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8/18/2019 Aod Modelling
1/23
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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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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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 .
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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
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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
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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 lo w r a t e s u s i n g n o n - r o t a t i n g a n d
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F i g . 4 M i x i n g t i m e s i n t h e A O D m o d e l b a t h a s a f u n c t i o n o f g a s fl o w r a t e a t t h e
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
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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 ;
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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,
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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 .
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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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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
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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.
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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
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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
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