www.
inf
o
rmacjain
s
tal
.
c
o
m
.
pl12/202515
Ź
r
ó
d
ł
a
c
i
ep
ł
a
i
e
n
e
r
g
ii
e
l
e
kt
r
yc
z
n
e
j
I
n
t
r
o
d
u
ct
i
on
I
n la
s
t decade
s
, the ev
o
luti
o
n
o
f c
o
m-
puter calculati
o
n capacitie
s
permitted t
o
devel
o
p C
A
E
–
t
y
pe pr
o
gram
s
(C
o
mputer
A
ided
E
ngineering)
.
The aim
o
f the C
A
E
pr
o
gram
s
i
s
t
o
perf
o
rm
s
imulati
o
n
s
u
s
ing
mathematical and ph
y
s
ical m
o
del
s
at vari-
o
u
s
level
s
o
f preci
s
i
o
n
.
O
ne
o
f the m
o
s
t
imp
o
rtant applicati
o
n
s
o
f the C
A
E
t
y
pe
t
oo
l i
s
the C
F
D
field (C
o
mputati
o
nal
F
luid
Dy
namic
s
), permitting the
s
imulati
o
n
o
f
fl
ow
phen
o
mena, even ta
k
ing int
o
acc
o
unt
the c
o
mbu
s
ti
o
n
.
There i
s
a need here t
o
dif-
fer the C
A
E
t
oo
l
s
and the mathematical
and ph
y
s
ical m
o
del
s
.
The C
A
E
t
oo
l
s
are the
implementati
o
n
o
f mathematical and ph
y
s
-
ical m
o
del
s
int
o
c
o
mputer envir
o
nment
s
.
The mathematical and ph
y
s
ical m
o
del
s
u
s
ed in C
A
E
are a
s
et
o
f m
o
del
s
permitting
t
o
de
s
cribe vari
o
u
s
phen
o
mena
o
ccurring
in real life
.
The m
o
s
t
o
f thi
s
m
o
del
s
w
ere
k
n
ow
n even bef
o
re the c
o
mputer
s
era
.
The
appariti
o
n
o
f p
ow
erful c
o
mputer
s
permit-
ted t
o
u
s
e the
s
e m
o
del
s
, at vari
o
u
s
degree
s
o
f e
x
actitude, t
o
perf
o
rm
s
imulati
o
n
s
.
The
m
o
del
s
u
s
ed in C
A
E
are
s
till enhanced, b
y
c
o
ntinu
o
u
s
s
tudie
s
permitting t
o
c
o
mpare
the C
A
E
re
s
ult
s
and real phen
o
mena
.
T
o
da
y
, the ne
x
t C
A
E
t
oo
l
s
can be cited a
s
e
x
ample
:
A
n
s
y
s
,
F
luent,
A
baqu
s
,
O
pen-
F
o
am ect
.
The u
s
e
o
f the
s
e C
A
E
t
oo
l
s
per-
mitted fir
s
t t
o
reduce the pr
o
duct
s
elab
o
ra-
ti
o
n time and fund
s
reducing the number
o
f
perf
o
rmed pr
o
t
o
t
y
pe
s
.
Then, the C
A
E
t
oo
l
s
permitted t
o
di
s
c
o
ver and/
o
r under
s
tand
phen
o
mena b
y
the deep anal
y
s
i
s
o
f g
oo
d
qualit
y
s
imulati
o
n
s
[
1, 2
].
C
A
E
t
oo
l
s
permit
t
o
be m
o
re efficient and ec
o
n
o
mical in
term
s
o
f pr
o
duct
s
devel
o
pment and in
ph
y
s
ical phen
o
mena better under
s
tanding
.
The ga
s
micr
o
turbine
s
are devi
s
e
s
that
are
w
idel
y
u
s
ed in vari
o
u
s
applicati
o
n
s
:
in
aviati
o
n t
o
p
ow
er dr
o
ne
s
, in the aut
o
m
o
tive
indu
s
tr
y
a
s
car’
s
range e
x
tender
s
(e
.
g
.
Jag-
uar C
X
75), in the energ
y
indu
s
tr
y
a
s
electri-
cal (and heat) generat
o
r
s
.
G
a
s
micr
o
tur-
bine
s
pre
s
ent man
y
advantage
s
,
s
uch a
s
l
ow
n
o
i
s
e level, cheap de
s
ign and
o
pera-
ti
o
n, l
ow
emi
ss
i
o
n
s
, large t
y
pe
o
f fuel appli-
cabilit
y
, etc
.
The
s
e criteria are the rea
s
o
n f
o
r
the ga
s
micr
o
turbine device
s
w
ildl
y
u
s
e
.
[
3
]
The ga
s
micr
o
turbine
s
are device
s
that are
o
ften equipped
o
f diffu
s
i
o
n c
o
mbu
s
ti
o
n
Ź
r
ó
d
ł
a
c
i
ep
ł
a
i
e
n
e
r
g
ii
e
l
e
kt
r
yc
z
n
e
j
/
S
ou
rc
e
s
of
h
ea
t
a
n
d
e
l
e
ctr
i
c
i
ty
N
u
me
ri
c
a
l
Ev
a
l
u
a
t
i
on
of
t
h
e
E
q
u
ili
b
ri
u
m
C
o
mb
u
st
i
on
Mo
de
l
i
n
M
e
t
h
a
n
e
M
i
c
r
o
t
u
r
b
i
n
e
s
N
u
me
r
yc
z
n
a
o
c
e
n
a
m
o
de
l
u
r
ó
w
no
w
ag
o
w
eg
o
s
pa
l
a
n
i
a
w
m
i
k
r
o
t
u
r
b
i
n
a
c
h
me
t
a
no
wyc
h
J
E
A
N-
M
AR
C
F
Ą
F
ARA
,
ZI
EMO
W
I
T
M
A
L
E
CH
A
,
AR
TU
R
J
Ę
DR
US
Y
N
A
DO
I 10
.
36119/15
.
2025
.
12
.
2
T
o
da
y
w
hen preparing a C
F
D
s
tud
y
, there i
s
a need t
o
ma
k
e a c
o
mpr
o
mi
s
e bet
w
een the re
s
ult
s
accurac
y
(applied
m
o
del
s
) and the c
o
mputati
o
nal c
o
s
t
.
I
n thi
s
s
tud
y
the n
o
n-premi
x
ed equilibrium c
o
mbu
s
ti
o
n m
o
del i
s
a
ss
e
ss
ed b
y
a c
o
mparative numerical meth
o
d,
w
hen applied t
o
diffu
s
i
o
n t
y
pe ga
s
micr
o
turbine c
o
mbu
s
t
o
r methane p
ow
ered
.
I
n
o
rder t
o
ma
k
e it, a diffu
s
i
o
n t
y
pe ga
s
micr
o
turbine c
o
mbu
s
t
o
r methane p
ow
ered
s
imulati
o
n
w
a
s
d
o
ne t
w
ice, u
s
ing
o
ne time the n
o
n-premi
x
ed equilibrium c
o
mbu
s
ti
o
n m
o
del and
s
ec
o
nd time the
s
tead
y
diffu
s
i
o
n flamelet c
o
mbu
s
ti
o
n
m
o
del (
w
ith the u
s
e
o
f
G
ri-
M
ech 3
.
0 mechani
s
m),
w
hich i
s
s
uitable f
o
r thi
s
s
pecific applicati
o
n
.
The thermal
o
perati
o
n
parameter
s
o
f b
o
th
s
imulati
o
n
s
w
ere c
o
mpared and their anal
y
s
i
s
s
h
ow
n that equilibrium m
o
del permit
s
t
o
o
btain
s
accurate thermal re
s
ult
s
, c
o
mpared t
o
m
o
re c
o
mple
x
and accurate c
o
mbu
s
ti
o
n m
o
del a
s
the
s
tead
y
diffu
s
i
o
n flamelet
m
o
del
.
Ke
ywo
rd
s
:
G
a
s
M
icr
o
turbine;
D
iffu
s
i
o
n T
y
pe
Co
mbu
s
t
o
r;
Co
mbu
s
ti
o
n
M
o
del
s
;
C
F
D
;
G
ri-
M
ech 3
.
0
.
W
s
p
ó
łc
z
e
ś
nie, p
o
dc
z
a
s
pr
z
y
g
o
t
owyw
ania badań C
F
D
, i
s
tnieje
ko
niec
z
n
o
ś
ć
z
nale
z
ienia
ko
mpr
o
mi
s
u międ
z
y
d
ok
ładn
o
ś
cią
wy
ni
ków
(
z
a
s
t
o
s
ow
an
y
mi m
o
delami) a
ko
s
z
tem
o
blic
z
eni
owy
m
.
W niniej
s
z
y
m badaniu m
o
del
s
pala-
nia r
ów
n
ow
ag
ow
eg
o
t
y
pu d
y
fu
z
y
jneg
o
z
o
s
tał
o
ceni
o
n
y
met
o
dą p
o
r
ów
na
w
c
z
ej anali
z
y
numer
y
c
z
nej, pr
z
y
z
a
s
t
o
-
s
ow
aniu g
o
d
o
d
y
fu
z
y
jnej
ko
m
o
r
y
s
palania mi
k
r
o
turbin
y
ga
z
ow
ej
z
a
s
ilanej metanem
.
A
b
y
teg
o
d
oko
nać, pr
z
epr
o
-
w
ad
z
o
n
o
d
w
u
k
r
o
tnie
s
y
mulację d
y
fu
z
y
jnej
ko
m
o
r
y
s
palania
:
ra
z
z
wyko
r
z
y
s
taniem r
ów
n
ow
ag
ow
eg
o
m
o
delu
s
pa-
lania d
y
fu
z
y
jneg
o
, a drugi ra
z
z
u
ż
y
ciem m
o
delu
s
palania d
y
fu
z
y
jneg
o
o
parteg
o
o
pł
o
m
yk
i (
„
flamelet
”
z
j
.
ang
.
–
z
wyko
r
z
y
s
taniem mechani
z
mu reag
ow
ania
G
ri-
M
ech 3
.
0),
k
t
ó
r
y
je
s
t
o
dp
ow
iedni dla teg
o
r
o
d
z
aju
z
a
s
t
o
s
ow
ań
.
P
o
r
ów
nan
o
cieplne parametr
y
prac
y
o
bu
s
y
mulacji, a ich anali
z
a
wyk
a
z
ała,
ż
e m
o
del r
ów
n
ow
ag
owy
p
o
z
w
ala
u
z
y
s
k
ać bard
z
o
z
bli
ż
o
ne
wy
ni
k
i (a
z
atem
w
iar
y
g
o
dne)
w
p
o
r
ów
naniu
z
bard
z
iej
z
ł
o
ż
o
n
y
m i prec
y
z
y
jn
y
m m
o
de-
lem
s
palania, ja
k
im je
s
t m
o
del
s
palania d
y
fu
z
y
jneg
o
o
parteg
o
o
pł
o
m
yk
i
.
Sł
ow
a
k
luc
z
ow
e
:
mi
k
r
o
turbin
y
ga
z
ow
e, d
y
fu
z
y
jne
ko
m
o
r
y
s
palania, m
o
dele
s
palania,
C
F
D
,
G
ri-
M
ech 3
.
0
.
Jean-
M
arc
F
ąfara http
s
:
//
o
rcid
.o
rg/0000-0002-3636-1188, e-mail
:
jean-marc
.
fafara
@
p
w
r
.
edu
.
pl,
Z
iem
ow
it
M
alecha http
s
:
//
o
rcid
.o
rg/0000-0001-8560-760
X
, e-mail
:
z
iem
ow
it
.
malecha
@
p
w
r
.
edu
.
pl,
A
rtur Jędru
s
y
na http
s
:
//
o
rcid
.o
rg/0000-0002-9728-9861, e-mail
:
A
rtur
.
jedru
s
y
na
@
p
w
r
.
edu
.
pl
‒
Wr
o
cła
w
Univer
s
it
y
o
f Science and
Techn
o
l
o
g
y
(WUST),
F
acult
y
o
f
M
echanical and P
ow
er
E
ngineering,
D
epartment
o
f Cr
yo
genic
s
and
A
er
o
nautical
E
ngineering, Wr
o
cła
w
, P
o
land
.
1612/2025
www.
inf
o
rmacjain
s
tal
.
c
o
m
.
pl
Ź
chamber
s
.
The diffu
s
i
o
n c
o
mbu
s
t
o
r are
o
lder techn
o
l
o
gicall
y
s
o
luti
o
n
s
, in
w
hich the
o
x
idi
z
er and fuel are
s
upplied
s
eparatel
y.
