J. Aerosp. Technol. Manag. vol.4 número3

LIST OF SYMBOLS

Cp 6SHFL¿FKHDWDWFRQVWDQWSUHVVXUH K 7KHUPDOFRQGXFWLYLW\

L +HDWRIDEODWLRQPHOWLQJS\URO\VLV q +HDWÀX[

T 7HPSHUDWXUH t 7LPH

V ,QWHUIDFHYHORFLW\ Y 7DQJHQWLDOFRRUGLQDWH

İ (PLVVLYLW\

ȡ 'HQVLW\

ı %ROW]PDQFRQVWDQW

INTRODUCTION

$HURG\QDPLFKHDWLQJLQVSDFHDQGVXERUELWDOYHKLFOHVLVD FRQVHTXHQFHRIWKHK\SHUVRQLFÀLJKWZLWKLQWKHDWPRVSKHUHLH EHORZNPRIDOWLWXGH'HSHQGLQJRQWKHYHORFLW\DQGWUDMHF

-WRU\WKHDLUWHPSHUDWXUHDURXQGWKHQRVHWRSPD\VXUSDVVž& DWWKHVWDJQDWLRQSRLQW0DFKDGRDQG3HVVRD)LOKRDE,Q VXFKVLWXDWLRQDHURG\QDPLFKHDWLQJSOD\VDYHU\LPSRUWDQWUROH LQWKHYHKLFOHGHVLJQ%HVLGHVWKHKLJKWHPSHUDWXUHVHIIHFWVRQ WKHPHFKDQLFDOEHKDYLRURIWKHVWUXFWXUHDQGRQERDUGGHYLFHV

LWLVPDQGDWRU\WRSUHVHUYHWKHSD\ORDGE\XVLQJDQHI¿FLHQW WKHUPDOSURWHFWLRQV\VWHP736736GHVLJQLVDFULWLFDODVSHFW RIWKHURFNHWGHVLJQVLQFHLWVXQGHUGLPHQVLRQLQJPD\UHVXOW LQWKHORVVRIWKHSD\ORDGDQGWKHRYHUGLPHQVLRQLQJLPSOLHV LQLQFUHDVLQJZHLJKWDQGFRVW$ORQJWKH\HDUVDEODWLYHPDWH

-ULDOVKDYHEHHQHIIHFWLYHO\XVHGDV736RIVSDFHYHKLFOHV,Q WKHVHSURFHVVHVWKHNLQHWLFHQHUJ\RIWKHURFNHWLVFRQYHUWHG LQWRKHDWZKLFKFRQVXPHVWKH736WKURXJKDEODWLRQ5RJDQ DQG+XUZLF],WLVDFRPSOH[SKHQRPHQRQUHODWHGZLWK GLYHUVHVLPXOWDQHRXVSK\VLFDOSURFHVVHV6LOYD

7KHDEODWLRQLVXVXDOO\FDOFXODWHGWKURXJKVLPSOL¿HGPRGHOV WKDWFRQVLGHUDVLQJOHSKDVHFKDQJHDWFRQVWDQWWHPSHUDWXUH 6XFK DSSURDFK LV QRW DOZD\V DSSOLFDEOH DQG PD\ EHFRPH JUHDWO\ LQDFFXUDWH 0DFKDGR DQG 3HVVRD )LOKR D E $OVR WKH FKDUDFWHUL]DWLRQ RI WKH DEODWLYH SURSHUWLHV XQGHU WKLVDSSURDFKLVGLI¿FXOWVLQFHLWSUHVHQWVGLIIHUHQWYDOXHVIRU GLIIHUHQWSURFHVVHVRIPHDVXUHPHQW'D&RVWDet al7KH VWXG\RIWKHDEODWLYHSURFHVVHVFDQEHJURXSHGLQWKUHHFDWHJR

-ULHVHQJLQHHULQJPRGHOVQXPHULFDOPHWKRGVFRPSXWDWLRQDO ÀXLGG\QDPLFV±&)'GLUHFWVLPXODWLRQ0RQWH&DUOR±'60& HWFDQGH[SHULPHQWDOPHWKRGV7KHWZRODVWGHPDQGJUHDW LQYHVWPHQWRIWLPHDQGUHVRXUFHV7KH¿UVWLVUHFRPPHQGHGLQ WKHLQLWLDOVWDJHVRIVSDFHYHKLFOHVGHYHORSPHQW

7KH FRXSOLQJ EHWZHHQ KHDW WUDQVIHU SURFHVVHV LQ WKH VXUIDFHDQGZLWKLQWKHOD\HUVUHSUHVHQWVDQDGGLWLRQDOGLI¿

-FXOW7KHH[WHUQDOKHDWH[FKDQJHRFFXUVE\FRQYHFWLRQDQG UDGLDWLRQDQGWKHKHDWWUDQVIHUWRWKHZDOO736DQGVWUXFWXUH KDSSHQVE\FRQGXFWLRQ7KHFRQYHFWLYHKHDWWUDQVIHUFRHI

-¿FLHQWFDQEHHVWLPDWHGWKURXJKVRPHHQJLQHHULQJPHWKRGV EDVHGRQHPSLULFDOUHVXOWV,QRUGHUWRREWDLQWKHWHPSHUDWXUH

Simulation of Ablation in a Composite Thermal Protection

System via an Interface Tracking Method

Humberto Araujo Machado*

,QVWLWXWRGH$HURQiXWLFDH(VSDoR6mR-RVpGRV&DPSRV63±%UD]LO 8QLYHUVLGDGHGR(VWDGRGR5LRGH-DQHLUR5HVHQGH5-%UD]LO

Abstract: In this work, the two-dimensional computational simulation of the ablative process in a composite used in rocket thermal protection systems via an interface tracking method was presented. The ablative model considers the pres-ence of two simultaneous moving fronts, the pyrolysis and char fronts. The results were compared with some experimental data, showing better agreement than the one-front model. Such procedure will allow a more accurate dimensioning of rocket thermal protection systems, contributing for project optimization.

Keywords: Ablation, Composite, Moving boundary, Computational simulation.

