade
s
w
ith the finite v
o
lume me
s
h la
y
er
applied in the central part
o
f the fl
ow
channel
:
a) fr
o
nt vie
w
, b) meridi
o
nal vie
w
Ry
s
.
3
.
M
o
del p
ow
ier
z
chni
owy
ł
o
pate
k
w
irni
k
a
z
p
ow
ł
ok
ą nał
o
ż
enia
o
bjęt
o
ś
ci
s
ko
ńc
z
o
n
y
ch
w
ś
r
o
d
kow
ej c
z
ę
ś
ci
k
anału
pr
z
epł
ywow
eg
o:
a
)
w
id
ok
z
pr
z
o
du,
b
)
w
id
ok
w
r
z
ucie p
o
łudni
kowy
m
F
ig
.
4
.
Surface m
o
del
o
f a 1/
z
s
ect
o
r
o
f the impeller
w
ith the finite v
o
lume me
s
h la
y
er applied in the central
part
o
f the fl
ow
channel
:
a) fr
o
nt vie
w
, b) enlarged vie
w
o
f the me
s
h in the blade leading-edge regi
o
n
Ry
s
.
4
.
M
o
del p
ow
ier
z
chni
owy
1/
z
c
z
ę
ś
ci
w
irni
k
a
z
p
ow
ł
ok
ą nał
o
ż
enia
o
bjęt
o
ś
ci
s
ko
ńc
z
o
n
y
ch
w
ś
r
o
d
kow
ej c
z
ę
ś
ci
k
anału pr
z
epł
ywow
eg
o:
a
)
w
id
ok
z
pr
z
o
du, b
)
p
ow
ię
k
s
z
o
n
y
w
id
ok
s
iat
k
i
w
o
b
s
z
ar
z
e
k
ra
w
ęd
z
i natarcia ł
o
pat
k
i
F
ig
.
5
.
Schematic repre
s
entati
o
n
o
f the b
o
undar
y
c
o
nditi
o
n
s
applied
t
o
the individual
s
urface
s
o
f the impeller ge
o
metric m
o
del
:
a) b
o
undar
y
c
o
nditi
o
n t
y
pe
s
defined f
o
r the 1/
z
s
ect
o
r m
o
del
o
f the impeller;
b) i
s
o
metric vie
w
o
f the 3
D
m
o
del
o
f the 1/
z
s
ect
o
r
o
f the impeller
w
ith the defined b
o
undar
y
c
o
nditi
o
n t
y
pe
s
.
1 - inlet regi
o
n, 2 - r
o
tating
regi
o
n a
ss
o
ciated
w
ith the impeller blade
s
, 3 -
o
utlet regi
o
n, 4 - impeller
blade, 5 - c
y
lindrical mea
s
urement
s
urface
Ry
s
.
5
.
Schemat nał
o
ż
enia daneg
o
t
y
pu
w
arun
ków
br
z
eg
owy
ch
na p
o
s
z
c
z
eg
ó
lne p
ow
ier
z
chnie ge
o
metr
y
c
z
neg
o
m
o
delu
w
irni
k
a
:
a
)
z
defini
ow
ane t
y
p
y
w
arun
ków
br
z
eg
owy
ch dla m
o
delu 1/
z
c
z
ę
ś
ci
w
irni
k
a, b
)
w
id
ok
i
z
o
metr
y
c
z
n
y
na m
o
del 3
D
1/
z
c
z
ę
ś
ci
w
irni
k
a
z
e
z
defini
ow
an
y
mi t
y
pami
w
arun
ków
br
z
eg
owy
ch; 1 -
o
b
s
z
ar
w
l
o
t
owy
,
2 -
o
b
s
z
ar ruchu
wy
mu
s
z
o
neg
o
ł
o
pat
k
ami
w
irni
k
a, 3 -
o
b
s
z
ar
wy
l
o
t
owy
,
4 - ł
o
pat
k
a
w
irni
k
a, 5 - c
y
lindr
y
c
z
na p
ow
ier
z
chnia p
o
miar
ow
a
in
s
tal
.
pc
z
.
pl
9/202625
W
o
d
o
c
i
ąg
i
i
k
a
n
a
li
z
a
c
j
a
n
n
The numerical
s
imulati
o
n
o
f the fluid fl
ow
w
a
s
perf
o
rmed u
s
ing
A
n
s
y
s
F
luent 2020
R
2
.
D
efining a given pr
o
ce
ss
in C
F
D
s
o
ft
w
are
inv
o
lve
s
s
electing appr
o
priate mathematical
m
o
del
s
that de
s
cribe the phen
o
mena under
c
o
n
s
iderati
o
n, f
o
ll
ow
ed anal
o
g
o
u
s
l
y
t
o
s
o
lving differential equati
o
n
s
, b
y
s
pecif
y
ing
b
o
undar
y
c
o
nditi
o
n
s
.
I
n the calculati
o
n
s
o
f
the
s
emi-
o
pen and cl
o
s
ed centrifugal impel-
ler, the
k
-
ε
turbulence m
o
del (
R
eali
z
able,
E
nhanced Wall Treatment)
w
a
s
applied
w
ith default
s
etting
s
(
M
o
del c
o
n
s
tant
s
:
C2-
E
p
s
il
o
n
=
1,9; TK
E
Prandtl Number
=
1;
T
DR
Prandtl Number
=
1,2)
.
A
cc
o
rding t
o
the
A
NS
Y
S d
o
cumentati
o
n
[
14, 15
]
, the
E
nhanced Wall Treatment i
s
rec
o
mmended
f
o
r the
k
-
ε
turbulence m
o
del and i
s
particu-
larl
y
s
uitable f
o
r fl
ow
s
w
ith
s
tr
o
ng pre
ss
ure
gradient
s
, fl
ow
s
eparati
o
n, fl
ow
s
inv
o
lving
r
o
tating
w
all
s
, and highl
y
three-dimen
s
i
o
nal
near-
w
all fl
ow
,
w
hich are characteri
s
tic
feature
s
o
f centrifugal pump impeller
s
.
