HWAHAK KONGHAK Vol. 39, No. 1, February, 2001, pp. 96-102(Journal of the Korean Institute of Chemical Engineers)

Finite Element Method

†****

* **

(2000 9 27 , 2000 11 27 )

Fines Behavior Analysis in Blast Furnace with Finite Element Method

Jin-Kyung Chung†, Jung-Hee Kim*, Yong-Ok Jeong* and Pan-Wook Park**

Technical Research Laboratories, POSCO, 699 Kumhodong, Kwangyang, Chonnam 544-090, Korea*School of Chemical Engineering, Pukyong National University, Pusan 608-739, Korea

**Department of Chemical Engineering, Pusan National University, Pusan 609-735, Korea(Received 27 September 2000; accepted 27 November 2000)

! "#$. % &'( )*+

,- . /0 12 Ergun34 567 8%9 : ;<. FEM(Finite Element Method)

2 2=>? 2@A$. 2@ B &'CD &EFG<B < FG H4 I JKL M

N8 O P QRQS? O 9- /3B T7 2@A$. 2@ B &'( US4

V WX -, YZ : [- \? ]^4 _ `4 a b W#$. cO d2 efgh ,- b_

2@ 2 O ,-iB jk B lm n )_A?o ,- 10% " pq 1.5-2 m- " `?

rst$. ,- u pv wx 20-30% rsy?o z|~ B z|~ 10-

20% ,- rsy$.

Abstract − Fines behaviors are considered as main factors in determining the operation states of blast furnace with PCI(Pul-

verized Coal Injection). The gas velocity and pressure distribution in blast furnace was analyzed by Ergun equation with two

dimensional FEM(Finite Element Method). The theoretical model to predict the pressure drop was used under assumption that

the interaction force between gas and powder is main resistance factor in fines flow through packed bed. To estimate the pow-

der hold-up, the model is combined with the experimental result on the fines velocity in gas stream. The size of fines is most

important factor in determining the concentration of fine in blast furnace together with density and feeding rate. Both of the

measured and calculated results show that 10% fines concentration is at 1.5-2 m distance from tuyere tip. The results of 2-D

numerical analysis on the distribution of fines concentration in blast furnace shows 20-30% in deadman and 10-20% above the

root of cohesive zone.

Key words: Blast Furnace, Pulverized Coal Injection, FEM, Fines Accumulation

†E-mail: jkchung@posco.co.kr

1.

. ! "#$ % &'( )*+

,- &$ 10-25 m. /, 012 345 6 & ,- 100 m

7. Fig. 18 9:; <= > ?/ @A! B C

DE A FG H%I$ J KLG M/ N

O! PQ RS$( A! H%IT UV2 VWX. V

8 Y5 PE Z@[! CO$I ?/ \M](

DE _M PE V2 ( Z4( M/8( N

a! b(pig iron), ?/8( N $I$ YMc d. e

8( H%I POf g Z@[! CO$I Of@( hi 7

8j kMM KLD lJ! mm= ?nM $I$ op q

mi r s o2 tRS u hi M e8( $K Tv5

Dw[1].

xyU xV, H%I g B y, N/8( pd z g

zD | C * E~8( 5 y YMm

t 5 y / $IT LGS +2 \M9

96

Finite Element Method 97

/J |JM* o, op8 x d.

( $I y 4q5 2?. y

$M* 8 W ( q\ p Mc i

v$ s. $IT8 y 1- ? fM* $I= yE ?

( Ergun type[2] qE yE +D ?

( ¡ ¢8 !M y £\¤ ¥2 9: £\

¦~ FM* y qE +8 M lM

$§M. ©ª8 x y j $M $§M.

