CRS4 CediRi e aSvi

Centro di Ri er a, Sviluppo e

Studi Superiori in Sardegna

Uta - (CA)

Programma ENEA-MURST

Obiettivo 6

Validazione e rilas io del odi e ARES

by:

M. Tali e, S. Chibbaro and M. Mulas

1 Test Case Des ription 3

2 Numeri al Simulations 5

3 Results 8

4 Dis ussion 17

5 Further investigation 19

5.1 Non adiabati TFC model with adiabati walls . . . 20

5.2 Non adiabati TFC model with isothermal walls . . . 26

6 Sensitivity to turbulen e models 32

7 Con lusions 37

Referen es 38

Abstra t

Thisreport on ludesthea tivitiesofthese ondyearoftheproje t. During

these ondyearavarietyofturbulen emodelstogetherwithapartiallypremixed

ombustion modelwere developed [1℄, [2℄. Implementation ofthe models into

the new Ares ombustion ode and their validation was the obje tive of the

present report. Tothe authors' knowledge however, there are no partiallypre-

mixed ben hmarks available in the literature, so that a thorough validation of

thisissue hastobe postponed tothe nalyear.

The test ase proposed has been presented in the First European Test for

Combustion Modeling Workshop, 1995 Aussois Fran e [3℄, by the Laboratoire

de Combustion et Detonique de l'ENSMA (hereinafter referred as ENSMA).

This test ase is appealing be ause even though it is geometri ally simple, it

reprodu es themain features that an o ur ina tual industrial ombustors.

Itisa wellknownfa tthatpremixedamesare unstable,therefore,inorder

to be used in pra ti al appli ations they have to be stabilized. This is usually

donebyindu ing thepresen eofstationaryvortexesintothemain owinorder

to an hor the ame. A simple way toa hieve this result is toput an obsta le

insidethe ombustion hamber. Thea tual geometri al ongurations used in

the industrial ombustors are omplex andexperimental measurements are not

easytobe found.

The test ase is des ribed in Chapter I. In Chapeter II the most relevant

parameters used for the omputations are indi ated. Chapter III presents the

resultswhi hhavebeen obtained.

The results show that the originalTFC modelformulation is not su ient

toprovidegoodquantitativeandalsoqualitativeresultsintermsoftemperature

and velo ity elds. The reason of su h a failure has been investigated using

alsotheFluent ode,asillustratedinChapterIV.Thethorough omprehension

of de ien iesof the ombustion modelled topartial res heduling ofthe third

and nal year ofthe proje t, during whi h the development ofa non adiabati

versionof the TFCmodelwillbe arriedout.

Finally, in Chapter V, given the fa t that ombustion and turbulen e are

strongly oupled, the sensitivity of the results to dierent turbulen e models

has been evaluated. In parti ular, the se ond order losure turbulen e model

(ReynoldsStress Model)whi his availablein Fluent,has beentested.

1 Test Case Des ription

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 dimensions

For ahydro arbon fuelgiven by C

x H

y

, thestoi 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

fa irg

m

ffuelg



= 4:76a

1 MW

fa irg

MW

ffuelg

whereMW

fa irg

andMW

ffuelg

arethemole ularweightofairandfuel, 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 Reynolds number based

onthe hannel heightis Re =17810, whereas the orresponding valuebasedonthe

The hemi al rea tion whi h des ribes the ombustion pro ess is given by:

C

3 H

8

+5(O

2

+3:76N

2

)!CO

2

+4H

2

O+(5 5)O

2

+18:8N

2 (1)

equivalen e ratio  0.65

fuel massfra tion Y

C

3 H

8

0.04

oxygen mass fra tion Y

O

2

0.2237

nitrogen mass fra tion Y

N

2

0.7363

mixture temperature T

unb

[K℄ 273.0

mixture density 

unb

1.3059

adiabati ame temperature T

a dia b

[K℄ 1780.0

spe i heat C

P

1614

heat of ombustion H

omb

[J/kg℄ 5010 6

Table 2: Mixture omposition and properties

The mixture omposition together with other quantities of interest are reported

in table 2, where the equivalen e ratio of the mixture is expressed by:

= (A=F)

fstoi g

(A=F)

Measurements are available for non-rea tive andrea tive ow onditions andthe

des riptionoftheexperimentalresults anbefoundinreferen e[3℄. Theexperiments

have found the eviden e of the existen e of two vortexes downstream the obsta le.

