15089 Numerical Modeling of Combustion -Gasification

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Numerical Model ing of Combustion and Gasif icat ion Processes using the Discrete Part ic le

Method

Mehrdad Shahnam Madhava Syamlal

Fluent Incorporated

3647 Collins Ferry Road Suite A

Morgantown WV 26505

Daniel Cicero

Department of Energy National Energy Technology Laboratory

P.O. Box 880

Morgantown WV 26507

A B S T R A C T

A methodology for model ing combust ion and gasi f icat ion

proce sses in a transport gasifier is describ ed in this paper. A

t ranspor t gasi f ier i s an eff icient means of conver t ing carbon-

based feedstock in to synthesis gas , which can be used to

produce high-value l iquid fuels , value-added chemicals , and

hydrogen for fuel cel ls amo ng other th ings. The system

consists of three mai n parts: mixing zone, riser, and the solids

return loop. The t ranspor t gasi f ier operates as a comb ustor at

startup. Coal is injected into the syste m at the top part of the

mixing zone. The devolat i l ized species are col lected and the

remaining unburned carbon in the coal , char , i s redi rected back

to the uni t. Addi t ional combu st ion takes p lace at the lower

por t ion of the mixing zon e where the recycled char and hot

burner ai r meet . As oxy gen in the system is depleted , the uni t

moves f rom the combustor mode in to gasi f icat ion mode.

Steam is in jected in to the system to prom ote s team gasi f icat ion

of hot recycle char . Addi t ional gasi f icat ion can take p lace wi th

carbon dioxide in the gas s tream. The gas-sol id f low regimes

encountered in the system vary f rom locat ion to location. Flow

in the recycle char return loop can be character ized as a dense

f low.Flow in the mixing zone and the r i ser can be character ized

as a dilute flow for input condit ions under consideration. The

goal of th is manus cr ip t i s to descr ibe the ap proach taken to

model the combust ion and gasi f icat ion process in the d i lu te

f low zones encountered in the mixing zone a nd the r i ser . I t is

assumed that the unit has reached i ts steady state condit ion.

Ti me averaged equat i ons o f mass , momen t um, energy , and

species t ranspor t are solved for the gaseous phase wi th

F L U E N T TM sof tware. The sol id par t icle f low is s imulated

using the discrete part icle metho d. In this approac h, the solid

phase equat ions of mom ent um and energy are solved in a

Lagrang ian f rame of reference. Heat , mass t ransfer, and

momen t um exchange t o and f rom t he par t i c l es a r e compu t ed

and added to the cont inuos phase as a source or s ink term

Coal devolat i l izat ion , gasi f icat ion and combust ion react ions

were included in the model through user def ined funct ions.

The discrete par t icle method works wel l when the f low is

sufficiently dilute that part icle-part icle interactions can be

neglected . This impl ies that the f low volume f ract ion needs to

be as low as 10-12 . Alth oug h the flow condit ions in the

current s tudy have volume f ract ions lower than the

recommended volume f ract ion l imi t , we found that the large

mass f low rate of par t icles relat ive to the mass f low rate of the

gaseous phase causes numerical instabi l i t ies . A novel approach

has been implemented which l imi ts the heat t ransfer rates

betwe en the two phases and s tabi lizes the calculat ions. The gas

phase tempera ture f ield obtained wi th the modif ied d iscrete

par t icle method agrees fav orably wi th avai lable data.

I N T R O D U C T I O N

Coal i s the most widely used sol id fuel consumed by the

powe r generat ion indust ry . Because of economic and

envi ronmental considerat ions, the need exis t s to improve the

eff iciency of coal comb ust ion process . Computat ional Fluid

Dynamics(CFD) has widely been used as a tool to opt imize

equipment designs and combust ion eff iciency of coa

combustors . An effect ive technique in model ing of coa

combust ion has been the Lagrangian discrete phase technique.

In th is approach, coal par t icles o f known size d is t r ibut ions and

proper t ies are in jected in to the combustor and t racked in a

Proceedings of2000 International Joint Power Generation Conference

Miami Beach, Florida, July 23-26, 2000

IJPGC2000-15089

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L a g ra ng i a n f a s h i on t h roughou t t h e c om pu t a t i ona l dom a in .