I
n thi
s
k
ind
o
f c
o
mbu
s
t
o
r the c
o
mbu
s
ti
o
n i
s
n
o
n-premi
x
ed, ev
o
lving fr
o
m rich t
o
leam
mi
x
ture, permitting g
oo
d flame
s
tabilit
y
and
s
afe c
o
mbu
s
t
o
r
o
perati
o
n
.
Thi
s
device
s
can
be p
ow
ered b
y
vari
o
u
s
fuel (jet-
A
, ga
s
o
-
line, petr
o
l,
w
a
s
te ga
s
, methane, ect
.
), but
o
ne
o
f the m
o
s
t p
o
pular fuel i
s
methane
.
A
cc
o
rding t
o
the ab
o
ve, it mu
s
t be
den
o
ted that actuall
y
man
y
ga
s
micr
o
tur-
bine
s
methane p
ow
ered are de
s
igned and
that the
o
ne
o
f m
o
s
t efficient de
s
ign t
oo
l
s
i
s
the C
F
D
d
o
main
.
I
n
o
rder t
o
enhance the
de
s
ign pr
o
ce
ss
o
f the
s
e device
s
, there i
s
a need t
o
u
s
e C
A
E
t
oo
l
s
permitting t
o
m
o
del the ph
y
s
ical phen
o
mena a
s
:
fluid
fl
ow
, c
o
mbu
s
ti
o
n, and radiati
o
n
[
3
].
O
ne
o
f the m
o
s
t p
o
pular C
F
D
t
oo
l able t
o
ma
k
e
it i
s
A
n
s
y
s
F
luent
[
4
].
A
s
e
x
p
o
s
ed ab
o
ve,
the applied mathematical and ph
y
s
ical
m
o
del
s
can be implemented at vari
o
u
s
degree
s
o
f e
x
actitude
.
A
s
e
x
p
o
s
ed bef
o
re, the diffu
s
i
o
n t
y
pe
c
o
mbu
s
t
o
r
s
are
w
idel
y
u
s
ed in the ga
s
micr
o
turbine
s
.
I
n
o
rder t
o
numericall
y
anal-
y
s
e the
s
e
k
ind
o
f device
s
, there i
s
a need t
o
u
s
e a n
o
n-premi
x
ed c
o
mbu
s
ti
o
n m
o
del,
applied t
o
C
F
D
meth
o
d
s
.
The
o
ften applied
c
o
mbu
s
ti
o
n m
o
del
s
are the finite-rate
chemi
s
tr
y
w
ith the
E
dd
y
D
i
ss
ipati
o
n
M
o
del
(
E
D
M
)
[
5
–
8
]
o
r the
E
dd
y
D
i
ss
ipati
o
n
C
o
ncept (
E
D
C)
[
9
–
13
]
, C
o
mp
o
s
iti
o
n P
D
F
Tran
s
p
o
rt
[
14
–
16
]
and the
s
tead
y
diffu-
s
i
o
n flamelet m
o
del
[
17
–
20
].
E
dd
y
-di
ss
ipati
o
n m
o
del
–
The m
o
del
all
ow
s
f
o
r the calculati
o
n
o
f the reacti
o
n
rate ba
s
ed
o
n a
s
imple c
o
mbu
s
ti
o
n mecha-
ni
s
m (preferabl
y
t
wo
-
s
tep mechani
s
m), ta
k
-
ing turbulence int
o
acc
o
unt
.
The m
o
del
d
o
e
s
n
o
t
s
upp
o
rt the
s
imulati
o
n
o
f detailed
c
o
mbu
s
ti
o
n mechani
s
m
s
,
w
hich re
s
ult
s
fr
o
m
the fact that it d
o
e
s
n
o
t c
o
n
s
ider chemical
k
inetic
s
and a
ss
ume
s
that all reacti
o
n
s
pr
o
-
ceed at the
s
ame rate
–
an inc
o
rrect
a
ss
umpti
o
n a
s
the number
o
f reacti
o
n
s
in
the c
o
mbu
s
ti
o
n mechani
s
m increa
s
e
s
.
The
m
o
del i
s
o
f general-purp
o
s
e u
s
e f
o
r c
o
m-
bu
s
ti
o
n pr
o
ce
ss
m
o
delling; it i
s
c
o
mputa-
ti
o
nall
y
efficient but d
o
e
s
n
o
t
s
upp
o
rt
wo
r
k
w
ith c
o
mple
x
c
o
mbu
s
ti
o
n
k
inetic
s
,
w
hich
limit
s
it
s
applicabilit
y
and accurac
y.
E
dd
y
-di
ss
ipati
o
n-c
o
ncept(
E
D
C)
m
o
del
–
The m
o
del i
s
a
s
ignificantl
y
impr
o
ved and e
x
tended ver
s
i
o
n
o
f the
E
dd
y
-
D
i
ss
ipati
o
n
M
o
del
.
I
t acc
o
unt
s
n
o
t
o
nl
y
f
o
r turbulence in the calculati
o
n
s
but
al
s
o
include
s
chemical
k
inetic
s
.
Thi
s
all
ow
s
f
o
r the implementati
o
n
o
f detailed c
o
mbu
s
-
ti
o
n mechani
s
m
s
.
The m
o
del i
s
relativel
y
accurate and can be c
o
n
s
idered a gener-
al-purp
o
s
e m
o
del f
o
r c
o
mbu
s
ti
o
n pr
o
ce
ss
s
imulati
o
n
s
.
Since it
s
o
lve
s
tran
s
p
o
rt equa-
ti
o
n
s
f
o
r each
s
pecie
s
during pr
o
ce
ss
ing, it
i
s
highl
y
demanding in term
s
o
f c
o
mputa-
ti
o
nal re
s
o
urce
s
,
w
hich can
s
ignificantl
y
increa
s
e c
o
mputati
o
n time
.
C
o
mp
o
s
iti
o
n P
D
F
Tran
s
p
o
rt
–
I
t i
s
an
alternative m
o
del t
o
the
F
inite-
R
ate Chem-
i
s
tr
y
appr
o
ach, in
w
hich
s
o
lving the aver-
aged
s
pecie
s
equati
o
n
s
i
s
replaced b
y
c
o
mputing the derivative
o
f the
s
e equa-
ti
o
n
s
at a
s
elected l
o
cati
o
n and appr
o
x
i-
mating them u
s
ing a pr
o
babilit
y
den
s
it
y
functi
o
n (P
D
F
)
.
The P
D
F
ha
s
a dimen
s
i
o
n
o
f
N
+
1,
w
here N i
s
the number
o
f
s
pecie
s
included in the c
o
mbu
s
ti
o
n mechani
s
m
.
Thi
s
appr
o
ach all
ow
s
f
o
r b
y
pa
ss
ing highl
y
n
o
nlinear reacti
o
n rate
s
.
The m
o
del
o
ffer
s
g
oo
d accurac
y
and i
s
al
s
o
c
o
n
s
idered
a general-purp
o
s
e m
o
del f
o
r c
o
mbu
s
ti
o
n
pr
o
ce
ss
s
imulati
o
n
s
.
Unf
o
rtunatel
y
, it i
s
al
s
o
c
o
mputati
o
nall
y
demanding and i
s
char-
acteri
z
ed b
y
l
o
ng c
o
mputati
o
n time
s
.
The N
o
n-Premi
x
ed
M
o
del appr
o
ach i
s
ba
s
ed
o
n determining mean temperature,
den
s
it
y
, and ma
ss
fracti
o
n
s
o
f chemical
s
pecie
s
u
s
ing the mi
x
ture fracti
o
n and it
s
variance
.
Thi
s
m
o
del ta
k
e
s
int
o
acc
o
unt the
influence
o
f turbulence
o
n c
o
mbu
s
ti
o
n
.
E
quilibrium
M
o
del
–
the m
o
del a
ss
ume
s
a
s
tate
o
f chemical equilibrium,
w
hich i
s
n
o
t entirel
y
accurate f
o
r reacti
o
n
s
that, in
realit
y
, d
o
n
o
t reach equilibrium
.
Stead
y
D
iffu
s
i
o
n
F
lamelet
M
o
del
–
thi
s
m
o
del
all
ow
s
f
o
r the inclu
s
i
o
n
o
f detailed chemi-
cal c
o
mbu
s
ti
o
n
k
inetic
s
(the chemi
s
tr
y
can
be in n
o
n-equilibrium
s
tate, but cl
o
s
e t
o
)
.
The
s
elected c
o
mbu
s
ti
o
n m
o
del i
s
c
o
mpu-
tati
o
nall
y
efficient
.
The main limitati
o
n
s
o
f the
E
quilibrium
c
o
mbu
s
ti
o
n m
o
del c
o
mpared t
o
the
F
lame-
let m
o
del are li
s
ted bel
ow:
l
E
quilibrium m
o
del ma
y
n
o
t predict
intermediate
s
pecie
s
(C
O
, N
Ox
, etc
.
)
a
s
accuratel
y
a
s
F
lamelet m
o
del, that
re
s
o
lve
s
finite rate
k
inetic
s
ma
k
ing p
o
s
-
s
ible t
o
capture p
o
llutant f
o
rmati
o
n
and inc
o
mplete c
o
mbu
s
ti
o
n, e
s
pecial-
l
y
in regi
o
n
s
w
ith rapid mi
x
ing, quench-
ing,
o
r flame e
x
tincti
o
n;
l
E
quilibrium m
o
del a
ss
ume
s
the entire
d
o
main a
s
unif
o
rm equilibrium pr
o
d-
uct
s
,
w
hile
F
lamelet m
o
del retain
s
s
pa-
tial gradient
s
acr
o
ss
the flame fr
o
nt
(thic
k
ne
ss
, temperature, radical di
s
tri-
buti
o
n);
l
E
quilibrium m
o
del predict
s
a
s
table
flame in pre
s
ence
o
f fuel and
o
x
idi
z
er,
w
hile
F
lamelet m
o
del ta
k
e
s
int
o
acc
o
unt the
s
calar di
ss
ipati
o
n rate,
ma
k
ing p
o
ss
ible t
o
predict l
o
cal e
x
tinc-
ti
o
n and reigniti
o
n in turbulent fl
ow
s
;
l
E
quilibrium m
o
del a
ss
ume
s
in
s
tanta-
ne
o
u
s
mi
x
ing and chemi
s
tr
y
w
hile
F
lamelet m
o
del treat
s
mi
x
ing (
s
calar
di
ss
ipati
o
n rate) and chemi
s
tr
y
;
l
E
quilibrium m
o
del re
s
ult
s
are in
s
en
s
i-
tive t
o
fl
ow
s
train, turbulence, and mi
x
-
ing rate
s
c
o
mpared t
o
F
lamelet m
o
del
that ta
k
e
s
the
s
e phen
o
mena int
o
acc
o
unt;
l
E
quilibrium generall
y
pr
o
vide
s
adia-
batic flame temperature,
w
hile
F
lame-
let m
o
del include
s
heat l
o
ss
e
s
and
finite-rate effect
s
, leading t
o
m
o
re real-
i
s
tic temperature
s
.
B
a
s
ed
o
n the ab
o
ve, it can be
s
tated
that the
s
electi
o
n
o
f c
o
mbu
s
ti
o
n m
o
del i
s
a c
o
mpr
o
mi
s
e bet
w
een re
s
ult accurac
y
and c
o
mputati
o
nal time
.
The N
o
n-Pre-
mi
x
ed
E
quilibrium c
o
mbu
s
ti
o
n m
o
del i
s
a m
o
del that a
ss
ume
s
the c
o
mbu
s
ti
o
n
o
ccur
s
in the chemical equilibrium
.
I
n the
ga
s
micr
o
turbine, the c
o
mbu
s
ti
o
n time i
s
reduced b
y
the
s
h
o
rt length
o
f the c
o
mbu
s
-
ti
o
n chamber
.
I
t mean
s
that the c
o
mbu
s
ti
o
n
ma
y
s
be n
o
t
o
n it
s
chemical equilibrium
.
A
t
the
s
ame time, the c
o
mbu
s
ti
o
n in ga
s
micr
o
turbine i
s
s
tr
o
ngl
y
turbulent, due t
o
it
s
de
s
ign
.
A
s
the turbulence
o
f a flame
increa
s
e
s
, it
s
chemical rate increa
s
e
s
.
Thi
s
phen
o
men
o
n c
o
uld permit t
o
m
o
ve cl
o
s
er
t
o
the chemical equilibrium
.