Theee tofthisre ir ulation zoneisthestabilizationoftheame. Thelongitudinal

extension of the re ir ulation zone has been measured to be equal to 4x=H along

the ombustor axis.

2 Numeri al Simulations

The numeri alsimulation of theENSMA test asehas been arried outby usingthe

odes ARES and Fluent. The two odes have been run using, as far as possible,

the same onditions,su h asnumeri als hemes, physi almodelsand omputational

grid.

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 thethree ross-se tions onwhi hexperimental dataare 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, plus the  log(!) model. The Fluent omputations have been arried out

by making use of the  family models only, be ause the  log(!) model was

not available in the version 5.5 of the ode. The Spalart and Allmaras one-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 modelis that it is not

possible to learly assignthe in oming ow a hosen turbulen e intensity (ora given

proleofturbulentkineti energy). Thevalidationofthemodelishen epostponedto

a su essive task. Inlet proles (transversal distributions) for the average quantities

u; and " have been imposed at the inlet se tion and are those reported in gures

3 and 4. The value of  and " have been omputed from the measured proles 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

In the aseof the  log(!) model, the log(!) prole has been imposedatthe

inlet se tion. It an been omputed from the orresponding  and  ones by using

1 2 3

4

0.01 0.03 0.06

Figure 2: Blo ks topology (up); mesh detail around the obsta le (bottom)

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

log(!) =log









Wall fun tions havebeen used at solid walls. At the outlet se tion, the pressure

value of 101325 [Pa℄ has been imposed.

TheTFCpremixed ombustionmodelhasbeenusedforthepresent omputation.

An exhaustive des riptionof themodel ould be foundin [4 ℄and[5℄. The inlet value

of the progress variable ~has been set to zero (unburned mixture).

The QUICK spatial dis retization s heme has been used for both ARES and

FLUENT omputations. The linear system integration method used in the ARES

ode was the BICGSTAB,pre onditioned by using the ADI algorithm. In the Fluent

−2 −1 0 1 2 y/H

0 2 4 6 8 10

average x−velocity

Figure 3: x-velo ity distribution 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

3 Results

Inthegures5 and6thenormalized residualsoftheresolvedequationsarereported.

Both odes havebeen started from the oarser grid level solution. Convergen e has

to be onsidered ata more than satisfa tory level and nosigni ant modi ation of

the obtained solutions have been found after someextra 100 iterations.

0 200 400 600 800 1000

iteration

−8

−6

−4

−2 0 2

log

10(RES/RES0)

x−velocity y−velocity pressure κ ε progress var.ble

0 200 400 600 800 1000

iteration

−8

−6

−4

−2 0 2

log

10(RES/RES0)

x−velocity y−velocity pressure κ ε progress var.ble

0 200 400 600 800 1000

iteration

−11

−10

−9

−8

−7

−6

−5

−4

−3

−2

−1 0

log

10(RES/RES0)

x−velocity y−velocity pressure κ log(ω) progress var.ble

Figure 5: Ares: onvergen e history;  left; RNG   enter;  log(!) right

0 200 400 600 800 1000

iteration

−8

−6

−4

−2 0 2

log 10 (RES/RES 0 )

x−velocity y−velocity continuity κ ε

progress var.ble

0 200 400 600 800 1000

iteration

−8

−6

−4

−2 0 2

log 10 (RES/RES 0 )

x−velocity y−velocity continuity κ ε

progress var.ble

Figure 7 showsthe omputed progress variable e

ontour plotstogether withthe

streamlines for Ares al ulations. The gures 8 and 9 show the omputed progress

variable e

ontour plotsfor Fluent al ulations.

Standard kappa-epsilon

RNG kappa-epsilon

kappa-log(omega)

Contours of Progress Variable Feb 08, 2002 FLUENT 5.5 (2d, dp, segregated, ke) 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Contours of Progress Variable Feb 08, 2002 FLUENT 5.5 (2d, dp, segregated, ke) 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

The gures 10, 11 and 12 show the omparison of the omputed temperature

proles to the experimental data at x=H = 1:04167; 3:125 and 6:25 from the

obsta le.

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment Ares Fluent

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment Ares Fluent

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment Ares k−log(ω)

Figure 10: Temperature prole at x=H = 1:04167;   left; RNG   enter;

k log(!) right.