A
s
imilar appr
o
ach empl
oy
ing the
k
-
ε
turbu-
lence m
o
del
w
a
s
ad
o
pted in
[
16
]
,
w
here
the m
o
del
w
a
s
s
h
ow
n t
o
pr
o
vide g
oo
d
agreement
w
ith e
x
perimental re
s
ult
s
and
accuratel
y
predict the fl
ow
field in a centri-
fugal pump
.
The
s
o
luti
o
n pr
o
ce
ss
f
o
r a full
y
defined
s
tead
y
-
s
tate pr
o
blem i
s
carried
o
ut b
y
pre-
s
cribing a certain number
o
f iterati
o
n
s
.
There
i
s
n
o
univer
s
al criteri
o
n f
o
r a
ss
e
ss
ing
s
o
luti
o
n
c
o
nvergence
.
F
o
r
s
o
me cla
ss
e
s
o
f pr
o
blem
s
,
m
o
nit
o
ring re
s
idual
s
(imbalance
s
) after
each c
o
mputati
o
nal iterati
o
n i
s
helpful;
h
ow
ever, f
o
r
o
ther t
y
pe
s
o
f pr
o
blem
s
, thi
s
appr
o
ach ma
y
lead t
o
mi
s
leading c
o
nclu-
s
i
o
n
s
.
Theref
o
re, g
oo
d practice i
s
t
o
a
ss
e
ss
c
o
nvergence n
o
t
o
nl
y
ba
s
ed
o
n re
s
idual
s
fr
o
m
s
ucce
ss
ive iterati
o
n
s
but al
s
o
o
n appr
o
-
priatel
y
integrated quantitie
s
and b
y
verif
y
-
ing ma
ss
and energ
y
balance
.
Numerical fl
ow
s
imulati
o
n
s
,
w
ith b
o
un-
dar
y
c
o
nditi
o
n
s
c
o
rre
s
p
o
nding t
o
n
o
minal
o
perating parameter
s
(
Q
=
500 dm³/min,
n
=
3060 rpm),
w
ere perf
o
rmed f
o
r a five--
bladed
s
emi-
o
pen impeller
w
ith an a
x
ial
clearance
o
f 0,5 mm a
s
w
ell a
s
f
o
r a cl
o
s
ed
impeller
.
A
s
a re
s
ult
o
f 500 c
o
mputati
o
nal
iterati
o
n
s
, c
o
nvergence
o
f all variable
s
(c
o
ntinuit
y
, m
o
mentum)
w
a
s
achieved at a
level
s
ignificantl
y
l
ow
er than the default
thre
s
h
o
ld value
o
f 10
–
³
.
A
dditi
o
nall
y
, c
o
nvergence
w
a
s
verified
u
s
ing the v
o
lumetric fl
ow
rate and the ave-
rage pre
ss
ure and vel
o
cit
y
at the impeller
inlet and
o
utlet,
w
hich are
k
e
y
variable
s
characteri
z
ing the fl
ow.
A
nal
y
s
i
s
o
f the
variati
o
n
o
f the
s
e parameter
s
o
ver
s
ucce
ss
i-
ve iterati
o
n
s
s
h
ow
s
(
F
ig
.
6) that after appr
o
-
x
imatel
y
220 iterati
o
n
s
, their value
s
s
tabili-
z
e, indicating c
o
nvergence
o
f the
s
o
luti
o
n
.
A
grid independence
s
tud
y
w
a
s
al
s
o
c
o
n-
ducted, c
o
nfirming the reliabilit
y
and accu-
rac
y
o
f the
o
btained re
s
ult
s
.
The average
An
a
l
ys
i
s
a
n
d
d
i
sc
u
ss
i
on
of
r
e
s
u
l
ts
F
l
o
w s
i
m
u
l
a
t
i
on
r
e
s
u
l
ts
fo
r
a
s
em
i
-
o
pe
n
i
mpe
ll
e
r
F
ig
.
6
.
Characteri
s
tic
s
o
f the variati
o
n
o
f c
o
ntr
o
l quantitie
s
o
ver
s
ucce
ss
ive c
o
mputati
o
nal iterati
o
n
s
perf
o
rmed
f
o
r a five-bladed
s
emi-
o
pen impeller
w
ith an a
x
ial clearance
o
f 0,5 mm
.
The individual pl
o
t
s
s
h
ow
the variati
o
n
o
f the f
o
ll
ow
ing parameter
s
:
a) v
o
lumetric fl
ow
rate at the impeller
o
utlet, b) mean vel
o
cit
y
at the impeller
o
utlet, c) mean
s
tatic pre
ss
ure at the inlet t
o
the blade-driven fl
ow
regi
o
n, and d) mean
s
tatic pre
ss
ure at the impeller
o
utlet
Ry
s
.
6
.
C
hara
k
ter
y
s
t
yk
i
z
mian
w
iel
ko
ś
ci
ko
ntr
o
ln
y
ch na dr
o
d
z
e
ko
lejn
y
ch iteracji
o
blic
z
eni
owy
ch
wyko
nan
y
ch
dla p
ó
ł
o
t
w
arteg
o
w
irni
k
a pięci
o
ł
o
pat
kow
eg
o
o
w
iel
ko
ś
ci
s
z
c
z
elin
y
0,5 mm
.
P
o
s
z
c
z
eg
ó
lne
wyk
re
s
y
pr
z
ed
s
ta
w
iają
z
mianę na
s
tępując
y
ch parametr
ów:
a
)
s
trumienia
o
bjęt
o
ś
ci na
wy
l
o
cie
z
w
irni
k
a,
b
)
pręd
ko
ś
ci
ś
redniej na
wy
l
o
cie
z
w
irni
k
a, c
)
ś
rednieg
o
ci
ś
nienia
s
tat
y
c
z
neg
o
na
w
l
o
cie d
o
o
b
s
z
aru
ruchu
wy
mu
s
z
o
neg
o
ł
o
pat
k
ami
w
irni
k
a, d
)
ś
rednieg
o
ci
ś
nienia
s
tat
y
c
z
neg
o
na
wy
l
o
cie
z
w
irni
k
a
the impeller and the fr
o
nt
w
all
o
f the
pump head at the
o
utlet
w
a
s
s
elected a
s
the the fluid i
s
di
s
turbed
.