Hea t and mass t rans fe r to / f rom pa r t i c le s a re ca lcu la ted a long

each t ra jec to ry and a re used a s the coupl ing mechanism

be tw een the gas phase and the so l id phase . A ma jor

as sumpt ion in the Lagrang ian d i s c re te phase mode l i s tha t the

in te rac t ion of so l id pa r t i c le s i s neg lected . As a re su lt th is

approach i s on ly app l icab le to d i lu te f lu id -pa r t i c le f lows w here

the so l id phase vo lume f rac t ion i s l e s s than 10%. S ince mos t

coa l burn ing com bus tors a re ope ra ted in the d i lu te f low reg ion ,

(e . g . low vo lume f rac t ion and low so l id - to -gas phase mass

load ing) , the Lagrang ian d i s c re te phase mode l can be used to

cap ture the rma l and hydrodynamic cha rac te r i s t i c s o f typ ica l

coa l burn ing com bus tors . How ever , i f so l id to gas phase mass

load ing i s h igh enough , th i s mode l may ove r -pred ic t the

• t empera tu re f ie ld . This work has bee n unde r taken to fo rmula te

and implement a me thodology which wi l l e l im ina te the

tempera ture ove rpred ic t ion encounte red in Lagra ng ian d i s c re te

phase mode l .

Coupled S olution

In the Lagrang ian d i s c re te phase mode l , pa r t i c le

mo me ntum and ene rg y equa t ions a re so lved a long each pa r t i c le

t ra jec to ry . Cons ide r the pa r t i cle ene rgy equa t ion :

d T p = h a p ( T f - T p + S p

(1)

mpCp d'--7

W here the f i r s t te rm o n the r igh t hand s ide i s the in te rphase

hea t t rans fe r be tween the so l ids and the sur rounding gas and

the s econd te rm on the r igh t ha nd s ide , Sp . represen t s any

addi t iona l hea t source o r s ink con t r ibu t ions . Dur ing the t ime

in tegra t ion of the pa r t i c le ene rgy equa t ion in each

compu ta t iona l con t ro l vo lume , the loca l gas phase t empera tu re ,

T f

i s he ld cons tan t . I f the hea t t rans fe r ra te be tween the two

phases i s sma l l , keep ing the gas phase t empera tu re cons tan t

dur ing t ime in tegra t ion of pa r t i c le ene rgy equa t ion i s

accep tab le . How ever , i f the hea t trans fe r rate be tween the so l id

and the gas phase i s l a rge , ho ld ing the loca l gas t empera tu re

cons tan t dur ing t ime in tegra t ion of equa t ion (1 ) l eads to

exces s ive ene rgy t rans fe r be tween the pa r t i c le s and the gas

phase . The exces s ive ene rgy t rans fe r causes unrea l is t i c ho t o r

co ld spo t s in the gas t em pera tu re f i e ld .

I t i s pos s ib le to p reven t such unrea l i s t i c hea t t rans fe r

be tween the phases by a t igh te r the rma l coupl ing be tween the

so l id phase and the gas phase . The ma in idea i s to so lve the

f lu id -phase ene rgy equa t ion coupled wi th the pa r t i c le -phase

ene rgy equa t ion du r ing the pa r t i c le - t rack ing phase on a ce l l -by-

ce l l bas i s. To ach ieve th i s goa l , f i r s t cons ide r the f lu id phase

ene rgy equa t ion :

,O f Cpf v f .V T f = V .k f V T f -F J transfer+ S f ( 2 )

W h e r e Y t r a n s f e r i s the in te rphase hea t t rans fe r be tween the

so l id and the gas phases . By in tegra t ing th i s equa t ion ove r a

con t ro l vo lume , the d i s c re f i zed fo rm of the f lu id phase en e rgy

equa t ion i s ob ta ined :

a c ( T f ) C = Z a n b ( T f ) n b + b + J tra nsfe rA V C ( 3 )

nb

Where ac , anb and b are the center coeffic ient , the

ne ighbor ing coe f f i c ien t , and the source t e rm respec t ive ly and

A V e i s ce l l vo lume . The pa r t i c le ene rgy equa t ion is so lved by

tak ing seve ral t ime s teps wi th in a computa t iona l ce l l. The

d isc re t ized fo rm of equa t ion (1) ov e r a time s tep i i s

i

m p C p T ~ T ~ - - h A p ( T f - T ~ ) + S p

A t ~

(4)