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment Ares Fluent

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment Ares Fluent

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment Ares k−log(ω)

Figure 11: Temperature prole at x=H = 3:125;   left; RNG   enter;

k log(!) right.

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment Ares Fluent

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment Ares Fluent

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment Ares k−log(ω)

Figure 12: Temperature prole at x=H = 6:25;   left; RNG   enter;

Thegures10,11and12showasubstantialagreementbetweenAresandFluent

results. The dieren e between the omputed and the experimental temperature is

about 400 K at the se tion nearest to the obsta le and about 280 K at the two

se tions further downstream.

However, it must be reminded here that, when using the TFC model, the tem-

perature represents a quantity derived from the al ulated progress variable ~as:

T =T

b

~ +T

u

(1: ~) (2)

and what itis a tually shown in the pi tures is the progress variable.

Figure 13,showsthe distributionofthestreamwisevelo ity omponent alongthe

ombustor axis. The true measured ri ir ulation region an be learly ompared to

the al ulated ones, previously shown in gure 7.

−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

Ares Fluent experiment

−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

Ares Fluent experiment

−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

Ares k−log(ω) experiment

Figure 13: x-velo ity distribution along the ombustor axis;  left; RNG  

enter; k log(!) right.

Proles of streamwise and rosswise omponents of the velo ity are shown in

0 0.5 1 1.5 y/H

−5 0 5 10 15 20 25

x−velocity ^experiment Ares

Fluent

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity ^experiment Ares

Fluent

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity ^experiment Ares k−log(ω)

Figure 14: x-velo ity prole at x=H = 1:04167;   left; RNG   enter;

k log(!) right.

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity ^experiment Ares

Fluent

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity ^experiment Ares

Fluent

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity ^experiment Ares k−log(ω)

Figure 15: x-velo ityproleatx=H =3:125; left;RNG  enter; k log(!)

right.

0 0.5 1 1.5

y/H 0

5 10 15 20 25 30 35 40

x−velocity

experiment Ares Fluent

0 0.5 1 1.5

y/H 0

5 10 15 20 25 30 35 40

x−velocity

experiment Ares Fluent

0 0.5 1 1.5

y/H 0

5 10 15 20 25 30 35 40

x−velocity

experiment Ares

Figure 16: x-velo ityproleatx=H =6:25; left; RNG  enter; k log(!)

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 Ares Fluent

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 Ares Fluent

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 Ares k−log(ω)

Figure 17: y-velo ity prole at x=H = 1:04167;   left; RNG   enter;

k 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 Ares Fluent

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 Ares Fluent

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 Ares

Figure 18: y-velo ityproleatx=H =3:125; left;RNG  enter; k 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 Ares Fluent

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 Ares Fluent

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 Ares

Figure 19: y-velo ityproleatx=H =6:25; left; RNG  enter; k log(!)

Finally, the gure 20 shows the proles of turbulent kineti energy at x=H =

1:04167. The ARES RNG   model provides a general good agreement with

experimental data, even though the maximumvalueappears underestimated.

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

κ

experiment Ares Fluent

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

κ

experiment Ares Fluent

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

κ

experiment Ares k−log(ω)

Figure 20: turbulent kineti energy proleat x=H=1:04167;  left; RNG  

enter; k log(!) right.

4 Dis ussion

From the analysis of the pi tures shownin the previous se tion someissues deserve

further investigation and better omprehension:

[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 implemented into Ares;

[2 ℄ streamlines pattern and velo ity eldsdownstream

proles of rosswise velo ity omponents far downstream of the obsta le

suggest thatthe streamlines donot bend toward the ombustor axis, as found

by most of the al ulations; again the RNG model of Ares gives the orre t

qualitative 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 400 K the measured level; in referen e [3 ℄ 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

AresRNG results determine the least degree of ameopening, also om-

pared toFluent RNG results; the  log(!) resultsshow the maximumlevel,

followed by the standard  ;

[5 ℄ temperature proles

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 proles; apparently the worst slope is that produ ed by Ares

RNG model, whi h is the steepest one: this is in ontradi tion to the previous

[6 ℄ ee ts of turbulen e model

turbulen e modelling seemsto play afundamental roleforthe orre t sim-

ulation of the ri ir ulating vorte es and the amefront opening as well;

[7 ℄ Ares versus Fluent

though the results of the two odes are very similar to ea h other, Ares

gives better results in almost all situations, and parti ularly when the RNG

turbulen e model is used.