Thi
s
i
s
reflected in the
verificati
o
n parameter, and the me
s
h inde-
s
treamline pattern
s
and ultimatel
y
lead
s
t
o
pendence
s
tud
y
w
a
s
perf
o
rmed u
s
ing ada- fluctuating fl
ow
behavi
o
r
w
ithin the inter-
ptive me
s
h refinement ba
s
ed
o
n the pre
ss
ure blade regi
o
n
.
gradient
.
The me
s
h
w
a
s
iterativel
y
refined inThe di
s
tributi
o
n
o
f
s
tatic pre
ss
ure (
F
ig
.
8)
regi
o
n
s
w
ith the highe
s
t pre
ss
ure gradient
s
w
a
s
determined at a di
s
tance
o
f 5 mm fr
o
m
until the variati
o
n in the predicted pump the impeller
s
hr
o
ud
.
I
n the inlet regi
o
n,
head bet
w
een t
wo
c
o
n
s
ecutive refinement
s
a
z
o
ne
o
f reduced pre
ss
ure can be
o
b
s
e-
w
a
s
bel
ow
2
%
.
F
o
r the anal
y
z
ed 1/
z
rved
.
A
s
the fluid fl
ow
s
thr
o
ugh the interbla-
s
ect
o
r
o
f the cl
o
s
ed impeller, the final c
o
m- de channel
s
,
s
tatic pre
ss
ure increa
s
e
s
in
s
ta-
putati
o
nal me
s
h c
o
n
s
i
s
ted
o
f 167380 cell
s
ge
s
a
s
the impeller blade
s
tran
s
fer m
o
men-
and 185589 n
o
de
s
.
F
o
r the
s
emi-
o
pen tum t
o
s
ucce
ss
ive fluid la
y
er
s
.
impeller, the ad
o
pted me
s
h-independence
criteri
o
n
w
a
s
s
ati
s
fied u
s
ing a c
o
mputati
o
nal
me
s
h
w
ith 358895 cell
s
and 387500
n
o
de
s
.
Ry
s
.
7
.
Pr
z
ebieg linii prądu
wy
z
nac
z
o
n
y
B
a
s
ed
o
n the numerical calculati
o
n
s
perf
o
rmed f
o
r a five-bladed
s
emi-
o
pen
impeller
w
ith an a
x
ial clearance
o
f
0,5 mm, the
s
treamline pattern
s
h
ow
n in
F
ig
.
7
w
a
s
o
btained
.
A
nal
y
s
i
s
o
f the
s
tre-
amline traject
o
rie
s
al
o
ng the impeller fl
ow
channel indicate
s
that the
y
are arranged
w
ithin the interblade pa
ss
age
s
in acc
o
r-
F
ig
.
7
.
Streamline pattern
o
btained fr
o
m numerical
d
na
a
l
n
m
ce
o
t
w
i
o
it
n
h
.
t
A
he
dd
im
iti
p
o
e
n
l
a
le
ll
r
y
’
s
,
i
a
m
s
p
a
o
r
s
e
e
s
d
ul
r
t
o
o
ta
f
t
t
i
h
o
e
-
w
s
im
ith
ul
a
a
n
ti
o
a
n
x
s
ia
f
o
l
r
cl
a
ea
fi
r
v
a
e
n
-
c
b
e
la
o
d
f
e
0
d
,5
s
e
m
m
m
i-
o
pen impeller
fl
ow
o
ccurring in the clearance bet
w
een
na p
o
d
s
ta
w
ie pr
z
epr
ow
ad
z
o
n
y
ch
s
y
mulacji
ca
s
ing, the circumferential m
o
ti
o
n
o
f
p
nu
ię
m
c
e
i
o
r
ł
y
o
c
p
z
a
n
t
y
k
c
o
h
w
d
e
l
g
a
o
p
o
ó
ł
w
o
t
i
w
el
a
ko
rt
ś
e
c
g
i
o
s
z
w
c
z
ir
e
n
l
i
i
k
n
a
y
0,5 mm
The ma
x
imum
s
tatic pre
ss
ure value
s
o
btained directl
y
at the blade
o
utlet c
o
rre-
s
p
o
nd t
o
the head generated b
y
the real
impeller
.
N
o
te that the
s
tatic pre
ss
ure value
s
s
h
ow
n in the legend
o
n the left are pred
o
-
minantl
y
negative acr
o
ss
m
o
s
t
o
f the range
.
Thi
s
i
s
becau
s
e, during the
s
o
luti
o
n
o
f the
g
o
verning equati
o
n
s
,
s
tatic pre
ss
ure i
s
refe-
renced t
o
bar
o
metric pre
ss
ure,
w
hich i
s
s
pe-
cified at the impeller
o
utlet rather than at the
inlet
.
The pr
o
file
s
o
f ab
s
o
lute vel
o
cit
y
deter-
mined directl
y
at the blade
o
utlet (
F
ig
.
9a)
fall
w
ithin a range that appr
o
x
imatel
y
c
o
r-
re
s
p
o
nd
s
t
o
the re
s
ult
s
o
btained fr
o
m the
de
s
ign calculati
o
n
s
, f
o
r
w
hich the ab
s
o
lute
vel
o
cit
y
at the impeller
o
utlet
w
a
s
13,9 m/
s
.
F
ig
.
9b pre
s
ent
s
the pr
o
file
s
o
f ab
s
o
lute
vel
o
cit
y
o
n the blade
s
urface
s
,
w
h
o
s
e di
s
tri-
buti
o
n al
o
ng the impeller radiu
s
reflect
s
the
increa
s
e in linear vel
o
cit
y
due t
o
r
o
tati
o
nal
m
o
ti
o
n at c
o
n
s
tant angular vel
o
cit
y.