The in te rphase hea t t rans fe r fe l t by the f lu id phase f rom the

part ic le t rack ove r t ime s tep i is

J~r ans f erAVc = h A p ( T t~ T f ) (r h ~ / /~ p ) A t i

( 5 )

where / rhP /m ] i s the num ber f l °w ra te ° f pa r t i cle s f ° r

the pa r t i c le t rack under cons ide ra t ion . The accumula ted

in te rphase hea t t rans fe r f rom a l l the t ime s teps N with in the

ce l l can be found by in tegra t ing ( summing) the above

express ion:

i=N

J, ,~, , :erA V e = Z h A p (T ip T I ) (r h ~ /~ p ] A t i

(6)

i=1

By combin ing equa t ions (3 ) and (6 ) , the fo l lowing

disc re t ized fo rm o f the f lu id phase ene rgy equa t ion i s ob ta ined :

i=N

a c T = Z a n b ( Tf )nb + b + Z h A p ( T] - T f) lr h P ~ m p ) A t i

nb i=1

( 7 )

Equa t ions (4 ) and (7 ) fo rm a s e t o f N + 1 equa tions fo r

T f

a nd

T i

( i = 1 , N ) . S imul taneous so lu t ion of the above

P

equa t ions wi l l ensure tha t the numer ica l so lu t ion wi l l no t

pe rmi t any unrea l i s t i c hea t t rans fe r. The above eq ua t ion s e t can

be eas i ly gene ra l i zed fo r mul t ip le pa r ti c le t racks. How ever ,

so lv ing such an equa t ion s e t i s cpu in tens ive and imprac t i ca l .

An a l t e rna te approach fo r so lv ing equa t ions (4 ) and (7 ) i s

desc r ibed be low.

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Temp erature Limiter Algorithm

I t i s p roposed t ha t dur i ng t he pa r t i c l e t r ack ing ca l cu l a t i on ,

t he i n t e rphase hea t t r ans f e r t e rm,

J t r a n s f e r be

b o u n d e d b y a

l o w e r a n d a n u p p e r th r e s h o l d w h i c h a r e c h a r a c t e r iz e d b y

m i n i m u m a n d m a x i m u m c o n v e c t i v e he a t t r an s f e r co e f f ic i e n t

b e t w e e n th e g a s a n d s o li d p h a s e s . T h e m i n i m u m i n t e rp h a s e

h e a t t r a n s f e r t e r m o c c u r s w h e n t h e h e a t t r a n s f e r c o e f f i c ie n t , h ,

a p p r o a c h e s z e r o . T h e p a r t ic l e te m p e r a t u r e c a n b e c a l c u l a te d

f r o m ( 4 ) to b e

S ; A t i

T ; ] mm

T; 1

I - -

(8)

m p C p

T o d e t e r m i n e t h e u p p e r t e m p e r a t u r e t h r e s h o l d w h e n t h e

c o n v e c t i v e h e a t t ra n s f e r c o e f f i c i e n t a p p r o a c h i ts m a x i m u m , a n

aux i l i a ry gas t emp era tu r e fi e l d , T} , is de fm ed . The aux i l i a ry

gas t empera tu r e can i nc r ease o r dec r ease dur i ng pa r t i c l e

t r ac k i n g c a l c u l a ti o n s d e p e n d i n g o n w h e t h e r h e a t i s t r a n s f e r re d

t o o r f r o m t h e g a s p h a s e . T h e d i s c r e t iz e d p a r t ic l e e n e r g y

equa t i on i n te rms o f t he aux i l i a ry gas t empe ra tu r e i s

i

m p C p T ; T ; - I - h A p : - T ; ) S p

A t ~

(9)