As reminded previously in the text, the temperature versus the progress variable

relationmustalsobetakeninto a ountwhendis ussingtheresults. TheTFCmodel,

asdevelopedandimplementedintoAres ode,is adiabati andnonheat- ondu ting.

The modelisadiabati be ause, sin e T =T(~ ),onlythe 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, annotbe simulated. Themodelisalsononheat ondu tingbe ause thereisno

way to diuse internal energy in a stream of burned gases ( ~=1). In other words,

a burned stream annot be ooled, whi h represents amodel limitation.

Whether the heat ondu tion loss through the walls, or the heat diusion within

the burned stream of gas, or both of them, are responsible for the lower tempera-

tures, the omputed density elds are mu h lower than the measured ones and, as

a onsequen e, the velo ity elds are also ae ted due to the ontinuity equation.

The higher velo ity levels might inturn intera t with the turbulen e modeland gen-

erate at the enda mu h smallerri ir ulating region. In other words, there is a hain

rea tion ofee ts thatmustbe understood. The betterbehaviour of the AresRGN

turbulen e model might, in the end, havebeen determined by han e only.

If it is true that a major failure is determined by the adiabati and non heat

ondu ting hara ter of the TFC model, then a model upgrade is needed and the

ombustion modelextensionto heat ondu ting asemustbe s heduled in the third

and nal year of the proje t. In the following se tions, Fluent non adiabati TFC

5 Further investigation

The examination of the experimentalresults showsthatthe a tual ow eld is har-

a terized by a stream of high temperature ombustion produ ts surrounded by a

stream of old mixture. Moreover the ex hange of thermal energy throughout solid

walls should be taken into a ount. In fa t, even ignoring the heat ow through

the external walls seems reasonable enough, the hypothesis of adiabati ity ouldn't

be applied to the obsta le walls. In other words, two me hanisms are to be put in

eviden e, by whi h thermal energy is transfered:

 thermal energy is diused from hot to old mixture;

 thermalenergy isdrained out the systemthroughout the obsta le walls due to

ondu tion.

The ne essity of in luding somehow energy into the mathemati al modelin order to

get amore a uratedes ription ofthe physi al behavior of thesystem,suggested to

makeuseofthenonadiabati version oftheTFCmodelwhi h isavailableinFluent.

A omplete des riptionof the model anbe foundin[6℄. In the s ope ofthe present

workitisonlyimportanttoremindthat,a ordinglytothenonadiabati formulation,

the energy equation, written in terms of stati enthalpy, is solved together with the

progress variable equation, being the hemi al sour e term in the energy equation

proportional via the heat of ombustion H

omb

and the fuel massfra tion Y

f

, to the

~

equation sour e term and being the lo al density omputed as:

=



u T

u

T

where the temperature T is derived from the energy equation and al ulated as:

T = h

p

instead of:

T =T

a d

~ +T

u

(1 ~)

as in the adiabati TFC model.

In order to weight the relative importan e of the two previously mentioned me ha-

betweenthe uidow andsolidwalls, two setsof al ulations havebeen arriedout.

At rst, the non adiabati version of the TFC model has been used, together with

adiabati ondition at solid walls. So that, the only dieren e with the TFC simu-

lation dis ussed in the previous hapter, was the version of the ombustion model,

only (non adiabati vs adiabati ). Then, isothermal onditions have been applied

to the solid wall limiting the omputational domain. Thus, in this se ond set of

simulation not only energy diusion, but also the energy ow from the ombustion

hamber to the obsta le walls was taken into a ount. In order to be able to set a

reasonable value for the obsta le wall temperature, the fully 3D oupled solid-uid

problem has been solved. Thermal energy an be ex hanged between the obsta le

and the external world via ondu tion. By the resolution of the 3D problem the

orre t temperature value to be assigned atthe solid walls has been determined.

5.1 Non adiabati TFC model with adiabati walls

Figures 21, 22 and 23 show the temperature proles atthe 3 se tions. Figures 24,

25and 26and gures27, 28and 29show the streamwiseand the rosswise velo ity

omponents respe tively, at the same ombustor se tions. All gures ompare the

adiabati to the non adiabati modelimplemented in Fluent.