M/8( H%I + b, $ «MM M//¬

N $I$ ?n5. H%I ­I®8( k5 b¯ £\

°' H%I /y yM* H%I xy d. 5± Q² ³

/¬ LGS+ xyU xV char2 pM* H%I xy g

Z@$I= 4´ JM, \M* /$ |JG d.

xy \E |J o op8 xµ. +

2 ?nM $Iq xy ¶ j·j y¸ %c G]

2? f5. q xy ¶j ·j ]

xy |J sc G. 2?8( q\ ¹5.

2 ,? M +8 sS( , 2? ²$ r ·

GS s[3-11]. +8( xº¡$ ?n£\M]( »¼G

\J hold-up M L¡ O½F8( |JGS¾ J

»¼GSmm ¿ yT 8( J 1À ~J hold-up 5.

y j8 ,5 ªÁÂE2 M* FEM(Finite Element Method)8

+8( y |J \#F8 ,5 ² Ãm ¿.

Ä ²8( ª[ 8( ÅÆÇd ÂE= y e |J

?È2 FEM8 B5 ÂE2 1` yB4( ~5 yB

r#É ²ÊM¡ MË.

2.

e8( y |J¤ ²M ( e $I g ¨ y32 ²

M* 8 y \ ÌÍ ·'Î 5. 5 y |J e

$I g ¨y38 xÏ ( ?ÐÐl8 s Ñ r s

. y j * $m ÒJ! ¦Ó ²Ô9 $K ~5 ¦

Ó ªÁJ ³^ ²M . ( 5 $Ij g ¨

y3 = y j8 Ð5 ªÁªJ ÂE2 ÂÕM* e8( y

\8 , Bi r s.

2-1.

+8( $I £\j2 BM ( Ergun Ö@

KM* FMË[12].

(1)

*(

± ? ~ M] ×E > d.

(2)

Ø8 xy M] ×E >.

(3)

ÙlÚM8( (3) ÛS( ÜÝ8( ²M, ¨

xyM* vV/ JyÝ8( q ²MË. = >

(2), (3) Þ( ÛS( q rß( tolerance)

i àám ÞMË.

jj j 3âã ²»8 1äM* Mk5 $~MË

Ï 'å= > 9:æ r s.

(4)

Ø8 xy M] ×E >.

(5)

q 5 (5)2 ÛS( j 3âã ψ2 ²M xy

M* q ²MË.

2-2. Ergun

e $I 8 ,5 j g ¨ ²M ( ç (3)

E (5)2 Û M* ÜÝ8( è g ÙlÚ JM

8 weighted residual JM* vV h JyM] ¦~

weighted residual ³`p GSÎ 5. à q¤ C ¨

ÜMË, q e²/8( ª[ KLj

0~MË. ( (3), (5) è g ÙlÚ JE weighting

factor(W) jL weak form ¥ZM] 'å E > ²+.

(Weak form)

Weak foam ¥Zd r éê¬ ëì M ( í?

4r(shape function) NA, NB2 jLM*

ZM] 'åE > Galerkin form ¥Zd. 2 @

º ¦~ ~îM* éê¬8 2 ²M $§M,

Newton method2 FM* vV/ JyÝ8( rßd $I

j 3âã ²i r s[13].

(Galerkin form)

2-3.

Yamaoka C[4] $I ²8 y 34d Ùï2 ðè

jLMË. y$ 8 ( rñG Ê? y rñò

E ÐóM* Y5 , 2? ²yÎ8( fGSm smt

+T8( y rñ8 Ð5 ² î Ãm ¿ô. y

WJ! £\?È8 õöM* ?È ò ×E > ÷øMË.