5HFHLYHG $FFHSWHG

DXWKRUIRUFRUUHVSRQGHQFHKXPEHUWRKDP#LDHFWDEU

SUR¿OHDQGWKHKHDWORDGWKHHQHUJ\FRQVHUYDWLRQHTXDWLRQ KDVWREHVROYHG$FRPPRQDSSURDFKLVWRFRQVLGHUWKHKHDW FRQGXFWLRQDVRQHGLPHQVLRQDOLQWKHQRUPDOGLUHFWLRQUHOD

-WLYHWRWKHORFDOVXUIDFH+RZHYHUVXFKK\SRWKHVLVEHFRPHV LQDFFXUDWHDVWHPSHUDWXUHJUDGLHQWVLQWKHWDQJHQWLDOGLUHF

-WLRQWKHFKDQJHRIPDWHULDORUDJUHDWWKLFNQHVVYDULDWLRQ RFFXU0D]]RQLet al$VDQH[DPSOHWKH736RIWKH 6$5$VXERUELWDOSODWIRUPZKLFKKDVEHHQGHYHORSHGE\WKH ,QVWLWXWHRI$HURQDXWLFVDQG6SDFH,$(VKRZQLQ)LJ UHSUHVHQWVDW\SLFDOVLWXDWLRQLQZKLFKWKHRQHGLPHQVLRQDO DSSURDFK PD\ UHVXOW LQ DQ DSSUHFLDEOH GHYLDWLRQ LQ WKH WHPSHUDWXUHGLVWULEXWLRQDQGDEODWLRQSUR¿OH,WLVUHPDUNDEOH WKDWLQWKLVFDVHDVPDOOGHYLDWLRQLQWKHVXUIDFHJHRPHWU\ GXHWRDEODWLRQPD\UHVXOWLQDFRQVLGHUDEOHLQFUHDVHLQWKH UHHQWU\WUDMHFWRU\XQFHUWDLQW\

Si-Phenolic

Al

R280

R300

20

)LJXUH7KH6$5$VXERUELWDOSODWIRUPSUR¿OHDQGLWV736LQGHWDLO

7KHIXOOFDOFXODWLRQXVLQJDGLVFUHWHPHWKRGLPSOLHVJUHDW FRPSXWDWLRQDOHIIRUWLQFOXGLQJJULGJHQHUDWLRQDQGVROXWLRQRI DERXQGDU\PRYLQJSUREOHP$QDOWHUQDWLYHWRWKHVHRSWLRQV PD\EHWKHXVHRIWKHLQWHUIDFHWUDFNLQJPHWKRGSURSRVHG E\8QYHUGL 7U\JJYDVRQZKLFKDOORZVREWDLQLQJD VROXWLRQIRUWKHFRXSOHGDEODWLRQFRQGXFWLRQSUREOHPLQWKH ZKROHGRPDLQFRQVLGHULQJWKHIXOOSK\VLFDOPRGHO

7KHREMHFWLYHRIWKLVZRUNZDVWRSUHVHQWDFRPSXWDWLRQDO VLPXODWLRQRIWKHDEODWLYHSURFHVVYLDWKHLQWHUIDFHWUDFNLQJ PHWKRGDSSOLHGWRDPXOWLOD\HUDEODWLYHPRGHO6XFKSURFH

-GXUHZLOODOORZDSSO\LQJPRUHFRPSOH[PRGHOVIRUDEODWLRQ WDNLQJLQWRDFFRXQWWKHSUHVHQFHRIVHYHUDODEODWLYHDQGVWUXF

-WXUDOOD\HUVDQGSURYLGLQJDPRUHDFFXUDWH736GLPHQVLRQLQJ

PHYSICAL PROBLEM

,QWKLVZRUNWKHDEODWLRQPRGHOSURSRVHGIRUDFRPSRVLWH PDWHULDO FRQVLGHUHG WKH SUHVHQFH RI WZR OD\HUV WKH YLUJLQ

PDWHULDODQGWKHFKDUOD\HUZKLFKDSSHDUVDIWHUWKHS\URO\VLV IURQW7ZRPRYLQJIURQWVZHUHDFFRXQWHGWKHS\URO\VLVDQG WKHDEODWLRQIURQWRIWKHFKDUOD\HU%RWKDSSHDUHGDWFRQVWDQW DQGVSHFL¿FWHPSHUDWXUHV7KHK\SRWKHVHVFRQVLGHUHGIRUWKH PDWKHPDWLFDOPRGHOZHUH

‡ VROLGPDWHULDOVDUHLVRWURSLFZLWKFRQVWDQWSURSHUWLHV ‡ WKHS\URO\VLVIURQWLVFRQVLGHUHGWRKDYH]HURWKLFNQHVV

DQGWKHS\URO\VLVUHDFWLRQKDSSHQVDWFRQVWDQWWHPSHUDWXUH DQGHQWKDOS\

‡ FKDUOD\HUUHFHVVLRQLVVXSSRVHGWRRFFXUGXHWRR[LGDWLRQ RUVXEOLPDWLRQDWFRQVWDQWWHPSHUDWXUH

‡ DEVHQFHRIPHOWLQJOD\HU

‡ WKHUHVXOWLQJJDVHVIXOO\UHDFWDQGSHUIHFWO\PL[ZLWKWKH H[WHUQDODLUOD\HUZLWKRXWLQÀXHQFHRYHULWVSURSHUWLHV ‡ DLULVFRQVLGHUHGDSHUIHFWJDV

‡ UDGLDWLRQLVDEVRUEHGRUHPLWWHGE\WKHH[WHUQDOVXUIDFH KRZHYHULWLVQRWWUDQVPLWWHG

:KHQDKHDWÀX[LVLPSRVHGWRWKHH[WHUQDOVXUIDFHWKH 736ZDUPVDVDSXUHWUDQVLHQWKHDWFRQGXFWLRQSUREOHPXQWLO WKHDEODWLRQWHPSHUDWXUHLVUHDFKHG2QFHWKH736VXUIDFH UHDFKHV WKH DEODWLRQ WHPSHUDWXUH LWV WKLFNQHVV LV UHGXFHG WKHUHIRUHDWUDQVLHQWDQGFRXSOHGSUREOHPRIKHDWFRQGXFWLRQ DQGPRYLQJERXQGDU\DSSHDUV

7KHVHWRIHTXDWLRQVXVHGWRUHSUHVHQWWKHSK\VLFDOSURE

-OHP LV ZULWWHQ DFFRUGLQJ WR WKH LQWHUIDFH WUDFNLQJ PHWKRG -XULF7KH736DQGWKHDLUDURXQGLWDUHUHSUHVHQWHG DVSDUWVRIDFRQWLQXRXVGRPDLQRIFDOFXODWLRQ7KHDSSOLFD

-WLRQRIWKHHQHUJ\FRQVHUYDWLRQSULQFLSOHWRDQLQ¿QLWHVLPDO YROXPHHOHPHQWRIWKHPDWKHPDWLFDOGRPDLQOHDGVWRDSDUWLDO GLIIHUHQWLDOHTXDWLRQIRUWKHWHPSHUDWXUHQDPHO\(T

( . . ) _.

t C T

K T Q

p

’ ’