Maximumtemperaturesfalltoabout1500Kwhenusingthenonadiabati model,

re overing the measured values, apart fromthe se tion losest to the obsta le. The

rosswisevelo ity omponent atse tionx=H =1:04167doesn't seemtobeee ted

too mu h by the errors made in the evaluation of the temperature eld, showing no

signi ant dieren e between the results obtained by using the two models. At the

two remaining se tions further downstream the hannel, the ee t of the energy

diusion be omes more evident, so thatthe maximumerror made in the evaluation

of the velo ity is redu ed by around 4 to 9 m=s depending onthe turbulen e model

used and on the examined lo ation.

Some improvement in the results ould be also observed for the rosswise om-

ponent of velo ity. The most signi ant ee 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 maximumlevel of the temperature is well

the rosswisedire tion isstillpoorly evaluated omparedto themeasures, andmight

depend upon the turbulen e model.

The examination of gures 30 and 31 shows no signi ant improvement in the

resolution of both the turbulent kineti energy and axial distribution of the longitu-

dinal velo ity omponent, by using the non adiabati TFC model.

Apartfromthe bettertemperaturelevel, theseresultsremainpoorerwithrespe t

to the bestAres results.

0 0.5 1 1.5 y/H

0 250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment ad.TFC n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment ad.TFC n. ad. TFC + ad. walls

Figure 21: Adiabati TFC vs non adiabati TFC with adiabati wall onditions:

temperature prole atx=H =1:04167;   left; RNG   right.

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment ad.TFC n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment ad.TFC n. ad. TFC + ad. walls

Figure 22: Adiabati TFC vs non adiabati TFC with adiabati wall onditions:

temperature prole atx=H =3:125;   left; RNG   right.

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment ad.TFC n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750 2000

Temperature (K)

experiment ad.TFC n. ad. TFC + ad. walls

Figure 23: Adiabati TFC vs non adiabati TFC with adiabati wall onditions:

0 0.5 1 1.5 y/H

−5 0 5 10 15 20 25

x−velocity

experiment ad. TFC n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity

experiment ad. TFC n. ad. TFC + ad. walls

Figure 24: Adiabati TFC vs non adiabati TFC with adiabati wall onditions: x-

velo ity prole atx=H =1:04167;   left; RNG   right.

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity

experiment ad. TFC n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity

experiment ad. TFC n. ad. TFC + ad. walls

Figure 25: Adiabati TFC vs non adiabati TFC with adiabati wall onditions: x-

velo ity prole atx=H =3:125;   left; RNG   right.

0 0.5 1 1.5

y/H 0

5 10 15 20 25 30 35 40

x−velocity

experiment ad. TFC n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H 0

5 10 15 20 25 30 35 40

x−velocity

experiment ad. TFC n. ad. TFC + ad. walls

Figure 26: Adiabati TFC vs non adiabati TFC with adiabati wall onditions: x-

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 ad. TFC n. ad. TFC + ad. walls

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 ad. TFC n. ad. TFC + ad. walls

Figure 27: Adiabati TFC vs non adiabati TFC with adiabati wall onditions: y-

velo ity prole atx=H =1:04167;   left; RNG   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 ad. TFC n. ad. TFC + ad. walls

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 ad. TFC n. ad. TFC + ad. walls

Figure 28: Adiabati TFC vs non adiabati TFC with adiabati wall onditions: y-

velo ity prole atx=H =3:125;   left; RNG   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 ad. TFC n. ad. TFC + ad. walls

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 ad. TFC n. ad. TFC + ad. walls

Figure 29: Adiabati TFC vs non adiabati TFC with adiabati wall onditions: y-

0 0.5 1 1.5 y/H

−5 0 5 10 15 20 25

κ

experiment ad. TFC n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

κ

experiment ad. TFC n. ad. TFC + ad. walls

Figure 30: Adiabati TFC vs non adiabati TFC with adiabati wall onditions: 

prole atx=H =1:04167;   left; RNG   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

ad. TFC n. ad. TFC + ad. walls experiment

−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

ad. TFC n. ad. TFC + ad. walls experiment

Figure 31: Adiabati TFC vs non adiabati TFC with adiabati wall onditions: x-

velo ity distribution along the ombustor axis;   left; RNG   right

5.2 Non adiabati TFC model with isothermal walls

As mentioned before, the fully 3D oupled uid - solid problem has been solved in

orderto determine the obsta le walls temperature. Infa t, whereas itis straightfor-