Us ing t he f l u i d phase ene rgy equa t i on , ( 7 ) , t he aux i l i a ry

gas t empe ra tu r e can be w r i t t en a s:

i N

a c T : = Z a n b T f ) n b + b + Z h A p T ; - T f ) l h P ~ m I t i

n b

i=1 P

Or

a c T } = a c r : - 1 + h A p T ; - T f ) p

( 10)

w h e r e

a c t ~ = Z a n b ( T f )nb + b

n b

C o m b i n i n g e q u a t i o n s ( 9 ) a n d ( 1 0 ) a n d n o t i n g t h a t a t

m a x i m u m i n te r p h a s e h e a t t r a n s f e r c o n d i ti o n , b o t h t h e p a r t i c l e

t e m p e r a t u r e a n d t h e a u x i l i a r y g a s t e m p e r a t u r e a p p r o a c h t h e

same equ i l i b r i um va lue , Tp = T} ,

T; Jm~ --

c ( r h p / ~ T i - l+ S ; ( r h P ~ m e ) A t i

a c T : - ' + m p

k

/ m p J P

( 11)

E q u a t i o n s ( 8 ) a n d ( 1 1 ) c a n b e u s e d a s l o w e r a n d u p p e r

boun ds fo r t he pa r t i c l e t emp era tu r e f i e ld . I n t he t echn iqu e

d e s c r i b e d a b o v e , t h e l o w e r a n d u p p e r p a r t i c l e t e m p e r a t u r e

t h r e sh o l d s a r e o n l y u s e d i f p a r ti c l e t e m p e r a t u r e c a l c u l a te d b y

equa t i on (4 ) a r e ou t s i de o f t he t emp era tu r e l imi t s.

Oxidizer Limiter Algorithm

I n t h e L a g r a n g i a n d i s c r e t e p h a s e m o d e l , g a s e o u s p h a s e

prope r t i e s , ( i .e . ox id i ze r mass f r ac t i on) a r e he ld cons t an t dur i ng

pa r t i c l e t r a j ec t o r i e s ca l cu l a t i ons . For com bus t i ng pa r t i c l e s th i s

a s s u m p t i o n w i l l l e a d t o a n e x c e s s i v e a m o u n t o f o x i d i z e r b e i n g

ava i l ab l e f o r com bus t i on dur i ng pa r t i c l e t r a j ec t o ry ca l cu l a ti ons

i n pa r t i cu l a r i f mu l t i p l e t r a j ec t o r i e s tr ave l t h rough a con t ro

v o l u m e . T h i s p r o b l e m c a n b e e l i m i n a t e d b y n o t i n g th a t t h e

r a te , a t w h i c h o x i d i z e r i s s u p p l ie d t o e a c h c o n t r o l v o l u m e h a s t o

b e e q u a l o r g r e a t e r t h a n t h e r a te a t w h i c h o x i d i z e r i s c o n s u m e d

i n t h e s a m e c o n t r o l v o l u m e d u r i n g c o m b u s t io n . I n a g i v e n

c o n t r o l v o l u m e , o n c e t h e r a t e o f c o n s u m p t i o n o f o x i d i z e r

becomes g r ea t e r t han t he supp ly r a t e , combus t i on i s ha l t ed .

P a r t i c l e s t r a v e l i n g t h r o u g h t h e c o n t r o l v o l u m e s w i t h d e p l e t e d

ox id i ze r , w i l l no t co mbu s t .

Results

The t echn iq ue ou t l i ned a~bove i s i ncorpora t ed i n t o

F L U E N T 5 .4 C F D s o f t w a r e . C o a l c o m b u s t i o n a n d g a s i f ic a t io n

ins i de a t r anspor t gas i f i e r a r e used t o va l i da t e t he approach

presen t ed i n t h i s man usc r i p t . ; r he t r anspor t gas i f i e r ope r a t ed by

t h e E n e r g y & E n v i r o n m e n t a l R e s e a r c h C e n t e r a t t h e U n i v e r s it y

of No r t h Dakot a i s s e l ec t ed fo r t h i s purpose . The gas i f i e r i

used t o conver t coa l i n t o syn thes i s gas. F igure 1 shows t he

g e o m e t r y o f th e c o m b u s t o r / g a s if i e r u n i t. C h a r e n t er s t h e

