Centre for Advan ed Studies,
Resear h and Development in Sardinia
Uta - (CA)
Programma ENEA-MURST
Obiettivo 8
Development of a non-adiabati premixed model into
the Ares ombustion ode
by:
M. Tali e and M. Mulas
Computational Fluid Dynami s Area
1 Non-adiabati TFC Equations 3
2 Test ase des ription 5
2.1 Numeri al simulation . . . 7
2.2 Results. . . 10
2.3 Dis ussion . . . 22
2.3.1 Adiabati model. . . 22
2.3.2 Non adiabati model . . . 23
3 Con lusion 25
The present report somehow represents the summa of the a tivities whi h
havebeen arried out duringthe thirdand on lusiveyearofthe proje t. In [3℄
thene essityofmodifyingtheoriginalgoalofthepresenttask,hasemerged. In
fa t, the resear h work arried out in [3℄ has shown that the original adiabati
formulation of the TFCmodel wasnot suÆ ient toa hieve aqualitatively and
quantitatively fair des ription of the uiddynami elds (velo ity and temper-
ature) insidea ombustion hamber whenever the energy di usion phenomena
annot benegle ted, whi his the asein thea tual industrialburners.
Inthesame report[3℄itwasdis ussedthe how theTFC modelformulation
ouldbemodi ed inorder totakeintoa ountthe di usionofthermalenergy,
andthenonadiabati versionoftheTFCmodelavailableinthe odeFluentwas
testedagainsttheENSMAexperimental ombustortest ase[1℄. Theobtained
results were su h to make advisable toreformulate the original on lusive task
oftheproje tinordertoimplementthenonadiabati versionoftheTFCmodel
intothe ode Ares.
In Chapter 1 a brief summary of the model will be presented. Interested
readers ould nda more detaileddes ription in [3℄or in [2℄. InChapter 2 the
validationofthe modelagainstthe ENSMA ombustorwillbeillustrated. Both
theadiabati andnonadiabati TFCmodelshavebeenused,andthe al ulation
has been repeated by using all the two-equationsturbulen e models whi h are
availableinAres,namelytheStandardandRNG modelsandthe log(!)
version of the Wil oxmodel. The Spalart & Allmaras one-equation turbulen e
model, whi h is also available in Ares, has not been used here for its intrinsi
limitation in dealing with given pro les of the turbulent quantities at the inlet
se tion.
An a urate des ription of the TFC adiabati formulation an be found in [5 ℄ and
[4 ℄. The nal modelequation writes as:
( ~)
t +
(u~
i
~ )
x
i
=
x
i
D
t
~
x
i
!
+ _
W (1)
The progress variable sour e term _
W whi h appeares in equation 1 is modeled
as:
_
W =U
t
u
jr j=AGu 0f
3
4 g
U f
1
2 g
l
f
1
4 g
` f
1
4 g
t
u
jr j (2)
Where the turbulent velo ity u tuation u 0
and the turbulent lenght s ale `
t an
be expressed as fun tions of the turbulent kineti energy and its dissipation rate.
Their a tual formulation depends onthe hoosen turbulent model.
The expression ofthestret hfa torG whi h appearesinequation 2 anbe found
again in [5 ℄ and [4℄.
In the adiabati TFC model, the energy equation is not solved and it is de fa to
repla ed by the progress variable equation, only. Thus temperature is omputed at
post-pro essing stage as:
T =T
b e
+(1 e
)T
u
Themathemati almodelis losedbyaddinganextra onstitutiverelation,namely
an appropriate equation of state. By usingthe un ompressible form of the ideal gas
law, density an be omputed as:
=
u T
u
T
(3)
Equation 3, by writing the temperature T a ording to equation 1, be omes:
=
u T
u
T
b e +
( 1 e
)
T
u
After somealgebra, the nalexpression for the omputationofdensity, be omes:
=
1
e
=
b +(1
e
)T
u
(4)
Equations 1 and 4 put in eviden e how temperature or density depend on the
progress variable eldonly, andnopossibilityexistsinthemodeltoex hange thermal
energy between uid regions atdi erent temperature levels.