ward to set the hannel walltemperature atthe samevalue ofthe old ow stream,

namely 273K, nothing is known about the temperature whi h exists at the obsta-

le surfa e. In the experimental apparatus the obsta le is not ooled and it an

ex hange thermal energy with the external world by ondu tion only, its extremities

beingkept atthe sametemperatureoftheexternalwalls. Inabsen eof experimental

data for the temperature distribution over the obsta le surfa e, the 3D uid - solid

oupled omputation has been then arried out. The gure 32 shows the tempera-

ture ontour plot over the obsta le surfa e and the temperature distribution along

the obsta le axis. The examof gure 32suggests thatfar enough fromthe hannel

walls, the obsta le surfa e temperature assumes the quasi- onstant value of 600 K

a ross the hannel width. This valuehas beenimposed attheobsta le wallinallthe

2D omputations.

Contours of Static Temperature (k)

FLUENT 5.5 (3d, dp, segregated, ke) Feb 04, 2002 6.00e+02

5.67e+02

5.35e+02

5.02e+02

4.69e+02

4.36e+02

4.04e+02

3.71e+02

3.38e+02

3.06e+02

2.73e+02

Z Y

X

Static Temperature

FLUENT 5.5 (3d, dp, segregated, ke) Feb 01, 2002 Position (m)

(k) Temperature Static

0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 6.00e+02

5.75e+02

5.50e+02

5.25e+02

5.00e+02

4.75e+02

4.50e+02

4.25e+02

4.00e+02

3.75e+02 y-coordinate-21

Figure 32: Temperature distribution over the obsta le surfa e (left) and along the

obsta le axis (right).

The examof gures 33 to38 shows thatnosigni ant improvements havebeen

the ow velo ity omponents. Also gures 42 and 43 don't reveal any important

improvement of the results a ura y.

The only observed ee ts whi h have been obtained by using the isothermal

onditions at solid walls, are on the temperature, espe ially at the se tion x=H =

1:04167, as shown in gure 39. The maximumtemperaturevalue has been lowered

by about 20 K with respe t to the orresponding value whi h was omputed by the

useofadiabati onditionsatsolidwalls. Hen e,eventhoughithasbeenproventhat

some ee t exists on the temperature distribution due to the ex hange of thermal

energybetweentheowandtheobsta lewall(whosetemperaturehasbeenevaluated

to be around 600 K), nevertheless this me hanism of energy transfer is not su h to

justifytheexperimentalvalueoftemperaturewhi hhasbeenmeasuredatthese tion

x=H =1:04167. Theremustbesomeothermorerelevantphysi alme hanismwhi h

gives reason of su h behavior. A ording to [3℄ it has been experimentally observed

that the vortex systemdownstream the obsta le shows a pulsatile behavior, namely

itmovesba kand forth alongthe hannelaxis. This movement ouldbe responsible

fortheentrapmentofgasatlower temperatureinthe zonerightbehindtheobsta le,

whi h would lead to a lower value of the average temperature. This ee t, whi h

is of strongly unsteady nature, has not been a ounted for in anyway in the present

simulation, whi h presents only stationary results.

0 0.5 1 1.5 y/H

−5 0 5 10 15 20 25

x−velocity

experiment n.ad. TFC + T

FIX walls n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity

experiment n.ad. TFC + T

FIX walls n. ad. TFC + ad. walls

Figure 33: Adiabati vs non adiabati wall onditions: x-velo ity distribution at

x=H =1:04167;  left; RNG   right.

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity

experiment n.ad. TFC + T _FIX walls n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity

experiment n.ad. TFC + T _FIX walls n. ad. TFC + ad. walls

Figure 34: Adiabati vs non adiabati wall onditions: x-velo ity distribution at

x=H =3:125;   left; RNG   right.

0 0.5 1 1.5

y/H 0

5 10 15 20 25 30 35

x−velocity

experiment n.ad. TFC + T _FIX walls n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H 0

5 10 15 20 25 30 35

x−velocity

experiment n.ad. TFC + T _FIX walls n. ad. TFC + ad. walls

Figure 35: Adiabati vs non adiabati wall onditions: x-velo ity distribution at

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 n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

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 n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

Figure 36: Adiabati vs non adiabati wall onditions: y-velo ity distribution at

x=H =1:04167;  left; RNG   right.

