Aod Modelling

8/18/2019 Aod Modelling

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Journal of Shanghai University Eng lish Ed ition ), 2 0 0 2 , 6 ( 1 ) : 1 - 2 3

A r t i c l e I D 1 0 0 7 -6 4 1 7 (2 0 0 2 )0 1 -0 0 0 1 -2 3

P h y s ic a l a n d M a t h e m a t i ca l M o d e l i n g o f t h e A r g o n O x y g e n D e c a r b u r i z a ti o n

R e f i n i n g P r o c e s s o f S t a i n l e s s S t e e l

W E I J i - H e @ ~ @ )

School of Materials Science and Engineering, Shanghai University, Shanghai 200072 , China

A b s t ra c t T h e a v a i l a b le s tu d ie s in th e l i t e r a tu re o n p h y s ic a l a n d m a th e m a t i c a l m o d e l in g o f th e a rg o n -o x y g e n d e c a rb u r i z a t io n (A O D )

p ro c e s s o f st a in l e s s s t e e l h a v e b r i e f ly b e e n r e v ie w e d . T h e l a t e s t a d v a n c e s m a d e b y th e a u th o r w i th h i s r e s e a rc h g ro u p h a v e b e e n s u m -

mar ized . W ate r mode l ing was used to inves t iga t e the f lu id f low and mix ing char ac te r is t ic s in the ba th o f an 18 t AOD vesse l , a s we l l a s

th e b a c k -a t t a c k a c t io n o f g as j e t s a n d i t s e f fe c t s o n th e e ro s io n a n d w e a r o f t h e r e f r a c to ry l i n in g , w i th s u f f i c i e n t ly fu l l k in e m a t i c sim -

i l a r i ty . T h e n o n - ro ta t in g a n d ro t a t in g g a s j e t s b lo w n th ro u g h tw o a n n u la r t u y e re s , r e s p e c t iv e ly o f s t r a ig h t - tu b e a n d s p i r a l - f la t t u b e

ty p e , w e re e m p lo y e d in th e e x p e r im e n t s . T h e g e o m e t r i c s im i l a r i ty r a t io b e tw e e n th e m o d e l an d i t s p ro to ty p e ( in c lu d in g th e s t r a ig h t -

tu b e ty p e tu y e re s ) w a s 1 :3 . T h e in f lu e n c es o f t h e g a s f lo w ra t e , t h e a n g le in c lud e d b e tw e e n th e tw o tu y e re s a nd o th e r o p e ra t in g p a -

ra m e te r s , a n d th e s u i t a b i l i t y o f t h e s p i r a l t u y e re a s a p ra c t i c al a p p l i c a t io n , w e re e x a m in e d . T h e s e l a t e s t s tu d ie s h a v e c l e a r ly a n d s u c -

c e s s fu l ly b ro u g h t t o l i g h t t h e f lu id f lo w a n d m ix in g c h a ra c te r i s t i c s i n th e b a th a n d th e o v e ra l l f e a tu re s o f t h e b a c k -a t t a c k p he n o m e n a o f

g a s j e t s d u r in g th e b lo w in g , a n d h a y e o f fe re d a b e t t e r u n d e r s t a n d in g o f th e r e f in in g p ro c e s s . B e s id e s , m a th e m a t i c a l m o d e l in g fo r t h e

re f in in g p ro c e s s o f s t a in l e s s st e e l w a s c a r r i e d o u t a n d a n e w m a th e m a t i c a l m o d e l o f t h e p ro c e s s w a s p ro p o s e d a n d d e v e lo p e d . T h e m o d -

e l p e r fo rm s th e r a t e c a l c u la t io n s o f t h e r e f in in g a n d th e m a s s a n d h e a t b a l a n c es o f t h e s y s t e m . A l s o , t h e e f f e c t s o f t h e o p e ra t in g f a c -

to r s , i n c lu d in g a d d in g th e s l ag m a te r i a l s , c ro p e n d s , a n d s c ra p , a n d a l lo y a g e n t s ; t h e n o n - i s o th e rm a l c o n d i tio n s ; t h e c h a n g e s in th e

a m o u n t s o f m e ta l a n d s l a g d u r in g th e r e f in in g ; a n d o th e r f a c to r s w e re a l l c o n sid e re d . T h e m o d e l w a s u se d to d e al w i th a n d a n a ly z e th e

a u s t e n i t i c s t a in l e s s s t e e l m a k in g ( in c lu d in g u l t r a - lo w c a rb o n s t e e l ) a n d w a s t e s t e d o n d a ta o f 32 h e a t s o b ta in e d in p ro d u c in g 30 4 g ra d e

s t e e l i n a n 1 8 t A O D v e s s el . T h e c h a n g e s in th e b a th c o m p o s i t io n a n d t e m p e ra tu re d u r in g th e r e f in in g p ro c e s s w i th t im e c a n b e a c c u -

ra t e ly p re d ic t e d u s in g th i s m o d e l . T h e m o d e l c a n p ro v id e s o m e v e ry u s e fu l i n fo rm a t io n a n d a r e l i a b le ba s i s fo r o p t im iz in g th e p ro c e s s

p ra c t i c e o f t h e r e f in in g o f s t a in l e s s s t e e l a n d c o n t ro l o f t h e p ro c e s s in r e a l - t im e a n d o n l in e .

K e y w o rd s s t a in l e s s s t e e l , a rg o n -o x y g e n d e c a rb u r i z a t io n (A O D ) p ro c e s s , f l u id f lo w a n d m ix in g , b a c k -a t t a c k p h e n o m e n o n , n o n - ro ta t -

in g a n d ro t a t in g g a s j e t s , d e c a rb u r i z a t io n , w a te r m o d e l in g , m a th e m a t i c a l m o d e l in g .

1 Introduction

C o m p a r e d t o t h e o t h e r r e f i n i n g p r o c e s s e s o f s t a i n -

l e ss s t e e l , t h e a r g o n - o x y g e n d e c a r b u r iz a t i o n ( A O D )

p r o c e s s h a s a n u m b e r o f o b v i o u s a d v a n t a g e s . S i n c e t h e

f i r s t A O D v e s s e l w a s c o m p l e t e d a n d p u t i n t o o p e r a t i o n

i n 1 9 6 8 , t h i s s e c o n d a r y s t e e l m a k i n g t e c h n o l o g y h a s

b e e n a p p l ie d e x t e n s i v e l y a n d d e v e l o p e d r a p i d l y

t h r o u g h o u t t h e w o r l d . I t n o t o n l y h a s b e c o m e t h e

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

h i g h c h r o m i u m a l l o y s , b u t i t c a n a ls o b e u s e d t o m a k e

a l m o s t a l l s t e e l s . A t p r e s e n t , o v e r 7 5 % o f t h e

Rece ived Nov . 22 , 2001

P ro je c t s u p p o r t e d b y th e N a t io n a l N a tu ra l S c ie n c e F o u n d a t io n o f

China (59474016)

W E I J i - H e , P h . D . , P r o f . , E - m a i l : j i h e w @ e a s t d a y , c o m

w o r l d ' s s t a i n l e s s s t e e l o u t p u t a r e p r o d u c e d u s i n g t h i s

p r o c e s s .

I n t h i s r e f i n i n g p r o c e s s , s e v e r a l a n n u l a r t u b e t y p e

t u y e r e s a r e u s u a l l y u s e d t o c a r r y o u t h o r i z o n t a l s i d e

b l o w i n g a n d i n j e c t i o n . T h e m o t i o n o f th e f l u i d s i n t h e

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

t h e h e a t a n d m a s s t r a n s f e r , a n d i s v e r y a d v a n t a g e o u s

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

t h e h o m o g e n e i t y o f b a t h c o m p o s i t io n a n d t e m p e r a -

t u r e . O n t h e o t h e r h a n d , a s a n i m p o r t a n t a p p l i c a t i o n

o f t h e s u b m e r g e d g a s i n j e c t io n t e c h n i q u e , t h e m o s t

s e r i o u s s h o r t c o m i n g o f t h e A O D p r o c e s s i s t h e s h o r t

l i fe o f t h e r e f r a c t o r y l i n i n g . A n o b v i o u s f e a t u r e i s th e

n o n - u n i f o r m w e a r a n d e r o s i o n o f t h e l in i n g . I t is

c l o s e l y r e l a t e d t o t h e g a s b l o w i n g c o n d i t i o n s a n d t h e

f l u id m o t i o n p a t t e r n s i n t h e b a t h . T h e b a c k - a t t a c k

a c t i o n o f g as j e t s , w h i c h o c c u r s a l l in t h e m e t a l l u r g i c a l

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


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Journal of Shanghai University

ferred to as an important factor in bringing about this

situation. Invest igating and obtaining a clear under-

standing of fluid flow phenomena and mixing charac-

teristics as well as back-attack action during the AOD

process, mathematically modeling this process will

contribute towards the improvement and optimization

of the installation design and blowing technology, and

computer control of the process in real-time and on-

line.

The fluid flow and mixing in the AOD vessels with

different capacities have been investigated by some

resea rcher s using water modeling [1-4]. Thes e studies,

to different extents, provided some useful information

for understand ing the practical process. In all previ-

ous studies of this type, however, a tube tuyere has

been used to model an annular tube tuyere, and multi-

tuyere blowing has been replaced with single tuyere

blowing [2-4]. Mor eover, the gas blowing rates used

for the model units have not been adequately deter-

mined. Thus, kinematic similarity between the model

and its prototype has not been fully maintained.

To improve the state of the gas jet at the tuyere

outlet and the fluid flow pattern, and thus to suppress

and eliminate the back- atta ck action of gas jets and

alleviate the erosion to the lining, many studies have

been conducted, e. g- Ref. [5 - 19]. Some schemes,

e. 9. , those that altered the circular pipe tuyer e into

flattened types with dif fere nt flatness values [~' 6.9]

and spiral types with differ ent s truct ures [7] , reduced

the width of the annular slit (the subtuyere) as was

p o s s i b l e [ 7 91, have been evaluated. The results avail-

able now showed that raising the blowing pressure,

using the flat-, micro-hole assembling- or spiral-type

tuyere, reducing the width of the annular slit (the

subtuyere) of an annular tube tuyere and others may

all decrease the back-attack frequency, to different

extent s. The state of a gas jet at the out let of an an-

nular tube tuyere could markedly be changed to a

forced rotating motion when the tuyere was altered to

one with a spiral s tru ctu re (71 . Under a certai n blowing

condition, the rotating motion of the jet could effec-

tively decrease the mechanical erosion of the ref racto-

ry lining by the fluid flow. Howeve r, the fluid flow

and mixing phenomena in an AOD bath with rotating

gas jets have not been studied. Moreo ver, there

would indeed be quite a few something in common for

the r elevant back-attack behaviors of gas jets in differ-

ent submerged gas blowing processes. As a result of

differ ent gas blowing directions , howeve r, the corre-

sponding gas jets must have different behaviors and

features, and there will also be some differences be-

tween their back-attack action. Fur the rmo re, all the

previous investigations also have not made stricter

calculations for the gas outlet parameters of the

tuyere; the sites taken for measuring the back-attack

pressure have mostly been positioned inside the

tuyere. Therefore, that cannot necessarily bring to

light the overall situation of the back-attack phe-

nomenon.