2

2 t

= +

ZKHUHKLVWKHWKHUPDOFRQGXFWLYLW\DQGQLVDVRXUFHWHUP WKDWWDNHVLQWRDFFRXQWWKHQHWKHDWH[FKDQJHDWWKHERXQGDU\ (T

( )

Q q x x dA

A f

d

=

#

ZKHUHxLVWKHSRVLWLRQLQWKHFRRUGLQDWHV\VWHPįx - x_f LV D 'LUDF GHOWD IXQFWLRQ ZKLFK LV QRQ]HUR RQO\ DW WKH LQWHUIDFHSRVLWLRQ

x_f , dALVDVXUIDFHHOHPHQWRIWKHLQWHUIDFHDQG

qLVWKHVRXUFHWHUPRIHQHUJ\SHUVXUIDFHXQLWRIWKHLQWHU

)RUWKHH[WHUQDOFKDUOD\HUWKLVZRXOGEHDVLQ(T

( )

q LV qe T tF T

4 4

t fv

= + + 6 - 3@

ZKHUH

VLVWKHLQWHUIDFHYHORFLW\ T_FLVWKHLQWHUIDFHWHPSHUDWXUH T_’LVWKHH[WHUQDOWHPSHUDWXUH LLVWKHKHDWRIDEODWLRQDQG

q_eLVWKHSUHVFULEHGH[WHUQDOKHDWÀX[

)RUWKHS\URO\VLVIURQWLWLVVLPSOL¿HGDVLQ(T

q=tL Vp

ZKHUHL_PLVWKHS\URO\VLVKHDW

$OVRWKHPDVVÀX[RIUHVXOWLQJJDVHVLVQHJOHFWHGGXHLWV ORZGHQVLW\ZKHQFRPSDUHGWRWKHVROLGPDWHULDO,QGHHG WKH VSHFL¿F PDVV LQ (TV DQG LV WKH LQWHUIDFH GHQVLW\ ZKLFKZDVREWDLQHGIURPWKHPHDQDYHUDJHRIWKHWZRSKDVHV VHSDUDWHGE\WKLVIURQW

$OWKRXJKWKHDLULVLQFOXGHGLQWKHGRPDLQWKLVUHJLRQ LVFRQVLGHUHGDGLDEDWLFDQGWKHKHDWFDSDFLW\DQGWKHUPDO FRQGXFWLYLW\DUHDVVXPHGWREHQXOO2QFHDEODWLRQRUS\URO\

-VLVWHPSHUDWXUHVDUHUHDFKHGWKHWHPSHUDWXUHMXPSFRQGLWLRQ EHFRPHV(T

TF=TA=0

ZKHUHT_AZLOOEHWKHDEODWLRQRUWKHS\URO\VLVWHPSHUDWXUH DFFRUGLQJWRWKHLQWHUIDFH

Solution Method

7KHPRYLQJERXQGDU\SUREOHPZDVVROYHGE\WKHLQWHU

-IDFHWUDFNLQJPHWKRGLQWURGXFHGE\8QYHUGL 7U\JJYDVRQ DQGHPSOR\HGE\-XULFLQVROYLQJSKDVHFKDQJH SUREOHPV,QWKLVPHWKRGD¿[HGXQLIRUP(XOHULDQJULGLV JHQHUDWHGZKHUHWKHFRQVHUYDWLRQODZVDUHDSSOLHGRYHUWKH FRPSOHWHGRPDLQ7KHLQWHUIDFHDFWVDVD/DJUDJHDQUHIHUHQWLDO ZKHUHDPRYLQJJULGLVDSSOLHG7KHLQVWDQWDQHRXVSODFHPHQW RIWKHLQWHUIDFHRFFXUVWKURXJKWKHFRQVWDQWUHPHVKLQJRIWKH PRYLQJJULGDQGHDFKDUHDRIWKHGRPDLQLVFKDUDFWHUL]HGE\ WKHLQGLFDWRUIXQFWLRQZKLFKLGHQWL¿HVWKHSURSHUWLHVRIWKH ZDOODQGWKHDLUDURXQGLW

7KLV PHWKRG DOORZV UHSUHVHQWLQJ DQ\ JHRPHWU\ XVHG LQ WKH 736 DQG DOVR WKH FKDUDFWHUL]DWLRQ RI HYHU\ OD\HU VHSDUDWHO\,WLVDFFRPSOLVKHGZLWKRXWKLJKLQFUHDVHLQWKH FRPSXWDWLRQDO FRVW DQG GRHV QRW QHHG DQ\ SUHSURFHVVLQJ FRQVWUXFWLRQRIXQVWUXFWXUHGJULGRUFRRUGLQDWHWUDQVIRUPD

-WLRQ ,Q WKLV ZRUN WKLV PHWKRG LV HPSOR\HG WR HVWLPDWH WKH DEODWLYH SHUIRUPDQFH RI WKH736 FRQVLGHULQJ D WZR GLPHQVLRQDODSSURDFKLQERWKWKHKHDWFRQGXFWLRQDQGWKH PRYLQJERXQGDU\SUREOHP

Interface tracking method for one moving interface 7KHLQWHUIDFHLVUHSUHVHQWHGDVDSDUDPHWULFFXUYHRu ZKHUH WKH QRUPDO DQG WDQJHQW YHFWRUV DQG FXUYDWXUH DUH H[WUDFWHG7KHLQWHUIDFHSRLQWVDUHLQWHUSRODWHGE\D/DJUDQJH SRO\QRPLDOZKLFKDOORZVWRREWDLQWKHJHRPHWULFSDUDPHWHUV DQG UHPHVKHV WKH FXUYH NHHSLQJ WKH GLVWDQFHd EHWZHHQ FXUYHSRLQWVZLWKLQWKHLQWHUYDOGKZKHUHhLVWKH GLVWDQFHDPRQJWKH¿[HGJULGSRLQWVDVVKRZQLQ)LJ

n

Lagrangean point at interface

I , J

X Y

k

d

h

_R

_(u)

)LJXUH(XOHULDQDQG/DJUDQJHDQPHVKHV

7KH LQGLFDWRU IXQFWLRQ LV XVHG WR UHSUHVHQW WKH GLIIHUHQW SKDVHV)RUWKHVLPSOHFDVHRIRQO\WZRSKDVHVLWYDULHVIURP DLUWRVROLGDQGLVLWQXPHULFDOO\FRQVWUXFWHGXVLQJWKH LQWHUIDFHFXUYHWRGHWHUPLQHDVRXUFHWHUPGx7KHMXPSRI WKHLQGLFDWRUIXQFWLRQDFURVVWKHLQWHUIDFHLVGLVWULEXWHGRYHUWKH ¿[HGJULGSRLQWV\LHOGLQJDJUDGLHQW¿HOGLQWKHPHVK(T