ç y ¤ “+ O½ù ¶ Jú ûM y ”

P∇– f1 f2 Gg+( )Gg=

f1 1501 εg–

ϕpdp

------------ µg

gc

----- 1

εg3ρg

---------- f2 1.751gc

----1 εg–

εg3ϕpdpρg

----------------------

=,=

a0 1 f1 f2 Gg+( )⁄=

P∇–1a0

----Gg=

∇ a0 P∇–( ) ∇ Gg 0=⋅=⋅

Ggnew Ggold– ≤

ψ∇– Gs=

∇ ψ∇–( ) ∇ Gs 0=⋅=⋅

W∫ raz∂2P

∂z2--------dΩ W∫ ar

∂∂r----- r

∂P∂r------

dΩ 0=⋅+⋅

W CANAA 1=

n

∑ P NBdBB 1=

n

∑=,=

∂NA

∂z---------- az

∂NB

∂z----------

B 1=

n

∑ dB

∂NA

∂r----------ar

∂NB

∂r----------

B 1=

n

∑ dB+⋅ 0=A 1=

n

∑

Fig. 1. Schematic diagram of a blast furnace.

HWAHAK KONGHAK Vol. 39, No. 1, February, 2001

98

~ M, + O½ü y J O½ù εkg, ý· þj

2 ρk M* y¤ Hk2 ÿÊM ×E > r s.

Hk= (1−εkg) ρk (6)

5± y T g $I= ? °'( £\M £\8

,M* £\ M GS¾( ~??È8(

×E > íÐl2 9:æ r s.

(7)

*( Fk,g: $I= y ?

: y¤8 ?úM T

Rk: £\

yE +L¡ ? ¢E s9 ?n£\

u Äl8( WM ¢ uv! uM

Ë. 2 y ¢8 sS( £\¤ ¥2 9: Rk

£\ ( ×E > r s.

(8)

*( β Y·~lr( 1/2 ek,p Ylr( 0.9~j.

ρp, dp L¡ þj g ³Ù, εg + O½ù, Uk y j

( Y !( yE $I j W Mm ¿

. $I8 L¡= 4´ yE ? JG

G. ¨©ª ∆P/L ×E > r s.

(9)

*( Fp,g $I= +L¡ ? Ergun J

M* ~îM] ×E > r s.

(10)

*( Ug $IOj

9 ª[ ~d E ld Allenh8( ?ú5 Ö2 ·

Ë. y j2 ²M E~8( Ergun/¬ ²5

8 !5 d[4, 5]. Kusakabe C[11] 5 ÒJ!

5l2 ½ÞM ªÁªJ $I= y 2? W m»¦~

²MË.

+8( 2? Ùï xy Ofq¤ Gk, xy ?

nj Uk g \J hold-up! Hd 8 ×E > Ðl 9:.

(11)

+8( y |JíÈ ~J hold-upE \J hold-up $

m 9 r s. y *( ³m ¿ Ùï2 ~J hold-up

M. ªÁªJ ²5 H%I8( ~J hold-up × E

>. 5

(12)

\J hold-up +2 ³ y 8 Â~G

ªÁªJ ²5 8( \J hold-up × E > 9

:;.

(13)

Ï ~J hold-upE \J hold-up¤ Õ5 hold-up¤

×E > 9:æ r s.

(14)

*( Fr Frouder2, Re Reynoldsr2 9:. ×E >

r s.

*( Gk xy w¤q¤[Kg/(m2s)], Gg w¤q¤[Kg/

(m2s)]y y32 ²M ( Yamaoka 6 (10)E Kusakabe

ªÁ (14)2 M* $I, y 2 ? W e8( $I

g y B FEM ªWMË.

Fig. 2 (3), (10), (14)2 è $I g y B 5

éê¬ ëì (j2 9:.

3.

3-1.