For the non-adiabati model, the solution of the energy transport equation is
needed in order to ompute the a tual temperature distribution. Combustion is
energy equation in terms of enthalpy writes as:
t (
e
h)+
x
i (
e
u
i e
h) =
x
i
+
t
p
x
i e
h
!
+S
h; hem
(5)
where S
h; hem
represents theenthalpy sour e termdueto the hemi alrea tions.
In the non adiabati TFC formulation, S
h; hem
is modeled as:
S
h; hem
= _
WH
omb m
f
(6)
being:
_
W the average spe i produ t formation date;
H
omb
the heat of ombustion for burning 1 kg of fuel;
m
f
the fuel massfra tion of unburnt mixture
The term _
W is omputed a ording to expression 2.
The temperature an be omputed from the enthalpy equation 5 by:
T = e
h
p
(7)
and an be introdu ed in equation 3 to ompute the density eld.
The experimental set-up is shown in gure 1, where a longitudinal se tion of the
ombustion hamber is represented.
y
Lch H Hch
o
L
x
Figure 1: Test Case Geometry.
A premixed mixture of propane and air ows through a hannel, where a square
se tion bar has been inserted. The hannel and obsta le dimensions are those re-
ported in table 1
Channel Obsta le
L
f hg
(mm) H
f hg
(mm) W
f hg
(mm) L (mm) H (mm) W (mm)
2200 28:8 160 5 9:6 160
Table 1: Geometri dimension
For a hydro arbon fuel given by C
fxg H
fyg
, the stoi hiometri rea tion an be
written as:
C
x H
y
+a(O
2
+3:76N
2
) ! xCO
2
+(y=2)H
2
O+3:76aN
2
where: a=x +y=4.
The stoi hiometri air to fuel ratio is given by:
(A=F)
fstoi g
=
m
a ir
m
fuel
= 4:76a
1 MW
a ir
MW
fuel
where MW
a ir
and MW
fuel
are the mole ular weight of air and fuel, respe tively.
The temperature of the mixture at the inlet se tion is 273K and the mass-
ow per unit of hannel thi kness is equal to 0:2722Kg=m=s, orresponding to a
maximumspeed of the main ow of 8:2m=s. The resulting Reynoldsnumber based
on the hannel height is Re = 17810, whereas the orresponding value based on
the obsta le height is Re = 5937.
The hemi al rea tion whi h des ribes the ombustion pro ess is given by:
fuel mass fra tion Y
C
3 H
8
0.04
oxygen mass fra tion Y
O
2
0.2237
nitrogen massfra tion Y
N
2
0.7363
mixture temperature T
unb
273.0
adiabati ame temperature T
a dia b
1780.0
mixture density
unb
1.3059
heat of ombustion H
omb
[J/Kg℄ 50.0
spe i heat C
P
1614
Table 2: Mixture omposition and properties
C
3 H
8
+5(O
2
+3:76N
2
) ! CO
2
+4H
2
O+(5 5)O
2
+18:8N
2
The mixture omposition together with other quantities of interest are reported
in table 2, where the mixture equivalen e ratio is de ned as:
= (A=F)
stoi
(A=F)
Measurements are available for non-rea tive andrea tive ow onditions andthe
des riptionoftheexperimentalresults anbefoundinreferen e[1℄. Theexperiments
have found the eviden e of the existen e of two vortexes downstream the obsta le.
Thee e tofthisre ir ulation zoneisthestabilizationofthe ame. Thelongitudinal
extension of the re ir ulation zone has been measured to be equal to 4x=H along
the ombustor axis.
Figure 2 shows the grid topology of the 4-blo k mesh used, and an enlargement of
the omputational domain around the obsta le. In the same gure, the positions of
the three ross-se tions on whi h experimental data are available, are also shown.