( ) ( )

G x I n x x dAf

A

d d

= =

#

+RZHYHU VXFK UHSUHVHQWDWLRQ LV QRW FRQYHQLHQW IRU D GLVFUHWHQXPEHURISRLQWVVLQFHWKH/DJUDQJLDQSRLQWVx_kGR QRWQHFHVVDULO\FRLQFLGHZLWKWKH(XOHULDQJULGSRLQWVx_i,j7KH GLVWULEXWLRQIXQFWLRQLVXVHGWRUHSUHVHQWWKHLQWHUIDFHGLVFRQ

-WLQXLW\DVDFRQWLQXRXVDQGVPRRWKIXQFWLRQ6XFKIXQFWLRQLV VLPLODUWRWKH*DXVVLDQGLVWULEXWLRQRQHDQGLWVYDOXHGHSHQGV RQWKHGLVWDQFH_x_ij - x_k_EHWZHHQWKH/DJUDQJHDQDQG(XOHULDQ SRLQWV(T

( ) [( ) / ] . [( ) / ]

D x

h

f x x h f y y h

,

i j k

k i k j

2

= - -

ZKHUHD_{i j} LV WKH GLVWULEXWLRQ IXQFWLRQ IRU D SRLQWk LQ WKH /DJUDQJHDQPHVKZLWKUHVSHFWWRDQ(XOHULDQSRLQWx_i ,y_j 2QHVKRXOGQRWHWKDWLQFUHDVLQJhUHVXOWVLQDWKLFNHULQWHUIDFH

7KHIXQFWLRQfLVWKHSUREDELOLW\GLVWULEXWLRQ)LJUHODWHG WRWKHGLVWDQFHhDV(TDDQGE

( )

( )

/ ( )

f x

f x

f x

if x

if x

if x

1 2 2

0

1

1 2

2

1

1 1

#

$

=

*

( ) 3 2. 1 4.

f x x x x

8

4

1

2

= - + + - E

0.0 0.2 0.4 0.6 0.8 1.0

x

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

f(x)

)LJXUH3UREDELOLVWLFGLVWULEXWLRQSUR¿OH

7KHGLYHUJHQFHRIWKHJUDGLHQW¿HOGLVIRXQGE\QXPHULFDO GHULYDWLRQRI3RLVRQ¶VHTXDWLRQ(T

.

I G

2

d

d =

'HVSLWHEHLQJFRQVLGHUHGFRQVWDQWVLQHDFKSKDVHWKH SURSHUWLHVLQVLGHWKHGRPDLQPXVWEHWUHDWHGDVYDULDEOHV LQ WKH IRUPXODWLRQ$ JHQHULF SURSHUW\IȡCp RUK LV H[SUHVVHGDV(T

( )x 0 ( 1 0) ( , )I x t

z =z + z -z

ZKHUHIDQGI1DUHWKHSURSHUW\YDOXHVIRUSKDVHVDQG

DFFRUGLQJWRWKHLUYDOXHVRILQGLFDWRUIXQFWLRQUHVSHFWLYHO\ 7KHFRXSOLQJEHWZHHQWKHPRYLQJPHVKDQGWKH¿[HG JULG LV GRQH DW HDFK WLPH VWHS WKURXJK WKH GLVWULEXWLRQ IXQFWLRQZKLFKLVXVHGWRUHSUHVHQWWKHVRXUFHWHUPVLQ WKH EDODQFH HTXDWLRQV DQG WR LQWHUSRODWH WKH ¿HOGV ZLWK LQ¿QLWHVLPDO GLVFRQWLQXLWLHV LQWR D ¿QLWH WKLFN UHJLRQ DW WKHLQWHUIDFH,QDVLPLODUPDQQHUWKLVIXQFWLRQLVXVHGWR LQWHUSRODWHWKH¿HOGYDULDEOHVIURPWKH(XOHULDQJULGWRWKH LQWHUIDFH7KHHTXDWLRQVXVHGWRGLVWULEXWHWKHVRXUFHWHUP LQWKH¿HOGDQGLQWHUSRODWHYDULDEOHVWRWKHLQWHUIDFHDUH (TVDQG

( ) .

Qi j, q D xk i j, k s

k

k

T

=

/

( )

T h T D x, ,

,

k i j i j k

i j

2

=

/

ZKHUHǻs_kLVWKHDYHUDJHRIWKHVWUDLJKWOLQHGLVWDQFHVIURPWKH SRLQWkWRWKHWZRRQHVRQHLWKHUVLGHRIx_kDQGFRUUHVSRQGV WRWKHDUHDFRQFHUQHGWRWKHSRLQWx_kLQWKHLQWHUIDFHVXUIDFH (TXDWLRQLVWKHGLFUHWL]HGIRUPRI(TLQZKLFKWKH'LUDF GHOWDIXQFWLRQZDVUHSODFHGE\WKHGLVWULEXWLRQIXQFWLRQD_{i , j} ZKLFKLVDOVRGRQHLQ(T

7KHLQLWLDOLQWHUIDFHVKDSHRuLV¿UVWVSHFL¿HGDQGWKHQ WKHLQGLFDWRUIXQFWLRQLVFRQVWUXFWHG)URPWKHLQLWLDOFRQGL

-WLRQV WKH SURSHUW\ DQG WHPSHUDWXUH ¿HOGV DUH GHWHUPLQHG 2XWRIWKHDEODWLYHSHULRGWKHLQWHUIDFHWHPSHUDWXUHLVNHSW EHORZWKHDEODWLRQRQHDQGWKHHQHUJ\HTXDWLRQLVVROYHGDVD SXUHKHDWFRQGXFWLRQSUREOHPYLDWKH¿QLWHYROXPHPHWKRG HPSOR\LQJDQH[SOLFLWWLPHPDUFKLQJVFKHGXOH

8VLQJWKHFXUUHQWYDOXHRIVUHVXOWIRUWKHSUHYLRXVWLPH VWHSWKHLQWHUIDFHSRLQWVDUHWUDQVSRUWHGWRDQHZSRVLWLRQ FDOFXODWHGH[SOLFLWO\WKURXJKWKHHTXDWLRQV n= dx_f / dt.n ZKHUHnLVWKHQRUPDOXQLWDU\YHFWRU