With respect to mathematical modeling for the AOD

process, numerous models have been proposed and de-

veloped to attempt to accomplish optimization and

computer control of the process. Some of them are

based on mass and hea t balances E2°2S3, and some of

them are in t erm s of the process k inet ics [26-28J and the

the rmodynamics with mass balance C291. A real -time

online control model for the refining process has also

been developed and applied E3°1. Thes e studies, to dif-

ferent extents, also offered some useful information

for understanding and improving the process practice.

Howev er, all these available models for the refining of

stainless steel have not reflected and described fully

the real situations of the process and, to a certain de-

gree , have all this or that shortcomings. Using these

models, in fact, it is difficult to predict quantitatively

and accurately the changes in the chemical composi-

tion and temperature of the bath during the practical

process and the influence of the relevant factors, as

well as their interactions.

Therefore, it is still needed, and is of important

theoretical and practical meaning, to study furth er

and more deeply this process. Considering these situa-

tions, the AOD refining of stainless s teel was investi-

gated by the author with his research group in recent

years, taking the process in an 18 t vessel for exam-

ple. The latest studies and advances made on physical

and mathematical modeling of the refining process are

summarized as follows.

2 P h y s i c a l M o d e l i n g o f t h e A O D

Process [31 3~3

2 1 S i m i l a r i ty c o n d i t i o n s a n d d e t e r m i n a t i o n o f

gas blowing r a t e f o r m o d e l

In the AOD process, the gas is horizontal ly blown


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Vol. 6 No. 1 Mar.2002 WEI J.H. • Physical and Mathematical Modeling of the Argon-Oxygen Decarburization .. . 3

into the bath from the side wall near the bottom of the

vessel, through several tuyeres ( 46 ) . The motion of

the liquid outside the gas-liquid two-phase flow in this

syst em is gas driven. The motion of the liquid outside

the gas-liquid two-phase flow will be due to gas agita-

tion and be independent of the turbulent and viscous

force characterized by the Reynolds number. The

buoyancy, inertial force and gravity will mainly gov-

ern the motion of the gas side blowing streams.

Therefore, the modified Froude number

F r

could al-

so be chosen as a decisive dimensionless number for

this system:

= pa ug ~p g~ (1)

F r p ~ - p ~ g d p i g d

where ug is the veloci ty of gas, m. s 1 ; [)~j ind ,,~ are,

respectively, the density of the gas and the liquid, kg

• m-a ; g is the acceleration due to gravity, m' s- 2; d

is the characteristic dimension of the syst em, m. To

maintain the kinematic similarity of the fluids in the

prototyp e and its model, accordingly, their modified

Froude numbers need to be kept equal, besides main-

taining their geometric similarity. Taking d to be the

tuyer e diamete r, the following relationship can be de-

rived from (

F r ) , , = ( F r ) p :

P f I O p ~ g l m ) 1 / 2 P r i m ) 1 / 2

d . , ) 5 /2

Q m = Q p ( p ~ o ) ~ p i p p a p ~ ( 2 )

where subscripts m and p indicate respectively the

model and its prototype; Q is the volume flow rate of

gas at the standard sta te, Nm 3 h- 1 ; pg0 is the density

of the gas used at the standard state, kg Nm-3 ; and

pg is the density of the gas at the tuyere outlet.

Obviously, for a given original and model system,

the gas densities at the tuyere outlets both for the

model and the vessel, Pgm and p g p , are the two key

parameters, and they are closely related to the gas

flow properti es in a tuyere. In order to ensure that

the kinematic similarity between the model and its

prototy pe was as high as possible, the corresponding

values were determined on the basis of theoretical cal-

culations of the parameters of the gas streams in the

tuyeres. During calculation it was assumed that the

gas streams in the tuyere used for the water modeling

would all be adiabatic friction flows. The correspond-

ing flows in the tuyere used for practical refining were

treated as heating friction processes since they all

have a marked heating friction f eatu re [36391. In addi-

tion, the gases would be heated by the molten steel

and expand after enter ing the bath. Correspondingly,

their densities would be reduced. An appropr iate re-

sponse would be to increase the gas blowing rates for

the model. This is true principally for the gas stream

of the main tuy ere. The results of theoretical calcula-

tions and estimation of the heat transfer between the

gas jet and the liquid steel in the AOD vessel showed

that the outlet temperature of the subtuyere gas

stream would have reached or slightly exceeded the

average value of the gas in the bath.

Another factor that needs to be considered is CO

formation during refining. The averag e utilization ra-

tio of 02 is about 40%-50% for the AOD refining of

austen itic stainless steel [4°7. This means t hat the gas

flow rate of the main tuyere for the model should be

further raised to simulate the practical effect. All of

these considerations would improve markedly the

kinematic similarity of fluid flows between the model

and its prototype.

For the blowing refining of austenitic stainless

steel in an AOD vessel of 18 t capacity, the gases used

for the main tuyere and subtuyere are, respectively,

mixed 02 : N2 gas (4 : 1 ) and N2 in the initial (f ir st )

stage of the refining; and mixed 02: Ar gas (3:2) and

Ar in the second (middle) period of the refining . With

a geometric similarity ratio of the model to its proto-

type (including the straight tube tuyeres) of 1:3, and

with modeling of the various gases used for refining

with air, calculations for the initial and middle stages

of blowing were conducted under conditions of heating

friction flow of the gases in a practical tuye re. As far

as the values of Q,~ are concerned, the calculated re-

sults showed that the difference for the two blowing

stages was not too large. The calculated results for

the middle period of blowing (not including the effect

of CO formation on the value of Q,~) with some relat-

ed parameters are presented in Table 1.


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Table 1 G a s b l o w i n g r a t e s u s e d f o r 1 8 t A O D v e s s e l a n d i t s m o d e l i n m i d d l e b l o w i n g s t a g e a n d v a l u e s o f r e l a t e d p a r a m e t e r s

1 8 t A O D v e s s e l M o d e l ( 1 : 3 )

P a r a m e t e r M a i n t u y e r e S u b t u y e r e M a i n t u y e r e ( * ) S u b t u y e r e

1 2

G a s b l o w in g r a t e ( Q ) , N m 3 h i 500 x 2 100 x 2 7.9 1 x 2

p~0 , kg Nm - 3 1 . 4392 + 1 . 6343 + 1 .184 4 +

p g , k g ' m 3 4 . 2 4 3 0 1 . 2 6 11 1 . 2 8 8 2

L iqu id m a s s in ba th ( M~ ) , t 18 .0 0

pL, kg- m - 3 7370 #

L iq u id l e v el h e i g h t i n b a t h ( H ) , m 1 . 1 0

D e p t h o f t u y e r e ( H z ) , m 0 . 9 5

Ga s in le t p re s s u re (P z ) , MPa 1 . 3272 1 . 3996 0 . 1671

Gas

o u t l e t p r e s s u r e ( P z ) , M P a 0 . 4 9 9 6 0 . 2 7 4 6 0 . 1 0 31

G a s i n l et t e m p e r a tu r e ( T 1 ) , K 3 2 3 . 0 3 2 3 . 0 2 9 8 . 0 0

G a s o u t l e t t e m p e r a t u r e ( T 2 ) , K 5 2 6 . 4 0 1 0 5 2 . 1 0 2 8 5 . 2 1

F r c a l cu l a te d f r o m g a s b l o w i n g r a t e 8 4 8 . 4 4 7 3 5 . 0 0 8 4 8 . 4 2

G a s o u t l e t v e l o c it y c a lc u l at e d f r o m F r ( u g ) , m s - l 4 1 6 . 5 2 6 0 5 . 5 0 1 6 0 . 7 6

G a s o u t l e t v e l o c it y c a l cu l a te d t h e o r e t ic a l l y ( u g ' ) , m s - z 4 1 6 . 2 0 6 0 4 . 4 2 1 6 0 . 1 3

1 1 . 3 2 x 2 3 . 6 2 5 x 2

1 . 1 8 4 4 + 1 . 1 8 4 4 +

1 . 2 6 4 5

0 . 1 1 3 2

1000 +

0 . 3 7

0 . 3 2

0 . 2 1 4 2

0 . 1 0 3 1

2 9 8 . 0 0

2 9 0 . 0 0

7 3 5 . 0 0

1 2 8 . 6 0

1 2 8 . 0 0

* 1 a n d 2 a r e , r e s p e c t i v e l y , f o r t h e c a s e s w h e r e h e a t e x p a n s io n o f m a in t u y e r e g a s a f t e r e n t r y i n t o b a th o f A O D v e s s e l w a s n o t a n d w a s c o n s i d e re d .

+ Re f . [36 - 38] ; ~ : Re f . [41 ] .

2 . 2 E x p e r i m e n t a l c o n d i t i o n s

Manometer 14

m e t e r ~

V a l v e ~

~740

- ,

| A n n u l a rerel

Cumpresse~ a i r , ,~ with s tra ight- I

. ~ ~ tube or spiral- I

t~uner fiat main tuyerd

/

1

AOD model

Pressure sensor

I ~467 P I

Dynamic resista-I [ l,ight-beam

nee strain-mater ~ oscilloscope

YD-2t type) [ I SCl6Atype)

a)

T

o 10~ 10 ~10°' 10 o

10°10 I ~ ~'10

1 0 . 1 ~ 0 ' 10~Vl0

5:3:

b)

F i g . 1

i t s t u y e r e p o si t io n a r r a n g e m e n t ( b )

Fig. 1 a) is a schematic diagram showing the di-

mensions of the model apparatus of an 18 t AOD vessel

that was used for the experiments. Seventeen tuye re

positions were fixed on its side wall, and the maxi-

mum angular separation of two tuyeres being 150 °, as

shown in Fig. 1 b) . The inner tube of the tuyere

S c h e m a t i c d i a g r am o f m o d e l a p p a r a t u s o f 1 8 - t A O D v e s s e l u s e d f o r w a t e r m o d e l i n g e x p e r i m e n t ( a ) a n d

used for the model was made of brass; the outer tube

of the tuyere was a circular pipe made of red copper.

The structure and cross-section of the straight tube

tuyere are presented in Fig. 2 a) and b), respective-

ly.