C
o
mpa
r
a
t
i
v
e
a
n
a
l
ys
i
s
of
t
h
e
e
n
e
r
g
y
c
onv
e
r
s
i
on
i
n
s
em
i
-
o
pe
n
a
n
d
c
l
o
s
ed
i
mpe
ll
e
r
s
B
a
s
ed
o
n the
s
treamline pattern
s
s
h
ow
n
in
F
ig
.
10 f
o
r b
o
th impeller
s
,
s
ignificant fluc-
tuati
o
n
s
o
ccur in the interblade regi
o
n
o
f
the
s
emi-
o
pen impeller
.
The
s
e are cau
s
ed
b
y
turbulent di
s
turbance
s
in the b
o
undar
y
la
y
er l
o
cated near the
s
tati
o
nar
y
fr
o
nt
w
all
o
f the ca
s
ing
.
A
s
the impeller blade
s
m
o
ve
in pr
o
x
imit
y
t
o
the ca
s
ing
w
all, the fluid
b
o
undar
y
la
y
er i
s
peri
o
dicall
y
di
s
rupted,
leading t
o
large vel
o
cit
y
gradient
s
bet
w
een
adjacent fluid la
y
er
s
.
Thi
s
, in turn, re
s
ult
s
in
fluctuating di
s
turbance
s
in the
s
treamline
pattern
s
.
The pr
o
file
s
o
f turbulent
k
inetic energ
y
(
F
ig
.
11)
w
ere
o
btained u
s
ing the
k
–
ε
turbu-
lence m
o
del applied in the calculati
o
n
s
.
A
nal
y
s
i
s
o
f the c
o
nt
o
ur di
s
tributi
o
n
o
f turbu-
lent
k
inetic energ
y
in the central part
o
f the
fl
ow
channel
o
f the
s
emi-
o
pen impeller cle-
arl
y
reveal
s
regi
o
n
s
o
f ver
y
inten
s
e turbulent
di
s
turbance
s
.
The
s
e
o
ccur immediatel
y
26
9/2026in
s
tal
.
pc
z
.
pl
W
F
ig
.
8
.
Static pre
ss
ure di
s
tributi
o
n pr
o
file
in a five-bladed
s
emi-
o
pen impeller
Ry
s
.
8
.
Pr
o
fil r
o
z
k
ładu ci
ś
nienia
s
tat
y
c
z
neg
o
w
p
ó
ł
o
t
w
art
y
m
w
irni
k
u pięci
o
ł
o
pat
kowy
m
F
ig
.
9
.
Vel
o
cit
y
pr
o
file
s
in a five-bladed
s
emi-
o
pen impeller determined
:
a) in the fluid d
o
main,
and b) al
o
ng the blade edge
s
Ry
s
.
9
.
Pr
o
file pręd
ko
ś
ci
w
p
ó
ł
o
t
w
art
y
m
w
irni
k
u pięci
o
ł
o
pat
kowy
m
wy
z
nac
z
o
ne
:
a
)
w
o
b
s
z
ar
z
e pł
y
nu,
o
ra
z
b
)
na
k
ra
w
ęd
z
iach ł
o
pate
k
F
ig
.
10
.
Streamline pattern
s
o
btained fr
o
m numerical
s
imulati
o
n
s
f
o
r the impeller
:
a) a five-bladed
s
emi-
o
pen
impeller
w
ith an a
x
ial clearance
o
f 0,5 mm, and b) a cl
o
s
ed impeller
Ry
s
.
10
.
Pr
z
ebieg linii prądu
wy
z
nac
z
o
n
y
na p
o
d
s
ta
w
ie pr
z
epr
ow
ad
z
o
n
y
ch
s
y
mulacji numer
y
c
z
n
y
ch
dla
w
irni
k
a
:
a
)
p
ó
ł
o
t
w
arteg
o
pięci
o
ł
o
pat
kow
eg
o
o
w
iel
ko
ś
ci
s
z
c
z
elin
y
0,5 mm,
o
ra
z
b
)
z
am
k
nięteg
o
d
ow
n
s
tream
o
f the blade
o
utlet, a phen
o
-Profile
s
of turbulent
k
inetic energ
y
(
F
ig
.
12)
men
o
n n
o
t
o
b
s
erved
w
ith the cl
o
s
ed impel-
w
ere
o
btained
o
n a c
y
lindrical
s
urface that
ler
.
I
n the pump’
s
h
y
draulic part,
s
uch fluctu- inter
s
ect
s
b
o
th impeller
s
.
I
n the ca
s
e
o
f the
ati
o
n
s
ma
y
c
o
ntribute t
o
energ
y
c
o
nver
s
i
o
n
s
emi-
o
pen impeller, the f
o
rmati
o
n
o
f v
o
rtical
l
o
ss
e
s
w
ithin the v
o
lute ca
s
ing
.
A
dditi
o
nall
y
,
s
tructure
s
can be
o
b
s
erved in the central
F
ig
.
11 pr
o
vide
s
in
s
ight int
o
turbulent di
s
tur- regi
o
n
o
f the interblade channel,
w
hich
bance
s
that ari
s
e
w
ithin the interblade chan- d
o
e
s
n
o
t
o
ccur in the ca
s
e
o
f the cl
o
s
ed
nel
o
f the
s
emi-
o
pen impeller
.
impeller
.
F
ig
.
11
.
Pr
o
file
s
o
f turbulent
k
inetic energ
y
determined f
o
r the impeller
:
a) a five-bladed
s
emi-
o
pen impeller
w
ith an a
x
ial clearance
o
f 0,5 mm, and b) a cl
o
s
ed impeller
Ry
s
.
11
.
Pr
o
file energii
k
inet
y
c
z
nej turbulencji
wy
z
nac
z
o
ne dla
w
irni
k
a
:
a
)
p
ó
ł
o
t
w
arteg
o
pięci
o
ł
o
pat
kow
eg
o
o
w
iel
ko
ś
ci
s
z
c
z
elin
y
0,5 mm
o
ra
z
b
)
z
am
k
nięteg
o
in
s
tal
.
pc
z
.
pl
9/202627
A
x
ial vel
o
cit
y
pr
o
file in a five-bladed
s
emi-
o
pen impeller (
F
ig
.