0 0.5 1 1.5

y/H

−3

−2.5

−2

−1.5

−1

−0.5 0 0.5 1 1.5 2

y−velocity

experiment n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H

−3

−2.5

−2

−1.5

−1

−0.5 0 0.5 1 1.5 2

y−velocity

experiment n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

Figure 37: Adiabati vs non adiabati wall onditions: y-velo ity distribution at

x=H =3:125;   left; RNG   right.

0 0.5 1 1.5

y/H

−3

−2.5

−2

−1.5

−1

−0.5 0 0.5 1

y−velocity

experiment n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H

−3

−2.5

−2

−1.5

−1

−0.5 0 0.5 1

y−velocity

experiment n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

Figure 38: Adiabati vs non adiabati wall onditions: y-velo ity distribution at

0 0.5 1 1.5 y/H

0 250 500 750 1000 1250 1500 1750

Temperature (K)

experiment n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750

Temperature (K)

experiment n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

Figure 39: Adiabati vs non adiabati wall onditions: temperature distribution at

x=H =1:04167;  left; RNG   right.

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750

Temperature (K)

experiment n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750

Temperature (K)

experiment n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

Figure 40: Adiabati vs non adiabati wall onditions: temperature distribution at

x=H =3:125;   left; RNG   right.

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750

Temperature (K)

experiment n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750

Temperature (K)

experiment n. ad. TFC + T

_FIX

walls n. ad. TFC + ad. walls

Figure 41: Adiabati vs non adiabati wall onditions: temperature distribution at

0 0.5 1 1.5 y/H

−5 0 5 10 15 20 25

κ

experiment n. ad. TFC + T _FIX walls n. ad. TFC + ad. walls

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

κ

experiment n. ad. TFC + T _FIX walls n. ad. TFC + ad. walls

Figure 42: Adiabati vs non adiabati wall onditions:  distribution at x=H =

1:04167;   left; RNG   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

n. ad. TFC + T FIX walls n. ad. TFC + ad. walls experiment

−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

n. ad. TFC + T FIX walls n. ad. TFC + ad. walls experiment

Figure 43: Adiabati vs non adiabati wall onditions: x-velo ity distribution along

6 Sensitivity to turbulen e models

Analysis of the results obtained sofar has put in eviden e that:

 the non adiabati formulation of the TFC model helps in obtaining a slightly

more orre t des ription of the velo ity elds;

 more a urateresultsintermsofvelo ity omponentproles ouldbea hieved

by using the RNG   turbulen e model, whi h gives a better evaluation of

the turbulent kineti energy eld, and a far betterevaluation of the dimension

of the ri ir ulating region behind the obsta le;

 Ares performs better than Fluent in genaral, and parti ularly better when

adopting the RNG standard  model.

Itseemedworthyto verifywhetherafurther improvementof theresultsa ura y

ould be a hieved by using a se ond order losure turbulen e model, su h as the

Reynolds Stress Model (RSM), whi h is also available in Fluent.

The gures 47, 48 and 49 show a dramati improvement of the results in terms

both of the longitudinal and transversal velo ity omponents.

The RSM model is the only one whi h is able to give the orre t, even still

qualitative,transversalvelo ityproleatthese tionx=H =1:04167. Theagreement

with the experimental values be omes good also in quantitative terms at the two

se tions further downstream the hannel. As a onsequen e, also the longitudinal

velo ity distribution along the hannel axis, as shown in gure 50, is more orre tly

simulated, even though the length of the re ir ulation zone is still underestimated.

The gure 50 also showsthe turbulent kineti energy distribution at the se tion

x=H = 1:04167, and gives reason why the RSM model is able to provide better

results in terms ofvelo ity t. The a tual turbulent kineti energy distribution is far

better apturedbythe RSMmodel,bothfromaquantitativeandqualitative pointof

view. The omputeddistribution tstheexperimentaldatafromabout y=H =0:7

on,anditappearstobeinfairlygoodqualitativea ordan eforvaluesofy=H <0:7,

whereas the familymodelsdofail. The onlyRNG modelgivesasomehow

qualitative a ordan e with the experimental data in the range of y=H >0:7.