'HQVLW\DQGVSHFL¿FKHDWDUHFDOFXODWHGDWWKHQHZLQWHU

-IDFHSRVLWLRQ

V n+1LVHVWLPDWHGYLD1HZWRQLWHUDWLRQVXVLQJDQXPHULFDO UHOD[DWLRQVFKHGXOH(T

+HDWÀX[qFURVVLQJWKHLQWHUIDFHLVFDOFXODWHGWKURXJK (TXDWLRQVRUGHSHQGLQJRQWKHLQWHUIDFHDQGGLVWULE

-XWHGLQWRWKH¿[HGJULGWKURXJK(T

$FFRUGLQJWRWKHERXQGDU\FRQGLWLRQVHQHUJ\HTXDWLRQ (TLVXVHGWRREWDLQWKHWHPSHUDWXUHDWWLPHVWHSn+1 7HPSHUDWXUH LV LQWHUSRODWHG WR ¿QGT_F DW WKH LQWHUIDFH

XVLQJ(T

7KHWHPSHUDWXUHMXPSFRQGLWLRQLVWHVWHGDQGLILWLVORZHU WKDQ WKH UHDFKHG WROHUDQFH WKH ¿HOGV RI YLVFRVLW\ DQG FRQGXFWLYLW\DUHXSGDWHGIRUWKHQHZSRVLWLRQDQGRQHVWHS LQWLPHLVDGYDQFHG,IWKDWLVQRWWKHFDVHDQHZHVWLPDWH IRUV n+1LVFDOFXODWHGDQGWKHSURFHVVUHWXUQVWRVWHS

7KHFRQYHUJHQFHFULWHULRQXVHGLQVWHSLVWKHUHVLGXDOLQ (T2QFHLWKDVUHDFKHGWKHGHVLUHGWROHUDQFHFRQYHUJHQFH IRULQWHUIDFHYHORFLW\LVDVVXPHG2WKHUZLVHWKHYHORFLW\LV FRUUHFWHGYLD1HZWRQ,WHUDWLRQVJLYHQDV(T

. ( )

Vn 1 Vn R T

~

=

-+

ZKHUHȦLVDUHOD[DWLRQIDFWRUDQGRTLVWKHUHVLGXDOIRU WKHWHPSHUDWXUHMXPSFRQGLWLRQDWWKHLQWHUIDFH,WHUDWLRQVDUH UHSHDWHGXQWLORTLQHYHU\SRLQWEHFRPHVVPDOOHUWKDQWKH SUHVFULEHGWROHUDQFH7KHRSWLPXPYDOXHIRUȦLVIRXQGE\ WHQWDWLYHDWWKHFDOFXODWLRQEHJLQQLQJ

7KHPHWKRGZDVFRPSDUHGZLWKWKHDQDO\WLFDOVROXWLRQIRU DVLPSOHSKDVHFKDQJHSUREOHP5XSHUWL-UUHVXOWLQJ LQDQH[FHOOHQWDJUHHPHQWDVLWFDQEHVHHQLQ)LJ6PDOO RVFLOODWLRQV LQ GDWD SRLQWV DUH FRQVHTXHQFHV RI WKH YLVXDO H[WUDFWLRQRIWKHSRLQWV

Extension to various moving interfaces

:KHQWKHUHLVPRUHWKDQRQHLQWHUIDFHDQLQGLFDWRUIXQF

-WLRQI_mLVFUHDWHGIRUHDFKRQHLQRUGHUWRFKDUDFWHUL]HHYHU\ UHJLRQFRQFHUQHGWRWKHLQWHUIDFHVLQGLYLGXDOO\7KHUHIRUHLQ DUHJLRQmWKDWFRUUHVSRQGVWRDVSHFL¿FSKDVHRUPDWHULDOD JHQHULFSURSHUW\LVHVWLPDWHGDV(T

Ig

m m

m NFC

1 z= z

=

/

ZKHUHNFC LV WKH QXPEHU RI LQWHUIDFHV7KH /DJUDQJHDQ JULGVIRUDOOLQWHUIDFHVKDYHWKHVDPHYDOXHVIRUWKHSDUDP

-HWHUVhDQGdVKRZQLQ)LJDQGDUHFRQVWUXFWHGIURPD SDUWLFXODUSDUDPHWULFFXUYHR_muIg_iLVWKHJOREDOLQGLFDWRU IXQFWLRQIRUDUHJLRQ mREWDLQHGIURPWKHLQGLFDWRUIXQFWLRQ RIHDFKLQWHUIDFHFDOFXODWHGDVGHVFULEHGEHIRUH,WLVJLYHQ DV(TDDQGE

Igm=Im-1-Im D

1 0

I0= ;INFC= E

0.2 0.4 0.6 0.8 1 -2

-1.6 -1.2 -0.8 -0.4 0

Vi(t)

-2 -1.6 -1.2 -0.8 -0.4 0

time

D'LPHQVLRQOHVVDEODWLRQYHORFLW\ZLWKGLPHQVLRQOHVVWLPH

0.2 0.4 0.6 0.8 1 0

0.2 0.4 0.6 0.8 1

Xi(t)

0 0.2 0.4 0.6 0.8 1

time

,IWKHUHDUHPRUHWKDQRQHPRYLQJLQWHUIDFHWKHVRXUFH WHUPQ_mIRUHYHU\LQWHUIDFHKDVWREHH[WUDFWHGIURPDPRGL

-¿HGIRUPRI(T(T

( )

Qm qm m x xFm k, dAm

A k

d

=

/ #

$FWXDOO\DFFRUGLQJWRWKHQXPHULFDOPHWKRG(TZLOO EHXVHGWRFDOFXODWHWKHVRXUFHWHUPLQHYHU\LQWHUIDFH7KH WRWDODPRXQWRIKHDWJHQHUDWHGZLOOEHWKHVXPPDWLRQRIKHDW VRXUFHVRIDOOLQWHUIDFHV(T

Q Qm

m

=

/

7KH FRQYHUJHQFH FULWHULRQ DQG YHORFLW\ FRUUHFWLRQ DUH WKHVDPHDVWKDWIRUWKHFDVHRIRQHLQWHUIDFHEXWWKH\DUH H[WHQGHGWRDOOLQWHUIDFHVDWHDFKWLPHVWHS,WPXVWEHSRLQWHG RXWWKDWDOWKRXJKDGLIIHUHQW/DJUDQJLDQPHVKLVQHFHVVDU\IRU HDFKLQWHUIDFHDXQLTXH(XOHULDQPHVKLVXVHGDQGDSSOLHGLQ (TIRUHYHU\LQWHUIDFH

RESULTS AND DISCUSSION

7KHFRPSXWDWLRQDOFRGHZDVHPSOR\HGWRVLPXODWHDRQH GLPHQVLRQDODEODWLRQSURFHVVDOLNHWKDWFRQGXFWHGE\%DUURV LQZKLFKPDWHULDOVDPSOHVZHUHH[SRVHGWRDSODVPD MHWDQGKDGWKHLUWHPSHUDWXUHDQGKHDWÀX[PHDVXUHG