Ta
k
ing int
o
acc
o
unt b
o
th phen
o
mena (
s
h
o
rt length
and high turbulence level), the c
o
mbu
s
ti
o
n
in ga
s
micr
o
turbine device
s
s
eem
s
n
o
t t
o
be t
oo
far fr
o
m the equilibrium c
o
mbu
s
ti
o
n,
ma
k
ing thi
s
m
o
del partiall
y
applicable
.
The aim
s
o
f thi
s
paper i
s
t
o
c
o
mpare the
N
o
n-Premi
x
ed Stead
y
D
iffu
s
i
o
n
F
lamelet
m
o
del,
k
n
ow
n t
o
be accurate f
o
r ga
s
micr
o
turbine c
o
mbu
s
ti
o
n m
o
delling,
w
ith
the
E
quilibrium m
o
del, rarel
y
(n
o
t) u
s
ed f
o
r
thi
s
purp
o
s
e, under the thermal a
s
pect
.
The
C
F
D
s
tud
y
w
ill be c
o
nducted u
s
ing a
s
elf-
de
s
igned c
o
mbu
s
ti
o
n chamber f
o
r meth-
ane p
ow
ered ga
s
micr
o
turbine
o
f ab
o
ut
40
k
W
o
f mechanical
o
utput p
ow
er
.
A
fter calculati
o
n
s
, the t
wo
m
o
del
s
ther-
mal pr
o
prietie
s
w
ill be c
o
mpared
.
A
s
the
N
o
n-Premi
x
ed Stead
y
D
iffu
s
i
o
n
F
lamelet
m
o
del i
s
k
n
ow
n t
o
pr
o
vide accurate re
s
ult
s
,
if it
s
re
s
ult
s
w
ill be
s
imilar t
o
the
s
e
o
f the
N
o
n-Premi
x
ed
E
quilibrium, it
w
ill mean
that the N
o
n-Premi
x
ed
E
quilibrium m
o
del
i
s
s
uitable and accurate f
o
r methane p
ow
-
ered ga
s
micr
o
turbine diffu
s
i
o
n t
y
pe
c
o
m-bu
s
t
o
r
s
.
I
n thi
s
s
tud
y
, the thermal
pr
o
prietie
s
w
ill be chec
k
ed
.
I
f the u
s
e
o
f the N
o
n-Premi
x
ed
E
quilib-
rium m
o
del
w
ill be p
o
s
itivel
y
a
ss
e
ss
ed in
thi
s
s
pecific applicati
o
n, it
w
ill permit t
o
engineer
s
and
s
cienti
s
t
s
t
o
perf
o
rm ea
s
ier
and u
s
ing m
o
re ba
s
ic c
o
mbu
s
ti
o
n m
o
del
f
o
r preliminarie
s
thermal anal
y
s
e
s
o
f c
o
m-
bu
s
t
o
r
s
.
I
t
w
ill permit t
o
o
pen ne
w
applica-
ti
o
n
s
t
o
the
s
tudied c
o
mbu
s
ti
o
n m
o
del
.
17
www.
inf
o
rmacjain
s
tal
.
c
o
m
.
pl
12/2025
Ź
r
ó
d
ł
a
c
i
ep
ł
a
i
e
n
e
r
g
ii
e
l
e
kt
r
yc
z
n
e
j
E
l
s
e, the paper
w
ill permit t
o
prevent t
o
n
o
t
u
s
e thi
s
m
o
del f
o
r the
s
e
o
r
s
imilar purp
o
s
e
s
.
A
cc
o
rding t
o
literature revie
w
, thi
s
a
s
pect
o
f the n
o
n-premi
x
ed equilibrium c
o
mbu
s
-
ti
o
n m
o
del
w
a
s
n
o
t
y
et
s
tudied
.
S
t
u
d
y c
a
s
e
c
o
mb
u
st
o
r
a
n
d
o
pe
r
a
t
i
n
g
c
on
d
i
t
i
on
s
The ann
o
unced re
s
earch need t
o
be
perf
o
rmed
o
n a methane p
ow
ered ga
s
micr
o
turbine
w
hich
o
perati
o
n parameter
s
are defined
.
T
o
re
s
p
o
nd t
o
thi
s
demand,
a ga
s
micr
o
turbine c
o
mbu
s
ti
o
n chamber
w
a
s
calculated, de
s
igned and 3
D
m
o
del
w
a
s
created, u
s
ing S
o
lid
E
dge C
AD
t
oo
l
[
21
].
Thi
s
c
o
mbu
s
t
o
r i
s
de
s
igned f
o
r
a 40
k
W
o
utput mechanical ga
s
micr
o
tur-
bine
.
The c
o
mbu
s
ti
o
n chamber
o
perati
o
n
parameter
s
are li
s
ted in Table 1
.
Thi
s
device
de
s
ign i
s
pre
s
ented in
F
igure 1
.
I
n the pa
s
t,
thi
s
c
o
mbu
s
t
o
r
w
a
s
alread
y
u
s
ed in
o
ther
re
s
earch
[
3, 22
].
T
ab
l
e
1
.
O
pe
r
a
t
i
on
pa
r
ame
t
e
rs
of
t
h
e
u
s
ed
me
t
h
a
n
e
p
o
w
e
r
ed
ga
s
m
i
cr
o
t
u
r
b
i
n
e
O
perati
o
nC
o
mbu
s
t
o
r inlet C
o
mbu
s
t
o
r
o
utlet
parameter
s
s
ecti
o
n
s
ecti
o
n
p*
[k
Pa
]
325312
p
[k
Pa
]
307301
T*
[
K
]
4331185
T
[
K
]
4261175
N
u
me
ri
c
a
l
me
t
ho
d
s
C
a
l
c
u
l
a
t
i
on
d
o
ma
i
n
The 3
D
m
o
del
o
f c
o
mbu
s
ti
o
n chamber
w
a
s
created u
s
ing S
o
lid
E
dge
s
o
ft
w
are
[
21
]
,
w
hile it
s
w
aterfl
ow
m
o
del, enabling
numerical calculati
o
n
s
,
w
a
s
generated
ba
s
ed
A
n
s
y
s
F
luent-
M
e
s
hing
s
o
ft
w
are
[
4
].
The generati
o
n
o
f c
o
mputati
o
nal me
s
h i
s
o
ne
o
f m
o
s
t imp
o
rtant
s
tep
s
in c
o
nducting
numerical
s
tudie
s
o
f c
o
mbu
s
ti
o
n chamber
s
.
T
o
generate a me
s
h
o
f the c
o
mbu
s
ti
o
n
chamber, tetrahedral element
s
are
o
ften
u
s
ed, a
s
the
y
have alread
y
pr
o
ven accu-
rac
y
in numerical calculati
o
n
s
o
f c
o
mbu
s
-
t
o
r
s
in the pa
s
t
[
18, 19, 25
].
The u
s
e
o
f thi
s
element all
ow
s
f
o
r the filling
o
f highl
y
c
o
m-
ple
x
c
o
mputati
o
nal d
o
main ge
o
metrie
s
w
hile maintaining acceptable me
s
h qualit
y
parameter
s
(S
k
e
w
ne
ss
,
O
rth
o
g
o
nalit
y
, and
A
s
pect
R
ati
o
)
.
R
ecentl
y
,
s
ignificant eff
o
rt
s
have been made t
o
devel
o
p numerical
me
s
he
s
build fr
o
m p
o
l
y
hedral element
s
.
Similar t
o
tetrahedral element
s
, p
o
l
y
hedral
element
s
all
ow
f
o
r
o
btaining g
oo
d c
o
mpu-
tati
o
nal re
s
ult
s
w
hile
s
imultane
o
u
s
l
y
impr
o
v-
ing me
s
h qualit
y
[
26, 27
].
Theref
o
re, p
o
l
y
-
hedral element
s
w
ere
s
elected f
o
r building
the c
o
mputati
o
nal me
s
h
.
F
ir
s
tl
y
, the me
s
h cell
s
w
ith a ma
x
imum
length
o
f 0
.
8 mm
w
ere applied f
o
r thi
s
re
s
earch
.
Then, the v
o
lume me
s
h
w
a
s
gener-
ated and impr
o
ved b
y
appl
y
ing the value
o
f
0
.
45 a
s
the cell de
s
ired
o
rth
o
g
o
nal qualit
y.
F
inall
y
, five b
o
undar
y
la
y
er
s
w
ere generat-
ed in
o
rder t
o
limit the
Y
+
value at le
ss
than
300
.
A
cc
o
rding t
o
the literature
[
18, 25
]
,
the
o
btained calculati
o
n d
o
main me
s
h i
s
s
ufficient t
o
pr
o
vide reliable re
s
ult
s
.
Table 2
s
h
ow
s
the qualit
y
parameter
s
o
f the
o
btained
me
s
h
s
y
s
tem,
w
hile
F
igure 2 pre
s
ent
s
the
me
s
h
o
f the calculati
o
n d
o
main
.
M
a
t
h
ema
t
i
c
a
l
m
o
de
l
s
Numerical
s
tudie
s
o
f a 3
D
c
o
mbu
s
ti
o
n
chamber
w
ere carried
o
ut u
s
ing
A
n
s
y
s
F
lu-
ent
s
o
ft
w
are
[
4
].
The f
o
ll
ow
ing ph
y
s
ic
o
-
chemical pr
o
ce
ss
e
s
w
ere m
o
delled
:
turbu-
lent fl
ow
, n
o
n-premi
x
ed c
o
mbu
s
ti
o
n in the
ga
s
pha
s
e, and heat tran
s
fer b
y
radiati
o
n
w
ithin the c
o
mputati
o
nal d
o
main
.
The
s
e
k
e
y
phen
o
mena
w
ere m
o
delled t
o
o
btain
accurate c
o
mparative numerical re
s
ult
s
.
M
o
del
o
f the turbulent fl
ow
F
o
r the fl
ow
de
s
cripti
o
n, the
RA
NS
(
R
e
y
n
o
ld
s
-
A
veragedNavier-St
ok
e
s
)
appr
o
ach
w
a
s
ch
o
s
en,
w
hich i
s
ba
s
ed
o
n
the averaged Navier-St
ok
e
s
equati
o
n
s
.
T
o
de
s
cribe turbulence, the
R
eali
z
able
k
-
ε
m
o
del
w
a
s
applied,
w
hich i
s
w
idel
y
u
s
ed
in man
y
indu
s
trial and
s
imilar applicati
o
n
s
.
Thi
s
m
o
del all
ow
s
f
o
r fl
ow
m
o
delling
w
ith
acceptable accurac
y
at a l
ow
c
o
mputa-
ti
o
nal c
o
s
t
.
F
o
r near-
w
all fl
ow
, the
“
E
nhanced Wall Treatment
”
appr
o
ach
w
a
s
applied
.
Thi
s
all
ow
s
c
o
mputing the
fl
ow
in the near-
w
all regi
o
n
w
hen the n
o
r-
mali
z
ed di
s
tance fr
o
m the
w
all i
s
le
ss
than
o
r equal t
o
unit
y
(
y
+
≤
1),
o
r b
y
u
s
ing
a near-
w
all functi
o
n called the
“
E
nhanced
Wall
F
uncti
o
n
”
(
y
+
>
1)
.
Thi
s
i
s
an
o
ptimal
s
o
luti
o
n
w
hen the phen
o
mena
o
ccurring in
the near-
w
all regi
o
n are n
o
t critical, a
s
i
s
the ca
s
e in thi
s
c
o
mputati
o
nal
s
tud
y.
M
o
del
o
f the radiati
o
n
I
n the inve
s
tigated c
o
mbu
s
ti
o
n cham-
ber, the d
o
minant heat tran
s
fer mechani
s
m
i
s
radiati
o
n
.
T
o
de
s
cribe thi
s
phen
o
men
o
n,
the
D
i
s
crete
O
rdinate
s
(
D
O
) m
o
del
[
18
]
w
a
s
u
s
ed,
w
hich treat
s
the c
o
mputati
o
nal
d
o
main a
s
a mi
x
ture
o
f gra
y
ga
s
e
s
.
The t
wo
main c
o
mp
o
und
s
that affect
s
ignificantl
y
ab
s
o
rpti
o
n and emi
ss
i
o
n capabilitie
s
in the
c
o
mbu
s
ti
o
n
z
o
ne (
w
ithin the c
o
mbu
s
ti
o
n
chamber) are carb
o
n di
o
x
ide and
w
ater
s
team
.
T
o
accuratel
y
m
o
del the menti
o
ned
pr
o
pertie
s
o
f the ga
s
mi
x
ture, the Weighted
Sum
o
f
G
ra
y
G
a
s
e
s
M
o
del (WS
GGM
)
w
a
s
s
elected
.