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Vol. 6 No. 1 Mar. 2002 WEI J. H. : Physical and Mathematical Modeling of the Argon-Oxygen Decarburization .. . 5

I q 290

~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t ° - -

1., 326 -1

D l =

D =8

(a)

~ _ 4

Fig 2

(b) (c)

Structu re (a) and cross-sections with dimensions of straight tube tuyere (b ) and (main tu yere ) spiral-flat tuy ere (c)

used for the model of 18-t AOD vessel

A n a n n u l a r s p i r a l - f l a t t u y e r e o f i n s e r t i n g a s p i r a l

f l a t i n to t h e c e n t r a l t u b e ( t h e m a i n t u y e r e ) w a s e m -

p l o y e d t o o b t a in a r o t a t i n g g a s j e t . A c r o s s - s e c t i o n

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

F i g . 2 ( c ) ; t h e r e l e v a n t p i tc h w a s 4 6 . 5 7 m m . I t h a s a

b e t t e r g a s b l o w i n g p e r f o r m a n c e [ 3z ' 33l

T h e m i x i n g t i m e i n t h e b a th ( r m ) , w h i c h w a s d e -

f i n e d a s r 0 . 9 5 , w a s m e a s u r e d b y t h e e l e c t r i c a l c o n d u c -

t i v i t y m e t h o d . A s a t u r a t e d K C1 s o l u t i o n w a s a d d e d t o

t h e l i q u i d s u r f a c e n e a r t h e w a l l a b o v e t h e s e c t o r z o n e

b e t w e e n t h e t w o t u y e r e s . F o r e a c h e x p e r i m e n t a l p o in t

a t e ac h o p e r at i n g m o d e , t h e m e a s u r e m e n t w a s r e p e a t -

e d a t le a s t 5 - 6 t i m e s , a n d t h e n a n a r i t h m e t i c a l m e a n

v a l u e o f t h e r e s u l t s o b t a in e d w a s t a k e n . P o l y s t y r e n e

p a r t i c le s o f 1 m m d i a m e t e r a n d 0 . 9 7 g c m - 3 d e n s i t y

w e r e u s e d as a t r a c e r ; a n S L V - 2 0 a d j u s ta b l e la s e r

g e n e r a t o r w i t h f r e q u e n c y s c a n n i n g p r o v i d e d a l as e r

s l i t l i g h t so u r c e .

T h e b a c k - a t ta c k f r e q u e n c y a n d i n t e n s i t y o f a g a s j e t

w e r e c o n t i n u o u s l y d e t e c t e d a n d m o n i t o r e d u s i n g a n

a n t i - w a t e r p r e s s u r e s e n s o r m a d e s p e c ia l ly . T h e s i te o f

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

j u s t c l o se t o t h e t u y e r e o u t l e t ( F i g . l a ) . T h e r e f r a c -

t o r y l in i n g w a s m o d e l e d w i t h b o r i c ac i d c a s t - p l a t e o f

1 0 0 x 1 0 0 × 1 0 m m f o r t h e e x p e r i m e n t o f t h e r e f r a c -

t o r y l i n i n g e r o s i o n a n d w e a r .

T h e i n f l u e n c e s o f th e g a s b l ow i n g r a t e , t h e a n g u l a r

s e p a r a t i o n o f th e t w o t u y e r e s a n d t h e t y p e o f t u y e r e

o n t h e s t i r r in g a n d f lo w c o n d i t io n s , t h e m i x i n g t i m e ,

t h e s ta b i l i t y o f t h e b l o w i n g p r o c e s s , t h e b a c k - a t t a c k

a c t i o n a n d t h e e r o s i o n a n d w e a r o f t h e l i n i n g w e r e e x -

a m i n e d . F o r c o m p a r i s o n w i t h t h e p r a c ti c a l p r o c e s s a n d

t h e r e a l t u y e r e u s e d , t h e v a l u es o f Qm f o r t h r e e o t h e r

c a s e s w e r e a l so d e t e r m i n e d . T h e s e w e r e a s s u m e d t o

c o r r e s p o n d r e s p e c t i v e l y t o a d i a b a t i c f r i c t i o n f l o w o f

t h e g a s i n t h e t u y e r e , t o a d i a b a t ic f r i c t i o n f l o w o f t h e

g a s i n t h e t u y e r e w i t h g a s h e a t i n g e x p a n s i o n , a n d t o

a d i a b a t ic f r i c t i o n f lo w o f t h e g a s in t h e t u y e r e w i t h g a s

h e a t i n g e x p a n s i o n a n d t h e f o r m a t i o n o f C O . T h e o p e r -

a t i n g m o d e s u s e d a r e s h o w n i n T a b l e 2 .


6/23


Table 2 All operat ing modes examin ed

Assumed condition of gas s tream in AOD tuyere ~'~

Total gas blowing rate for two tuyere s. Nm3 h -t

Q.,l(formain tuyeres)

Q.~2(for su btuyer es)

I II III IV V

1 1+3 1+3+ 4 2 2+3

12.94 20.12 25.34 15.82 22.64

3.97 6.026 6.026 6.53 6.53

Blowing pressur e of main tuye re/ subt uyere + A B C D E

(gauge value), MPa 0.066/0.07 0.135/0.125 0.185/0.125 0.09/0.137 0.16/0.137

No. 1 2 3 4+ 5+ 6+ 7 8 9

Angle included between the two tuy ere s, 0, °( ') 0 20 40 60 80 100 115 130 150

1-adiabatic friction flow; 2- heating friction flow; 3-considering gas heating expansion; 4- considering formation of CO.

~ 0 ° corresponds to single tuyere blowing.

+ for rotating gas jet and study of back-attack action

Corresponding to the blowing pressures of A- E in

Table 2, the gas blowing rates of the spiral-flat type

tuyer e were , respec tively, the values of I - V. For

the erosion and wear experiments of the refractory

lining, the pressures used for the two types of tuyer es

were all taken to be the value of E. In this case, the

gas blowing rate of the main-tuyere of the straight-

tube type tuyere was relevantly 27.58 Nm~ h-1

2 . 3 h e f e a t u r e s o f gas st irring a n d l i q u i d flow

i n t h e b a t h

It can be seen from the experimental process that

the gas blown horizontally into the bath through an

annular tube type tuyere from the side wall near the

bottom of the vessel , was in the form of a jet and

formed a few very large bubbles near the tuyere out-

let. Under the combined action of the inertial force

and the buoyancy, the gas jet gradually acquired an

upward motion after penetrating a certain distance a-

long the horizontal direction in the bath liquid. At the

same time, the liquid around it was continuously

sucked in, a gas-liquid two-phase flow was formed,

and a great quantity of small bubbles was generated.

Also, the cross-sectional area of the two-phase stream

was gradually enlarged . At the liquid surface of the

bath, the gas inside the two-phase str eam escaped into

the gaseous phase. Simultaneously, the kinetic ener-

gy of the liquid was changed into potential energy,

thus leading to the liquid surface level at the center of

the two-phase zone being higher than the surface level

around the zone. This pa rt of the liquid had downward

motion owing to the force of gravity and flowed to-

wards the peripheral wall of the vessel along the radial

direction. This brought about fluctuating motion of

the entire liquid surface of the bath and formed a sta-

tionary wave under the obstruction of the wall. The n,

this part of the liquid had downward motion along the

side wall. During this process , it was again drawn in-

to the two-phase stre am, forming vortexes and eddies

of varyi ng sizes. In the process of gas escape, a con-

siderable part of the gas was also drawn into the bath

by the falling liquid and again turned into small bub-

bles by interaction of the gas jet with the liquid

stream. These bubbles flowed with the liquid stream

and floated up and escaped again during circulatory

motion. From beginning to end, the liquid of the bath

underwent very active stirring and circulatory motion

during blowing. Th er e was no obvious dead zone any-

wher e in the bath. An increase in the gas flow rate in-

tensified the gas agitation, but did not alter these

kinds of feat ures of the liquid flow in the bath. Corre-

spondingly, the fluctuation and wave motion of the

bath surface were aggravated and its stability was re-

duced.

The influence of the angle included between the

two tuyeres on features of gas stirring and liquid flow

in the bath was very marked and may even govern the

stability of blowing refining, particularly with a larger

gas flow rate. When the angular separation between

the two t uye res was below 40 °, the two gas streams

inters ected and merge d, with their interacti on in-

creasing as they rose in the bath. This made the bath

liquid surface more dynamic. The smaller the angular

separation, the more serious this situation became.

When the angle included between the two tuyeres was

beyond 115 ° , the two gas str eams even tual ly collided


7/23

Vol. 6 No. 1 Mar. 2002 WEI J. H. • Physical and Mathematical Modeling of the Argon-Oxygen Decarburization .. . 7

h e a d o n w i t h i n c r e a s e i n t h e a n g l e . T h i s a ls o r e s u l t s

i n l o w e r s t a b i l i ty o f t h e b a t h l i q u i d s u r f a c e . W i t h a g a s

b l o w in g r a t e c o r r e s p o n d i n g t o I I I in T a b l e 2 , a t a n g u -

l a r s e p a r a ti o n s o f 2 0 ° an d ~ 1 3 0 ° t h e r e w e r e v i o l e n t

o sc i l l a t i o n a n d sp l a sh i n g o f t h e l i q u i d a t t h e b a t h su r -

f a c e. T h i s n o t o n l y m a k e s t h e b l o w i n g p r o c e s s d i f fi -

c u l t t o s t a b i l i z e b u t a l s o g r e a t l y i n t e n s i f i e s e r o s i o n o f

t h e r e f r a c t o r y w a l l b y t h e f l u i d s . W i t h a l l th e g a s

b l o w i n g r a t e s u s e d , a t a n g u l a r s e p a r a t i o n s o f 6 0 ° -

1 0 0 ° , t h e l iq u i d s u r f a c e s o f t h e b a t h r e m a i n e d r e l a -

t i v e l y s m o o t h a n d s t e a d y . A s f a r a s t h e s t a b i l i t y o f t h e

b l o w i n g p r o c e s s i s c o n c e r n e d , i t i s i n e x p e d i e n t f o r t h e

a n g l e i n c lu d e d b e t w e e n t h e t w o t u y e r e s t o b e e x c e s -

s i v e l y l a r g e o r s m a l l .

W h e n a s p i r al a n n u l a r t u b e t u y e r e w a s u s e d , t h e

g a s j e t w a s o b v i o u s l y r o t a t i n g n e a r t h e t u y e r e o u t l e t.

T h e d i s c h a r g e a n g l e o f t h e j e t a t t h e t u y e r e o u t l e t d id

n o t n o t i c e a b l y e n l a r g e . I t s r o ta t i n g v e l o c i t y d e c r e a s e d

c o n s i d e r a b l y w i th d i s t a n c e f r o m t h e t u y e r e o u t l e t .