The gures 44 to 46 show the omputed temperature proles at the usual se -

omputed by using the RSM model is equal to about 1460 K, providing an extra

gain of around 30 K on the value whi h was omputed by using the RNG  

model. As a general omment,the temperature gradient appears better resolved by

the RSM model at all the examined lo ations, even the width of the burned zone

seems underestimated, espe ially at the se tion x=H =6:25.

A more a urate tuning of the TFC model parameters ould most probably x

this dis repan y. Be ause the aim of the present omputation was only to give a

somehow quantitative measure of the inuen e of the turbulen e modeling on the

quality of the results, it has not been onsidered relevant to further investigate the

matter.

0 0.5 1 1.5 y/H

0 250 500 750 1000 1250 1500 1750

Temperature (K)

experiment Std κ−ε RNG κ−ε RSM

Figure 44: Temperature prole at x=H =1:04167.

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750

Temperature (K)

experiment Std κ−ε RNG κ−ε RSM

Figure 45: Temperature prole atx=H =3:125.

0 0.5 1 1.5

y/H 0

250 500 750 1000 1250 1500 1750

Temperature (K)

experiment

Std κ−ε

RNG κ−ε

RSM

0 0.5 1 1.5 y/H

−5 0 5 10 15 20 25

x−velocity

experiment Std κ−ε RNG κ−ε RSM

0 0.5 1 1.5

y/H

−3

−2.5

−2

−1.5

−1

−0.5 0 0.5 1 1.5 2

y−velocity

experiment Std κ−ε RNG κ−ε RSM

Figure 47: x=H = 1:04167: x-velo ity distribution (left); y-velo ity distribution

(right).

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

x−velocity

experiment Std κ−ε RNG κ−ε RSM

0 0.5 1 1.5

y/H

−3

−2.5

−2

−1.5

−1

−0.5 0 0.5 1 1.5 2

y−velocity

experiment Std κ−ε RNG κ−ε RSM

Figure 48: x=H =3:125: x-velo ity distribution (left);y-velo ity distribution(right).

0 0.5 1 1.5

y/H 0

5 10 15 20 25 30 35

x−velocity

experiment Std κ−ε RNG κ−ε RSM

0 0.5 1 1.5

y/H

−3

−2.5

−2

−1.5

−1

−0.5 0 0.5 1 1.5 2

y−velocity

experiment

Std κ−ε

RNG κ−ε

RSM

−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 Std κ−ε RNG κ−ε RSM

0 0.5 1 1.5

y/H

−5 0 5 10 15 20 25

κ

experiment Std κ−ε RNG κ−ε RSM

Figure 50: x-velo ity distribution along the hannel axis (left); turbulent kineti

energy distribution at x=H =1:04167 (right).

7 Con lusions

Thepresentedworkhadstartedfromtheattemptofsimulatingthepremixedrea tive

owinthe experimentalENSMA ombustor,byusingthe TFCpremixed ombustion

model. The apparently simple test ase had soon appeared to be a very tough one

instead, hallenging the two odes used (Aresand Fluent) andmakingvery di ult

to nd good agreement with the experiemental measures.

The di ulties en ountered were related to the TFC ombustion model and to

the turbulen e model as well. The investigations arried out with the two odes

put in eviden e the need for extending the TFC model to non-adiabati and heat-

ondu ting apabilities. This work will be done during the third year of the proje t,

re-designing the a tivities of Obje tive no. 8.

A strong ee t due to the turbulen e models was also found. Ares results were

better then Fluent ones, whenever a omparison with the same turbulen e model

was possible. The bestsolution wasfound with RNG  model implementedinto

Ares, slightly betterthan Fluent results with a full Reynolds Stress Model.

Referen es

[1℄ Stalio E. Mulas M. and Tali e M. Development and Implementation of Turbu-

len e Models in the Combustion Code Ares. Te hni al Report CRS4-TECH-

REP-00/95, CRS4 Resear h Centre, November 2000.

[2℄ Tali e M. and Mulas M. Development of a Partially Premixed Combustion

Model. Te hni al Report CRS4-TECH-REP-01/54, CRS4 Resear h Centre,

Mar h 2001.

[3℄ First European Test for Combustion Modelling Workshop. Aussois, Fran e,

February 5-10, 1995.

[4℄ Zimont, V.L., Polifke, W., Bettelini, M. Weisenstein W. An E 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.

[5℄ 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, O tober 1999.

[6℄ Fluent In . Fluent 5 User's Guide. Fluent In ., 1998.