Thi
s
m
o
del acc
o
unt
s
f
o
r the
radiative pr
o
pertie
s
o
f the flue ga
s
c
o
mp
o
-
nent
s
ba
s
ed
o
n e
x
perimental
s
tudie
s
[
26
]
and i
s
w
idel
y
applied in numerical calcula-
ti
o
n
s
o
f c
o
mbu
s
ti
o
n chamber
s
.
The cham-
ber
w
all
s
w
ere a
ss
umed t
o
behave a
s
blac
k
b
o
d
y
s
urface
s
[
27
].
M
o
del
s
o
f the n
o
n-premi
x
ed c
o
mbu
s
ti
o
n
B
o
th, the N
o
n-Premi
x
ed
E
quilibrium
C
o
mbu
s
ti
o
n
M
o
del and the Stead
y
D
iffu-
s
i
o
n
F
lamelet C
o
mbu
s
ti
o
n
M
o
del a
ss
ume
the u
s
e
o
f a
“
L
ook
-up Table
”
(generated
F
i
g
u
r
e
1
.
M
e
t
h
a
n
e
p
o
w
e
r
ed
ga
s
m
i
cr
o
t
u
r
b
i
n
e
c
o
mb
u
st
o
r
de
s
i
g
n
ed
fo
r
CF
D
r
e
s
ea
rc
h
F
i
g
.
2
C
o
mb
u
st
o
r c
a
l
c
u
l
a
t
i
on
d
o
ma
i
n
v
i
e
w
T
ab
l
e
2
.
C
o
mb
u
st
o
r
me
s
h
q
u
a
li
ty
pa
r
ame
t
e
rs
M
a
x
imum
s
k
e
w
ne
ss
[
-
]
Number
o
f
M
a
x
imum
M
inimum
cell
s
a
s
pect rati
o
o
rth
o
g
o
nal
[
milli
o
n
s
][
-
]
qualit
y
[
-
]
5
.
838
.
30
.
8950
.
435
1812/2025
www.
inf
o
rmacjain
s
tal
.
c
o
m
.
pl
Ź
during pre-pr
o
ce
ss
ing
s
tep) and
s
everal
calculated c
o
efficient
s
during pr
o
ce
ss
ing
(
s
uch a
s
the mean mi
x
ture fracti
o
n and it
s
variance, the mean
s
calar di
ss
ipati
o
n rate,
and the mean enthalp
y
) t
o
retrieve c
o
m-
bu
s
ti
o
n pr
o
ce
ss
mean parameter
s
(
s
pecie
s
ma
ss
fracti
o
n, temperature, and den
s
it
y
)
.
i
i
ii
ii
―
i
N
o
n Premi
x
ed
E
quilibrium C
o
mbu
s
ti
o
n
M
o
del
The in
s
tantane
o
u
s
c
o
mbu
s
ti
o
n parame-
ter
s
,
F
,
s
uch a
s
s
pecie
s
ma
ss
fracti
o
n, tem-
perature, and den
s
it
y
, are calculated ba
s
ed
o
n the available chemical
s
pecie
s
included
in the c
o
mputati
o
n
s
, the general la
w
s
o
f
chemical reacti
o
n
s
, the l
o
cal enthalp
y
level
(in the ca
s
e
o
f n
o
n-adiabatic pr
o
ce
ss
), and
the availabilit
y
o
f
o
x
idi
z
er and fuel,
w
hich
are de
s
cribed u
s
ing the mi
x
ture fracti
o
n
.
The
available chemical
s
pecie
s
and the enthal-
p
y
level
s
are defined during the pre-pr
o
-
ce
ss
ing
s
tep b
y
s
pecif
y
ing the fuel and
o
x
i-
di
z
er
s
pecie
s
and partiall
y
b
y
their
tempera-ture
s
.
The mi
x
ture fracti
o
n ta
k
e
s
value
s
fr
o
m 0 (pure
o
x
idi
z
er) t
o
1 (pure
fuel)
.
B
a
s
ed
o
n thi
s
s
et
o
f variable
s
and their
range
s
, t
o
geth-er
w
ith the general chemical
reacti
o
n la
w
s
, the in
s
tantane
o
u
s
value
s
o
f
the parameter
s
de
s
cribing the c
o
mbu
s
ti
o
n
pr
o
ce
ss
at equi-librium,
F
, are calculated
f
o
r each
s
tate,
w
here
F
=
F
(f,H)
.
Here, a
n
o
n-adiabatic
B
eta-t
y
pe pr
o
babilit
y
den
s
it
y
functi
o
n (P
D
F
) p
=
p (f, H) i
s
u
s
ed
.
I
n
o
rder t
o
s
implif
y
the calculati
o
n
s
, the
ne
x
t a
ss
umpti
o
n i
s
d
o
ne
:
the enthalp
y
fluc-
tuati
o
n
s
are independent
o
f the enthalp
y
level
.
Thi
s
a
ss
umpti
o
n c
o
nduct
s
t
o
the u
s
e
o
f mean enthalp
y
in
s
tead
o
f the in
s
tanta-
ne
o
u
s
enthalp
y.
B
ecau
s
e
o
f that, it can be
n
o
ted that
F
=
F
(f,H) and 1
=
p(f)
.
The integrati
o
n
o
f the in
s
tantane
o
u
s
parameter
s
F
w
ith the pr
o
babilit
y
den
s
it
y
functi
o
n (P
D
F
) p all
ow
s
f
o
r the generati
o
n
o
f
the L
ook
-up Table (in the ca
s
e f
o
r the N
o
n-
Premi
x
ed
E
quilibrium C
o
mbu
s
ti
o
n
M
o
del)
thr
o
ugh the f
o
ll
ow
ing equati
o
n (3
.
1)
:
(3
.
1)
‒
―
―
‒
――
The re
s
ult
o
f the
s
e calculati
o
n
s
i
s
the
generati
o
n
o
f a databa
s
e that can be u
s
ed
during the pr
o
ce
ss
ing
s
tep, u
s
ing the val-
ue
s
o
f the f
o
ll
ow
ing parameter
s
:
f , f
’2
and
H, calculated u
s
ing the appr
o
priate tran
s
-
p
o
rt equati
o
n
s
during pr
o
ce
ss
ing
s
tep
.
Thi
s
L
ook
-up Table return
s
the mean value
s
o
f
parameter
s
de
s
cribing the c
o
mbu
s
ti
o
n pr
o
-
ce
ss
(ma
ss
fracti
o
n
o
f the i-th
s
pecie
s
,
den
s
it
y
, and temperature)
:
Y
i
,
r
o
ra
z
T
.
Stead
y
D
iffu
s
i
o
n
F
lamelet C
o
mbu
s
ti
o
n
M
o
del
The in
s
tantane
o
u
s
c
o
mbu
s
ti
o
n param-
eter
s
F
i
,
s
uch a
s
s
pecie
s
ma
ss
fracti
o
n,
iii
temperature, and den
s
it
y
, are calculated
ba
s
ed
o
n the c
o
mbu
s
ti
o
n mechani
s
m
implemented f
o
r the calculati
o
n
s
(in thi
s
s
tud
y
ca
s
e,
G
R
I
-
M
ech 3
.
0), the availabil-
it
y
o
f
o
x
idi
z
er and fuel de
s
cribed b
y
the
mi
x
ture fracti
o
n and it
s
variance, a
s
w
ell a
s
the
s
calar di
ss
ipati
o
n rate
.
The enthalp
y
i
s
al
s
o
t
o
be ta
k
en int
o
acc
o
unt
w
hen a n
o
n-
adiabatic
s
y
s
tem i
s
treated
.
B
a
s
ed
o
n thi
s
s
et
o
f variable
s
and their value range
s
,
s
elected mechani
s
m, the in
s
tantane
o
u
s
parameter
s
de
s
cribing the c
o
mbu
s
ti
o
n pr
o
-
ce
ss
in a
s
tate deviating fr
o
m equilibrium
(e
x
pre
ss
ed b
y
the
s
calar di
ss
ipati
o
n rate)
are calculated,
F
,
w
here
F
=
F
(f,
c
,H)
.
E
ach
o
f the
s
e
c
s
tate
s
i
s
referred t
o
a
s
a
“
flamelet
”.
T
o
generate the flamelet
s
truc-
ture parameter
s
f
o
r each
s
calar di
ss
ipati
o
n
rate
c
, equati
o
n
s
(3
.
2) f
o
r each
s
pecie
s
and
o
ne energ
y
equati
o
n (3
.
3) are
s
o
lved
:
(3
.
2)
(3
.
3)
ii
―
i
The databa
s
e
o
f flamelet
s
u
s
ed in thi
s
c
o
mbu
s
ti
o
n m
o
del
w
a
s
generated ba
s
ed
o
n the
G
R
I
-
M
ech 3
.
0 c
o
mbu
s
ti
o
n mecha-
ni
s
m
[
28
].
Thi
s
mechani
s
m include
s
53
chemical
s
pecie
s
and 325 chemical reac-
ti
o
n
s
.
A
ppr
o
priate
s
et
s
o
f flamelet
s
(and
later the L
ook
-up Table)
w
ere generated
f
o
r numerical c
o
mbu
s
ti
o
n calculati
o
n
s
.
A
ir
w
a
s
s
implified t
o
a ma
ss
fracti
o
n
o
f 23
%
o
x
y
gen and 77
%
nitr
o
gen
.
I
n
o
rder t
o
s
implif
y
the calculati
o
n
s
, the ne
x
t a
ss
ump-
ti
o
n i
s
d
o
ne
:
the enthalp
y
fluctuati
o
n
s
are
independent
o
f the enthalp
y
level
.
Thi
s
a
ss
umpti
o
n c
o
nduct
s
t
o
the u
s
e
o
f mean
enthalp
y
in
s
tead
o
f the in
s
tantane
o
u
s
enthalp
y.
B
ecau
s
e
o
f that, it can be n
o
ted
that
:
F
=
F
(f,
c
,H) and p
=
p(f,
c
)
.
I
n
o
rder t
o
generate the L
ook
-up Table,
the in
s
tantane
o
u
s
parameter
s
o
f the c
o
m-
bu
s
ti
o
n pr
o
ce
ss
, den
o
ted b
y
F
, mu
s
t be
integrated
w
ith the pr
o
babilit
y
den
s
it
y
functi
o
n (P
D
F
) p
.
The integrati
o
n i
s
per-
f
o
rmed u
s
ing the f
o
ll
ow
ing relati
o
n (3
.
4)
:
(3
.
4)
‒
―
――
‒
――
The re
s
ult
o
f the calculati
o
n
s
i
s
the gen-
erati
o
n
o
f a databa
s
e (L
ook
-up Table)
o
f
the f
o
ll
ow
ing parameter
s
:
f , f
’2
,
c
and H
.
The L
ook
-up Table return
s
the parameter
s
mean value
s
de
s
cribing the c
o
mbu
s
ti
o
n
pr
o
ce
ss
(ma
ss
fracti
o
n
o
f the i-th
s
pecie
s
,
den
s
it
y
, and temperature)
:
Y
i
,
r
o
ra
z
T
.
B
oun
da
r
y c
on
d
i
t
i
on
s
A
fter the me
s
h generati
o
n, the imple-
mentati
o
n
o
f the mathematical m
o
del
s
, the
b
o
undar
y
c
o
nditi
o
n
s
w
ere applied, a
s
de
s
cribed in the ne
x
t table 3
.
T
ab
l
e
3
.
T
h
e
b
oun
da
ry c
on
d
i
t
i
on
s
b
o
undar
y
T
y
pe
D
e
s
ignati
o
n
o
f the
o
f b
o
undar
y
Parameter
s
c
o
nditi
o
n
c
o
nditi
o
n
A
ir inlet
M
a
ss
fl
ow=
0
.
251
k
g/
s
;
Turbulent
I
nten
s
it
y=
15
%
;
M
a
ss
F
l
ow
Turbulent Vi
s
c
o
s
it
y
R
ati
o=
10;
I
nletT
o
tal Temperature
=
433 K;
M
ean
M
i
x
ture
F
racti
o
n
=
0;
M
i
x
ture
F
racti
o
n Variance
=
0;
F
uel inlet
M
a
ss
fl
ow=
0
.