H o w e v e r , b e c a u s e o f i n e r ti a l f o r c e , t h e a s ce n d i n g

g a s - l iq u i d t w o - p h a s e f l o w a n d t h e l i q u id a r o u n d i t c o n -

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

T h e c r o s s - s e c t i o n a l a r e a o f t h e t w o - p h a s e f l o w w a s

s l i g h t l y l a r g e r t h a n w h e n t h e s t r a i g h t - t u b e t u y e r e w a s

u s e d . A s g a s f l o w r a t e w a s i n c r e a s e d , t h e r o t a t i n g

m o t i o n b e c a m e m o r e i n t e n s e , a n d t h e s iz e o f t h e t w o -

p h a s e f lo w r e g i o n b e c a m e l a r g e r . M a n y s m a l l b u b b l e s

w e r e f o r m e d n e a r t h e t u y e r e o u t l e t in t h e r o t a t i n g

m o t i o n o f t h e g a s j e t . L a r g e b u b b l e s , w h i c h f r e q u e n t -

l y a p p e a r w h e n a n o n - r o t a t i n g j e t i s u s e d , s e l d o m o c -

c u r r e d e v e n a t t h e h i g h e s t g a s f lo w r a t e . A t a g i v e n

g a s fl o w r a t e , t h e d is t a n c e p e n e t r a t e d b y t h e r o t a t in g

j e t a l o n g t h e h o r i z o n t a l d i r e c t i o n i n t h e b a t h w a s

s l i g h tl y l e s s t h a n th a t o f a n o n - r o t a t in g j e t . H o w e v e r ,

t h e c i r c u l a t o r y m o t i o n v e l o c i t y o f t h e l i q u id a n d t h e

r e l a t e d i n t e n s i t y o f t h e v o r t e x e s a n d e d d i e s w e r e l a rg -

e r , r e s u l t i n g i n t h e l i q u id s u r f a c e o f th e b a t h b e i n g

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

T h e p o s i t i o n t h e i n c l u d e d a n g l e ) o f t h e tw o t u y -

e r e s a l s o s t r o n g l y a f f e c t e d t h e g a s a g i t a t i o n a n d l i q u i d

f l o w i n t h e b a t h w h e n r o t a t i n g g a s j e t s a r e u s e d . T h e

e f f e c t s o f t h is p a r a m e t e r w e r e m o r e s e n s i t iv e t h a n

w h e n n o n - r o t a t i n g g a s j e t w e r e u s e d a n d w e r e m o r e

r e l a t e d t o t h e s t a b i l i t y o f t h e b l o w i n g p r o c e s s , p a r t i c -

u l a r l y a t t h e h i g h e r g a s f l o w r a t e s . A t t h e g i v e n g a s

f l o w r a t e s t e s t e d , t h e l i qu i d o n t h e b a t h s u r f a c e w a s

r e l a t iv e l y b o t h a c t iv e a n d s t e a d y w h e n t h e a n g u l a r

s e p a r a t i o n b e t w e e n t h e t w o s p i r a l - f l a t t u y e r e s w a s

8 0 ° ; a s t a t i o n a r y w a v e w i t h a s h o r t e r w a v e l e n g t h w a s

o n t h e s u rf a c e . H o w e v e r , t h e b lo w i n g p r o c e s s w a s

f a i r ly s m o o t h a n d s t e a d y , w i t h n o v i o l e n t s p la s h i n g o f

t h e l iq u id o n t h e b a t h s u r f a c e , e v e n a t t h e m a x i m u m

g a s fl o w r a t e u s e d I I I in T a b l e 2 ) . W h e n t h e a n g u l a r

s e p a r a t i o n s o f 6 0 ° a n d 1 0 0 ° w e r e u s e d , o s c i l l a ti o n s a n d

f l u c t u a ti o n s o f l ar g e a m p l i t u d e w e r e o f t e n f o r m e d o n

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

W i t h r e s p e c t t o t h e s t a b i l i t y o f t h e b l o w i n g p r o c e s s ,

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

t w o t u y e r e s , w h e n u s i n g t h e r o t a t in g g a s j e t s , w a s

n a r r o w e r t h a n w h e n u s i n g t h e n o n - r o t a t i n g j et s .

T h e d i f f e r e n t b a c k - at t a ck p h e n o m e n a o f t h e t w o

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

e x p e r i m e n t s , a n d w i ll b e d e s c r i b e d l a te r .

2 4 M i x i n g t im e in b a t h a n d e f f e c t s o f an g u la r

separat ion be tween two tuyeres and gas f low rate

F i g s . 3 a n d 4 s h o w t h e r e s u l t s o f t h e m i x i n g t i m e

m e a s u r e d e x p e r i m e n t a l l y in t h e A O D m o d e l b a th w i t h

n o n - r o t a t i n g a n d r o t a t i n g g a s j e t s. H e r e , F i g . 3 p r e -

s e n t s t h e r e s u l t s o f m i x i n g t i m e a s a f u n c t i o n o f t h e

a n g l e in c l u d ed b e t w e e n t w o t u y e r e s a t t h e g i v e n g a s

f l o w r a t e s , a n d F i g . 4 s h o w s t h e r e s u l t s o f th e m i x i n g

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

s e p a r a t i o n s . I t is v e r y c l e a r th a t t h e A O D p r o c e s s u n -

d e r t h e o p e r a t i v e c o n d i t i o n s w i t h n o n - r o t a t i n g a n d r o -

t a t i n g g a s j e t s h a s e x c e l l e n t m i x i n g e f f i c i e n c y .

I t c an b e s e e n f r o m F i g . 3 t h a t w i t h n o n - r o t a t i n g

g a s j e t , r,~ w a s s h o r t e s t i n t h e a n g u l a r r a n g e o f 60 ° -

1 0 0 ° r e d u c i n g t o a m i n i m u m v a l u e a t 8 0 ° ) . F i g . 4 i l-

l u s t r a t e s t h a t , w i t h a g a s f l ow r a t e r a n g e c o r r e s p o n d -

i n g to I I , I V a n d V i n T a b l e 2 , t h e r e w a s a n i n t e r v a l

w i t h th e s h o r t e s t m i x i n g t i m e . T h e c h a n g e s i n r m

w i t h 0 a n d Q m a l l s h o w e d a p a r a b o l ic f e a t u r e .

T h e r e l a t i o n s h i p s b e t w e e n t h e m i x i n g t i m e i n t h e

A 0 D b a t h , t h e an g l e i n cl u d e d b e t w e e n t h e t w o t u y -

e r e s , a n d t h e g i v e n g a s f l o w r a t e s c o m p l e t e l y c o r r e -

s p o n d t o t h e s t i r r i n g a n d f l o w c o n d i t i o n s i n t h e b a t h .

Q u a l i t a t iv e l y , a t a g i v e n g a s f lo w r a t e , a n e x c e s s i v e l y

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

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

e f f e c t i v e s t i r r i n g p o w e r , t h u s l e a d i n g to a d e c r e a s e i n

m i x i n g e f f i c ie n c y . T h e a u t h o r h o p e s t o d e v e l o p te c h -

n o l o g y t h a t w i ll e n s u r e b o t h a s h o r t e r m i x i n g t i m e a n d

a n a c t i v e a n d s t a b l e b a t h . F o r t h e p r a c t i c a l p r o c e s s ,

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


8/23

Journal o f Shanghai Univers i t y

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o - - S t r a i g h t - t u b e t u y e r e

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g i v e n i n c l ud e d t u y e r e a n g l e s u s i n g n o n - r o t a t i n g a n d r o t a t i n g g a s j e t s


9/23

Vol. 6 No. 1 Mar.

2002

WEI J. H. : Physical and Mathematical Modeling of the Argon-Oxygen Decarburization .. . 9

m i x i n g t im e b u t a c c o r d i n g t o th e a c t u a l r e q u i r e m e n t o f

t h e r e f in i n g r e a c t i o n s , i t s a d j u s t a b i l i t y a n d f l e x i b i li t y

a r e n o t so go o d . T h e r e f o r e , t h e i n f l u e n c e o f t h e a n g u -

l a r s e p a r a t i o n i s m o r e s i g n i f i c a n t a n d m a y b e t a k e n a s

a b a s i s f o r s e l e c t i n g a n e f f i c i e n t t u y e r e a r r a n g e m e n t .

I t w a s p r e s u m e d t h a t t h e s i t u a t i o n w i t h t h e g a s f l o w

r a t e c o r re s p o n d i n g t o V in T a b l e 2 m i g h t p e r h a p s b e

c l o s e r t o p r a c t i c e . A t th i s g as b l o w i n g r a t e , t h e a n g u -

l a r r a n g e o f 6 0 ° - 1 0 0 ° o f f e r s m o r e e f f i c i e n t t u y e r e p o -

s i t i o n . O b s e r v a t i o n s a n d e x p e r i m e n t a l r e s u l t s a l l i n d i -

c a t e d t h a t , i n t h i s c a s e , n o t o n l y t h e m i x i n g e f f e c t i v e -

n e s s w a s b e t t e r b u t al s o th e b l o w i n g p r o c e s s w a s

s m o o t h e r a n d s t e a d i e r. T h i s r e c o m m e n d e d r a n g e o f

a n g u l a r s e p a r at i o n o f th e t w o s t r a i g h t - t u b e t u y e r e s is

l a r g e r t h a n t h e v a l u e ( 5 4 ° ) o b t a i n e d b y L e a c h

et

al.

[13 f r o m t h e r e s u l t s o f w a t e r m o d e l i n g f o r a 1 6 t

A O D v e s s e l , w h i c h m a y p r o b a b l y b e r e l a t e d t o t h e u s e

o f si n g le t u b e t y p e t u y e r e s i n t h e i r e x p e r i m e n t s .

T h e m i x i n g t i m e s i n t h e b a t h w i t h r o t a t i n g g a s j e t s

w e r e s im i l a r t o th o s e f o r u s in g t h e s t r a i g h t - t u b e t u y -

e r e s . I n t h e o p t i m a l o p e r a t i n g r a n g e o f 6 0 ° - 1 0 0 ° f o r

t h e s t r a i g h t - t u b e t u y e r e s , t h e a n g u l ar s e p a r a t io n w a s

l e s s s e n s i t i v e f o r t h e tw o s p i r a l - f la t t u y e r e s . C o m p a r -

a t i v e l y , t h e m i x i n g e f f i c i e n c y a t 8 0 ° w o u l d b e b e s t . A t

g i v e n a n g u l a r s e p a r a t io n s b e t w e e n t h e t u y e r e s a n d g a s

f l o w r a t e s , t h e m i x i n g t i m e s u s i n g t h e s p i r a l - fl a t tu y -

e r e s w e r e s l i g h t l y s h o r t e r t h a n t h a t w i t h t h e s t r a i g h t -

t u b e tu y e r e s . T h e r e f o r e , u s i n g t h e s p ir a l -f l a t t u y e r e s

w i ll r e s u l t i n a h i g h e r m i x i n g e f f i c i e n c y . C o n s i d e r i n g

t h e o v e r a l l e f f e c t s o n t h e s t a b i l i t y o f th e b l o w i n g p r o -

c e s s ( t h e s u r f a c e e f f e c t s ) a n d t h e m i x i n g e f f i c i e n c y i n

t h e b a t h , t h e a n g u l a r s e p a r a t i o n o f 8 0 ° w a s t h e o p t i -

m a l p o s i t i o n f o r t h e t w o s p i r a l - f l a t t u y e r e s .