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

7KHPDVVORVVUDWHZDVWKHSDUDPHWHUFKRVHQLQRUGHUWR FRPSDUH H[SHULPHQWDO GDWD DQG QXPHULFDO UHVXOWV 'XULQJ WKHH[SHULPHQWWKHPDVVORVVUDWHZDVHYDOXDWHGFRPSDULQJ WKHVDPSOHPDVVDIWHUDSHULRGRIH[SRVXUHWRWKHSODVPDMHW 7KHUDWHZDVREWDLQHGGLYLGLQJWKHPDVVORVVE\WKHWLPHRI H[SRVXUH7KHVDPHSURFHVVZDVHPSOR\HGWRREWDLQWKHPHDQ PDVVORVVUDWHLQWKHVLPXODWLRQV+RZHYHUWKHFDOFXODWLRQ RIWKHPDVVORVVUDWHZDVGRQHLQVWDQWDQHRXVO\WKURXJKWKH

LQWHJUDWLRQDWHDFKWLPHVWHSZKLOHWKHH[SHULPHQWDOPHWKRG VKRZHGWKH¿QDOUHVXOWDIWHUWKHVHOHFWHGSHULRG

7KH PDWHULDO XVHG LQ WKH VDPSOHV ZDV WKH TXDUW] SKHQROLFUHVLQ6L3KHQROLF7KHIUDFWLRQRIUHVLQZDVQRW VSHFL¿HGLQWKHZRUNRI%DUURVYDU\LQJIURPWR UHVXOWVIURPWKHUPRJUDYLQRPHWULFDQDO\VLV6DPSOHV ZHUHÀDWF\OLQGHUVZLWKWKLFNQHVVRIPPDQGGLDPHWHUV RIDQGPP7KHSURSHUWLHVXVHGLQWKHVLPXODWLRQDUH SUHVHQWHGLQ7DEOH

7DEOH 3URSHUWLHVRIWKHTXDUW]SKHQROLFUHVLQ

3URSHUW\ 2QHIURQW

PRGHO

7ZRIURQWPRGHO 9LUJLQ &KDU

K:Pž&

Cp-NJž&

ȡNJP

İ

+HDWRIDEODWLRQ0-NJ _-

-$EODWLRQWHPSHUDWXUHž& ž _-

-+HDWRIS\URO\VLV0-NJ -

-3\URO\VLVWHPSHUDWXUHž& - ž

-+HDWRIPHOWLQJVXEOLPDWLRQ

0-NJ - -

0HOWLQJWHPSHUDWXUHž& - - ž

_{'D&RVWDHWDO*UHJRULHWDO7LFNHWDO}

_{:LOOLDPVDQG&XUU\6DYYDWLPVNLL}

7KHRQHGLPHQVLRQDOKHDWFRQGXFWLRQSUREOHPZDVVROYHG FRQVLGHULQJSUHVFULEHGKHDWÀX[LQWKHZDUPHGIDFHDQGDGLD

-EDWLFVXUIDFHLQWKHRSSRVLWHRQHDVERXQGDU\FRQGLWLRQV7KH LQLWLDOWHPSHUDWXUHZDVž&.

+HDWÀX[HVRIDQG 0:P_{ZHUHLPSRVHGWRWKHZDUPHGIDFH$FFRUGLQJ}

WR%DUURVWKHKHDWÀX[RYHUWKHVXUIDFHZDVFRQWUROOHG E\WKHSRZHURIWKHSODVPDWRUFKDQGLWVGLVWDQFHIURPWKH VDPSOHVXUIDFHDQGWKHUHVXOWXQFHUWDLQW\LQWKHHYDOXDWLRQRI KHDWÀX[HVYDULHGIURPWR0:P_{GHSHQGLQJRQWKH}

KHDWÀX[YDOXH

SRLQWVJULGZHUHXVHG

,Q )LJ WKH PDVV ORVV UDWHV DUH SUHVHQWHG DORQJ WKH WLPHRIH[SRVXUHWRWKHSODVPDMHWÀDPHIRUHDFKYDOXHRI WKHSUHVFULEHGKHDWÀX[7KHRQHIURQWPRGHOKLJKO\RYHU

-HVWLPDWHVWKHYDOXHVZKHQFRPSDUHGWRWKHH[SHULPHQWDO UHVXOWV7KHWZRIURQWPRGHOVOLJKWO\XQGHUHVWLPDWHVWKHVH YDOXHVDOWKRXJKLWLVFORVHUWRH[SHULPHQWDOGDWD)RUWKH PLQRUYDOXHVRIKHDWÀX[WKHLQLWLDOVKDSHVRIWKHFXUYHV REWDLQHGIURPWKHQXPHULFDOVLPXODWLRQVDUHIDUIURPWKH H[SHULPHQWDO UHVXOWV ,W PLJKW EH D FRQVHTXHQFH RI WKH QXPHULFDOWUHDWPHQWVLQFHLQERWKQXPHULFDOPHWKRGVWKH DEODWLRQYHORFLW\WHQGVWRLQ¿QLWHDWWKHLQVWDQWZKHQDEODWLRQ VWDUWV6LQFHWKHLQWHJUDWLRQLVGRQHDWHYHU\WLPHVWHSWKH UHODWLYHZHLJKWRIWKLVLQLWLDOSHULRGEHFRPHVLPSRUWDQWLQ WKHUHVXOWIRUWKHORZKHDWÀX[HVEHFDXVHWKHVWDELOL]DWLRQRI WKHSURFHVVWDNHVPRUHWLPHLQWKHVHFDVHV,WLVDOVRLPSRU

-WDQWWRFRQVLGHUWKHGLIIHUHQWZD\VWKHUDWHVDUHFDOFXODWHG

Two-front Experimental O ne-front

0 10 20 30 40 50 60 70 80 90 100 time, s

0 0.04 0.08 0.12 0.16 0.2

Mass loss rate, kg/m

2 .s

D0:P

0 10 20 30 40 50 60 70 80 90 100 time, s

0 0.05 0.1 0.15 0.2 0.25

Ma

s

s l

os

s r

a

te

, kg

/m

2.s

Experimental O ne-front Two-front

E0:P

0 10 20 30 40 50 60 70 80 90 100 time, s

0 0.05 0.1 0.15 0.2 0.25

Mass loss rate, kg/m

2.s

Experimental O ne-front Two-front

F0:P

0 10 20 30 40 50 60 70 80 90 100 time, s

0 0.1 0.2 0.3

M

a

s

s l

o

ss

r

a

te

, kg

/m

2.s

Experimental One-f ront Two-f ront

G0:P

0 10 20 30 40 50 60 70 80 90 100 time, s

0 0.1 0.2 0.3 0.4

Mass loss rate, kg/m

2.s

Two-front O ne-front Experimental

H0:P

7KH PHDVXUHPHQWV DUH GRQH LQ ¿QLWH LQWHUYDOV ZKLOH WKH QXPHULFDOUDWHVDUHFDOFXODWHGLQVWDQWDQHRXVO\DWHDFKWLPH VWHS+RZHYHUIRUWKHPDMRUYDOXHVRIKHDWÀX[DOORIWKHP SUHVHQWWKHVDPHEHKDYLRUFXUYHVKDSH