004874
k
g/
s
;
Turbulent
I
nten
s
it
y=
15
%
;
M
a
ss
F
l
ow
Turbulent Vi
s
c
o
s
it
y
R
ati
o=
10;
I
nletT
o
tal Temperature
=
300 K;
M
ean
M
i
x
ture
F
racti
o
n
=
1;
M
i
x
ture
F
racti
o
n Variance
=
0;
Pre
ss
ure
O
utlet
Static Pre
ss
ure
=
0 Pa;
Turbulent
I
nten
s
it
y=
15
%
;
Turbulent Vi
s
c
o
s
it
y
R
ati
o=
10;
Ex
hau
s
t
B
ac
k
fl
ow
T
o
tal
Temperatu-
re
=
1200 K;
M
ean
M
i
x
ture
F
racti
o
n
=
0;
M
i
x
ture
F
racti
o
n Variance
=
0;
WallWall
Stati
o
nar
y
Wall;
N
o
Slip;
N
o
Heat
Ex
change;
I
nternal
E
mi
ss
ivit
y=
1;
O
paque Wall;
D
iffu
s
e
F
racti
o
n
o
f
R
adiati
o
n
=
1;
-
O
perating
O
perating pre
ss
ure
=
301
k
Pa,
c
o
nditi
o
n
s
G
ravit
y
o
ff;
R
e
s
u
l
ts
a
n
d
D
i
sc
u
ss
i
on
G
a
s
m
i
c
r
o
t
u
r
b
i
n
e
ma
i
n
o
pe
r
a
t
i
on
pa
r
ame
t
e
r
s
When dealing
w
ith a ga
s
micr
o
turbine
c
o
mbu
s
ti
o
n chamber, the m
o
s
t imp
o
rtant
o
perati
o
n parameter
s
are the t
o
tal pre
ss
ure
dr
o
p thr
o
ugh the device and the t
o
tal tem-
perature at the
o
utlet
.
A
dditi
o
nall
y
the
o
ut-
let
s
tatic temperature
w
ill be treated
.
The
t
o
tal pre
ss
ure dr
o
p
w
a
s
calculated u
s
ing
the equati
o
n 4
.
1
.
The
o
perati
o
n parame-
ter
s
are pre
s
ented in the table 4
.
A
s
it can
be
s
een the relative difference
s
bet
w
een
b
o
th c
o
mbu
s
ti
o
n m
o
del
s
are ver
y
s
mall
.
(4
.
1)
T
ab
l
e
4
.
C
o
mb
u
st
o
r
ma
i
n
o
pe
r
a
t
i
on
pa
r
ame
t
e
rs
N
o
n Premi
x
ed N
o
n Premi
x
ed
E
quilibrium C
o
m- Stead
y
F
lamelet
bu
s
ti
o
n
M
o
del
M
o
del
Δ
p*
[
%
]
10
.
08 10
.
09
T3*
[
K
]
1231 1241
T3
[
K
]
1217 1229
A
cc
o
rding t
o
the pre
s
ented re
s
ult
s
, the
t
o
tal pre
ss
ure dr
o
p
o
ccurring in the c
o
mbu
s
-
ti
o
n chamber i
s
ver
y
s
imilar f
o
r b
o
th c
o
mbu
s
-
ti
o
n m
o
del
s
:
10
.
08
%
f
o
r the n
o
n-premi
x
ed
www.
inf
o
rmacjain
s
tal
.
c
o
m
.
pl12/202519
Ź
r
ó
d
ł
a
c
i
ep
ł
a
i
e
n
e
r
g
ii
e
l
e
kt
r
yc
z
n
e
j
equilibrium c
o
mbu
s
ti
o
n m
o
del and 10
.
09
%
.
The relative difference bet
w
een b
o
th re
s
ult
s
i
s
ab
o
ut 0
.
06
%
,
w
hich i
s
neglectable
.
The
calculati
o
n
s
have
s
h
ow
n that the ch
o
ice
o
f
di
s
cu
ss
ed c
o
mbu
s
ti
o
n m
o
del
s
have n
o
impact
o
n the t
o
tal pre
ss
ure dr
o
p
.
Thi
s
i
s
a p
o
s
itive
o
b
s
ervati
o
n; the t
o
tal dr
o
p pre
s
-
s
ure i
s
n
o
t impacted
w
hen u
s
ing
s
impler
c
o
mbu
s
ti
o
n m
o
del (the n
o
n-premi
x
ed equi-
librium c
o
mbu
s
ti
o
n m
o
del) regarding a m
o
re
c
o
mple
x
m
o
del (
s
tead
y
diffu
s
i
o
n flamelet
c
o
mbu
s
ti
o
n m
o
del)
.
A
s
in the ca
s
e
o
f the e
x
hau
s
t ga
s
e
s
t
o
tal
temperature, thi
s
parameter i
s
n
o
t impacted
regarding the c
o
mbu
s
ti
o
n m
o
del ch
o
ice
.
The t
o
tal temperature
s
are ver
y
cl
o
s
e
s
:
1231 K f
o
r the equilibrium c
o
mbu
s
ti
o
n
m
o
del and 1241 K f
o
r the
s
tead
y
diffu
s
i
o
n
flamelet c
o
mbu
s
ti
o
n m
o
del
.
The e
x
hau
s
t
t
o
tal temperature i
s
higher in the flamelet
c
o
mbu
s
ti
o
n m
o
del c
o
mpared t
o
the equi-
librium c
o
mbu
s
ti
o
n m
o
del
.
O
n the
o
ne
hand, in the equilibrium c
o
mbu
s
ti
o
n m
o
del,
the c
o
mbu
s
ti
o
n i
s
a
ss
umed t
o
be at the
equilibrium
s
tate
–
the fuel
wo
uld be better
c
o
n
s
umed,
w
hile in the flamelet m
o
del,
w
here the c
o
mbu
s
ti
o
n
o
ccur
s
in a
s
tate near
t
o
equilibrium but
o
ut
o
f thi
s
o
ne,
w
hich
ma
y
s
lead t
o
le
ss
c
o
mplete c
o
mbu
s
ti
o
n
o
f
the fuel
.
O
n the
o
ther hand, the turbulence
phen
o
mena, the fuel and
o
x
idi
z
er avail-
abilit
y
, and c
o
mbu
s
ti
o
n m
o
del
s
difference
s
ma
k
e the interpretati
o
n
o
f the
s
e phen
o
me-
na and re
s
ult
s
e
x
tremel
y
c
o
mple
x
, m
o
re
c
o
mple
x
than
s
imple higher
o
r l
ow
er fuel
tran
s
f
o
rmati
o
n degree
.
The
s
e b
o
th
o
b
s
er-
vati
o
n
s
ma
k
e the difference
o
f ma
x
imum
temperature, at e
x
hau
s
t, f
o
r b
o
th c
o
mbu
s
-
ti
o
n m
o
del
s
, n
o
t reall
y
f
o
re
s
eeable
.
The
e
x
hau
s
t t
o
tal temperature
s
in b
o
th c
o
mbu
s
-
ti
o
n m
o
del
s
are ver
y
cl
o
s
e
s
:
0
.
82
%
,
w
hich
can be neglected in primar
y
engineering
and
s
cientific
s
tudie
s
.
Thi
s
reduced differ-
ence, in term
o
f the e
x
hau
s
t t
o
tal tempera-
ture, c
o
me
s
t
o
c
o
nfirm the idea that the high
turbulence
o
f the fl
ow
in the c
o
mbu
s
ti
o
n
chamber lead t
o
a fa
s
ter c
o
mbu
s
ti
o
n,
w
hich ma
k
e
s
the re
s
ult
s
fr
o
m b
o
th c
o
mbu
s
-
ti
o
n m
o
del
s
cl
o
s
e
s
.
Thi
s
i
s
a p
o
s
itive
o
b
s
er-
vati
o
n; the e
x
hau
s
t t
o
tal temperature i
s
n
o
t
impacted
w
hen u
s
ing
s
impler c
o
mbu
s
ti
o
n
m
o
del (the n
o
n-premi
x
ed equilibrium c
o
m-
bu
s
ti
o
n m
o
del) regarding a m
o
re c
o
mple
x
m
o
del (
s
tead
y
diffu
s
i
o
n flamelet c
o
mbu
s
-
ti
o
n m
o
del)
.
T
h
e
t
empe
r
a
t
u
r
e
pa
r
ame
t
e
r
s
a
n
a
l
ys
i
s
The temperature in
w
h
o
le liner v
o
lume
The mean and ma
x
imum
s
tatic tem-
perature in the
w
h
o
le liner v
o
lume
w
ill be
pre
s
ented and di
s
cu
ss
ed
.
The anal
y
s
i
s
o
f
T
ab
l
e
5
.
T
h
e
mea
n
a
n
d
ma
xi
m
u
m
t
empe
r
a
t
u
r
e
i
n
w
ho
l
e
c
o
mb
u
st
o
r
li
n
e
r r
ega
r
d
i
n
g
t
h
e
s
e
l
e
ct
ed
c
o
mb
u
st
i
on
m
o
de
l
M
o
del
[
%
N
o
n Premi
x
ed
E
quilibrium C
o
mbu
s
ti
o
n
N
o
n Premi
x
ed Stead
y
F
lamelet
M
o
del
M
o
del
s
parameter
s
]
relative diference
Tmed
[
K
]
Tma
x
[
K
]
Tmed
[
K
]
Tma
x
[
K
]
Tmed
[
K
]
Tma
x
[
K
]
757 2266 755 2297 0
.
26 1
.
37
F
i
g
u
r
e
3
.
the
s
e parameter
s
, e
s
peciall
y
the ma
x
imumapplicable, and the
s
impler equilibrium
c
o
mbu
s
ti
o
n temperature, i
s
crucial fr
o
mm
o
del i
s
adequate f
o
r preliminar
y
evalua-
a material heat re
s
i
s
tance
o
f the c
o
mbu
s
-ti
o
n
o
f mean v
o
lumetric
s
tatic temperature
ti
o
n chamber
s
tructure p
o
int
o
f vie
w.
The
s
ein micr
o
turbine c
o
mbu
s
ti
o
n chamber
s
.
parameter
s
are pre
s
ented in table 5
.
F
ir
s
t, the ma
x
imum v
o
lumetric
s
taticThe temperature map
s
anal
y
s
i
s
in the liner
temperature i
s
c
o
n
s
idered
.
I
n b
o
th c
o
m- The mean and ma
x
imum
s
tatic tem-
bu
s
ti
o
n m
o
del
s
, the pea
k
temperatureperature and the
s
tatic temperature unif
o
r-
in
s
ide the liner i
s
ver
y
s
imilar
:
2266 K f
o
rmit
y
inde
x
, thr
o
ugh
s
elected c
o
mbu
s
t
o
r
the n
o
n-premi
x
ed equilibrium m
o
del anda
x
ial
s
ecti
o
n
s
in the
w
h
o
le c
o
mbu
s
ti
o
n
2297 K f
o
r the
s
tead
y
diffu
s
i
o
n flameletchamber,
w
ill be pre
s
ented and di
s
cu
ss
ed
.
m
o
del, a relative difference
o
f
o
nl
y
1
.
37
%
.
The
s
tatic temperature unif
o
rmit
y
inde
x
i
s
Thi
s
agree
s
w
ith the
s
mall temperature dif-calculated appl
y
ing the equati
o
n 4
.
2
.
The
ference
o
b
s
erved at the c
o
mbu
s
t
o
r
o
utlet
.
a
x
ial
s
ecti
o
n
s
o
f the c
o
mbu
s
t
o
r are
s
h
ow
n
L
o
cal effect
s
—fuel/
o
x
idi
z
er availabilit
y
,
o
n the figure 3
.
The anal
y
s
i
s
o
f the
s
e
inlet c
o
nditi
o
n
s
, and turbulence—e
x
plainparameter
s
, e
s
peciall
y
the ma
x
imum c
o
m-
the min
o
r variati
o
n
s
bet
w
een m
o
del
s
.
bu
s
ti
o
n temperature, i
s
crucial fr
o
m a mate-
Since the ma
x
imum temperature
s
are near-rial heat re
s
i
s
tance p
o
int
o
f vie
w.
The
s
e
l
y
identical, the ch
o
ice
o
f m
o
del i
s
n
o
t criti-parameter
s
are pre
s
ented in table 6,
w
hile
cal f
o
r e
s
timating thi
s
parameter, and thetheir difference
s
bet
w
een b
o
th c
o
mbu
s
ti
o
n
s
impler equilibrium m
o
del i
s
s
ufficient f
o
rm
o
del
s
are pre
s
ented
o
n figure 4
.
initial anal
y
s
e
s
.
Sec
o
nd, the mean v
o
lumetric
s
tatic
temperature al
s
o
s
h
ow
s
negligible differ-
ence
s
:
757 K f
o
r the equilibrium m
o
del
and 755 K f
o
r the flamelet m
o
del (0
.
26
%
difference)
.