T a k i n g c o m p r e h e n s i v e l y a c c o u n t o f th e e f f e c t s o f

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

t w o tu y e r e s , t h e f o ll o w i n g r e l a ti o n s h i p s w e r e o b -

t a i n e d f r o m t h e e x p e r i m e n t a l d a t a :

f o r n o n - r o t a t i n g g a s j e t s ,

t tq ) -0 . 3 4 5 S / S 0 )0.075

22 • 04 ( Qm a ) - o. 072 ( ,~m2

2 0 ° _ 8 0 o )

r m = 3 0 1 7 ( ,~ . ~1

Qm2

S/ So ) 0 484 ,

n ) 0 . 0 4 2 -o22o

(80 ° - 150 o)

3 )

f o r r o t a t i n g g a s j e t s ,

1 4 . 6 1 ( Q m l ) -0.142 Qm2) 0 .1 39 ( S / S o ) -0.21,

(60 - 80 ° )

r m = 2 9 . 6 7 ( Q , , 1 ) - o . 1 5 o ( Q , , 2 ) - 0. 09 9 ( S / S o ) O . 2 9 ,

(80 ° - 100 ° )

( 4 )

w h e r e S a n d S o a r e , r e s p e c t i v e l y , t h e a r e a o f t h e

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

t u y e r e s a n d t h e c r o s s - s e c t i o n a l a r e a o f t h e b a t h , m z .

I t c a n b e s e e n t h a t i n t h e A 0 D p r o c e s s u s i n g t w o

t u y e r e b l o w i n g w i t h a n n u l a r s t r a i g h t - tu b e t y p e

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

p r o p o r t i o n a l t o Q a ( a < 0 ) a s i n th e c a s e o f g a s b l o w -

i n g i n a l a d l e u s i n g a s i n g l e t u b e t u y e r e . T h e g a s

s t r e a m o f th e s u b t u y e r e w o u l d b e a b le t o p r o v i d e a

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

t u y e r e F8] . W i t h r e s p e c t t o m i x i n g , s u i t a b l e i n c r e a s e i n

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

a d v a n t a g e o u s •

T h e r e la t i o n s h ip s s h o w n b y E q u a t i o n ( 4 ) a r e

s l i g h t l y d i f f e r e n t f r o m t h o s e w h e n u t i l iz i n g t h e

s t r a i g h t - t u b e t u y e r e s . T h e e x p o n e n t s o f Q ,, a a n d

Qm2

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

w i t h t h e r a n g e o f t h e a n g u l a r s e p a r a t i o n u s e d . I n a d -

d i t i o n , t h e n o n - r o t a t i n g j e t s f r o m t h e s u b t u y e r e a l s o

h a s a p h y s i c a l s h i e l d in g e f f e c t o n t h e r o t a t i n g g a s j e t s

o f t h e m a i n t u y e r e s , b u t c o m p a r e d t o t h a t o n a n o n -

r o t a t i n g j e t , t h e a ct io n i s e v i d e n t l y w e a k e n e d o w i n g

t o t h e r o t a t i n g m o t i o n o f th e m a i n t u y e r e j e t .

2 . 5 T h e g a s s t i r r in g e n e r g y a n d i ts r e l a t i o n s h i p

w i t h m i x i n g t i m e

R e g a r d i n g t h e g a s s t i r r i n g e n e r g y i n a g a s a g i t a t i o n

l a d le s y s t e m , t h e r e a r e d i f f e r e n t c a l c u l a t io n e q u a t i o n s

i n t h e l i t er a t u r e • T h e d i v e r g e n c e s o f t h e s e e q u a t io n s

a r e b a s i c a l l y d u e t o d i f f e r e n t c o n s i d e r a t i o n s f o r b u o y -

a n c y p o w e r a n d e x p a n s i o n w o r k d u r i n g f l o a ti n g u p o f

t h e b u b b l e s• A c t u a l l y , d u r i n g f l o a t i n g u p , e v e r y b u b -

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

g r a d u a l l y in c r e a s e s w i t h d e c r e a s e i n th e s t a t i c p r e s -

s u r e ; t h e b u o y a n c y s u f f e r e d i n c re a s e s c o r r e s p o n d -

i n g l y . O n t h e o t h e r h a n d , t h e b u b b l e it s e l f w o u l d a ls o

d o w o r k t o t h e l i q u i d w i t h i t s v o l u m e i n c r e a s i n g . T h a t

i s t o s a y , a s a b u b b l e f l o a t s u p w a r d , t h e r e a l b u o y a n -

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

p u r e b u o y a n c y a n d t h e o t h e r t o e x p a n s i o n . T h e f o r -

m e r w o u l d b e c a u s e d p u r e l y b y b u o y a n c y a n d t h e l a t -

t e r w o u l d r e s u l t f r o m a d e c r e a s e i n s t a t i c p r e s s u r e ;


10/23

10 J o u r n a l o f S h a n g h a i U n i v e r s i t y

they would not be equal [42]. In addition, the tempera-

ture of the gas stream after en try into the bath, Tg,

must be lower than the molten steel temperature, be-

cause it is impossible that the heat transfer rate be-

tween the gas stream and the bath is high enough to

allow equilibrium to occur in gas blowing process-

es [4345]. Moreover, the theoret ical calculations[36a9]

indicated that, under the experimental conditions, the

gas will discharge at subsonic velocity, the outlet

pressure being equal to the back pressure. However ,

the stream can still have a considerable velocity (for

instance, see Table 1) and a substantial kinetic ener-

gy. Therefore, it is inappropriate to neglect the effect

of the kinetic energy of the stream, although the re-

lated agitation efficiency is low [46]. Fur ther more,

isothermal expansion of the gas near the outlet does

not take place in a water modeling process.

Based upon the considerations above, the densities

of the gas agitation energy for the main tuyere and

subtuyere, era1 and e~2(W t- 1) were respectively es-

timated using the following equation:

8 m = £ b + 7 ] l ~T + 7 1 2 ~k

O. 1031

p l g H1 p ~ q H1

= M? m T ~ {[ 2 1 n ( l + - ~ - o

) - p o + p L g H l l +

r ] l ( 1 - 1 2 ) +

1

T2

Tg 7/2 ( ~ - ~ p g u g ) } (5)

where eb is the real buoyancy power , eT is the ex-

pansion power of the gas at a constant pressure near

the tuyere outl et, ek is the kinetic energy , P0 is the

atmosphere pressure. The various Tg were estimated

according to the method described in Ref. [47]; 7/1

and r/2 were taken to be 0.06 and 0.02 , respectively.

It is reasonable to believe that the above analysis and

Equation (5) are applicable both to a non-rotating gas

jet and to a rotating one. However, it is necessary to

determine the values of the related parameters for a

rotating gas jet, which were performed using a rea-

sonable and reliable appropriation methodE32'33] .

Not considering the energy loss as a result of the

interaction between the non-rotating streams of the

two straight-tube tuyeres, the total density of gas

stirring energy was appropriately 150 - 320 W t-~,

and 155 - 330 W t- 1 for the two rotat ing s treams of

the two spiral-flat tuyeres. These values are much

higher than those (4 . 5 - 8. 0 W ' t- ~ ) obtained by

Figueira and Szekely 3] in terms of two times of the

buoyancy power , and equivalent to the intensity of

induction agitation in a 50 t ASEA-SKF furnace as pre-

dicted by Nakanishi e t a l . ~ 48 3 As pointed out by

Figueira and Szekely 3], the k inematic simil arity of

the model to its prototype in their modeling experi-

ment was very poor. Their results do not necessarily

reflect the practical situation. The relationships be-

tween the mixing time and the densities of gas stirring

energy, obtained from the experimental data and the

calculated results, were as follows:

for non-rotating gas jets,

46.82(eml ) - °'°6° (era2) -0.320(S/So) -0.075,

(20 ° - 80 o)

rm =

4 3 . 9 1 ( e m l ) o . o a a ( e m 2 ) _ o . 2 1 o ( S / S o ) O . 4 S 4

(6)

(80 ° - 150 °)

for rotating gas jets,

{23.15(e~1) - 0 . 1 1 3 / x - 0 1 3 5/ - 0 . 2 1

~ m 2 J t S / S o ) ,

6 o ° _ 8 0 ° )

Vr~ = 4 4 . 0 4 ( e m l ) _ o . 1 2 O ( e m 2 ) _ o . o 9 8 ( S / S o ) O . 2 9 ,

(7)

( 8 0 1 0 0 )

These equations are in an identical form to Equations

(3) and (4).

2 6 D i m e n s i o n l e s s c o r r e l a ti o n o f m i x i n g t i m e

The dimensional analysis indicated that, for mixing

in the bath during the AOD process with two tuyere

blowing using an annular tube tuyere , the following

equation is valid:

2 2

U~ll Cm •g2 r m Dgl U (11 P g2 U g2 H e e

f ( d l d 2 p l g d l p ~q d2 D e d l d 2 p l

- ~ , ~ ) = 0 8 )

P~

where the subscripts 1 and 2 denote, respectively,

the appropriate parameters of the main tuyere and

subtuyere, and De is the equivalent diameter of the

bath. Taken u = u g l [ Q ~ l / ( Q ~ l + Qm2)] + ug2[ Q m 2 /

(Q,~I + Qm2)] and all, d2, d to be respectively the

equivalent diameters of the main tuyere and subtuyere

and the total of the two tuyeres combined into one

(the effective cross-sectional areas are accordingly

equal ), the corresponding dimensionless relationships

of the mixing time were obtained:

for non-rotating gas jets,


11/23

Vol.6 No. 1 M ar, 2 0 0 2 WEI J.H . • Physical and Mathematical Modeling of the Argon-Oxygen Decarburization .. . 11

2 6 2 1 2 . 0 1 ( F r l )0 .3 9 0 F r 2 - ) - o 1 11 S ~ S o ) - 0 .0 7 5

u r , , ( 2 0 ° - 8 0 ° )

d 3 0 5 8 8 . 9 2 ( F r l ) o . 4 5 1 ( F r 2 ) - ° . ° S T ( S / S o ) ° .4 84 ,

80 o -

150 ° )

( 9 )

f o r r o t a t i n g g a s j e t s ,

-urm _

t 3 0 7 8 7 4 9 ( F r l ) ° ' 3 3 7 ( F r 2 ) - ° ' ° ° 5 ( S / S ° ) - ° 2 1 , ( 6 0

- 80 ° )

- ~ 6 0 9 5 0 . 0 7 ( F r l . ) o . 3 3 1 ( F r 2 . ) - o . o 1 6 ( S / S o ) O . Z 9 ,

8 0 ° - l o o o )

( 1 0 )

E q u a t i o n s ( 9 ) a n d ( 1 0 ) d e m o n s t r a t e c l e a r ly t h a t

t h e g a s j e t f r o m t h e m a i n t u y e r e s t il l h a s a g o v e r n i n g

i n f l u e n c e o n t h e f l u id f lo w a n d m i x i n g i n t h e b a t h , a l -

t h o u g h t h e g a s j e t f r o m t h e s u b t u y e r e h a s a p h y s i c a l

s h i e l d i n g e f f e c t o n i t. C o m p a r a t i v e l y , t h e r o t a t i n g g a s

j e t o f t h e m a i n t u y e r e h a s a g r e a t e r e f f e c t t h a n t h e

n o n - r o t a t i n g g a s j e t . I t m a y b e r e a s o n a b l y a s s e r t e d

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

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

t y p e o n a c c o u n t o f t h e s u f f i c i e n t l y h i g h k i n e m a t i c s i m -

i l a r i ty o f t h e m o d e l t o i ts p r o t o t y p e u n d e r t h e e x p e r i -

m e n t a l c o n d i t i o n s . T h i s h a s b e e n c o n f i r m e d in p r a c -

t i c e d u r i n g t h e p r o d u c t i o n o f s ta i n l e s s s t e e l i n a n 1 8 t

A O D v e s s e l .