7KHURRWPHDQVTXDUHrmsHUURUZDVXVHGDVDPHDVXUH

-PHQWRIWKHDJUHHPHQWEHWZHHQWKHUHVXOWVDQGLVGH¿QHGDV (TVDQG

rms

n mi i I

n 2

T

=

/

m

m

m m

i

e

e s

T =

ZKHUHm_eDQGm_sUHIHUWRWKHPDVVORVVUDWHVH[WUDFWHGIURP %DUURV DQG IURP WKH FRPSXWDWLRQDO VLPXODWLRQ UHVSHFWLYHO\

7DEOHVKRZVDFOHDUDGYDQWDJHRIWKHWZRIURQWPRGHOD UHGXFWLRQWKDWH[FHHGHG

7DEOH &RPSDULVRQRIrmsIRUERWKPRGHOV

&DVH Q

0:P

rms

7ZRIURQW 2QHIURQW

7RWDOrms -

)LJXUHVKRZVWKHH[WHUQDOVXUIDFHWHPSHUDWXUHH[WUDFWHG IURPWKHVLPXODWLRQZLWKWKHWZRIURQWPRGHOFRPSDUHGWR WKHH[SHULPHQWDOPHDVXUHPHQWV%DUURV7HPSHUDWXUH XQFHUWDLQW\ZDVQRWDYDLODEOHLQWKHUHIHUHQFHDQGDOOGDWDIRU WKHH[SHULPHQWDOUHVXOWVZHUHFROOHFWHGYLVXDOO\$OWKRXJK¿QDO YDOXHVSUHVHQWDQLQFUHDVLQJGLVFUHSDQF\ZLWKWKHKHDWÀX[ LPSRVHGWKHEHKDYLRULVVLPLODUZKLFKDWWHVWVWKHSK\VLFDO FRKHUHQFHRIWKHPDWKHPDWLFDOPRGHOXVHGLQWKHVLPXODWLRQV 7DEOHVKRZVWKHWHPSHUDWXUHVZKHQVWHDG\VWDWHLVUHDFKHGDQG RQFHDJDLQHYLGHQFHVWKHLPSURYHPHQWLQWKHDJUHHPHQWZKHQ PRGHOVDUHFRPSDUHG7KHRQHIURQWPRGHOFRQVLGHUVWKDWWKH H[WHUQDOVXUIDFHVKRXOGEHDWDFRQVWDQWDEODWLRQWHPSHUDWXUH DQGWKHWZRIURQWRQHFRQVLGHUVWKHH[WHUQDOWHPSHUDWXUHRIWKH FKDUOD\HUZKLFKPLJKWEHH[SRVHGWRWKHDLU,IWKHDEVROXWH YDOXHVLQ.HOYLQRIWKH¿QDOWHPSHUDWXUHVDUHFRQVLGHUHGWKH DYHUDJHGHYLDWLRQLQWKHDEVROXWHWHPSHUDWXUHIDOOVIURP

WRZKLFKLVDUHGXFWLRQRIDOPRVW

,Q )LJ WKH WHPSHUDWXUH SUR¿OH DW WKH ¿QDO WLPH VHFRQGVLVVKRZQIRUWKHFDVHRIPD[LPXPKHDWÀX[7KH SRVLWLRQRIWKHH[WHUQDOVXUIDFHNHHSVFRQVWDQWVLQFHWKHPHOW

-LQJWHPSHUDWXUHRIWKHFKDULVQRWUHDFKHG7KHGLVSODFHPHQW two interfaces model

0,45 MW/m2 0,64 MW/m2 0,90 MW/m2 1,22 MW/m2 2,18 MW/m2

Barros (2008)

0 10 20 30 40 50 time (s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

Tempe

ratu

re (

oC)

)LJXUH5HVXOWVIRUWKHWZRIURQWPRGHOFRPSDUHGZLWKWKHH[SHU

-LPHQWDOGDWD%DUURVIRUWKHVXUIDFHWHPSHUDWXUH ZLWKWKHWLPH

7DEOH )LQDOVXUIDFHWHPSHUDWXUHV

&DVH ([SHULPHQWDO_{2QHIURQW'HYLDWLRQ7ZRIURQW'HYLDWLRQ}

ž& ž& ž&

ž& ž& ž&

ž& ž& ž&

ž& ž& ž&

ž& ž& ž&

$YHUDJH $YHUDJH

_{%DUURVDIWHUVHFRQGV$EODWLRQWHPSHUDWXUH([SHULPHQWDO}

YDOXHWDNHQDVUHIHUHQFHLQ._$IWHUVHFRQGV

0 500 1000 1500 2000 2500

T,

o

C

0.0005 0.001 X,_m 0

0.005

0.01

Y, m Pyrolysis front, t = 0

Char surface

Pyrolysis front, t = 90 s

RFFXUV LQ WKH S\URO\VLV IURQW FRQVLGHUHG EHLQJ LQLWLDOO\ DW PPIURPWKHH[WHUQDOVXUIDFHRQO\IRUFDOFXODWLRQ7KH WHPSHUDWXUHJUDGLHQWLVJUHDWHULQWKHFKDUWKDQLQWKHYLUJLQ PDWHULDO FRQ¿UPLQJ LWV HIIHFW DV D WKHUPDO LQVXODWRU 7KH H[WHUQDOVXUIDFHWHPSHUDWXUHDERXWž&LVYDVWO\VXSHULRU WRWKHS\URO\VLVRUWRWKHDEODWLRQRQHVIRUWKHRQHIURQWPRGHO :KHQFRPSDULQJWKHSHUIRUPDQFHRIERWKPRGHOVVRPH DVSHFWVRIWKHUHVXOWVVKRXOGEHDFFRXQWHGVXFKDVWKHXQFHU

-WDLQW\RIWKHH[SHULPHQWDOUHVXOWVWKHVLPSOHDSSURDFKXVHG LQWKHLUFRQVWUXFWLRQWKDWQHJOHFWVWKHLQÀXHQFHRIYDULRXV SK\VLFDOSURFHVVHVDQGYDOXHVRIWKHSURSHUWLHVXVHGLQWKH FDOFXODWLRQZKLFKZHUHH[WUDFWHGIURPVHYHUDOVRXUFHVDQG FRQVHTXHQWO\DUHVXEMHFWWRGLIIHUHQWHYDOXDWLRQFRQGLWLRQV 'HVSLWHDOOWKHVHDVSHFWVWKHWZRIURQWPRGHOFDQEHFRQVLG