Thi
s
indicate
s
that, de
s
pite their
different a
ss
umpti
o
n
s
—chemical equilibri-
um v
s
.
finite-rate chemi
s
tr
y
—b
o
th m
o
del
s
de
s
cribe the c
o
mbu
s
ti
o
n
s
imilarl
y
under the
highl
y
turbulent and ge
o
metricall
y
c
o
n-
s
trained c
o
nditi
o
n
s
o
f a ga
s
micr
o
turbine
c
o
mbu
s
t
o
r
.
High turbulence accelerate
s
chemical reacti
o
n
s
, pu
s
hing the
s
y
s
tem
cl
o
s
er t
o
equilibrium even
w
hen re
s
idence
V
i
s
u
a
li
s
a
t
i
on
of
t
h
e
cr
o
ss s
e
ct
i
on
s st
u
d
i
ed
of
t
h
e
time
s
are
s
h
o
rt
.
Thu
s
, b
o
th m
o
del
s
remain
c
o
mb
u
st
o
r
T
ab
l
e
6
.
T
h
e
mea
n
a
n
d
ma
xi
m
u
m
t
empe
r
a
t
u
r
e
,
a
n
d
i
ts
un
i
fo
r
m
i
ty
i
n
de
x,
i
n
c
o
mb
u
st
o
r cr
o
ss
-
s
e
ct
i
on
s
r
ega
r
d
i
n
g
t
h
e
s
e
l
e
ct
ed
c
o
mb
u
st
i
on
m
o
de
l
N
on
P
r
em
ix
ed
E
q
u
ili
b
ri
u
m
N
on
P
r
em
ix
ed
S
t
ead
y F
l
ame
l
e
t
Mo
de
l
s
pa
r
ame
t
e
r
s
r
e
l
a
t
i
v
e
C
o
mb
u
st
i
on
Mo
de
l
Mo
de
l
d
i
f
e
r
e
n
c
e
[%]
X [
m
] T
med
[
K
] T
ma
x
[
K
] UIT [
-
] T
med
[
K
] T
ma
x
[
K
] U
I
T
[
-
]
Tmed
[
%
]
Tma
x
[
%
]
U
I
T
[
%
]
0
.
00 859 2175 0
.
817 836 2234 0
.
819 2
.
73 2
.
69 0
.
29
0
.
01 835 2184 0
.
815 836 2267 0
.
817 0
.
21 3
.
77 0
.
18
0
.
02 889 2169 0
.
812 885 2258 0
.
814 0
.
48 4
.
11 0
.
24
0
.
03 845 2215 0
.
811 844 2281 0
.
813 0
.
19 2
.
99 0
.
26
0
.
04 927 2200 0
.
794 930 2253 0
.
793 0
.
28 2
.
38 0
.
19
0
.
05 976 2189 0
.
804 984 2237 0
.
802 0
.
86 2
.
21 0
.
26
0
.
06 952 2203 0
.
805 962 2261 0
.
803 1
.
04 2
.
66 0
.
22
0
.
0793022340
.
79993922740
.
7981
.
071
.
780
.
16
0
.
08 962
0
.
09 987
0
.
10 1007
0
.
11 946
0
.
12 998
0
.
13 1006
0
.
14 1199
0
.
151200
2205 0
.
786 973
2205 0
.
804 997
2204 0
.
810 1020
2219 0
.
781 970
2213 0
.
793 1019
1876 0
.
777 1020
1691 0
.
945 1209
16310
.
9511210
22650
.
7831
.
18
22610
.
8030
.
98
22670
.
8091
.
27
22610
.
7782
.
53
22750
.
7932
.
10
18570
.
7751
.
37
16980
.
9470
.
83
16510
.
9530
.
82
2
.
750
.
45
2
.
580
.
13
2
.
870
.
13
1
.
920
.
29
2
.
780
.
09
1
.
030
.
31
0
.
410
.
21
1
.
210
.
19
(4
.
2)
t
o
r, permit t
o
o
btain
s
imilar c
o
mbu
s
ti
o
n
de
s
cripti
o
n
w
hen appl
y
ing b
o
th c
o
mbu
s
ti
o
n
m
o
del
s
.
The N
o
n-Premi
x
ed
E
quilibrium
c
o
mbu
s
ti
o
n m
o
del a
ss
ume
s
that the c
o
m-
bu
s
ti
o
n
o
ccur
s
in the chemical equilibrium,
w
hile the
s
tead
y
diffu
s
i
o
n flamelet m
o
del
a
ss
ume
s
the reacti
o
n rate imp
o
rtance in
c
o
mbu
s
ti
o
n pr
o
ce
ss
.
I
n the ga
s
micr
o
turbine
c
o
mbu
s
t
o
r
s
, the c
o
mbu
s
ti
o
n time i
s
limited; it
wo
uld mean that the c
o
mbu
s
ti
o
n ma
y
s
be
n
o
t
o
n it
s
chemical equilibrium, leading t
o
the u
s
e
o
f
s
tead
y
diffu
s
i
o
n flamelet m
o
del
.
A
t the
s
ame time, the c
o
mbu
s
ti
o
n in ga
s
micr
o
turbine i
s
s
tr
o
ngl
y
turbulent
.
A
s
the tur-
bulence
o
f a flame increa
s
e
s
, it
s
chemical
rate increa
s
e
s
t
oo
; thi
s
o
b
s
ervati
o
n c
o
uld
permit t
o
m
o
ve cl
o
s
er t
o
the chemical equi-
librium, leading t
o
the u
s
e
o
f n
o
n-premi
x
ed
equilibrium c
o
mbu
s
ti
o
n m
o
del
.
Ta
k
ing that
int
o
acc
o
unt, the c
o
mbu
s
ti
o
n in ga
s
micr
o
-
turbine device
s
s
eem
s
n
o
t t
o
be t
oo
far fr
o
m
the equilibrium c
o
mbu
s
ti
o
n, ma
k
ing b
o
th
m
o
del
s
applicable
.
The behavi
o
ur
o
f the
mean c
o
mbu
s
ti
o
n
s
tatic temperature c
o
me
s
t
o
s
upp
o
rt thi
s
the
s
i
s
.
I
n the c
o
nte
x
t
o
f the
mean c
o
mbu
s
ti
o
n
s
tatic temperature, the
perf
o
rmed
o
b
s
ervati
o
n i
s
p
o
s
itive regarding
the i
ss
ue
o
f the
s
e re
s
earch
–
the ch
o
ice
o
f
the c
o
mbu
s
ti
o
n m
o
del i
s
n
o
t
o
f crucial
imp
o
rtance regarding the c
o
mbu
s
ti
o
n mean
s
tatic temperature
.
A
s
impler c
o
mbu
s
ti
o
n
m
o
del can be applied de
s
pite
o
f m
o
re c
o
m-
ple
x
c
o
mbu
s
ti
o
n m
o
del,
w
hen anal
y
s
ing
initiall
y
the mean
s
tatic temperature
.
The c
o
mbu
s
ti
o
n
s
tatic temperature uni-
f
o
rmit
y
inde
x
varie
s
al
o
ng the c
o
mbu
s
t
o
r
but remain
s
alm
o
s
t identical f
o
r b
o
th m
o
d-
el
s
:
0
.
777
–
0
.
951 f
o
r the n
o
n-premi
x
ed
equilibrium m
o
del and 0
.
775
–
0
.
953 f
o
r
the flamelet m
o
del
.
The relative difference
s
(0
.
09
–
0
.
45
%
) are negligible
.
I
t
s
behav-
i
o
ur mirr
o
r
s
that
o
f the mean c
o
mbu
s
ti
o
n
s
tatic temperature di
s
cu
ss
ed earlier, and
n
o
additi
o
nal phen
o
mena
w
ere n
o
ted
.
Thi
s
c
o
nfirm
s
again that the ch
o
ice bet
w
een the
t
wo
c
o
mbu
s
ti
o
n m
o
del
s
ha
s
n
o
s
ignificant
impact
o
n preliminar
y
thermal anal
y
s
i
s
o
f
ga
s
micr
o
turbine c
o
mbu
s
t
o
r
s
.
C
a
l
c
u
l
a
t
i
on
t
i
me
c
o
mpa
ri
s
on
be
tw
ee
n
b
o
t
h
app
li
ed
m
o
de
l
s
The calculati
o
n
s
f
o
r b
o
th c
o
mbu
s
ti
o
n
m
o
del
s
w
ere c
o
nducted
o
n the
s
ame c
o
m-
puter
.
Thi
s
hard
w
are
o
perati
o
n parameter
s
are li
s
ted bel
ow:
l
Pr
o
ce
ss
o
r
:
I
ntel(
R
)C
o
re(T
M
)
i9-14900K 3
.
20
G
H
z
; 24 ph
y
s
ical
c
o
re
s
:
8 Perf
o
rmance-c
o
re
s
(P-c
o
re
s
)
and 16
E
fficient-c
o
re
s
(
E
-c
o
re
s
);
l
R
am
:
128
GB
.
D
uring
o
perati
o
n,
o
nl
y
10 c
o
re
s
w
ere
dedicated f
o
r the
F
luent calculati
o
n
s
.
The
calculati
o
n time f
o
r the
E
quilibrium m
o
del
w
a
s
o
f 61380
s
,
w
hile f
o
r the
F
lamelet
m
o
del it
w
a
s
80220
s
.
The u
s
e
o
f the m
o
re
c
o
mple
x
m
o
del (
F
lamelet m
o
del), c
o
m-
pared t
o
the
E
quilibrium m
o
del, pr
o
v
ok
e
s
the calculati
o
n time increa
s
e
s
o
f ab
o
ut
30
%
.
Thi
s
value i
s
n
o
t
y
et neglectable,
w
hich i
s
al
s
o
an imp
o
rtant, l
ook
ed f
o
r,
advantage
o
f u
s
ing the
s
impler c
o
mbu
s
ti
o
n
m
o
del de
s
pite
o
f the m
o
re c
o
mple
x
o
ne,
f
o
r the thermal initial calculati
o
n
s
.
C
on
c
l
u
s
i
on
s
The pre
s
ent
s
tudie
s
permitted t
o
c
o
m-
pare the n
o
n-premi
x
ed equilibrium c
o
m-
bu
s
ti
o
n m
o
del t
o
the
s
tead
y
diffu
s
i
o
n
flamelet c
o
mbu
s
ti
o
n m
o
del, applied t
o
a ga
s
micr
o
turbine diffu
s
i
o
n t
y
pe c
o
mbu
s
-
ti
o
n chamber methane p
ow
ered
.
Three
gr
o
up
s
o
f
o
perati
o
n parameter
s
w
here
s
tudied
:
the main
o
perati
o
n parameter
s
,
the thermal
o
perati
o
n parameter
s
and the
calculati
o
n time
.
I
n term
s
o
f the main
o
perati
o
n param-
eter
s
, the t
o
tal pre
ss
ure dr
o
p and e
x
hau
s
t
ga
s
t
o
tal temperature
w
ere a
ss
e
ss
ed
.
A
dditi
o
nall
y
, the e
x
hau
s
t
s
s
tatic tempera-
ture
w
a
s
al
s
o
anal
y
z
ed
.
The pre
s
ent
s
tud-
ie
s
s
h
ow
ed that the ch
o
ice
o
f the di
s
-
cu
ss
ed c
o
mbu
s
ti
o
n m
o
del
s
ha
s
n
o
impact
o
n the
s
e main
o
perati
o
n parameter
s
, in
thi
s
s
pecific applicati
o
n ca
s
e, de
s
cribed
bef
o
re
.
I
n term
s
o
f the thermal
o
perati
o
n
parameter
s
, the ne
x
t parameter
s
w
ere
anal
y
z
ed
:
mean and ma
x
imum c
o
mbu
s
-
ti
o
n v
o
lumetric
s
tatic temperature, ma
x
i-
mum and mean c
o
mbu
s
ti
o
n
s
tatic temper-
ature and it
s
unif
o
rmit
y
inde
x
.
The pre
s
ent
s
tudie
s
s
h
ow
ed that the ch
o
ice
o
f the di
s
-
cu
ss
ed c
o
mbu
s
ti
o
n m
o
del
s
ha
s
n
o
impact
o
n the
s
e thermal
o
perati
o
n parameter
s
, in
thi
s
s
pecific applicati
o
n ca
s
e, e
x
cept
o
ne
:
the ma
x
imum c
o
mbu
s
ti
o
n
s
tatic tempera-
ture; the applicati
o
n
o
f the n
o
n-premi
x
ed
equilibrium c
o
mbu
s
ti
o
n m
o
del lead
s
t
o
l
ow
er value
s
o
f thi
s
parameter, reaching
even ab
o
ut 4
%
.