In order to assure grid independen e results, the omputations have been repeated
by usingtwo ner meshes whi h are obtained by doubling the number of ells ofthe
oarse grid. Table 3 gives the number of ells used in the x and y dire tions for
ea hblo kand for ea hgrid level. Resultsobtained with grid levelB de fa tomat h
those obtained with grid level C, and will be the only ones reported in the following.
As previouslymentioned, the stabilization ofthe amebehind the ameholder is
due to the presen e of two vortexes. Hen e, a orre t des ription of the turbulent
ow behavior is a riti al issue of the test ase simulation. The turbulen e models
whi h havebeen used were the two modelsof the family, namely standard and
RNG,plusthe log(!)model. The Spalartand Allmarasone-equation turbulen e
model whi h has been implemented into the ARES ode, has not been used in the
simulation. In fa t, an intrinsi limitation of that model is that it is not possible to
learly assign to the in oming ow a hosen turbulen e intensity (or a given pro le
of turbulent kineti energy). The validation of the model is hen e postponed to a
su essive task.
1 2 3
4
0.01 0.03 0.06
Figure 2: Blo ks topology (up); mesh detail around the obsta le (bottom)
Inlet pro les(transversal distributions)forthe average quantities u; and"have
been imposed at the inlet se tion and are those reported in gures 4 and 5. The
value of and "have been omputed from the measured pro les of p
u 0
2
and p
v 0
2
by using relations:
= 1
2
p
u 0
2
+2: p
v 0
2
; "=
2
uv
u
y
1 2 3
obstacle
Figure 3: Domain splitting for the ARES parallel al ulation
Level A Level B Level C
Bl NI NJ Cells NI NJ Cells NI NJ Cells
1 48 96 4608 96 192 18432 192 384 73728
2 32 64 2048 64 128 8192 128 256 32768
3 32 64 2048 64 128 8192 128 256 32768
4 96 96 9216 192 192 36864 384 384 147456
17920 71680 286720
Table 3: Mesh size
In the aseof the log(!) model, the log(!) pro le has been imposedatthe
inlet se tion. It an been omputed from the orresponding and ones by using
the relation:
log(!) =
−2 −1 0 1 2
y/H 0
2 4 6 8 10
average x−velocity
Figure 4: x-velo ity distrinution atinlet
−2 −1 0 1 2 y/H
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
average kinetic energy
−2 −1 0 1 2
y/H 20
40 60 80 100 120
average kinetic energy dissipation
Figure 5: and
Wall fun tions have been used at solid walls for the family al ulation,
whereas turbulent quantities have been integrated down to solid walls in the
log(!) ase. At the outlet se tion, the pressure value of 101325 [Pa℄ has been
imposed. Isothermal onditions have been imposed at solid walls. The in oming
ow temperaturevaluehas beenset to 273 K.Boththe adiabati and non adiabati
versions of the TFC premixed ombustion model have been used for the present
omputation. An exhaustive des riptionof theadiabati model ould be foundin [5 ℄
and [4 ℄.
Theinletvalueoftheprogress variable ~hasbeensettozero(unburnedmixture).
For theadiabati al ulationthe valueof the burned mixture density hasbeen set to
bnd
=0:20.
In the non adiabati ase isothermal onditions have been used at solid walls.
The temperature of the hannel walls havebeen set to 273 K,whereas the obsta le
walls temperature, a ordingly to the results already obtained in [3 ℄, was set to 600
K.
The QUICK spatial dis retization s heme has been used, and the linear system
was integrated by making use of the BICGSTAB, pre onditioned by the ADI algo-
rithm.