13), ba
s
ed
o
n
w
hich the nature
o
f the
o
ccurring v
o
rtical
s
tructure
s
can be a
ss
e
ss
ed
.
I
n turbulent fl
ow
devel
o
ping in the central regi
o
n
o
f the inter-
blade channel, an a
x
ial fl
ow
c
o
mp
o
nent i
s
o
b
s
erved,
w
hich ma
y
indicate the f
o
rmati
o
n
o
f v
o
rtice
s
acr
o
ss
the fl
ow
pa
ss
age
s
, a
s
rep
o
rted b
y
Papier
s
k
i et al
.
[
5
].
I
n the regi
o
n l
o
cated at the impeller bla-
de
o
utlet (
F
ig
.
13), the a
x
ial vel
o
cit
y
pr
o
file
s
d
o
n
o
t e
x
hibit an
y
v
o
rtical
s
tructure
s
o
rien-
ted perpendicular t
o
the impeller
s
hr
o
ud
.
Thi
s
indicate
s
the pre
s
ence
o
f ver
y
inten
s
e
turbulent fl
ow
at the blade
o
utlet
o
f
s
emi--
o
pen impeller
s
,
w
hich i
s
alm
o
s
t entirel
y
parallel t
o
the impeller
s
hr
o
ud
.
Thu
s
, the
vel
o
cit
y
vect
o
r
s
o
f the fluid la
y
er
s
f
o
rming
v
o
rtice
s
in the
o
utlet regi
o
n have pred
o
mi-
nantl
y
radial and circumferential c
o
mp
o
-
nent
s
.
I
n c
o
ntra
s
t, the a
x
ial c
o
mp
o
nent i
s
relativel
y
s
mall and a
ss
ume
s
averaged
value
s
c
o
mparable t
o
th
o
s
e in
o
ther part
s
o
f
the impeller fl
ow
channel
s
.
The rea
s
o
n f
o
r
thi
s
behavi
o
r ma
y
be the f
o
rmati
o
n
o
f a v
o
r-
te
x
bet
w
een the fr
o
nt
w
all
o
f the ca
s
ing and
the tip
o
f the blade
s
ide
s
urface
.
B
a
s
ed
o
n
the numerical anal
y
s
e
s
, the
s
e v
o
rtical
s
truc-
ture
s
reach their ma
x
imum inten
s
it
y
at the
center
o
f the impeller
o
utlet
.
A
t the
o
utlet
o
f the cl
o
s
ed impeller, the
vel
o
cit
y
i
s
s
ignificantl
y
higher than in the
ca
s
e
o
f the
s
emi-
o
pen impeller,
w
hich i
s
due
t
o
l
o
ss
e
s
cau
s
ed b
y
turbulent fl
ow
in the
h
y
draulic pa
ss
age
s
o
f the
s
emi-
o
pen impel-
ler
.
F
ig
.
14 pre
s
ent
s
the head H
=
f(
Q
) and
efficienc
y
η
=
f(
Q
) curve
s
f
o
r b
o
th impeller
s
,
s
h
ow
ing that the cl
o
s
ed impeller achieve
s
c
o
n
s
iderabl
y
higher head and efficienc
y.
I
n
the pre
s
ented re
s
ult
s
, the pump head (H)
w
a
s
determined ba
s
ed
o
n the fl
ow
parame-
ter
s
o
btained fr
o
m the C
F
D
s
imulati
o
n
s
,
w
herea
s
the h
y
draulic efficienc
y
(
η
)
w
a
s
calculated acc
o
rding t
o
the f
o
ll
ow
ing equ-
ati
o
n
:
P
P
η
=
hyd
r
au
lic
(1)
moto
r
h
y
draulic
m
o
t
o
r
w
here
:
P
–
h
y
draulic p
ow
er determi-
ned fr
o
m the C
F
D
s
imulati
o
n re
s
ult
s
, W;
P
–
electric m
o
t
o
r p
ow
er determined
fr
o
m the ad
o
pted m
o
t
o
r perf
o
rmance cha-
racteri
s
tic, W
.
The re
s
ult
s
o
f the numerical
s
imulati
o
n
s
f
o
r the
s
elected de
s
ign c
o
nfigurati
o
n
s
o
f the
cl
o
s
ed and
s
emi-
o
pen impeller
s
are quali-
tativel
y
c
o
n
s
i
s
tent
w
ith the e
x
perimental
inve
s
tigati
o
n
s
and numerical
s
imulati
o
n
s
rep
o
rted in
[
9
]
and
[
5
]
, re
s
pectivel
y.
A
dditi
o
nall
y
, the de
s
ign calculati
o
n
re
s
ult
s
w
ere c
o
mpared
w
ith the numerical
s
imulati
o
n re
s
ult
s
o
btained f
o
r the cl
o
s
ed
impeller
.
The applicati
o
n
o
f the de
s
ign pr
o
-
cedure de
s
cribed in
[
2
]
, implemented in
calc
n
n
PTC
M
athcad and
M
icr
o
s
o
ft
Ex
cel, enabled 52,1
%
.
The intr
o
ducti
o
n
o
f an a
x
ial clearan-
the devel
o
pment
o
f the impeller fl
ow
pa
ss
a- ce
o
f 0,5 mm re
s
ulted in an appr
o
x
imatel
y
ge ge
o
metr
y
,
w
hich
w
a
s
s
ub
s
equentl
y
11
%
reducti
o
n in head and a decrea
s
e in
rec
o
n
s
tructed in
A
NS
Y
S
B
lade
G
en h
y
draulic efficienc
y
o
f m
o
re than 6
%
.
2020
R
2
.
The calculated pump head
F
urtherm
o
re, a
s
s
h
ow
n in
F
ig
.
14, the
s
e dif-(H
)
w
a
s
27,5 m, re
s
ulting in a de
s
ign ference
s
bec
o
me increa
s
ingl
y
pr
o
n
o
unced
head
s
urplu
s
o
f H
=
1,5 m relative t
o
the a
s
the fl
ow
rate decrea
s
e
s
f
o
r b
o
th impeller
a
ss
umed n
o
minal head (H
=
26 m)
.