xyU L Ú8 ( q5 vVÓ M* yj

y32 #F5 ÂE= \Ú8( ~5 ª y j ?È=

1`M ( e y MË. ~rî2 M* mM

8( PQ RS$ L²! Q²2 o( 3.5 m, ³Ù

Fk g,

Hkg

gc

--------- Rk=–

Hkg

gc

---------

Rk1gc

----3β1 ek p,+

1 ek p,–----------------

1 εg–( )ρp 1 εkg–( )ρk dp dk+( )2

ρpdp3 ρkdk

3+----------------------------------------------------------------------Uk

2=

P∆L

------- Fp g, Fk g,+=

P∆L

------- 1 εkg–( )ρk 1 1gc

----32---

1 ek p,+1 ek p,–----------------

1 dk dp⁄+( )2

1 ρkdk3+ ρpdp

3⁄( )-------------------------------------

1 εg–( )dp

-----------------Uk2+

=

+150µg

gc

-----1 εg–

εgϕpdp

---------------- 2 1

ρg

-----ρgUg

εgεkg

------------- 1.75+

1gc

----1 εg–

εgϕpdp

----------------- 1

ρg

-----ρgUg

εgεkg

------------- 2

Gk Hd Uk×=

Hs ρk⁄ 0.71 ReFr2( )0.45–

=

Hd ρk⁄ 82 Gk Gg⁄( ) dk dp⁄( )0.3 ReFr2( )0.9–

=

εkg Ht ρk⁄ 7.5 82 Gk Gg⁄( ) dk dp⁄( )0.3+ ReFr2( )0.9–

= =

Fr Ug εg⁄( ) gdp( )⁄ 0.5= Re dp= Ugρg εgµg⁄,

Fig. 2. Flow chart for the calculation of fines concentration in blast fur-nace.

39 1 2001 2

Finite Element Method 99

0.15 m ë2 LM* e +D ÅÆÇ5. WA ñ

QNj$ 1,200oC, bNj 1,515oC, KLH%I LÙ

50 mm! à2 ü ªWMË.

Q²8( ²pD I2 Ü-M* ²pD ²yM

²pD Dp yBM* Ù¦ H%I p

FMË. I ²pD 20 cm ²y5 wM* Lj

c2 ~M* c ,1 T¤yÀ 9:.

!c ÅÆÇd I H%I ?È2 ÌÍ·] Q² "#8 V

, O ( p$ H%I ûM e%¦

þ5 ³ &'I( g Vº?È H%I )S+ e% ²

pGS s. V,2 ) H%I KLH%I8 1( Lj$

~j8 m9m ¿. ÿ] ?È *ï +. &'I( e%

WG /y H%I Lj %9 H%I F8 y Ã

* s ,. Ù¦ H%ILj2 FM* 3 mm

My 10%$ G mÝ î2 Q²/¬ ~M* 2 V

, %j ~ MË.

3-2.

/ ?È2 #FM ( 2 839- ÜÝE 759

- vV yiMË, Ùl Ú Q²#8 ¨E e~#8(

¨ ÙlÚ M *8 ª8( JMË.

Fig. 3 = > Ú8( Ergun8 5 e JyÝ8(

jy3 l-2 9: s. op . eT%8( $I

*ï / , e%E V, ³?/ 08( $K $I 1

2 r s. 5 aõ, 348( $I j$ 5VM

²h YM s. !c $I j$ 1 68 y |JGî

7c -?i r s.

4.

4-1. !"#$ %& '( )* +, -

Fig. 4 xyU L¤ 86 g 144 kg/t-p8( e +D Lj

8J cyÀ 9: s. xyU L¤ 86 kg/t-p à &'

I(/8( Lj$ 25 mmM! H%I T8( 50%2 ÖmM

s. xyU L¤ 144 kg/t-p à 25 mm M H%I$

70% 86 kg/t-p à· Ã. 8 ,5 @!( 144 kg/t-p à

KL H%I LÙ 51.3 mm 86 kg/t-p à! 48.9 mm· 9¸

: ;8j <²M xyU L¤ 144 kg/t-p à Q²?8( 25 mm

M H%I$ Ã xyU L¤8 ( e H%I

W C H%I y8 uS( Q²?8( H%I Lj$ J

c d ·5 <$ s[1]. !c yd H%I xV xyU

E 4´ Q²8( 1.5-2 m mÝ8 ípG &'I(8 c G

oop ¦M* b 5V2 $¾N.