The gures 6, 7 and 8 show the omparison of the omputed temperature pro les
to the experimental data at x=H = 1:04167, x=H = 3:125 and x=H = 6:25 from
the obsta le. The maximum value of the temperature whi h has been omputed
by using the adiabati TFC model is equal to the adiabati ame temperature of
the mixture, namely 1780 K. In fa t it ought to be re alled here that by using the
adiabati model, temperature is omputed at a post-pro essing stage as a fun tion
of the progress variable ~as:
T =T
a dia b
~ +T
unb
(1 ~)
From the exam of gures 6, 7 and 8 it an be seen that the error ommitted in
the evaluationofthe temperature atthe rst onsidered rossse tion, redu esfrom
some500Ktonearly 150K. Atthe twostations further downstreamthe ombustor
hamber, the maximumvalue of temperature is well aptured by the non adiabati
model,whereas the error whi h ismade by using theadiabati modelisstill ofabout
280 K.
Figure 10 shows the velo ity streamlines over the progress variable ontour plot
ba kground, for the non adiabati omputation. Analysis of the gure show the
in uen e of the di erent turbulen e models on the ri ir ulation region lenght. The
quantitative evaluation of the ri ir ulation region amplitude an be retrieved from
the gure 9, whi h shows the omparison of the streamwise velo ity omponent to
the experimental data.
Pro les of the streamwise and rosswise omponents of the velo ity are shown
in gures 11, 12, 13and 14, 15, 16respe tively.
The gure 17 shows the omputed turbulent kineti energy distribution at the
rst ross se tion from the obsta le.
The exam of gures from 18 to 28 allows to ompare the omputed results in
dependen e on the turbulen e model whi h has been used for the omputation.
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment adiabatic TFC non adiabatic TFC
Figure 6: temperature distribution at x=H =1:04167: RNG (left); Std
(middle); log(!) (right);
0 0.5 1 1.5 y/H
0 250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment adiabatic TFC non adiabatic TFC
Figure 7: temperature distribution at x=H = 3:125: RNG (left); Std
(middle); log(!) (right);
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment adiabatic TFC non adiabatic TFC
Figure 8: temperature distribution at x=H = 6:25: RNG (left); Std
(middle); log(!) (right);
−1 0 1 2 3 4 5 6 7 8
−6
−5
−4
−3
−2
−1 0 1 2 3 4 5 6 7 8 9 10
experiment adiabatic TFC non adiabatic TFC
−1 0 1 2 3 4 5 6 7 8
−6
−5
−4
−3
−2
−1 0 1 2 3 4 5 6 7 8 9 10
experiment adiabatic TFC non adiabatic TFC
−1 0 1 2 3 4 5 6 7 8
−6
−5
−4
−3
−2
−1 0 1 2 3 4 5 6 7 8 9 10
experiment adiabatic TFC non adiabatic TFC
Figure 9: x-velo ity distribution along the ombustor axis: RNG (left); Std
(middle); log(!) (right);
f 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
f 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
f 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Figure 10: Streamlines over progress variable ontour: Standard (top); RNG
(middle); log(!) (bottom);
0 0.5 1 1.5 y/H
−5 0 5 10 15 20 25
x−velocity experiment
adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
x−velocity experiment
adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
x−velocity experiment
adiabatic TFC non adiabatic TFC
Figure 11: x-velo ity distribution at x=H = 1:04167: RNG (left); Std
(middle); log(!) (right).;
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
x−velocity experiment
adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
x−velocity experiment
adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
x−velocity experiment
adiabatic TFC non adiabatic TFC
Figure 12: x-velo ity distribution at x=H = 3:125: RNG (left); Std
(middle); log(!) (right);
0 0.5 1 1.5
y/H 0
5 10 15 20 25 30 35 40
x−velocity
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H 0
5 10 15 20 25 30 35 40
x−velocity
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H 0
5 10 15 20 25 30 35 40
x−velocity
experiment adiabatic TFC non adiabatic TFC
Figure 13: x-velo ity distribution at x=H = 6:25: RNG (left); Std
(middle); log(!) (right);
0 0.5 1 1.5 y/H
−5
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2
y−velocity experiment
adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−5
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2
y−velocity experiment
adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−5
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2
y−velocity experiment
adiabatic TFC non adiabatic TFC
Figure 14: y-velo ity distribution at x=H = 1:04167: RNG (left); Std
(middle); log(!) (right);
0 0.5 1 1.5
y/H
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1
y−velocity experiment
adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1
y−velocity experiment
adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1
y−velocity experiment
adiabatic TFC non adiabatic TFC
Figure 15: y-velo ity distribution at x=H = 3:125: RNG (left); Std
(middle); log(!) (right);
0 0.5 1 1.5
y/H
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2 2.5
y−velocity
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2 2.5
y−velocity
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2 2.5
y−velocity
experiment adiabatic TFC non adiabatic TFC
Figure 16: y-velo ity distribution at x=H = 6:25: RNG (left); Std
(middle); log(!) (right);
0 0.5 1 1.5 y/H
−5 0 5 10 15 20 25
κ
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
κ
experiment adiabatic TFC non adiabatic TFC
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
κ
experiment adiabatic TFC non adiabatic TFC
Figure 17: turbulentkineti energydistribution atx=H =1:04167: RNG (left);
Std (middle); log(!) (right).