m i x i n g z o n e a n d c o m b u s t w i t h t h e b u r n e r a ir , w h i c h e n t e rs t h e

mix in g zone on t he s ide . The un i t i s ope r a t ed a t sub-

s t o i c h io m e t r i c c o n d i t io n s w h i c h l e a d s t o b u r n i n g o f a s m a l

f r ac t i on o f t he cha r . I nc r eases i n t he gas t empera tu r e w i l l he l p

w i t h g a s i f ic a t i o n o f t h e r e m i n d e r o f t h e c h a r. C h a r m a s s

l o a d i n g w h i c h i s d e f m e d a s m a s s f l o w r a te o f c h a r t o m a s s f l o w

r a t e o f c h a r a n d b u r n e r a i r c o m b i n e d i s 0 . 8 8 . A s i t is s e e n in

f i g u r e 1 , tw o s e c o n d a r y a i r p o r t s a r e u s e d d o w n s t r e a m o f t h e

burn e r a i r en t ry t o a s s i s t w i t h cha r comb us t i on . F r esh

p u l v e r i z e d c o a l i s i n t r o d u c e d a t t h e u p p e r p o r t i o n o f th e m i x i n g

zone t o rep l en i sh t he cha r s tock . F igure 2 i ll us t ra t e s t he

l oca t i on o f c ros s s ec t i ona l p l anes wh ere t he t empera tu r e f i e lds

a r e r epor t ed . F igure 3 shows t he t empera tu r e f i e l ds a l ong t he

t r ave r se d i r ec t i on on p l ane s A t h rou gh F , ( r e f e r to f i gure 2 )

A l t h o u g h t h e m a j o r i t y o f t e m p e r a t u r e d a t a p o i n t s l a y a l o n g t h e

a v e r a g e t e m p e r a t u r e a t e a c h p l a n e , t h e p r e s e n c e o f s p u r io u s h o

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and co ld spot s on e ach p l ane c an be se en . F igu re 4 shows the

t empe ra tu re f i e ld a c ross t he same c ross se c t iona l p l ane s when

the tempe ra tu re l im i t e r i s u sed . The un rea l i s ti c ho t and co ld

spo t s o f f i gu re 3 a re e limina t ed . Wh en the ox id i z e r l im i t e r i s

a l so a c t iva t ed , t he t empe ra tu re f i e ld va r i ance on p l ane s A

th rough E becomes ev en le ss a s i t i s show n in f i gu re 5. A

compa r i son o f t he a c tua l t empe ra tu re va lue s w i th the th re e

s imu la t ions pe r fo rme d i s g iven by t ab l e 1 . W hen the concep t

o f t empe ra tu re and o x id i z e r l im i te r s a re u sed , t he t empe ra tu re

f i e ld is p red ic t ed more a ccu ra t e ly . As d i scussed e a r l ie r , a t h igh

so l id to ga s mass load ing , t he a ssumpt ion o f cons t an t ga s pha se

p rope r t i e s , ( cons t an t ga s s t e am t empe ra tu re and ox id i z e r mass

f ra c t ion ) l e ads to unphys i c a l t empe ra tu re pa t t ems . W hen the

the rma l mass o f pa r t i c le s i s no t g re a t , ( l ow pa r t i c l e mass

load ing ) , t he d i sc re t e pha se mode l c an p red ic t t he t empe ra tu re

f i e ld r e a sonab ly w e l l .

Conclusion

A m e thod o logy ha s been in t roduced to e limina t e

un rea l is i t c tempe ra tu re va lue s . The concep t o f t empe ra tu re and

ox id i z e r l im i te r s ha s succe ss fu l ly been imp lem en ted and t e s t ed .

A com pa r i son o f meas u red and s imu la t ed t empe ra tu re f i e ld s

ind ic a te s t ha t t empe ra tu re s a re p red ic t ed more a ccu ra t e ly when

the t empe ra tu re and ox id i z e r l im i t er s a re u sed .