&'I(/y8( H%I c8 ,5 3 mm M y¤ 1

LG xyU Vp mÿ FGj M. Fig. 58 9:;

<= > y¤ 10%2 ü &'I( WÝ ²y5. ¶

Ð íÈ xyU L I2 FM Ùï 3 mmMy xyU

L¤ =$8 ( =$M ] TÐ I2 FM* T%8

xyU 7/8 V/2 M oxy-coal I Ùï \ xyU¤

LW 3 mmM y¤ Jc 9:>. 144 kg/t-p8( TÐ I

2 FM* xyU LM Ùï 3 mm M y¤ ¶Ð xyU

LI2 FM* xyU 86 kg/t-p LM Ùï rüE 1?

MË.

xyU L¤ g Ú8 V, u +8( y

j H%I ÅÆÇ oM* ! i r s. ÅÆÇd y dynanic

hold-upE static hold-up Õµ total hold-up¤ Ñ r s.

Fig. 48 ÅÆÇ WA ² wt%2 9: s. 10 mmM

WAT ,/y 3 mmM 2 r s.

+ uv L¡! H%I 10 mm? 10 mm? WA

Fig. 3. Calculated gas velocity distribution in furnace by 2D FEM.

Table 1. Operating conditions and raceway depth changes

PCR(kg/t-p)

Tf(oC)

Burning ratio(-)

Fines generation rate (kg/m2s)

Measured raceway depth(m)

186 2234 0.83 0.41 1.9197 2165 0.81 0.48 1.6130 2200 0.81 0.62 1.2124 2307 0.86 0.51 1.5144 2510 0.93 0.46 1.7186 2231 0.83 0.41 1.8

Fig. 4. Cumulative coke size distribution at tuyere level.(a) PCR: 86 kg/t-p and (b) PCR: 144 kg/t-p in blast furnace.

HWAHAK KONGHAK Vol. 39, No. 1, February, 2001

100

2 W Lj yîM* 9:S ·] k5 ñQ8@m8

( H%I b¯$ S9 ²h! 50-80 cm²h 25 mmM H%

I$ Ã Ñ r s ] H%I + WÝ A~G

80-100 cm y hold-up WÝ! 3 mmM % H%I yÀ

10%! mÝám Lj$ B 25 mm? H%I$ Ã 2

r s.

Table 1 *C8 DE( FS+ H%I ÅÆÇ ÂE/¬ FS+

xyU L¤ V, Nj= VÀ î V, %j2 9:

s. V, Nj Ùï oxy-coal Mm ¿ Ùï mr

T 5 V, Nj 9:. Oxy-coal M Ùï

oxy-coal¤ 1,000 Nm3/hrú 60oC Nj ?n s ²ÂE[14]

2 M* V, Nj2 A~MË. V, Nj/¬ xyU

VÀ A~ ×E > r s[15].

xyU VÀ =V,NjG0.03801−2.08 (16)

ª8( ~d V, Nj= &'I(8 ! y¤E

Ðl/¬ ²H. = 4´ 5 - Q²ú V,8( H%I x

yU yY¤ ×E > A~ ²MË. *( A1

ü 500 kg/t-p 0~MË.

yY¤(kg/m2/s) =

(17)

*( PCR: xyU L¤(kg/t-p)

*( η: VÀ(-)

*( cgas(PCRGη): xyUT $I¤(kg/t-p)

ICJ Ùï xyU L¤8 ( H%I yY¤ =$M

c GÏ A12 ü xyU L¤8 ( H%Iy l

GjK MË. !c Yd y T 1/3~j$ V, qL

GS &'I(8 $~MË. CJ xyUT

rV8 ( e solution loss 5V8 úM yY¤ 9

:[16]. LCJ xyU VÀ8 xyU ¡8( Y

G y¤ 9: s. 5 8 ¼b¤, W g Q²Mr2

:MÏ( yY q ²i r s. 2 Table 18 9:.