0 0.5 1 1.5 y/H
−5 0 5 10 15 20 25
κ
experiment RNG κ−ε Std κ−ε κ−log(ω)
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
κ
experiment RNG κ−ε Std κ−ε κ−log(ω)
Figure 18: turbulent kineti energy distribution at x=H =1:04167: adiabati model
(left); non adiabati model(right);
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
x−velocity experiment
RNG κ−ε Std κ−ε κ−log(ω)
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
x−velocity experiment
RNG κ−ε Std κ−ε κ−log(ω)
Figure 19: x-velo ity distribution at x=H = 1:04167: adiabati model (left); non
adiabati model (right);
0 0.5 1 1.5 y/H
−5 0 5 10 15 20 25
x−velocity experiment
RNG κ−ε Std κ−ε κ−log(w)
0 0.5 1 1.5
y/H
−5 0 5 10 15 20 25
x−velocity experiment
RNG κ−ε Std κ−ε κ−log(w)
Figure 20: x-velo ity distribution at x=H = 3:125: adiabati model (left); non
adiabati model (right);
0 0.5 1 1.5
y/H 0
5 10 15 20 25 30 35 40
x−velocity
experiment RNG κ−ε Std κ−ε κ−log(ω)
0 0.5 1 1.5
y/H 0
5 10 15 20 25 30 35 40
x−velocity
experiment RNG κ−ε Std κ−ε κ−log(ω)
Figure 21: x-velo ity distribution at x=H = 6:25: adiabati model (left); non adia-
bati model (right);
0 0.5 1 1.5 y/H
−5
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2
y−velocity experiment
RNG κ−ε Std κ−ε κ−log(ω)
0 0.5 1 1.5
y/H
−5
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2
y−velocity experiment
RNG κ−ε Std κ−ε κ−log(ω)
Figure 22: y-velo ity distribution at x=H = 1:04167: adiabati model (left); non
adiabati model (right);
0 0.5 1 1.5
y/H
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1
y−velocity experiment
RNG κ−ε Std κ−ε κ−log(ω)
0 0.5 1 1.5
y/H
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1
y−velocity experiment
RNG κ−ε Std κ−ε κ−log(ω)
Figure 23: y-velo ity distribution at x=H = 3:125: adiabati model (left); non
adiabati model (right);
0 0.5 1 1.5 y/H
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2 2.5
y−velocity
experiment RNG κ−ε Std κ−ε κ−log(ω)
0 0.5 1 1.5
y/H
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2 2.5
y−velocity
experiment RNG κ−ε Std κ−ε κ−log(ω)
Figure 24: y-velo ity distribution at x=H = 6:25: adiabati model (left); non adia-
bati model (right);
−1 0 1 2 3 4 5 6 7 8
−6
−5
−4
−3
−2
−1 0 1 2 3 4 5 6 7 8 9 10
experiment RNG κ−ε Std κ−ε κ− log( ω )
−1 0 1 2 3 4 5 6 7 8
−6
−5
−4
−3
−2
−1 0 1 2 3 4 5 6 7 8 9 10
experiment RNG κ−ε Std κ−ε κ−log(ω)
Figure 25: x-velo ity distribution along the ombustor axis: adiabati model (left);
non adiabati model (right);
0 0.5 1 1.5 y/H
0 250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment RNG κ−ε Std κ−ε κ−log(ω)
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment RNG κ−ε Std κ−ε κ−log(ω)
Figure 26: temperature distribution atx=H =1:04167: adiabati model (left); non
adiabati model (right);
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment RNG κ−ε Std κ−ε κ−log(ω)
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment RNG κ−ε Std κ−ε κ−log(ω)
Figure 27: temperature distribution at x=H = 3:125: adiabati model (left); non
adiabati model (right);
0 0.5 1 1.5 y/H
0 250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment RNG κ−ε Std κ−ε κ−log(ω)
0 0.5 1 1.5
y/H 0
250 500 750 1000 1250 1500 1750 2000
Temperature (K)
experiment RNG κ−ε Std κ−ε κ−log(ω)