I
t
s
h
o
- c
o
nfigurati
o
n
s
.
u
va
ld
lu
b
e
e
s
n
c
o
o
te
r
d
re
,
s
h
p
o
o
w
n
e
d
ve
t
o
r, t
t
h
h
a
e
t
p
th
e
e
r
c
f
o
a
r
lc
m
u
a
la
n
te
c
d
e
S
u
mma
r
y
parameter
s
o
f the c
o
mplete pump, inclu-
ding, am
o
ng
o
ther
s
, the h
y
draulic l
o
ss
e
s
The influence
o
f impeller de
s
ign
o
n the
o
ccurring in the v
o
lute ca
s
ing
.
The
s
e l
o
ss
e
s
energ
y
c
o
nver
s
i
o
n pr
o
ce
ss
w
a
s
inve
s
tigated
are n
o
t acc
o
unted f
o
r in the numerical b
y
c
o
mparing
s
emi-
o
pen and cl
o
s
ed impel-
m
o
del,
w
hich i
s
limited t
o
the impeller ler
s
under identical
o
perating c
o
nditi
o
n
s
.
d
o
main
.
C
o
n
s
equentl
y
, a
s
ignificantl
y
Numerical C
F
D
s
imulati
o
n
s
w
ere perf
o
rmed
higher head i
s
e
x
pected at the c
o
ntr
o
l
s
ec- t
o
e
x
amine internal fl
ow
behavi
o
r, including
ti
o
n directl
y
d
ow
n
s
tream
o
f the impeller vel
o
cit
y
and pre
ss
ure di
s
tributi
o
n
s
in the fl
ow
o
utlet in the numerical m
o
del
.
Thi
s
o
b
s
erva- channel
s
o
f b
o
th impeller
s
.
The anal
y
s
i
s
ti
o
n i
s
c
o
n
s
i
s
tent
w
ith the re
s
ult
s
pre
s
ented revealed that the
s
emi-
o
pen impeller i
s
m
o
re
in
F
ig
.
14
.
pr
o
ne t
o
fl
ow
di
s
turbance
s
, particularl
y
due
A
quantitative c
o
mpari
s
o
n
o
f the t
o
a
x
ial clearance,
w
hich pr
o
m
o
te
s
lea
k
age
numerical
s
imulati
o
n re
s
ult
s
(
F
ig
.
14) and the devel
o
pment
o
f turbulence
s
tructu-
indicate
s
that, at the n
o
minal fl
ow
rate re
s
.
The
s
e effect
s
re
s
ult in increa
s
ed energ
y
(
Q
=
500 dm³/min), the head and di
ss
ipati
o
n and le
ss
efficient m
o
mentum
h
y
draulic efficienc
y
o
f the cl
o
s
ed impeller tran
s
fer
w
ithin the fl
ow
pa
ss
age
s
.
reached 31,6 m and 58,7
%
, re
s
pectivel
y.
I
n
I
n c
o
ntra
s
t, the cl
o
s
ed impeller en
s
ure
s
c
o
ntra
s
t, the c
o
rre
s
p
o
nding value
s
f
o
r the a m
o
re c
o
ntr
o
lled fl
ow
envir
o
nment, limiting
s
emi-
o
pen impeller
w
ere 28,1 m and turbulence and reducing h
y
draulic l
o
ss
e
s
.
F
ig
.
12
.
Pr
o
file
s
o
f turbulent
k
inetic
energ
y
o
n a c
y
lindrical
s
urface
w
ith a radiu
s
o
f 45 mm, determined
f
o
r the impeller
:
a) a five-bladed
s
emi-
o
pen impeller
w
ith an a
x
ial
clearance
o
f 0,5 mm, and b) a cl
o
s
ed
impeller
Ry
s
.
12
.
Pr
o
file energii
k
inet
y
c
z
nej
turbulencji na p
ow
ier
z
chni
c
y
lindr
y
c
z
nej
o
pr
o
mieniu 45 mm
wy
z
nac
z
o
ne dla
w
irni
k
a
:
a
)
p
ó
ł
o
t
w
arteg
o
pięci
o
ł
o
pat
kow
eg
o
o
w
iel
ko
ś
ci
s
z
c
z
elin
y
0,5 mm
o
ra
z
b
)
z
am
k
nięteg
o
F
ig
.
13
.
A
x
ial vel
o
cit
y
pr
o
file
s
o
btained
o
n a c
y
lindrical
s
urface
w
ith a radiu
s
o
f 45 mm and
o
n a plane l
o
cated 5 mm
F
ig
.
14
.
Perf
o
rmance characteri
s
tic
s
H
=
f(
Q
) and
η
=
f(
Q
)
fr
o
m the
s
hr
o
ud
o
f a five-bladed
s
emi-
o
pen
o
f a
w
ith a five-bladed cl
o
s
ed impeller (
Z
) and a
s
emi-
o
pen
impeller
w
ith an a
x
ial clearance
o
f 0,5 mm
impeller
w
ith an a
x
ial clearance
o
f 0,5 mm (P0,5), determined
Ry
s
.
13
.
Pr
o
file pręd
ko
ś
ci
o
s
i
ow
ej
ba
s
ed
o
n numerical
s
imulati
o
n
s
perf
o
rmed in
A
n
s
y
s
F
luent
o
tr
z
y
mane na p
ow
ier
z
chni c
y
lindr
y
c
z
nej
Ry
s
.
14
.