I
n term
s
o
f the hard
w
are calculati
o
n
time, the u
s
e
o
f the m
o
re c
o
mple
x
m
o
del
(
F
lamelet m
o
del) lead
s
t
o
a calculati
o
n
time e
x
ten
s
i
o
n
o
f ab
o
ut 30
%
c
o
mpared t
o
the u
s
e
o
f the
s
impler m
o
del (
E
quilibrium
m
o
del)
.
Thi
s
value i
s
n
o
t negligible and
c
o
n
s
titute an advantage
w
hen primar
y
thermal calculati
o
n
s
are c
o
nducted
.
F
i
g
u
r
e
4
.
C
o
mb
u
st
o
r t
h
e
r
ma
l
o
pe
r
a
t
i
on
pa
r
ame
t
e
rs
,
t
h
r
ou
g
h
a
xi
a
l
cr
o
ss
-
-
s
e
ct
i
on
,
r
e
l
a
t
i
v
e
d
i
ff
e
-
r
e
n
c
e
s
be
tw
ee
n
app
li
ed
c
o
mb
u
st
i
on
m
o
de
l
s
The ma
x
imum c
o
mbu
s
ti
o
n
s
tatic temper-
ature varie
s
al
o
ng the c
o
mbu
s
t
o
r depending
o
n l
o
cal c
o
nditi
o
n
s
.
F
o
r b
o
th m
o
del
s
the
value
s
are cl
o
s
e
:
1631
–
2234 K f
o
r the n
o
n-
premi
x
ed equilibrium m
o
del and 1651
–
2281 K f
o
r the
s
tead
y
diffu
s
i
o
n flamelet
m
o
del
.
The relative difference
s
range fr
o
m
0
.
41
%
t
o
4
.
11
%
—
s
mall, th
o
ugh n
o
t entirel
y
negligible
.
The flamelet m
o
del generall
y
predict
s
s
lightl
y
higher pea
k
temperature
s
,
w
ith
o
ne l
o
cal e
x
cepti
o
n at
X
=
0
.
13
.
The
s
e difference
s
ari
s
e fr
o
m l
o
cal fuel
–
o
x
idi
z
er availabilit
y
, thermal and pre
ss
ure
c
o
nditi
o
n
s
, and turbulence level
s
, c
o
m-
bined
w
ith the inherent calculati
o
n differ-
ence
s
bet
w
een the m
o
del
s
.
Still, the pea
k
temperature
s
remain
s
ufficientl
y
cl
o
s
e t
o
c
o
n
s
ider b
o
th m
o
del
s
acceptable f
o
r pre-
liminar
y
engineering
o
r
s
cientific anal
y
s
e
s
.
T
y
picall
y
, the
s
impler equilibrium m
o
del
y
ield
s
s
lightl
y
l
ow
er ma
x
ima—up t
o
ab
o
ut
4
%
—but
s
uch deviati
o
n
s
remain t
o
lerable
.
Theref
o
re, the ch
o
ice
o
f c
o
mbu
s
ti
o
n m
o
del
i
s
n
o
t critical f
o
r e
s
timating the ma
x
imum
c
o
mbu
s
ti
o
n
s
tatic temperature, and the
s
impler n
o
n-premi
x
ed equilibrium m
o
del i
s
adequate f
o
r initial
s
tudie
s
.
The mean c
o
mbu
s
ti
o
n
s
tatic temperature
w
ill be then treated
.
The mean
s
tatic tem-
perature ev
o
lve
s
fr
o
m
s
ecti
o
n t
o
s
ecti
o
n,
depending
o
n the l
o
cal envir
o
nment c
o
ndi-
ti
o
n
s
.
The
s
e temperature
s
are ver
y
cl
o
s
e
s
f
o
r
b
o
th c
o
mbu
s
ti
o
n m
o
del
s
:
range fr
o
m 835 K
t
o
1200 K f
o
r the n
o
n-premi
x
ed equilibrium
c
o
mbu
s
ti
o
n m
o
del, ver
s
u
s
a range fr
o
m
836 K t
o
1210 K f
o
r the
s
tead
y
diffu
s
i
o
n
flamelet m
o
del
.
The relative difference f
o
r
thi
s
parameter ev
o
lve
s
fr
o
m 0
.
19
%
t
o
2
.
73
%
,
w
hich i
s
l
ow
difference, qua
s
i-
neglectable
.
R
ever
s
el
y
t
o
ma
x
imum c
o
m-
bu
s
ti
o
n
s
tatic temperature, there i
s
n
o
rule in
term
s
f
o
r
w
hich c
o
mbu
s
ti
o
n m
o
del the mean
c
o
mbu
s
ti
o
n temperature
w
ill be higher
o
r
l
ow
er than the
s
ec
o
nd
o
ne
.
I
t mean
s
that the
20
phen
o
mena
o
ccurring in
s
ide
o
f the c
o
mbu
s
-
Ź
A
cc
o
rding t
o
the ab
o
ve, the ch
o
ice
o
f
s
impler c
o
mbu
s
ti
o
n m
o
del (the n
o
n-pre-
mi
x
ed equilibrium c
o
mbu
s
ti
o
n m
o
del)
de
s
pite
o
f m
o
re c
o
mple
x
c
o
mbu
s
ti
o
n
m
o
del (the
s
tead
y
diffu
s
i
o
n flamelet m
o
del)
ha
s
n
o
crucial impact
o
n the thermal
o
perati
o
n parameter
s
w
hen applied t
o
a methane p
ow
ered ga
s
micr
o
turbine dif-
fu
s
i
o
n t
y
pe c
o
mbu
s
t
o
r
.
Simpler m
o
del can
be u
s
ed f
o
r thermal initial
s
tudie
s
in thi
s
s
pecific ca
s
e
.
N
o
me
n
c
l
a
t
u
r
e
i
p
p,i
s
‒
―
―
i
·
2
3
i
m
―
facei
area
i
―
M
‒
―
A
–
area
o
f facet defining anal
y
s
ed
s
urface
[
m
2
]
c
–
heat capacit
y
at c
o
n
s
tant pre
ss
ure
[
J/(
k
g
.
K)
]
c
–
mi
x
ture i-element heat capacit
y
at
c
o
n
s
tant pre
ss
ure
[
J/(
k
g
.
K)
]
c
–
methane (fuel) ma
ss
fl
ow
[k
g/
s
]
f
–
mi
x
ture fracti
o
n
[
-
]
f
–
mean mi
x
ture fracti
o
n
[
-
]
f
’2
–
mi
x
ture fracti
o
n variance
[
-
]
H
–
enthalp
y
[
J/
k
g
]
H
–
mean enthalp
y
[
J/
k
g
]
H
–
enthalp
y
o
f mi
x
ture i-element
[
J/
k
g
]
m
–
air ma
ss
fl
ow
entering the c
o
mbu
s
-
t
o
r
[k
g/
s
]
p
–
s
tatic pre
ss
ure
[
Pa
]
p*
–
t
o
tal pre
ss
ure
[
Pa
]
p(i,j,
k
…)
–
pr
o
babilit
y
den
s
it
y
functi
o
n
p*
–
t
o
tal pre
ss
ure at c
o
mbu
s
t
o
r’
s
inlet
[
Pa
]
p*
–
t
o
tal pre
ss
ure at c
o
mbu
s
t
o
r’
s
o
utlet
[
Pa
]
D
p*
–
t
o
tal pre
ss
ure dr
o
p in c
o
mbu
s
t
o
r
[
%
]
S
–
mi
x
ture i-element chemical reac-
ti
o
n rate
S
–
s
o
urce term due
s
o
lel
y
t
o
tran
s
fer
o
f
ma
ss
int
o
the ga
s
pha
s
e fr
o
m liquid
fuel dr
o
plet
s
o
r reacting particle
s
t
–
time
[
s
]
T
–
s
tatic temperature
[
K
]
T*
–
t
o
tal temperature
[
K
]
T
–
mean temperature
[
K
]
T
–
s
tatic temperature
o
n i-th facet
defining anal
y
s
ed
s
urface
[
K
]
Tma
x
–
ma
x
imum
s
tatic temperature
[
K
]
Tmed
–
mean
s
tatic temperature
[
K
]
T3*
–
t
o
tal e
x
hau
s
t temperature
[
K
]
U
I
plane
–
area averaged unif
o
rmit
y
inde
x
[
-
]
U
I
T
–
s
tatic temperature area averaged
unif
o
rmit
y
inde
x
[
-
]
Y
–
mean ma
ss
fracti
o
n
o
f the i-th
s
pe-
cie
s
[
-
]
Y
–
repre
s
ent
s
the c
o
ntributi
o
n
o
f the
fluctuating dilatati
o
n in c
o
mpre
ss
i-
ble turbulence t
o
the
o
verall di
ss
i-
pati
o
n rate
r
–
den
s
it
y
[k
g/m
3
]
–
mean den
s
it
y
[k
g/m
3
]
c
–
s
calar di
ss
ipati
o
n rate
[
1/
s
]
c
–
mean
s
calar di
ss
ipati
o
n rate
[
1/
s
]
C
onf
li
cts
of
I
n
t
e
r
e
st
:
The auth
o
r
s
declare n
o
c
o
nflict
o
f intere
s
t
.
R
E
F
E
R
E
N C
E
S
4 2
.
[
1
]
E
NC
Y
(available
o
nline
o
n the 15/07/2025)
.
E
v
o
luti
o
n
o
f C
AD
/C
A
M
S
y
s
tem
s
:
1970
–
2025
.
Lin
k:
http
s
:
//enc
y
cam
.
c
o
m/article
s
/
ev
o
luti
o
n-
o
f-cad-cam-
s
y
s
tem
s
-1970-2025/
[
2
]
E
NC
Y
(available
o
nline
o
n the 15/07/2025)
.
Under
s
tanding the
D
ifference
B
et
w
een C
AD
,
C
A
M
, and C
A
E
:
A
C
o
mprehen
s
ive
G
uide
.
Lin
k:
http
s
:
//enc
y
cam
.
c
o
m/article
s
/under
s
tan-
ding-the-difference-bet
w
een-cad-cam-
and-cae-a-c
o
mprehen
s
ive-guide/
[
3
]
J
.
-
M
.
F
ąfara and N
.
M
o
dliń
s
k
i (2023)
.
Nume-
rical
s
tud
y
o
f internal flue ga
s
recirculati
o
n
s
y
s
-
tem applied t
o
methane-h
y
dr
o
gen
p
ow
ered ga
s
micr
o
turbine c
o
mbu
s
t
o
r
.
C
o
mbu
s
ti
o
n
E
ngi-ne
s
, 2023,192(1), pp
.
63-77
.
http
s
:
/
/
d
o
i
.
o
rg/10
.
19206/C
E
-
152236
[
4
]
A
n
s
y
s
(available
o
nline
o
n the 15/07/2025)
.
A
n
s
y
s
F
luent,
F
luid Simulati
o
n S
o
ft
w
are
.
Lin
k:
http
s
:
//
www.
an
s
y
s
.
c
o
m/pr
o
duct
s
/fluid
s
/
an
s
y
s
-fluent
[
5
]
A.
C
.
M
angra (2020)
.
M
icr
o
ga
s
turbine c
o
m-
bu
s
ti
o
n chamber C
F
D
m
o
delling
.
I
O
P C
o
nf
.
Serie
s
:
M
aterial
s
Science and
E
ngineering,
916(2020),012064
.
http
s
:
//d
o
i
.
o
rg/10
.
1088/1757-899
X
/916/1/012064
[
6
]
A.
C
.
M
angra,
R.
Carlane
s
cu,
M
.
E
nache and
F
.
F
.
G
abriel (2022)
.
Numerical and e
x
peri-
mental inve
s
tigati
o
n
o
f a micr
o
ga
s
turbine
c
o
mbu
s
ti
o
n chamber
.
I
nternati
o
nal j
o
urnal
o
f
m
o
dern manufacturing techn
o
l
o
gie
s
, V
o
l
.
X
I
V,
N
o.
3 / 2022
.
I
SSN 2067
–
3604 / http
s
:
//
d
o
i
.o
rg/10
.
54684/ijmmt
.
2022
.
14
.
3
.
132
[
7
]
Q
.
Li, H
.
Y
ang,
Y
.
Wang and P
.
Wang (2015)
.
A
ccurac
y
impr
o
vement
o
f the m
o
dified
E
D
M
m
o
del f
o
r n
o
n-premi
x
ed turbulent c
o
mbu
s
ti
o
n
in ga
s
turbine
.