Figure 28: temperature distribution at x=H = 6:25: adiabati model (left); non
adiabati model (right);
2.3.1 Adiabati model
From the analysis of the pi tures shown in the previous se tion someremarks ould
be made:
[1 ℄ dimension of ri ir ulating region behind the obsta le
itis strongly underestimated; aremarkable ex eption is represented by the
simulation produ ed by the RNG model;
[2 ℄ streamlines pattern and velo ity eldsdownstream
pro les of rosswise velo ity omponents far downstream of the obsta le
suggest thatthe streamlines donot bend toward the ombustor axis, as found
bymost ofthe al ulations; again the RNGmodelgives the orre tqualitative
behaviour;
[3 ℄ temperature level
all models predi t a temperature level, right behind the obsta le, given
by the adiabati ametemperature whi h, as a matter of fa t, overestimates
of about 500 K the measured level; in referen e [1 ℄ it is suggested a power
loss through the solid bar due to heat ondu tion; moreover, the temperature
measures show a minimum level (about 1250 K) upstream, with respe t to
about 1500 K downstream, whi h anbe explained onlyby assuming a ertain
level of instability of the vorte es behind the obsta le whi h in turn may allow
fresh mixture to be entrained;
[4 ℄ ame opening
RNG results determine the least degree of ameopening; the log(!)
results show the maximumlevel, followed by the standard ;
[5 ℄ temperature pro les
this issue is tightly onne ted to the previous one due to the temperature
relation to the progress variable: all models fail to reprodu e the slope of
the temperature pro les; apparently the worst slope is that produ ed by the
RNG model, whi h is the steepest one: this is in ontradi tion to the previous
ommentsabout the RNG results;
[6 ℄ e e ts of turbulen e model
turbulen e modelling seemsto play afundamental roleforthe orre t sim-
variable relation must also be taken into a ount when dis ussing the results. The
TFC model,asin origin developedand implementedinto Ares ode, is adiabati and
non heat- ondu ting. The model is adiabati be ause, sin e T = T( ~), only the
progress variable equation is solved, with Neumann wall boundary onditions. As
a result, no isothermal wall onditions an ever be used, and the suggested heat
loss through the ondu tiong bar, annot be simulated. The modelis also non heat
ondu ting be ause there is no way to di use internal energy in a stream of burned
gases ~=1. In other words, a burned stream annot be ooled, whi h represents a
modellimitation.
Whether the heat ondu tion loss through the walls, or the heat di usion within
the burned stream of gas, or both of them, are responsible for the lower temper-
atures, the omputed density elds are mu h lower than the measured ones and,
as a onsequen e, the velo ity elds are also a e ted due to the ontinuity equa-
tion. The higher velo ity levelsmightin turn intera t with the turbulen e modeland
generate at the end a mu h smaller ri ir ulating region. In other words, there is a
hain rea tionofe e ts thatmustbe understood. The betterbehaviour oftheRGN
turbulen e model might, in the end, havebeen determined by han e only.
2.3.2 Non adiabati model
Themaximumtemperaturevaluefallstoabout 1500Kwhenusingthenonadiabati
model,re overingthemeasuredvalues,apartfromthese tion losesttotheobsta le.