= > V,8( y Y¤ xyU VÀ8 ( xyU

¡ Nt 'O H%I y8 y Yj :i v$ s×

2 r s. 5 xyU VÀ g H%I yY¤8 e

8 y hold-up V, u H%I +8 På g QR

W c MÏ op8 x ·!.

4-2. ./ FEM$ 0 +, 1

Fig. 6 Table 18 9:; xyU L Ú ~d y |J W

G , V, %j= yY¤ Ðl2 9:; yY

¤ =$8 ( V, %j$ M Ù *ï S 4

2 r s.

Fig. 7 xyU 200 kg/t-p LW VÀ 60, 80, 90% à e8(

y|J?T 9:; . l[ Ú xyU Lj$

75µm, þj$ 1,000 kg/t-p! MË. VÀ =$8 ( Q

²³? 08( U 5%~j y|J¤ 5V$ sV. e%8

(j 1 m~j y|J & 5V$ sV. e h8( y

j$ ð 9: aD8 5 y[ WE2 :M

m X5 8 !5 d.

Fig. 8 y þj ¥8 e y |J ?T 9:; .

l[ Ú y Lj$ 0.5 mm, y Y¤ 0.88 kg/m2/sÙ

ï8 ,( lMË. y þj$ ¥M Ùï xyU ,Y y

B9 flux2 Li à. y þj=$8 ( e8( y

|J j$ %c =$Mm ¿9 Q² ³?/= e%8( y|J

²h %$ U ZSm Ù 9: s.

Fig. 9 xyU 150 kg/t-p LW VÀ 60% Ú8( xyU Lj

y |J ?È2 9: s. Ê Lj! 75µm8( 0.5 mm

Lj$ [m Ùï 08( j$ 10%? =$M 2 r

s. e%8( y |J &j 1 m? =$M 9:>.

¸ aõ,2 ( ³?/ /y8 y WM

2 r s. Lj$ 1 mm! xyU L\ Ùï Q²³?/8 y

j$ 25% ?! o<¤ ²h pGS 08( $I

¦i d. ( xyU Lj Ðî 8( $

K TvMc ÐîÎ i !¡! 2 r s.

Fig. 10 VÀ 60%, Lj 75µm xyU L1 150 kg/t-p8

( 300 kg/t-p =$W Ùï e8( y j y32 F M

Ë. xyU L¤ =$8 ( e08( U 3% j$ =$

MË9 e% ?È ¥8 1M* î %m ¿ô. e% Ùï y

500 cgas–( ) cgas500-----------× 1

3--- 2

30------ cgas PCR 1 η–( )×+×+×

8500 86400⁄ 34⁄ 0.3925⁄ ×

Fig. 5. Difference in −−−−3 mm size fraction with various PCR, lance con-figuration and oxygen enrichment at tuyere level.

Fig. 6. The change of raceway depth and amount of fines generatedwith PCR.

39 1 2001 2

Finite Element Method 101

on

$ %c ¥MË. y |J WÝ j Q² #

$á]H× 2 r s.

Fig. 11 þj, Lj, y L¤ 1`5 ( Lj

75µm, y Of¤ 0.66 kg/m2/s(xyU 150 kg/t-p2 ü VÀ

80%W yY¤8 ú), þj 1,000 kg/m32 ü 1` ÷øMË

. þj$ 7,000 kg/m3 ¥i Ùï e0/8( ¥$ ^9

e%8( y |J ²h %$ =$G 2 r s. Lj2

1 mm =,W Ùï e08( yj ¥= 4´ e%8( y

|J ?n mc 9:9 2 r s. yY¤

=$j Lj=$8 y |J¤ ¥ ~j8 xm XM9 ?

ú5 x 2 r s.