-HUHGPRUHDFFXUDWHWKDQWKHRQHIURQWPRGHO

CONCLUSIONS

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¿UPLWVKLJKHUDFFXUDF\ ZKHQFRPSDUHGWRWKHRQHIURQWPRGHO

7KHPRYLQJERXQGDU\SUREOHPZDVVLPXODWHGYLDLQWHUIDFH WUDFNLQJPHWKRG7KHUHVXOWVGHPRQVWUDWHGWKDWWKHPHWKRGLV FDSDEOHRIFDSWXULQJWKHWHPSHUDWXUHSHDNDQGRIUHSUHVHQW

-LQJWKHDEODWLRQSURFHVVDVDPRYLQJERXQGDU\SUREOHPLQ WKH SUHVHQFH RI PRUH WKDQ RQH VLQJOH OD\HU 5HVXOWV VKDOO EHH[WUDFWHGIRUPRUHUH¿QHGPHVKHVLQRUGHUWRFKHFNWKH PHWKRGDFFXUDF\

7KLV DQDO\VLV FDQ EH DSSOLHG WR GLYHUVH UHJLRQV RI WKH URFNHWPRUHOD\HUVDQGRWKHUVKDSHV$PRUHUHDOLVWLFSK\VL

-FDOPRGHOIRUWKHDEODWLRQLQWKHFRPSRVLWHPDWHULDOPD\QRZ UHSODFHWKHVLPSOHRQHXVHGLQWKLVZRUN7KHLQFOXVLRQRIWKH ÀRZ¿HOGHIIHFWVOLNHLQMHFWLRQRIPDVVGXHWRVXEOLPDWLRQ VKDOODOVREHLQFRUSRUDWHGLQWRWKHVLPXODWLRQ,QIXWXUHZRUNV WKHHIIHFWRIWHPSHUDWXUHYDULDWLRQLQWKHS\URO\VLVDFFRXQWHG WKURXJKWKH$UUKHQLXVHTXDWLRQVKRXOGEHLQFOXGHG

ACKNOWLEDGEMENTS

7KHDXWKRUZRXOGOLNHWRWKDQNWKHConselho Nacional de Desenvolvimento Cientt¿co e Tecnolygico &13T WKH %UD]LOLDQ)HGHUDO$JHQF\IRU6FLHQFHDQG7HFKQRORJ\IRU WKHLU¿QDQFLDOVXSSRUWGXULQJWKLVZRUN

REFERENCES

%DUURV($³7KHUPDO3ODVPDIRU$EODWLRQLQ0DWHUL

-DOV8VHGLQ+HDW6KLHOGRI6SDFH6\VWHPV´,Q3RUWXJXHVH 06F'LVVHUWDWLRQ,7$6mR-RVpGRV&DPSRV%UD]LOS

'D&RVWD/(9/et al³9LDELOLW\6WXG\RI7KHUPDO 3URWHFWLRQIRU6$5$3ODWIRUP´,Q3RUWXJXHVH,$(&7$ 7HFKQLFDOQRWH17$6(1,$(&7$6mR-RVpGRV &DPSRV%UD]LO

*UHJRUL0/et al³3URSHUWLHVRI4XDUW]3KHQROLF &RPSRVLWHV IRU 7KHUPDO 3URWHFWLRQ 6\VWHPV´ WK _,$&

&RQJUHVV*ODVFRZ6FRWODQG

-XULF ' ³&RPSXWDWLRQV RI 3KDVH &KDQJH´ 3K' 7KHVLV8QLYHUVLW\RI0LFKLJDQ0LFKLJDQS

0DFKDGR+$³7KHUPDO3URWHFWLRQIRU$HURG\QDPLF +HDWLQJRIWKH6$5$6XERUEWLDO3ODWIRUP´,Q3RUWXJXHVH &21(05HFLIH%UD]LO

0DFKDGR+$DQG3HVVRD)LOKR-%D³$HURG\QDPLF +HDWLQJDW+\SHUVRQLF6SHHGV´3URFHHGLQJVRIWK%UD]LOLDQ &RQJUHVVRI0HFKDQLFDO(QJLQHHULQJ%UDVtOLD%UD]LO

0DFKDGR+$DQG3HVVRD)LOKR-%E³$HURG\QDPLF +HDWLQJRQ96%´(6$6\PSRVLXP9LVE\6ZHGHQ

0D]]RQL -$ DQG 3HVVRD )LOKR - % 0DFKDGR +$ ³$HURG\QDPLF+HDWLQJRQ96%6RXQGLQJ5RFNHW´ 3URFHHGLQJVRIWK%UD]LOLDQ&RQJUHVVRI0HFKDQLFDO(QJL

-QHHULQJ2XUR3UHWR0LQDV*HUDLV%UD]LO

5XSHUWL-U1-³6ROXWLRQRID2QH'LPHQVLRQDO$EOD

-WLRQ 0RGHO´ ,Q 3RUWXJXHVH 06F 'LVVHUWD-WLRQ 1D-WLRQDO ,QVWLWXWHIRU6SDFH5HVHDUFK±,13(6mR-RVpGRV&DPSRV %UD]LOS

6DYYDWLPVNLL$9³0HOWLQJ3RLQWRI*UDSKLWHDQG/LTXLG &DUERQ´3K\VLFV8VSHNKL9RO1RSS

6LOYD'9)05³(VWLPDWLYHRI7KHUPDO3URSHUWLHV RI$EODWLYH0DWHULDOV´,Q3RUWXJXHVH06F'LVVHUWDWLRQ )HGHUDO8QLYHUVLW\RI5LRGH-DQHLUR8)5-5LRGH-DQHLUR %UD]LOS

7LFN6-et al.³'HVLJQRI$EODWLYH7KUXVW&KDPEHUV DQG7KHLU0DWHULDOV´-RXUQDORI6SDFHFUDIW 5RFNHW9RO 1RSS

8QYHUGL62DQG7U\JJYDVRQ*³$)URQW7UDFNLQJ 0HWKRG IRU 9LVFRXV ,QFRPSUHVVLEOH 0XOWLÀXLG )ORZV´ -RXUQDORI&RPSXWDWLRQDO3K\VLFV9ROSS

:LOOLDPV6'DQG&XUU\'0³7KHUPDO3URWHFWLRQ 0DWHULDOV±7KHUPRSK\VLFDO3URSHUW\'DWD´1$6$5HIHU