2 . 7 B a c k - a t ta c k p h e n o m e n a o f g a s j e ts w i t h

s u b m e r g e d h o r i z o n t a l l y b l o w i n g

T h e b a c k - a t t a c k p h e n o m e n a o f t h e g a s j e t s w e r e

c l e ar l y o b s e r v e d d u r in g t h e e x p e r i m e n t s , n o m a t t e r

w h a t t h e s t r a i g h t - t u b e o r s p i ra l - fl a t t y p e t u y e r e w a s

u s e d . I n t h e c a s e o f t h e s t r a i g h t - t u b e t u y e r e u s e d ,

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

t h e t u y e r e o u t l e t w e r e s t r i k i n g b a c k w a r d t h e si d e w a l l

o v e r t h e t u y e r e o u t l e t u n d e r t h e o p p r e s s i o n o f t h e l i q -

u i d i n m o t i o n , a n d b r o k e n i n t o s m a l l b u b b l e s . A t t h e

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

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

r e c t i o n , a t t a c k i n g t h e f r o n t s u r f a ce o f t h e t u y e r e o u t -

l e t a n d t h e s i d e w a l l a r o u n d i t , t h u s c a u s i n g o n e b a c k -

a t ta c k . T h e n , t h e j e t w a s s t r e tc h i n g f o r w a r d u n d e r

t h e a c ti o n o f t h e s u c c e e d i n g f o l l o w - u p g a s , a n d c a r r y -

i n g w i t h i n i t s e lf t h e n e x t b a c k - a t t a c k . T h i s p r o c e s s

w a s r e p e a t e d l y c o n d u c t i n g i n th i s w a y .

T h e b a c k - a tt a c k p h e n o m e n o n o f a r o t a t i n g g a s j e t

d e m o n s t r a t e d i t s g e n e r a l f e a t u r e s d i f f e r e n t f r o m t h a t

o f a n o n - r o t a t i n g . A s m e n t i o n e d a b o v e , l a r g e b u b b l es

s e l d o m o c c u r r e d . M a n y s m a ll b u b b le s f o r m e d a t t h e

p l a c e n o t b e i n g f a r f r o m t h e t u y e r e o u t l e t w e r e s i m u l -

t a n e o u s l y s t r i k i n g t h e s i d e w a l l ; t h e r e s i d u a l g a s o f

t h e j e t w a s i n s w i r l in g c o n t r a c t i n g b a c k w a r d a n d a t -

t a c k i n g th e s u r f a c e o f t h e t u y e r e o u t l e t a n d t h e s i d e

w a l l a r o u n d i t. O b v i o u s l y , t h e b a c k -a t t ac k p h e n o m e n a

o f th e t w o k i n d s o f g a s j e t s h a v e r e s p e c t i v e l y t h e d i f -

f e r e n t c h a r a c t e r i s t ic s f r o m t h a t o f a b o t t o m - b l o w i n g

j e t .

T h e b a c k - a t t a c k p h e n o m e n o n o f a h o ri z o n t al g a s

j e t , i n a b r o a d s e n s e , s h o u l d i n c l u d e t h r e e p a r t s . O n e

i s t h e b a c k - a t t a c k a c t i o n o f t h e r e s i d u a l b u l k o f th e g a s

j e t a t t h e t u y e r e o u t l e t , w h i c h i s t h e b a c k - a t t a c k i n a

n a r r o w s e n s e . T h e s e c o n d is th e c o u n t e r a c t i o n o f t h e

j e t [ 14 1. T h e t h i r d i s t h e s t r i k i n g a c t i o n o f t h e b u b b l e s

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

t h e r e p r e s s i o n o f t h e l iq u i d i n m o t i o n . I n a d d i t i o n , t h e

b a c k - a t t a c k a c t i o n o f a g a s j e t w o u l d b e c l o s e l y r e l a t e d

t o t h e c i r c u l a t o r y m o t i o n o f t h e l i q u id i n t h e b a t h .

T h i s w o u l d b e t r u e a t l e a s t w i t h a h o r i z o n t a l g a s j e t .

I n t h e c a s e o f b o t t o m b l o w i n g , t h e a p p r o p r i a t e b a c k -

a t t a c k p h e n o m e n o n i s m a i n l y c o m p o s e d o f t h e f o r m e r

t w o a c t i o n s .

2 . 8 B a c k - a t t a c k fr e q u e n c i e s a n d p r e s su r e s o f

g a s j e t s w i t h s u b m e r g e d h o r i z o n t a l l y b l o w i n g

T h e d e t e r m i n e d r e s u l t s o n t h e b a c k - a t t a c k f r e q u e n -

c i e s o f t h e r o t a t i n g a n d n o n - r o t a t i n g j e t s w i t h t h e t w o

t u y e r e b l o w in g t h r o u g h t h e a n n u l a r t u b e t u y e r e a t t h e

g i v e n g as b l o w i n g r a t e s a n d b l o w i n g p r e s s u r e s a r e

s h o w n i n T a b l e s 3 a nd 4 , r e s p e c t i v e l y . T h e b a c k - a t-

t a ck f r e q u e n c i e s o f t h e r o t a t i n g a n d n o n - r o t a t i n g j e t s

a ll s h o w e d a r a is i n g t e n d e n c y w i t h a n i n c r e a s e i n g a s

b l o w i n g r a t e o r b l o w i n g p r e s s u r e o f t h e m a i n t u y e r e .

T h e i n f l u e n c e s o f th e a n g l e i n cl u d e d b e t w e e n t h e t w o

t u y e r e s o n t h e b a c k - a t ta c k f r e q u e n c y f o r t h e t w o k i n d s

o f g a s j e ts w e r e a l l n o t t o o l a rg e u n d e r t h e e x p e r i m e n -

t a l c o n d i t i o n s , o n l y t h e s i t u a t i o n a t t h e s m a l l g a s

b l o w i n g r a t e s w a s s e e m i n g l y e x c e p t io n a l . T h e d a t a in

T a b l e 3 a ls o in d i c a t e d t h a t t h e b a c k - a t t a c k f r e q u e n c y

o f a r o t a t i n g j e t w a s s l i g h t l y h i g h e r a t a s a m e g a s o u t -

l e t f l o w r a t e .

T h e d i f f e r e n c e o f o p e r a t i n g m o d e s s p e c i f ie d i n T a -

b l e s 3 a n d 4 i s th a t t h e r e w a s a h i g h e r g a s f l o w r a t e o f

t h e m a i n t u y e r e f o r th e s t r a i g h t - t u b e t y p e t u y e r e . A p -

p r o p r i a t e l y , t h e b a c k -a t t a ck f r e q u e n c y o f t h e r o t a t in g

g a s j e t w a s e v i d e n t l y d e c r e a s e d .


12/23

12 Journal of Shanghai University

Table 3 Determined re sults on back-attack frequencies of rotatin g and non-rotating gas jets with two tuye re blowing through annular-

tube tuyere a t the given gas blowing ra tes and angle included between the two tuyeres (Hz)

Gas blowing rate , Nma. h- 1

12 .94(main tuyeres ) 15 .82(main tuyeres ) 20 .12(m ain tuyeres ) 22 .64(m ain tuyeres ) 25 .34(m ain tuyeres )

4- 4-

3 .97(sub tuyeres ) 6 .53(sub tuyeres ) 6 . 026(sub tuyeres ) 6 .53(sub tuy eres ) 6 . 026(sub tuyeres )

Rotating Non-rota- Rotating Non-rota- Rotating Non-rota- Rotating Non-rota- Rotating Non-rota-

jet r ing jet je t r ing jet je t r ing jet je t r ing jet je t r ing jet

Angle included 60 ° (6) (3) (4) (2) (9) (10) (12) (8) (12) (12)

between the two 80* (6) (5) (5) (3) (9) (8) (9) (9) (11) (11)

tuyeres , O 100 ° (7 ) (8 ) (7 ) (3 ) (9 ) (9 ) (11) (9 ) (11) (13)

Table 4 Dete rmin ed resul ts on back-attack frequencies of rotati ng and non-rotating gas jets with two tuyere blowing through annular-

tube tuyere a t the given gas blowing pressures and angle included between the two tuyeres (Hz)

Gas blowing pressure

(gauge va lue ) , MPa

0 .066(m ain tuyeres ) 0 .09(m ain tuyeres ) 0 . 135(main tuyeres ) 0 .16(m ain tuyeres ) 0 . 185(main tuyeres )

÷ 4-

0.07 (sub tuye res) 0 . 137(subtuyeres) 0 .125 (subtu yeres ) 0 .13 7(su btuy eres) 0 . 125(subtuyeres)

Rotating Non-rota- Rotating Non-rota- Rotating Non-rota- Rotating Non-rota- Rotating Non-rota-

jet r ing jet je t r ing jet je t r ing jet je t r ing jet je t r ing jet

Angle included 60* (6) (8) (4) (6) (9) (12) (12) (15) (12) (17)

between the two 80° (6 ) (9 ) (5 ) (9 ) (9 ) (13) (9 ) (14) (11) (17)

tuyere s, t9 100 ° (7) (8) (7) (9) (9) (13) (11) (15) (11) (17)

Table 5 Determined resu lts on back-attack frequencies of rotatin g gas jet with single tuyere blowing throu gh single tube tuye re at the

given gas blowing pressures (f low rates)

Blowing p ressu re (gauge va lu e ) , MPa

Gas blowing rate , Nm3 h - 1

Back-attack frequency, Hz

0 . 0 6 6 0 . 0 9 0 . 1 3 5 0 . 1 6 0 . 1 8 5

6 .47 7 .91 10 .06 11 .32 12 .67

8 10 13 13 15

I t c a n a ls o b e c l e a r l y s e e n f r o m t h e d a t a i n T a b l e s 3

a n d 4 t h a t r e l a t i v e l y t o t h e g a s s t r e a m o f t h e s u b -

t u y e r e , t h e g a s s t r e a m f r o m t h e m a i n t u y e r e h a s a d e -

c i s iv e i n f l u e n c e o n th e b a c k - a t t a c k p h e n o m e n o n .