Fig. 12 ~d V, %j= 2Ö@ FEM ld V, %j

= Ðl2 9:; Ù *ï S M s× 2 r

s9 Ü,8( ?ú5 Ö2 9: s. 1.6 m348

( V, %j A~ 1`J ~M9 %j$ *ï _9 $ Ùï8

?ú5 Ö2 · s. rB 5 Q`2 9a

U 50 cm( V, u2 ~¸ #FM b8 U B

d. 5 :Mm XM* e%?È$

Fig. 8. Calculated 2-D fines accumulation diagram in BF.(a): at ρ=1,000 kg/m3, 0.5 mm size, FIR 0.88 kg/m2/s, η=60%, (b): atρ=3,500 kg/m3, and (c): at ρ=7,000 kg/m3(FIR: fine injection rate,η: PC combustion efficiency, ρ: fine density).

Fig. 9. Calculated 2-D fines accumulation diagram in BF.(a): at η=60%, 75µm size, PCR=150 kg/t-p, ρ=1,000 kg/m3, (b): at0.5 mm size, and (c): at 1 mm size(PCR: coal injection ratio, η: PCcombustion efficiency, ρ: fine density).

Fig. 10. Calculated 2-D fines accumulation diagram in BF.(a): at PCR=150 kg/t-p, 75µm size, η=60%, ρ=1,000 kg/m3, (b): atPCR=200 kg/t-p, and (c): at PCR=300 kg/t-p(PCR: coal injectiratio, η: PC combustion efficiency, ρ: fine density).

Fig. 7. Calculated 2-D fines accumulation diagram in BF.(a): at η=60%, 75µm size, PCR 200 kg/t-p, ρ=1,000 kg/m3, (b): atη=80%, and (c): at η=90%(PCR: coal injection ratio, η: PC com-bustion efficiency, ρ: fine density).

HWAHAK KONGHAK Vol. 39, No. 1, February, 2001

102

om-

9).

G9 -bG Ùï aD E y cJ¤ ?

:Mm XM* 8 y |J¤ ?n WE2 [,

Mm X5 8 !5 d.

5.

(1) +8( FEM8 $I g y3 #F= y j8 Ð

5 ªÁ ÂÕWd( y \ S #Fi r sV.

(2) xyU ¤ LW VÀ 20% 5VM · Lj$ 1 mm

=$M 8 y |J g j8 %c xc d.

(3) yY¤8 V, %j ¥ ªE r#F8 5 -

V, %j$ *ï %9 J Ùï2 [7M S M

Ë.

(4) yj$ & mh Q²³E e%( 20-30%2 9:

. aõ,= aõ, ³? 0/8( 10-20% y j2

9:.

di : diameter of i [m]

ek, p : repulsion factor [-]

Fr : Froude number [(Ug/eg)/(gdp)0.5]

Fi, j : interacted force between i and j [Kg/(m2s2)]

Gi : mass velocity of phase i [Kg/(m2s)]

gc : gravimetric conversion factor [1N/Kgf]

g : gravimetric force [m/s2]

Ht : total hold-up of powder [Kg/m3]

Hd : dynamic hold-up of powder [Kg/m3]

Hs : static hold-up of powder [Kg/m3]

P : pressure [Pa]

Rk : momentum through collision of powder [Kg/m3]

Re : Reynolds number [dpUgρg/εgµg]

Ui : velocity of i [m/s]

2345 67

β : correction factor of repulsion angle

εkg : voidage of powder

εg : voidage of packed bed

εk : volume fraction of powder in packed bed

ϕI : shape factor of powder

µi : viscosity of i [Kg/(ms)]

ρi : density of i [Kg/m3]

897

p : coke in blast furnace

g : gas

k : powder

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Fig. 11. Calculated 2-D fines accumulation diagram in BF.(a): at 75µm size, FIR 0.66 kg/m2s(η; 80%), ρ=1,000 kg/m3, (b):at ρ=7,000 kg/m3, (c): at 1 mm size, and (d): at FIR 0.88 kg/m2s(η;60%)(FIR: fine injection rate, η: PC combustion efficiency, ρ: finedensity).

Fig. 12. The measured and calculated raceway depth with PCR.

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