Ca
s
e
s
tudie
s
in thermal engine-
ering,6(2015)69
–
76
.
http
s
:
//d
o
i
.
o
rg/10
.
1016/j
.
c
s
ite
.
2015
.
07
.
002
[
8
]
A.
Sanja
y
Vibhute (2024)
.
Numerical
s
tud
y
o
f
different micr
o
ga
s
turbine c
o
mbu
s
t
o
r de
s
ign
c
o
nfigurati
o
n
s
f
o
r h
y
dr
o
gen
o
perati
o
n
.
M
a
s
ter
the
s
i
s
at Techni
s
che Univer
s
itat
D
arm
s
tadt,
R
evie
w
er
s
:
Pr
o
f
.
D
r
.
-
I
ng
.
Chri
s
tian Ha
ss
e and
D
r
.
-
I
ng
.
Hendri
k
Nic
o
lai
.
[
9
]
S
.
Serbin, K
.
B
urun
s
u
z
,
D.
Chen and J
.
K
ow
al
s
k
i
(2022)
.
I
nve
s
tigati
o
n
o
f the characteri
s
tic
s
o
f
a l
ow
emi
ss
i
o
n ga
s
turbine c
o
mbu
s
ti
o
n chamber
o
perating
o
n a mi
x
ture
o
f natural ga
s
and
h
y
dr
o
gen
.
P
o
li
s
hmaritimere
s
earch,
2(114)2022; V
o
l
.
29; pp
.
64-76
.
http
s
:
//d
o
i
.
o
rg/10
.
2478/p
o
mr-2022-0018
[
10
]
B
.
F
.
M
agnu
ss
en (1989)
.
M
o
deling
o
f P
o
llutant
f
o
rmati
o
n in
G
a
s
Turbine C
o
mbu
s
t
o
r
s
B
a
s
ed
o
n
the
E
dd
y
D
i
ss
ipati
o
n C
o
ncept
.
I
n
:
C
I
M
A
C C
o
n-
ference, 4-9 June 1989, Tianjin, China
.
[
11
]
R.
D
e
Ro
bbi
o
(2017)
.
I
nn
o
vative c
o
mbu
s
ti
o
n
anal
y
s
i
s
o
f a micr
o
-ga
s
turbine burner
s
upplied
w
ith h
y
dr
o
gen-natural ga
s
mi
x
ture
s
.
I
n
:
72nd
C
o
nference
o
f the
I
talian Thermal
M
achine
s
E
ngineering
A
ss
o
ciati
o
n,
A
T
I
2017, 6-8 Septem-
ber 2017, Lecce,
I
tal
y.
[
12
]
Y
.
M
u, H
.
Z
heng and
Z
.
Li (2009)
.
A
pplicati
o
n
o
f
E
dd
y
D
i
ss
ipati
o
n C
o
ncept
M
o
del in Simulati
o
n
o
f
G
a
s
Turbine C
o
mbu
s
t
o
r
.
I
n
:
2009
A
s
ia-Pacific
P
ow
er and
E
nerg
y
E
ngineering C
o
nference,
27-31
M
arch 2009, Wuhan, China
.
http
s
:
//
d
o
i
.o
rg/10
.
1109/
A
PP
EE
C
.
2009
.
4918181
[
13
]
A.
M
ardani (2017)
.
O
ptimi
z
ati
o
n
o
f the
E
dd
y
D
i
ss
ipati
o
n C
o
ncept (
E
D
C) m
o
del f
o
r turbu-
lence-chemi
s
tr
y
interacti
o
n
s
under h
o
t diluted
c
o
mbu
s
ti
o
n
o
f CH /H
F
uel, V
o
l
.
191, 2017,
pp
.
114-129
.
http
s
:
//d
o
i
.o
rg/10
.
1016/j
.
fuel
.
2016
.
11
.
056
[
14
]
A.R
U
y
an
w
aththa (2018)
.
C
F
D
M
o
delling
o
f
G
a
s
Turbine C
o
mbu
s
ti
o
n Pr
o
ce
ss
e
s
.
Do
ct
o
ral
D
i
ss
ertati
o
n at W
o
lf
s
o
n Sch
oo
l
o
f
M
echanical
E
lectrical and
M
anufacturing
E
ngineering
.
L
o
ughb
o
r
o
ugh Univer
s
it
y
[
15
]
F
.
Wang, L
.
X.
Z
h
o
u, C
.
X.
X
u and
G
.
M
.
G
o
ldin
(2008)
.
C
o
mpari
s
o
n bet
w
een a c
o
mp
o
s
iti
o
n
P
D
F
tran
s
p
o
rt equati
o
n m
o
del and an
A
S
OM
m
o
del f
o
r
s
imulating a turbulent jet flame
.
I
nter-
nati
o
nal J
o
urnal
o
f Heat and
M
a
ss
Tran
s
fer,
V
o
l
.
51,
I
ss
ue
s
1
–
2, 2008, pp
.
136-144
.
http
s
:
//d
o
i
.o
rg/10
.
1016/j
.
ijheatma
ss
tran
s
-fer
.
2007
.
04
.
031
[
16
]
R.
Y
adav,
A.
Ku
s
hari, V
.
Es
w
aran and
A.
K
.
Verma (2013)
.
A
numerical inve
s
tigati
o
n
o
f
the
E
ulerian P
D
F
tran
s
p
o
rt appr
o
ach f
o
r m
o
de-
ling
o
f turbulent n
o
n-premi
x
ed pil
o
t
s
tabili
z
ed
flame
s
.
C
o
mbu
s
ti
o
n and
F
lame, V
o
l
.
160,
I
ss
ue
3, 2013, pp
.
618-634
.
http
s
:
//d
o
i
.
o
rg/10
.
1016/j
.
c
o
mbu
s
tflame
.
2012
.
11
.
010
[
17
]
C
.A.
G
o
n
z
ela
z
, K
.
C
.
W
o
ng
o
ra
z
S
.
A
rmfield
(2008)
.
C
o
mputati
o
nal
s
tud
y
o
f a micr
o
-turbine
engine c
o
mbu
s
t
o
r u
s
ing large edd
y
s
imulati
o
n
and
R
e
y
n
o
ld
s
averaged turbulence m
o
del
s
.
A
N
ZI
A
M
J
o
urnal, 49(2008), pp
.
407-422
.
[
18
]
T
.
Such
o
c
k
i, P
.
Lampart
o
ra
z
P
.
Kl
o
n
ow
ic
z
(2014)
.
Numerical inve
s
tigati
o
n
o
f a
G
T
M
-140
turb
o
jet engine
.
O
pen
E
ngineering, 2015(5),
pp
.
478-484
.
[
19
]
V
.
Vilag, J
.
Vilag,
R.
Carlane
s
cu,
A.
M
angra
o
ra
z
F
.
F
l
o
rean (2019)
.
C
F
D
A
pplicati
o
n f
o
r
G
a
s
Tur-
bine C
o
mbu
s
ti
o
n Simulati
o
n
s
.
W
:
G
u
o
z
ha
o
Ji
o
ra
z
Jiujiang
Z
hu (2020), C
o
mputati
o
nal
F
luid
Dy
namic
s
Simulati
o
n
s
,
I
ntech
O
pen
.
http
s
:
//d
o
i
.
o
rg/10
.
5772/intech
o
pen
.
89759
[
20
]
R.
Kell
y
,
A.
Jemc
o
v, S
.
R
ida
o
ra
z
J
.
B
a
s
ani
(2019)
.
E
fficient
G
a
s
Turbine C
o
mbu
s
t
o
r Simula-
ti
o
n U
s
ing
F
ull Simulati
o
n
M
eth
o
d
o
l
o
g
y
(
F
S
M
)
.
http
s
:
//d
o
i
.o
rg/10
.
2514/6
.
2019-4260
[
21
]
S
o
lid
E
dge (available
o
nline
o
n the
17/07/2025)
.
S
o
lid
E
dge pr
o
duct devel
o
p-
ment
s
o
ft
w
are
.
Lin
k:
http
s
:
//plm
.
s
w.
s
iemen
s
.
c
o
m/en-US/
s
o
lid-edge/
[
22
]
J
.
-
M
.
F
ąfara and N
.
M
o
dliń
s
k
i (2023)
.
C
o
mpu-
tati
o
nal
F
luid
Dy
namic
s
(C
F
D
)
A
ss
e
ss
ment
o
f the
I
nternal
F
lue
G
a
s
e
s
R
ecirculati
o
n (
I
FG
R
)
A
pplied t
o
G
a
s
M
icr
o
turbine in the C
o
nte
x
t
o
f
M
o
re H
y
dr
o
gen-
E
nriched
F
uel U
s
e
.
E
nergie
s
,
16(18), 6703
.
http
s
:
//d
o
i
.o
rg/10
.
3390/
en16186703
[
23
]
M
.
,
G
iera
s
and T
.
, Stań
kow
s
k
i (2012)
.
C
o
mpu-
tati
o
nal
s
tud
y
o
f an aer
o
d
y
namic fl
ow
thr
o
ugh
a micr
o
turbine engine c
o
mbu
s
t
o
r
.
J
o
urnal
o
f
P
ow
er Techn
o
l
o
gie
s
, 92 (2), 68-79
.
I
SSN
2083-4195
.
[
24
]
M
.
, S
o
s
n
ow
s
k
i, J
.
, Kr
z
yw
an
s
k
i and
R.
,
G
nat
ow
-
s
k
a (2017)
.
P
o
l
y
hedral me
s
hing a
s
an inn
o
va-
tive appr
o
ach t
o
c
o
mputati
o
nal d
o
main di
s
cre-
ti
z
ati
o
n
o
f a c
y
cl
o
ne in a fluidi
z
ed bed CLC unit
.
E
3S Web
o
f C
o
nference
s
, 14
.
01027
.
http
s
:
//
d
o
i
.o
rg/10
.
1051/e3
s
c
o
nf/20171401027
[
25
]
Z
ahid
Q
ure
s
hi and Chan
A.
(2015)
.
A
s
tud
y
o
f
the effect
o
f element t
y
pe
s
o
n fl
ow
and turbu-
lence characteri
s
tic
s
ar
o
und an i
s
o
lated high-
ri
s
e building
.
I
n
:
E
leventh
I
nternati
o
nal C
o
nfer-
ence
o
n C
F
D
in the
M
ineral
s
and Pr
o
ce
ss
I
ndu
s
trie
s
, CS
I
R
O
,
M
elb
o
urne (
A
u
s
tralia), 7-9
december 2015
.
http
s
:
//
www.
cfd
.
c
o
m
.
au/
cfd_c
o
nf15/P
D
Fs
/035
I
QB
.
pdf
[
26
]
T
.
, Smith,
Z
.
, Shen and J
.
,
F
riedman (1982)
.
E
valuati
o
n
o
f C
o
efficient
s
f
o
r the Weighted Sum
o
f
G
ra
y
G
a
s
e
s
M
o
del
.
Tran
s
acti
o
n
s
o
f the
A
S
ME
, 104(4), pp
.
602
–
608
.
http
s
:
//d
o
i
.
o
rg/10
.
1115/1
.
3245174
[
27
]
F
.
,
F
uch
s
, V
.
,
M
eidinger, N
.
, Neuburger, T
.
,
R
eiter,
M
.
,
Z
ündel and
A.
, Hupfer (2016)
.
Chal-
lenge
s
in de
s
igning ver
y
s
mall jet engine
s
fuel
di
s
tributi
o
n and at
o
mi
z
ati
o
n
.
I
n
:
I
nternati
o
nal
S
y
mp
o
s
ium
o
n Tran
s
p
o
rt Phen
o
mena and
Dy
namic
s
o
f
Ro
tating
M
achiner
y
, Ha
w
aii
(H
o
n
o
lulu), 10-15
A
pril 2016
.
http
s
:
//hal
.
archive
s
-
o
uverte
s
.
fr/hal-01891309/d
o
cument
[
28
]
G
.
P
.
, Smith,
D.
M
.
,
G
o
lden,
M
.
,
F
ren
k
lach, N
.
W
.
,
M
o
riart
y
,
B
.
,
E
iteneer,
M
.
,
G
o
ldenberg, C
.
T
.
,
R.
K
.
,
B
ow
man, Han
s
o
n, S
.
, S
o
ng, W
.
C
.
,
G
ardiner, V
.
V
.
, Li
ss
ian
s
k
i, and
Z
.
,
Q
in (availa-
ble
o
nline
o
n the 28/07/2025)
.
Welc
o
me t
o
the
G
R
I
-
M
ech H
o
me Page! Lin
k:
http
:
//
www.
me
.
ber
k
ele
y.
edu/gri_mech/
n
21
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