Acknowledgments

T h i s w o r k h a s b e e n p e r f o r m e d u n d e r c o n t r a c t D E - A M 26

9 9 F T 4 0 5 7 5 f o r D e p a r t m e n t o f E n e r g y , N a t i o n a l E n e r g y

Techn o log y Labora to ry . The au tho rs wou ld l ike to t hank th

s t a f f o f F luen t W es t V i rg in i a o f f i c e i n pa r t icu l a r Dr . Mike

Pr inkey fo r a l l t he inva luab le d i scuss ions on fo rmu l i z ing th i s

app roach .

N O M E N C L A T U R E

A area

Cp spec i f i c hea t

h convec t ive hea t t r ans fe r coe f f i c i en t

m pa r t i c l e mass

m mass f l ow ra t e

S sou rce o r s ink t e rm

T Tempe ra tu re

t t ime

Subscripts

f f lu id

p par t ic le

L o c a t i o n

P lane D

N o l i m i te r W i t h t e m p e r a t u re W i t h t e m p e r a tu r e a n d M e a su r m e n t

(°k) l imi te r (°k) oxid izer l imi te rs (°k) (°k)

2000 1400 1310 1223

Tab le 1. A compa r i son o f s imu la t ed and a c tua l t empe ra tu re f i e ld in t he mix ing zone .

4

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Coal injection j _

Secondary

a ir in le t s ~ _ ~ ~gv Coa) in j ec t io n ~ / /

~ r ~ po r t ~ ~ / O utle t

Bum er air A v/ \ 1~'-

Figure 1. Com bustor/gasifiergeometry.

Mixing zone

Ciiiiiii~

plane F

plane E

plane D

plane C

plane B

plane A

Secondary air

inlets

~k

Figure 2.

Cross sectiona lplanes along he mixingzone w here temperaturevalu es are reported.

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3 0 0 0

2 5 0 0

•

2 0 0 0

•

1500

1000

500

u *

• 1 1

• I • : %

n ' ; , -

. . . ~ : ' .

- t ~

. . ~ •

• * ~ . ~ - - . . e ~ : ' r , . . : - b

. ' I t

-g

plane A

-0.05 0 0.05 0.1

Dis tance a lon g the t raverse di rect ion (m)

3 0 0 0

2 5 0 0

2 0 0 0

,~ 1500

E

1000

500

mm

ml

N

. g % , .

; . ; . % r - . r . ', r , . ~ . , ~ . . ~ . . . . .

• - ~ .

•

. ' '

plane C

, , , , I , , , , I , , , , I , , , ,

-0.05 0 0.05 0,1

Dis tance a lon g the t raverse di rect ion (m)

3 0 0 0

2 5 0 0

~ '

2 0 0 0 • •

E

lOOO . .

500

plane E

0 ' r ~ ~ I , , , , I r r i , [ r I , ,

-0.05 0 0.05 0.1

Di s t ance a l ong t he t r ave r se d i r ec t ion (m)

3 0 0 0

2 5 0 0

~ 2 o o o

•

1500

1000

500

u

• • m

o

ee

• o ° . ° ° ° t

. . . , 5 - : : : ; , - 5

° o w

e e

plane B

0 I i i i I I i i i I i r i r I i i i i

-0.05 0 0.05 0.1

Di s t ance a l ong t he t r ave r se d i r ec t i on (m)

3 0 0 0

2 5 0 0

, ~ . 2 o o o

~ 1 5 0 0

~ 1 0 0 0

500

, . . .

~ . . ~ . . ''w '~ 8 / • I . . .

plane D

t ~ i r I i i i r I T i i i I i i r I

-0.05 0 0.05 0.1

Di s t ance a l ong t he t r ave r se d i r ec ti on (m)

3 0 0 0

2 5 0 0

. ~ 2 0 0 0 - . .

ee

~ 1 0 0 0

%

500

plane F

0 , I r , , i l l r i r I r , r I

-0.05 0 0.05 0.1

Di s t ance a l ong t he t r ave r se d i r ec ti on (m)

F igure 3 .

Tem pera tu r e f i e l d a t c ros s s ec t i ona l p l anes A t h roug h E wi t ho u t t he t empera tu r e and ox id i ze r limi t er s .

