Finite Element Method

(1)

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 powder 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 e 8( $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

(2)

/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.

e 8( 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* e 8( 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, N_B2 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 û{M y ”

∇P

– =(f₁+f₂Gg)Gg

f₁ 150 1–ε_g ϕ_pd_p ---

 

  µ^g g_c --- 1

εg 3ρg

--- f₂ 1.751 g_c ---- 1–ε_g

εg 3ϕpd_pρg

---

 

 

 

, =

=

a₀=1 f⁄( ₁+f₂Gg)

∇P

– 1

a₀ ----Gg

=

∇⋅(–a₀∇P) ∇= ⋅Gg=0

Ggnew–Ggold≤

ψ

∇ – =G_s

∇⋅(–∇ψ) ∇= ⋅Gs=0

∫

W⋅^ra^z^∂_∂z---dΩ²^P2 +

∫

W⋅^a^r_∂r^{--- r}^∂^∂P^---_∂rdΩ=0

W C_AN_A

A=1

∑

n ,^P=_B

∑

ⁿ₌₁^N^B^d^B

=

∂N_A

--- a∂z _z ∂N_B ---∂z

B=1

∑

n ^d^B ^∂N---a_∂r^A _r ∂N_B ---∂r

B=1

∑

n ^d^B

⋅ + =0

A=1

∑

n

Fig. 1. Schematic diagram of a blast furnace.

(3)

~ M, + O½ü y J O½ù ε_kg, ý· þj 2 ρ_kM* y¤ Hk2 ÿÊM ×E > r s.

H_k= (1−ε_kg) ρ_k (6)

5± y T g $I= ? °'( £\M £\8 ,M* £\ M GS¾( ~??È8(

×E > íÐl2 9:æ r s.

(7)

*( F_k,g: $I= y ?

: y¤8 ?úM T

R_k: £\

u Äl8( WM ¢ uv! uM Ë. 2 y ¢8 sS( £\¤ ¥2 9: R_k

£\ ( ×E > r s.

(8)

*( β Y·~lr( 1/2 e_k,p Ylr( 0.9~j.

ρ_p, d_p L¡ þj g ³Ù, ε_g + 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%I 8( ~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 e 8( $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 F_{k g}_, H_kg

g_c ---=R_k –

H_kg g_c ---

R_k 1 g_c ----3β1 e+ _{k p}_,

1 e– _{k p}_,

---(1–ε_g)ρ_p(1–ε_kg)ρ_k(d_p+d_k)² ρ_pd_p³+ρ_kd_k³

---U_k²

=

∆P

---L =F_{p g}_, +F_{k g}_,

∆P

---L (1–ε_kg)ρ_k 1 1 g_c ----3

2---1 e+ _{k p}_, 1 e– _{k p}_,

--- (1 d+ _k⁄d_p)² 1+ρ_kd_k³⁄ρ_pd_p³

( )

---(1–ε_g) d_p ---U_k²

 + 

 

 

=

+150µ_g g_c --- 1–ε_g

ε_gϕ_pd_p ---

 

 ²1 ρ_g --- ρ_gU_g

ε_gε_kg ---

 

 +1.751 g_c ---- 1–ε_g

ε_gϕ_pd_p ---

 

 1

ρ_g --- ρ_gU_g

ε_gε_kg ---

 

 ²

G_k=H_d×U_k

H_s⁄ρ_k=0.71 ReFr( ²)^–^0.45

H_d⁄ρ_k=82 G( _k⁄G_g)(d_k⁄d_p)^0.3(ReFr²)^–^0.9

ε_kg=H_t⁄ρ_k={7.5+82 G( _k⁄G_g)(d_k⁄d_p)^0.3}(ReFr²)^–^0.9

Fr=(U_g⁄ε_g)⁄(gd_p)^0.5, Re= d_pU_gρ_g⁄ε_gµ_g

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

(4)

0.15 m ë2 LM* e +D ÅÆÇ5. WA ñ QNj$ 1,200^oC, bNj 1,515^oC, 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 û{M 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 1.9

197 2165 0.81 0.48 1.6

130 2200 0.81 0.62 1.2

124 2307 0.86 0.51 1.5

144 2510 0.93 0.46 1.7

186 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.

(5)

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 60^oC 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 e 8(

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 ( e 8( 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 e 8( 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–

( ) cgas

---500

× 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 generated with PCR.

(6)

$ %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): at ρ=3,500 kg/m³, and (c): at ρ=7,000 kg/m³(FIR: fine injection rate, η: PC combustion efficiency, ρ: fine density).

(a): at η=60%, 75µm size, PCR=150 kg/t-p, ρ=1,000 kg/m³, (b): at 0.5 mm size, and (c): at 1 mm size(PCR: coal injection ratio, η: PC combustion efficiency, ρ: fine density).

(a): at PCR=150 kg/t-p, 75µm size, η=60%, ρ=1,000 kg/m³, (b): at PCR=200 kg/t-p, and (c): at PCR=300 kg/t-p(PCR: coal injection ratio, η: PC combustion efficiency, ρ: fine density).

(a): at η=60%, 75µm size, PCR 200 kg/t-p, ρ=1,000 kg/m³, (b): at η=80%, and (c): at η=90%(PCR: coal injection ratio, η: PC combustion efficiency, ρ: fine density).

(7)

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:.

d_i : diameter of i [m]

e_{k, p} : repulsion factor [-]

Fr : Froude number [(U_g/e_g)/(gd_p)^0.5]

F_{i, j} : interacted force between i and j [Kg/(m²s²)]

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

g_c : gravimetric conversion factor [1N/Kg_f] g : gravimetric force [m/s²]

H_t : total hold-up of powder [Kg/m³] H_d : dynamic hold-up of powder [Kg/m³] H_s : static hold-up of powder [Kg/m³] P : pressure [Pa]

R_k : momentum through collision of powder [Kg/m³] Re : Reynolds number [d_pU_gρ_g/ε_gµ_g]

U_i : velocity of i [m/s]

2345 67

β : correction factor of repulsion angle ε_kg : voidage of powder

εg : voidage of packed bed

ε_k : volume fraction of powder in packed bed ϕ_I : shape factor of powder

µ_i : viscosity of i [Kg/(ms)]

ρ_i : density of i [Kg/m³]

897

p : coke in blast furnace

g : gas

k : powder

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(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: fine density).

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

Finite Element Method  