C
hara
k
ter
y
s
t
yk
i H
=
f
(
Q
)
i
η
=
f
(
Q
)
w
irni
k
a
o
pr
o
mieniu 45 mm
o
ra
z
na pła
s
z
c
z
y
ź
nie
pięci
o
ł
o
pat
kow
eg
o
z
am
k
nięteg
o
(
Z
)
o
ra
z
p
ó
ł
o
t
w
arteg
o
o
ddal
o
nej 5 mm
o
d tarc
z
y
w
irni
k
a
z
e
s
z
c
z
eliną
o
s
i
ow
ą 0,5 mm
(
P 0,5
)
,
wy
z
nac
z
o
ne
w
o
parciu
p
ó
ł
o
t
w
arteg
o
pięci
o
ł
o
pat
kow
eg
oo
pr
z
epr
ow
ad
z
o
ne
s
y
mulacje numer
y
c
z
ne
w
pr
o
gramie
o
w
iel
ko
ś
ci
s
z
c
z
elin
y
0,5 mm
A
n
s
y
s
F
luent
W
o
d
o
c
i
ąg
i
i
k
a
n
a
li
z
a
c
j
a
28
9/2026in
s
tal
.
pc
z
.
pl
W
n
C
o
n
s
equentl
y
, it achieve
s
better h
y
draulic
perf
o
rmance, reflected in higher head and
efficienc
y
value
s
.
The numerical
s
imulati
o
n
re
s
ult
s
o
btained in thi
s
s
tud
y
are qualitative-
l
y
c
o
n
s
i
s
tent
w
ith finding
s
rep
o
rted in previ
o
-
u
s
s
tudie
s
o
n thi
s
t
o
pic
.
The
s
tud
y
al
s
o
empha
s
i
z
e
s
the imp
o
rtance
o
f anal
y
z
ing
l
o
cal fl
ow
phen
o
mena, a
s
the
y
s
ignificantl
y
influence the machine’
s
gl
o
bal perf
o
rman-
ce
.
O
verall, the re
s
ult
s
dem
o
n
s
trate that
even
s
ubtle ge
o
metric difference
s
in impeller
de
s
ign can lead t
o
c
o
n
s
iderable variati
o
n
s
in energ
y
c
o
nver
s
i
o
n efficienc
y.
A
t the n
o
mi-
nal fl
ow
rate (
Q
=
500 dm³/min), the intr
o
-
ducti
o
n
o
f an a
x
ial clearance
o
f 0,5 mm
re
s
ulted in an appr
o
x
imatel
y
11
%
reducti
o
n
in head and a decrea
s
e in h
y
draulic effi-
cienc
y
o
f m
o
re than 6
%
.
F
urtherm
o
re, the
s
e
difference
s
bec
o
me increa
s
ingl
y
pr
o
n
o
un-
ced a
s
the fl
ow
rate decrea
s
e
s
f
o
r the ana-
l
y
z
ed impeller c
o
nfigurati
o
n
s
.
F
o
r e
x
ample, a
ss
uming a pump p
ow
er
o
f 4,4
k
W,
o
perati
o
n f
o
r 16 h per da
y
thr
o
-
ugh
o
ut the
y
ear, and a 6
%
reducti
o
n in
p
ow
er demand due t
o
the higher efficienc
y
o
f the cl
o
s
ed impeller, the annual electricit
y
s
aving
s
wo
uld am
o
unt t
o
appr
o
x
imatel
y
1,540
k
Wh
.
A
t an electricit
y
price
o
f
1 PLN/
k
Wh, thi
s
c
o
rre
s
p
o
nd
s
t
o
annual
s
aving
s
o
f appr
o
x
imatel
y
1540 PLN f
o
r
a
s
ingle pump
.
I
n indu
s
trial in
s
tallati
o
n
s
equ-
ipped
w
ith multiple pump
s
o
perating under
s
imilar c
o
nditi
o
n
s
, the cumulative energ
y
and c
o
s
t
s
aving
s
ma
y
theref
o
re bec
o
me
s
ignificant
.
F
uture re
s
earch ma
y
inve
s
tigate the
influence
o
f different a
x
ial clearance
s
o
n
perf
o
rmance parameter
s
, particularl
y
in
s
emi-
o
pen impeller
s
.
A
dditi
o
nall
y
, it
wo
uld
be valuable t
o
anal
y
z
e the impact
o
f impel-
ler de
s
ign variati
o
n
s
,
s
uch a
s
the number
o
f
blade
s
,
o
n fl
ow
s
tructure, energ
y
l
o
ss
e
s
,
and
o
verall pump efficienc
y.
I
t can al
s
o
be
valuable t
o
anal
y
z
e the difficultie
s
and c
o
s
t
s
o
f fabricating cl
o
s
ed impeller
s
c
o
mpared t
o
o
pen-de
s
ign impeller
s
in the c
o
nte
x
t
o
f the
pump’
s
higher head and
o
verall efficienc
y.
A
ck
no
w
l
edgeme
n
ts
Numerical calculati
o
n
s
w
ere perf
o
rmed
u
s
ing re
s
o
urce
s
pr
o
vided b
y
the Wr
o
cla
w
C
enter f
o
r Net
wo
r
k
ing and Superc
o
mputing
(
http
:
//
w
c
ss
.
pl
)
, grant n
o.
565
.
L
i
t
e
r
a
t
u
r
a
[
1
]
Ła
z
ar
k
ie
w
ic
z
S
z
.
, Tr
o
s
ko
lań
s
k
i T
.
A.
, P
o
mp
y
w
ir
o
-
w
e, W
y
da
w
nict
w
a Nau
kowo
-Technic
z
ne; War-
s
z
a
w
a, 1968
[
2
]
Jędral W
.
, P
o
mp
y
w
ir
ow
e, W
y
da
w
nict
wo
Nau
ko
-
w
e PWN, War
s
z
a
w
a, 2001
[
3
]
K
o
rc
z
a
k
A.
,
Rok
ita J
.
, P
o
mp
y
i u
k
ład
y
p
o
mp
ow
e
–
o
blic
z
enia i pr
o
je
k
t
ow
anie, W
y
da
w
nict
wo
P
o
li-
techni
k
i Ślą
s
k
iej,
G
li
w
ice, 1998
[
4
]
Stępnie
w
s
k
i
M
.
, P
o
mp
y
, W
y
d
w
anict
w
a Nau
ko
-
wo
-Technic
z
ne, War
s
z
a
w
a, 1978
[
5
]
Papier
s
k
i
A.
,
B
ła
s
z
c
z
yk
A.