H o w e v e r , a t a s a m e g a s b l o w i n g p r e s s u r e , t h e b ac k -

a t t a c k f r e q u e n c y o f th e r o t a t i n g g a s j e t w i t h t h e s i n g l e

t u y e r e b l o w i n g t h r o u g h t h e s i n g l e t u b e t u y e r e

m a r k e d l y i n c r e as e d ( T a b l e 4 a n d 5 ) . T h e r e w a s a

s i m i l a r p a t t e r n f o r t h e n o n - r o t a t i n g j e t . T h a t a p p e a r s

t o s h o w t h a t t h e g a s s t r e a m o f t h e s u b t u y e r e m a y a l le -

v i a t e t h e b a c k - a t t a c k p h e n o m e n o n t o a c o n s id e r a b l e

e x t e n t . T h e g a s s t r e a m o f t h e s u b t u y e r e a l s o h a s a n

e v i d e n t s h i e l d i n g e f f e c t o n t h e b a c k - a t t a c k a c t i o n

b e s i d e s t h e c o o l i n g a n d p h y s i c a l s h i e l d i n g e f f e c t s t o

t h e f l o w o f m a i n t u y e r e g a s [3 1-3 3] . A d d i t i o n a l l y , t h i s

e f f e c t i s e n h a n c e d w i t h a n i n c r e a s e i n i t s r e l a t i v e f l o w

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

w i t h t h e r e s u l t s o b t a i n e d b y C h o

et al

[131

I t s h o u l d b e p o i n t e d o u t t h a t t h e r e w o u l d a ll b e th e

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

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

t a c k i n g . A s a r e s u l t o f t h i s k i n d o f c h a r a c t e r i s t i c f o r a

h o r i z o n t a l g a s j e t , i t s e a c h b a c k - a t t a c k , i n f a c t , w i l l

a ll i n v o l v e t h e a c t i o n o f a g r o u p o f b u b b l e s i n c l u d i n g

t h e re s i d u a l b u l k o f t h e j e t . T h i s w a s f u l ly c o n f i r m e d

b y t h e o b t a i n e d b a c k - a t t a c k w a v e s s h o w n i n F ig . 5 . I t

c a n b e s e e n f r o m F i g . 5 t h a t t h e r e w a s c o r r e s p o n d -

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

b a c k - a t t a c k , a n d t h e p u l s e n u m b e r s i n c l u d e d i n e a c h

b a c k - a t t a c k w e r e r o u g h l y c l o se t o e a c h o t h e r a t t h e

g i v e n b l o w i n g p a r a m e t e r s .


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Vol. 6 No. 1 Mar. 2002 WE I J. H. : Physical and Mathematical Modeling of the Argon-Oxygen Decarburization . • • 13

k P a

+l .0

0.0:

-1.0)

I _ 0 , s -

onc back-attack

Rotating gas e t

k P a

+1.0

0.0

-1.0

i

I0 " ~ -~ l one ba ck-at ta ck

Non-rotatinggas e t

( a ) B lowing p re s s u re s o f the m a in tuye re a nd s ub tuye re ( ga uge va lue s ) : 0 .1 6 MPa a nd 0 . 137 MPa , 0 = 80 °

kPa

+1.0

0.0

-1,0

i o . z . . i

o n back-attack

Rotating gas je t

k a i

1.0

-1.0

I I

~ O. I s ~ one back-attack

Non-rotating gas jet

b) Blowing pressures of the main tuyere and subtuyere gauge values ): 0. 066 MPa and 0.07 MPa, 0 = 80*

Fig.5 Back-attack waves of gas jets for a part of operating modes during the AOD water modeling blowing

2 9 R a t e a n d a p p e a r a n c e o f e r o s io n a n d w e a r

o f r e f r a c t o r y l i n i n g w i t h h o r i z o n t a l l y s id e

b l o w -

i n g

T h e c h a n g e s i n t h e a v e r a g e r a t e o f e ro s i o n a n d

w e a r f o r t h e b o r i c a c id p l a t e w i t h t h e a n g l e i n c lu d e d

b e t w e e n t h e t w o t u y e r e s d u r i n g t h e w a t e r m o d e l i n g of

t h e A O D p r o c e s s u s i n g t h e d i f f e r e n t t y p e s o f t u y e r e

w e r e o b t a i n e d . I n t h e c a se o f t h e g a s b lo w i n g p r o c e s s

w i t h t h e s tr a i g h t - tu b e t y p e t u y e r e , t h e a v e r a g e e r o -

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

t r e a t m e n t o f 1 0 m i n w e r e 0 . 0 3 0 1 5 , 0 . 0 2 7 5 6 , 0 .

0 3 2 19 g ' s - 1 , r e s p e c t i v e l y fo r th e a n g u l a r s e p a ra t i o n s

b e t w e e n t h e t w o t u y e r e s o f 6 0 ° , 8 0 ° a n d 1 0 0 ° . T h e

e r o s i o n a n d w e a r r a t e o f th e l i n i n g w a s t h e l o w e s t a t

t h e a n g l e i n c l u d e d b e t w e e n t h e t w o t u y e r e s o f 80 ° .

W h e n t h e s p i r a l -f l a t t u y e r e w a s u s e d , t h e a v e r a g e

r a t e s w e r e e s s e n t i a l l y n o t r e l a t e d t o t h e a n g u l a r s e p a -

r a t io n b e t w e e n t h e t w o t u y e r e s , c o r r e sP o n d i n g l y ,

w e r e a ll 0 . 0 1 7 3 3 g s - ~ . C o m p a r i n g w i t h t h a t o f t h e

s t r a i g h t - t u b e t y p e t u y e r e , i t d e c r e a s e d b y 3 7 % -

4 6 % .

A f t e r t h e t r e a t m e n t o f 1 0 m i n , t h e b o r ic ac i d p l a t e s

w e r e m a r k e d l y c h a n g e d i n t o t h i n n e r , e s p e c i a l l y a t t h e

p e r i p h e r y t i g h t l y c lo s e to t h e t u y e r e o u t l e t . A s e r i e s

o f c o n c a v e p i t s a n d p o c k e d m a r k s w e r e f o r m e d i n a

r a t h e r l a r g e r a n g e n e a r a n d o v e r t h e t u y e r e o u t l e t . I t

i s e v i d e n t t h a t f o r t h e b o r i c a c id p l a t e s , t h e e r o s i o n o f

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

c a u s e t h e m c h a n g i n g m o r e u n i f o r m l y i n t o t h i n n e r .

T h e fo r m a t i o n o f t h e c o n c a v e p i t s a n d p o c k e d m a r k s


14/23

14 Journal o f Shanghai University

would be the resu lts of striking repeatedly by the bub-

bles with the back attacking of jet. Under the condi-

tions of the rotating gas jets, relativ ely, the pits and

marks formed were fewer, shallower and more uni-

form, and their distribution area was smaller. The re

were also some curved stripes. The kinds of appear-

ance characteristics of the treated boric-acid plates

like that are completel y corresponding to the observed

back-attack features of the gas jets, and reflect gener-

ally the actual situation about the damage of the re-

fractor y lining in the AOD process. In the practical

AOD process, the buoyancy stood by the bubbles

would be much larger, approximately over 7 times of

that for water modeling, and the zone formed the con-

cave pits and pockmarks will be farther from the

tuyere outlet.

2 . 1 0 U s i n g e f f e c t iv e n e s s a n d p r a c t i c a l s u i t a b i l-

i t y o f th e a n n u l a r m a i n t u y e r e ) s p i r a l - f l a t t y p e

tuyere

The results of the water modeling experiments in-

dicated that relatively to the annular straight-tube

tuye re, the annular spiral-flat type tuyere used is able

to become the gas stream of the main tuyere into be-

ing the rotating motion with a suitable intensity. That

can make the bath attain a better agitation, thus

reaching a better mixing efficiency. Furthermore, it

can decrease and even eliminate large bubbles, and

bring about a great number of small bubbles forming.

That will alleviate quite effectively the back-attack of

gas jet, decrease the non-uni formity and rate of the

erosion and wear of the refract ory lining, thus im-

proving the life of the refractory lining for the hori-

zontal side blowing processes including the AOD pro-

cess. Also, the utilization ratio of the oxygen gas and

the rates of the refining reactions will be enhanced

owing to marked increase in the reaction interface. It

should be said that this type of the tuyere possesses a

good latent using power and composite effectiveness

and well suites for industrial application.

M a t h e m a t ic a l M o d e l in g o f t he A O D

R e f i n i n g P r o c e s s o f S t a i n l e s s

S t e e l [ 4 9 5 1]

3 . 1 A n a l y s i s o f t h e A O D p r oc e ss

It is well known that in AOD stainless steel mak-

ing, the supplied oxygen is utilized to remove the car-

bon in the molten steel. The argon or ni tro gen)

blown simultaneously can decrease the partial pres-

sure of the carbon monoxide and promote decarboriza-

tion, thus achieving the eff ectiven ess and objective of

removing carbon and reducing the loss of chromium.

However, the silicon and manganese dissolved in the

molten steel can also absorb the blown oxygen and re-

strict the oxidation reactions of carbon and chromium.

There exists throughout the competitive oxidation of

the carbon, chromium, silicon, manganese, and other

elements dissolved in the steel during the whole refin-

ing process.

Moreover, at high carbon concentrations, there

would be insufficient oxygen to oxidize the carbon

transferred to the reaction interface from the bulk of

the molten steel. This means that at high carbon con-

centrations, the rate of decarburization would be pri-

marily related to the ra te of oxygen blow. When the

carbon content in the steel is decreased to a certain

low level, the rate of decarburization may change to

being controlled by the mass transfer of carbon to the

reaction interface from the liquid bulk. Correspond-

ingly, there is a critical point or a critical state in the

process like that in oxygen - converter steelmaking.

The oxygen gas entering the bath would also con-

tact the iron atoms as a matrix of stainless steel and

form iron oxide, but most of the iron oxide formed

would, subsequently, quickly be reduced by the car-

bon, chromium, silicon, manganese and other ele-

ments in the molten steel. This means that the iron

oxide formed also would be an oxidant for them, and

would be mainly an intermediate product of the gas

blowing refining. In addition, their oxidation, to a

certain extent, would be related to the supplied oxy-

gen rate even at low carbon concentration levels.

Furthermore, the bath always demonstrates an ob-

vious non-isothermal characteristic during the refining

process, which can directly and strongly influence the

equilibrium and rates of the various refining reac-

tions. Another featu re of the AOD process is that the

bath is strongly agitated by the gas streams. This can

very effectively promote and intensify the heat and

mass transfer and is very advantageous in accelerating

the refining reactions and improving the homogeneity

of the bath composition and temperature, as pointed

out previously.