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3000 3000

2500

2000

~ 1 5 0 0

E l

l o o o

. . • ~ - ~

• v

# ~

• • • i i . i

500

plane A

0

i i ~ r I r i ~ i I i i ~ i I i i ~ i

-0.05 0 0.05 0.1

Distan ce along the traverse direction (m )

3000

2500

,~, 200 0

~d

1500

~.

~ - . , : .- ~ - - ~ ~ ' ¢ 4 % ' , .' d ' h ' . - , r % - . . , , . .

1000

500

plane C

0

~ i r r I i i , , I , ~ , , I ~ , ~ ~

-0.05 0 0.05 0.

Dis tance a long the t raverse direction (m)

2500

~,~2000

•

1500

~ 1 0 0 0

500

3000

. : - . -

plane B

r I r l I i i r 1 [ 1 i i 1 I i I I I

-0.05 0 0.05 0.1

Dis tance a long the t raverse direct ion (m)

2500

2000

5OO

~ 1 0 0 0

500

plane D

0 ~ r I , , , , I , r , r I ~ ~ , ,

-0.05 0 0.05 0.1

Dis tance a lon g the t raverse direct ion (m)

3000

2500

2

~ 1 5 0 0

. d . ~ . . m l ~ I l q l V l l t ql ~ , ~ l m l l l , m w l ~ , ~ 8 D *

1000

500

plane E

0 , , , , I , r , , I , , ,

I r ~ ~

-0.05 0 0.05 0.1

Dis tance a long the t raverse direct ion (m)

3000

2500

~ 2 0 0 0

E

•

1500

~ 1 0 0 0

500

plane F

0 ~ r r I ~ ~ I r ~ I ~ r

-0.05 0 0.05 0.1

Dis tance a long the t raverse direct ion (m)

F igure 4. Tempera ture f i e ld a t c ros s s ec t iona l p lanes A th roug h E wi th the t empera tu re l im i te r .

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3 0 0 0 3 0 0 0

2 5 0 0

~ ' 2 0 0 0

1500

E

1000

•

500

plane A

0

I t I I I I I I I I I I 1 I I I I I I

lO105 0 0105 On1

Distance a lon g the t raverse di rect ion (m)

3 0 0 0

2 5 0 0

2 0 0 0

1500

E

1000

500

plane C

0

, I , , l , I l , i l I ~ l l l

-0.05 0 0.05 0.1

Dis tance a lo ng the t raverse di rect ion (m)

2 5 0 0

~,~ 20 00

E

~ 1 5 0 0

1000

500

plane B

0

I I I I I I I I I I I I I r l l I I I

-0.05 0 0.05 0.1

Di s t ance a l ong t he t r ave r se d i r ec t i on (m)

3 0 0 0

2 5 0 0

2 o o o

1 5 o o

1000

P h ~ r w . , u q ' ' q l Y ' l. , . l~ F ' . l ~ . . ~ Il i l , ,/ d u ~

5OO

plane D

0

l l l l I l i l i i i l l , i , l t l

-0.05 0 0.05 0.1

Di s t ance a l ong t he t r ave r se d i r ec ti on (m)

3 0 0 0

2 5 0 0

2 0 0 0

1500

1000

500

u ~ p m a u n d ~ ~ ~ l ~ a m ~ ( n l ~ i ~ m n m ~ p l N m m ~ m J l ~ l am a ml ~ m l ~ im m q m l I N •

plane E

, , , , I ~ r r , I , , , , I ~ , r r

-0.05 0 0.05 0.1

Di s t ance a l ong t he t r ave r se d i r ec t ion (m)

3 0 0 0

2 5 0 0

2 0 0 0

~ 1 5 0 0

gm,4w,O~l~ll~O~ , I~tl ,'ll p dmO~ilClFllm,llsm~,lwm,~bdm ~ e

~ 1 0 0 0

500

plane F

0 r r , I I r , ,

i i 1 , 1

l l , , , ,

-0.05 0 0.05 0.1

Di s t ance a l ong t he t r ave r se d i r ec ti on (m)

F igure 5 . Tem pera tu r e f i e l d a t c ros s s ec t i ona l p l anes A t h rough E wi t h t he tem pera tu r e and ox id i ze r l imi te r s .

8 Copyright (C) 2000 by ASME