,
M
ulti
o
bjective
o
ptimi-
z
ati
o
n
o
f the
s
emi-
o
pen impeller in a centrifugal
pump b
y
a multilevel meth
o
d, J
o
urnal
o
f The
o
reti-
cal and
A
pplied
M
echanic
s
; V
o
l
.
49, pp
.
327-341
[
6
]
F
arid
A.
,
E
l-
A
z
m
A
l
y
A.
A.
,
A
bdalla H
.
M
.
,
E
ffect
o
f
s
emi-
o
pen impeller
s
ide clearance
o
n centrifu-
gal pump cavitati
o
n incepti
o
n,
I
nternati
o
nal J
o
ur-
nal
o
f C
o
mputati
o
nal Ph
y
s
ic
s
Serie
s
, V
o
l
.
1(2),
pp
.
24-39,
D
O
I
:
10
.
29167/a1i2p24-39
[
7
]
M
o
u
s
m
o
uli
s
G
.
, Ka
ss
an
o
s
I
.
,
A
ggidi
s
G
.
,
A
nagn
o
-
s
t
o
p
o
ul
o
s
I
.
, Numerical
s
imulati
o
n
o
f the perf
o
r-
mance
o
f a centrifugal pump
w
ith a
s
emi-
o
pen
impeller under n
o
rmal and cavitating c
o
nditi
o
n
s
,
A
pplied
M
athematical
M
o
deling, V
o
l
.
89,
Part 2, 2021, pp
.
1814-1834,
D
O
I
:
10
.
1016/
j
.
apm
.
2020
.
08
.
074
[
8
]
Z
hang
F
.
, Heng
Y
.
, Liu
Q
.
, Ta
o
R.
,
Y
ang W
.
,
Z
hu
D.
,
X
ia
o
R.
,
O
ptimi
z
ati
o
n de
s
ign
o
f a
s
emi-
o
pen cen-
trifugal impeller u
s
ing
G
A
-
F
u
zz
y
l
o
gic c
o
mbina-
ti
o
n
s
trateg
y
, J
o
urnal
o
f
A
pplied
F
luid
M
echanic
s
,
V
o
l
.
16, N
o.
7, 2023, pp
.
1427-1441,
D
O
I
:
10
.
47176/jafm
.
16
.
07
.
1655
[
9
]
Ay
ad
A.
F
.
,
A
bdalla H
.
M
.
,
E
l-
A
z
m
A
l
y
A.
A.
,
E
ffect
o
f
s
emi-
o
pen impeller
s
ide clearance
o
n the centri-
fugal pump perf
o
rmance u
s
ing C
F
D
,
A
er
o
s
pace
Science and Techn
o
l
o
g
y
, V
o
l
.
47, 2015, pp
.
247-
255,
D
O
I
:
10
.
1016/j
.
a
s
t
.
2015
.
09
.
033
[
10
]
E
ffi
o
m S
.
O
.
,
A
bam
F
.
,
O
fem S
.
,
E
ffi
o
m P
.
-C
.
,
O
n
o
-
chie
O
.
,
I
nah
O
.
,
O
du P
.
, C
F
D
anal
y
s
i
s
and
h
y
draulic perf
o
rmance
o
f t
wo
-pha
s
e fl
ow
in
a centrifugal pump
w
ith r
o
t
o
d
y
namic multi-impeller
c
o
nfigurati
o
n
s
,
A
frican J
o
urnal
o
f
A
dvance
s
in
E
ngineering and Techn
o
l
o
g
y
, V
o
l
.
1, N
o.
2, 2025,
pp
.
5-27
[
11
]
M
an
s
o
ur
M
.
, Thévenin
D.
,
I
mpact
o
f blade t
w
i
s
ting
and tip clearance
o
n centrifugal pump perf
o
rman-
ce under air
–
w
ater t
wo
-pha
s
e fl
ow
,
I
nternati
o
nal
J
o
urnal
o
f Heat and
F
luid
F
l
ow
, V
o
l
.
112, 2025,
pp
.
1-19,
D
O
I
:
10
.
1016/j
.
ijheatfluidfl
ow.
2024
.
109682
[
12
]
Wang K
.
, Liu H
.
, Wang L
.
,
G
u
o
P
.
, Wang
Y
.
,
Y
ang
J
.
,
E
ffect
o
f particle
s
i
z
e
o
n v
o
rte
x
s
tructure and
er
o
s
i
o
n behavi
o
r
o
f
s
emi-
o
pen centrifugal pump,
E
nerg
y
, V
o
l
.
293, 2024, pp
.
1-20,
D
O
I
:
10
.
1016/
j
.
energ
y.
2024
.
130576
[
13
]
Wang K
.
, Jia
o
Z
.
, Wang
Y
.
,
Do
ng J
.
, Liu H
.
,
F
eng
J
.
,
Q
uantitative in
s
ight
s
int
o
the effect
o
f particle
s
t
ok
e
s
number
o
n the er
o
s
i
o
n behavi
o
r in
s
emi--
o
pen centrifugal pump
:
V
o
rte
x
-particle-
s
urface
interacti
o
n, P
ow
der Techn
o
l
o
g
y
, V
o
l
.
476, 2026,
pp
.
1-18,
D
O
I
:
10
.
1016/j
.
p
ow
tec
.
2026
.
122360
[
14
]
A
NS
Y
S,
I
nc
.
,
A
NS
Y
S
F
luent U
s
er’
s
G
uide,
Can
o
n
s
burg, 2020
[
15
]
A
NS
Y
S,
I
nc
.
,
A
NS
Y
S
F
luent The
o
r
y
G
uide,
Can
o
n
s
burg, 2020
[
16
]
B
aba
y
igit
O
.
,
O
z
g
o
ren
M
.
,
Ak
s
oy
M
.
H
.
, K
o
ca-
a
s
lan
O
.
,
Ex
perimental and C
F
D
inve
s
tigati
o
n
o
f
a multi
s
tage centrifugal pump including lea
k
age
s
and balance h
o
le
s
,
D
e
s
alinati
o
n and Water Treat-
ment, V
o
l
.
67, 2017, pp
.
28-40,
D
O
I
:
10
.
5004/
d
w
t
.
2017
.
20153