15/23

Vol. 6 No. 1 Mar .2002 WEI J. H. • Physical and Mathematical Modeling of the Argon-OxygenDecarburization . . . 15

3 . 2 M a t h e m a t i c a l m o d e l o f t h e p r o c e s s

Based on the previous analysis, a new mathemati-

cal model for the AOD refining process of stainless

steel has been proposed and developed, in which the

conditions and characteristics mentioned have all been

considered and noted.

3 . 2 . 1 B a s i c a s s u m p t i o n s o f t h e m a t h e m a t i c a l m o d e l

The initial assumptions of the new mathematical

model for the refining process were as follows:

1. The oxygen blown into the molten steel simulta-

neously oxidizes the carbon, chromi um, silicon, and

manganese dissolved in the steel and the iron as a ma-

trix; the iron oxide formed is also an oxidant for the

other elements and is essentially an intermediate

product of the refining process.

2. All the possible oxidation-reduction reactions

take place simultaneously and reach and establish a

combined equilibrium in competition at the liquid/bub-

ble in te rfaces [41' 52- 56]

3. At high carbon contents, the oxidation rates of

elements are primarily related to the supplied oxygen

rate; at low carbon concentration levels, the rate of

decarburization is mainly determined by the mass

transfer of carbon in molten steel.

4. The unabsorbed oxygen blown into the liquid

steel will escape from the bath and form C02 with CO

in the exhaust gas, rathe r than dissolving and accu-

mulating in the steel.

5. The bath composition and temperatu re are con-

tinually changing and are uniformly distributed at any

moment during the whole refining process.

6. The oxidation of elements in the steel other than

C, Cr, Si, and Mn is temporarily not taken into ac-

count; i. e . , the oxygen consumed by the other ele-

ments is ignored.

3 . 2 . 2 R e f i n i n g r e a c ti o n s c h e m e s

The oxidative reactions of the carbon, chromium,

silicon, and manganese dissolved in the molten steel

and the iron as a matrix of the steel by the blown oxy-

gen can be written as

1

[C] + ~O z = ICOI (11)

3

2[Cr ] + ~-02 = (Cr203) (12)

[Si] + 02 = (SiOz) (13 )

1

[Mn] + ~-O2 = (MnO) (14)

1

[Fe] + ~-O2 = (FeO) (15)

The following independent reaction equilibria in this

system can be produced from combinations of reaction

(11) through (14), respectively, with reaction (15):

[C] + (FeO) : {CO} + [F e] ,

Pco

A G c = A G ~ R T l n

(16)

a[¢] a FeO

2[Cr] + 3(FeO) = (Cr203) + 3[ Fe ],

a cr2o3

,AGcr = z~ G[=r R T ln z 3 (17)

a [Cr] a (FeO)

[Si] + 2(FeO) = (Si02) + 2[ Fe ],

a (sio2)

A G c = A G~ i R T l n 2 (18)

a[si] a (FeO)

[Mn] + (FeO) = (MnO) + [Fe],

AGMn = AC~n+ R T l n a MnO) (19)

a [Mn] a (~eO)

where ai--the activity of i component; AGi and z3G7

--the Gibbs free energy at the refining conditions and

the Gibbs free energy at the standard state for oxida-

tion reaction of i element, respectively, J. g- 1 ; R- -

the gas constant, J tool-1. K-1; T- -t he bath temper-

atur e, K. These all belong among the possible reac-

tions which occur in the system. Thermodynami cally,

the reaction schemes presented by reactions (11)

through (15) and reactions (16) through (19) can all

characterize the chemical-equilibrium feature of the

refining system but, kinetically, they are differen t,

the former being direct, and the latter being indirect.

3 . 2 . 3 R a t e e q u a t i o n s o f t h e p r o c e s s

At high carbon contents, the average loss rates of

the carbon, chromium, silicon and manganese dis-

solved in the steel in the competitive oxidation are,

separately,

Wm dE%C] _ 2 ~ o

- 100Mc dt 22400 xc (20)

Wm d [ % Cr ] _ 2T/Qo (21)

- 1.5 100Mc------~ d ~ 22400 Xcr

Wm d [ % S i ] _ 2r]Qo (22)

2 100Msi dt

2 2 4 0 0 x s i

Wm d[%Mn]

2 r l Q o

100MMn d t - 2 2 4 0 0 X M n (23)

At low carbon concentration levels, the average rate

of decarburization can be expressed as


16/23

16 Journa l of Shanghai University

- W m d [ C ] - A r e a P m k C ( [ C ] - [ C ] e )

( 2 4 )

d t

At t h i s t im e , t he f o l l owing r e a c t ion c a n a ppr opr i a t e ly

be c ons ide r e d :

( Cr 203) + 3 [ C] = 2 [ C r ] + 3 I COI ( 25)

Pa y ing a t t e n t io n to t he d i l u t i ng r o l e o f t he i ne r t ga s

( a r g o n o r n i t r o g e n ) a n d n o n - r e a c t in g o x y g e n , t h e fo l -

l owing e xpr e ss ion c a n be de r ive d :

d [ % C ] 1 2

d t : 2 - ( - 8 1 - ~ ) ( 2 6 )

w h e r e

10 0M c Q o( 1 - r ]) + Q~ .b

81 = -- Wm 22400 F

A re a P m k c _ P t

a [c r ] +

[ % C ] ( 2 7 )

Wm a CrxO Kcr _c

r o O m C l O O ) Q o < l - + Q s .

s

= 4 Wm [ C 3 ~ ~ 6 ( 2 8 )

a n d A r e a - - t h e to t al re a c t i o n i n t e r f a c e , c m 2 ; f c - - t h e

He n r i a n a c t i v i t y c oe f f i c i e n t o f c a rbon in m ol t e n s t e e l ;

k c - - t h e m a s s t r a n s f e r o f c a r b o n i n m o l t e n s t e e l , c m

s - l ; K c r . c - - t h e e q u il ib r iu m c o n s t a n t o f [ C ] - ( C r 2 0 3 )

r e a c ti o n ; M ~ - - t h e m o l e m a s s o f i s u b s t a n c e , g

m o l e - l ; P t - - t h e t o ta l d i m e n s i o n l e s s p r e s s u r e in t h e

A O D v e s s e l ; Q o - - t h e f lo w ra t e o f o x y g e n , N c m a

s - l ; Q s u b - -t h e to t a l f lo w r a t e o f i n e r t g a s , N c m a

s - 1 x i - - t h e d i s tr i b u t io n r a t io o f o x y g e n f o r / c o m p o -

ne n t i n l iqu id s t e e l ; W m - - th e m a ss o f l iqu id s t e e l , g ;

[ % / ] - - t h e m a s s p e r c e n t c o n ce n t ra t io n of i s o l u t e i n

m o l t e n s t e e l , m a s s -% ; [ % C ] e - - t h e e q u i l i b ri u m c o n -

c e n t r a t i o n o f c a r bon in m o l t e n s t e e l a t r e a c t ion in t e r -

f a c e , m a ss -% ; r l - - t h e u t i l i z a t ion r a t i o o f ox yg e n ;

-3

p m - - t h e d e n s i t y o f m o l t e n s te e l , g - c m

3 2 4 H e a t b a l a n c e o f t h e s y s t e m

T he he a t ba l a nc e e qua t ion i s

W m c p , m T + Q odt poCp .o Tg,o + QsubdtpsubCp,sub Tg,o +

Wm d[ C]AI . .1 d[ C r] ~ ~,,.

W ~ c p ,~ T + 1 - ~ ( ~ - ~ 'a i x C d - i £ M / C r - -

d [

% M n ] A u

d [ % S i ]

A H s i ) d t = W m [ 1

+

d t ~ - -M . d t

[ d [ % C ] + d [ % C r ] + d [ % M n ] + d [ % S i ] / d t I

\

d t d t d t d t

] l O O J

Cp,m( T +

d T ) +

Q o ( 1 - 7 ] ) d t p o % , o T g + Q ~u b

W m d [ % C ] ) d t M c o

dtp~.bC p.~.b Tg + ~ ( d t M----c

Cp,co Tg

W m d t ( d[ %C r ] M c r2°a d [ % M n]

+ Ws 100 d t 2M c r + d t

MMnO + d % s i] M sG / ] cp,~( T + d T ) + ( qlos~ +

MMn d t 2M si ]

q 5 ) d t ( 2 9 )

T h e a p p r o p r i a t e r i s i n g r a t e o f t h e b a t h t e m p e r a t u r e i s

d T _ / ~ / M c @ ~ d [ % C r ] M M n o d [ % M n ] ~_

d t c p , ~ l k ~ ~ + M Mn d t

M s G d [ % S i ] d [ % C ] + d [ % C r ] +

Msi dt ) - Cp'm T ( d t d t

df M n3 +d[ Si3 / 100

d t - - d t / -~ - m {Q O p o C p , o [( 1 - r ~ ) r g -

M c o d [ % C ]

T g , o l +

qloss + qs} + Cp.CO Tg M c dt

A H c d [ % C ] + A H c r d [ % C r ] + AH M n d[ % M n ]

d t d t d t

A H s i d [ S i ]

a t ) 1 / ( l O O C p ' m + l O O c p ' s W s / W m )

3 0 )

w h e r e q l o s s q 1 q 2 q 3 q 4 q u ; t h e r e f r a c t o r y

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

a m u l t i - l a y e r p l a t e ; q l , q 2 , q 3 a n d q 4 w e r e , r e s p e c -

t i v e l y , d e t e r m i n e d i n t e r m s o f t h e o n e - d i m e n s i o n a l

t r a n s i e n t h e a t - c o n d u c t i o n p r o b l e m s ; q 5 w a s t a k e n t o

b e W l c p , j A T a n d q u = ( q l + c / 2 + q 3 + q 4 ) x 1 5 % ;

q l - - t h e h e a t l o s s b y c o n d u c t i o n f r o m b o t t o m o f t h e

v e s s e l , J s - i ; q 2 - - t h e h e a t l o s s b y c o n d u c t i o n f r o m

t h e l o w e r o f t h e v e s s e l , J ' s - 1 ; q 3 - - t h e h e a t l o s s b y

c o n d u c t i o n f r o m t h e u p p e r o f t h e v e s s e l , J ' s - 1 ; q 4 - -

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

s - 1 ; q 5 - - t h e h e a t l o s s a b s o r b e d b y r e f r a c t o r y l i n i n g o f

t h e v e s s e l d u r i n g b a t h r i s i n g t e m p e r a t u r e , J s - l ;

q u - - t h e u n c e r t a i n h e a t l o s s o f t h e s y s t e m , J s - l ;

T g , T g o - - t h e t e m p e r a t u r e o f g a s a n d i t s i n i t i

Aod Modelling

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