It ought to be put in eviden e here that, even tough isothermal onditions have
been used at the obsta le solid walls, in order to take into a ount the ex hange
of thermal energy between the main ow and the obsta le itself, this me hanism of
energytransferseemsnotbeingsuÆ ienttogivereasonofthemeasuredtemperature
drop at the rst ross se tion behind the obsta le. A ording to [1℄ it has been
experimentally observed that the vortex system downstream the obsta le shows a
pulsatile behavior, namely it moves ba k and forth along the hannel axis. This
movement ould be responsible for the entrapment of gas at lower temperature
in the zone right behind the obsta le, whi h would lead to a lower value of the
averagetemperature. Thise e t, whi hisofstrongly unsteadynature,hasnotbeen
a ounted for in anyway in the present simulation, whi h presents only stationary
results.
The streamwise velo ity omponent at se tion x=H = 1:04167 doesn't seem
to be e e ted too mu h by the errors made in the evaluation of the temperature
eld,showing nosigni antdi eren ebetweenthe results obtainedbyusing thetwo
models. At the two remaining se tions further downstream the hannel, the e e t
of the energy di usion be omes more evident, so that the maximum error made in
the evaluation of the velo ity is redu ed by around 4 to 9m=s depending on the
Some improvement in the results ould be also observed for the rosswise om-
ponent of velo ity. The most signi ant e e ts are found for the standard
model, for whi h the relative maximumerror has been redu ed up to about 30%.
As expe ted, the most relevant improvement on the results are obtained in the
evaluation of the temperature eld. The maximum level of the temperature is well
apturedbythe model,aswellasthe amefront positionand thi kness. Di usionin
the rosswisedire tion isstillpoorlyevaluated omparedto themeasures, andmight
depend upon the turbulen e model.
The examination of gures 17, 18 and 9, 25 shows no signi ant improvement
in the resolution of both the turbulent kineti energy and axial distribution of the
longitudinal velo ity omponent, by using the non adiabati TFC model.
In the present work the implementation of the non adiabati version of the TFC
model and its validation have been presented. All the omputations have been also
arried out by making use of the adiabati version of the TFC model. The hoosen
test ase, namely the ENSMA ombustor, has proven itself to be a very tough one
and has represented a good hallange for testing the ombustion ode Ares. The
diÆ ulties whi h havebeenen ountered wererelated to the TFC ombustion model
as well as to the turbulen e models. The obtained results have shown the a ura y
improvement that ould be a hieved in the omputationof the temperature eld by
making use of the non adiabati version of the model. The more orre t evaluation
of the uid ow temperature has also determined an improvement in the omputed
velo ity pro les. A orre t des ription of the turbulent quantities proved to be an
important issue and the RNG model gave the best results in omparison to
both the standard and the log(!) .
[1℄ First European Test for Combustion Modelling Workshop. Aussois, Fran e,
February 5-10, 1995.
[2℄ Fluent In . Fluent 5 User's Guide. Fluent In ., 1998.
[3℄ Chibbaro S. Tali e M. and Mulas M. \Validazione del odi e ARES". Te hni-
alReport CRS4-TECH-REP-02/22,CRS4Resear hCentre, z.i.Ma hiareddu,
strada VI, 09010 Uta (Ca), February 2002.
[4℄ V. Zimont and M. Barbato. \Premixed and Partially Premixed Turbulent Com-
bustion: Theory and Modelling". Te hni al Report CRS4-TECH-REP-97/71,
CRS4 Resear h Centre, z.i. Ma hiareddu, strada VI, 09010 Uta (Ca),O tober
1999.
[5℄ Zimont, V.L., Polifke, W., Bettelini, M. Weisenstein W. An EÆ ient Compu-
tational Model for Premixed Turbulent Combustion at High Reynolds Numbers
Based on a Turbulent Flame Speed Closure. Journal of Engineering for Gas
Turbines and Power, 120, July 1998.
