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Mathematical Modeling of the Vacuum Chamber of RH-KTB Process.

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Dev. Chem. Eng. Mineral Process. 14(3/4), pp. 449-458,2006.
Mathematical Modeling of the Vacuum
Chamber of RH-KTB Process
Zong-Ze Huangl*, Yi-Sheng Chen2 and You-Duo He2
R & D Center, Baoshan Iron & Steel Co., Ltd., Shanghai 201900,
P. R. China
Inner Mongolia University of Science & Technology, Baotou 014010,
P. R. China
A mathematical model was developed for the simulation of gas flow, combustion and
heat convection in the vacuum chamber of RH-KTB process at Baosteel. Under
different conditions, the model was used to predict the influence of the top oxygen
blowing lance on the gas flow; chemical reactions and temperature distribution were
calculated. The optimum position of the lance is suggested for the RH-KTB process.
In recent years, the quality specifications for steel products have significantly
increased. Secondary refining processes now impose additional requirements and the
resultant increase in process complexity has hampered efforts to produce high-purity
steels in large quantities at low cost. The RH process that was originally developed
for the removal of hydrogen from steel is also used for decarburization, deoxidation,
inclusions removal, and composition control because it is easy to operate and has the
capability for large volume production. The functions of forced decarburization and
heating by oxygen blowing were added to facilitate the production of ultra low-carbon
steel, and also adding the function of desulfurization by flux refining. With these
improvements, the RH process has made rapid progress as a multifunctional
secondary refining facility [I-31.
There are three kinds of RH facilities at Baosteel, including RH-OB (RH with
oxygen blowing), RH-KTB (RH with top oxygen blowing) and RH-MFB (RH with
multifunction blowing). The capacity of the RH facility is 300 ton. These facilities
have a very important role in the production of clean steel. Based on hndamental
studies, many technologies were incorporated into the RH process for production of
ultra low carbon steel, pipeline steel, tin-plate steel, electrical steel, etc. These include
double slag deoxidation technology for ultra low-carbon steel, flux powder injection
for desulhrization, inclusions modification technology by calcium treatment [4].
The RH vacuum chamber has previously been considered as a semi-black box,
however, its complex internal processes and reactions need to be understood through
* Author for correspondence (zzhuang(
Zong-Ze Huang, Yi-Sheng Chen and You-Duo He
physical simulation experiments and mathematical simulations. For example,
water-modeling experiments can model processes such as circulatory flow,
decarburization, degassing, etc. [ 5 ] . High-temperature experiments are used to
investigate reactions such as desulfurization, decarburization, and inclusions
modification in the RH process. Certain process simulations such as post-combustion,
heat convection, and gas flow are conducted only by computer-based mathematical
modeling for reference to actual operations. Especially in the process of RH-KTB and
RH-MFB, the determination of the position of the top lance for different functions is
very important for the production of high quality steel at lower cost.
In this study, a 3D-mathematical model was developed for the simulation of gas
flow, combustion and heat convection in the vacuum chamber of an RH-KTB facility
at Baosteel. The optimum position of the lance for carrying out the heating and the
insulation of the molten steel are proposed.
Mathematical Model
The combustible gases of the RH vacuum chamber usually escape from the molten
steel in a circulatory motion. The amount of outlet gases follows the normal
distribution of irregular patterns, with the up-leg as the symmetry center. Diffising
gradually during their ascent, the outlet gasses are uniformly distributed at the end.
These gases generally consisted of circulating carrying gas (Ar or N2), decarburized
product (CO) and degassing products (H2and N2).The temperature of the outlet gases
is nearly the same as that of the molten steel. If oxygen is provided by an oxygen
lance at the top of the RH chamber, then the high-speed oxygen jet will move in the
direction opposite to the escaping rising gases and bring a strong agitation to the
liquid steel in the chamber. Meanwhile, the turbulent diffusing combustion reaction of
CO and O2takes place in the chamber where the combustion flame heats the molten
steel, and its heating efficiency depends on the lance position of KTB, hence the
shape and position of the combustion flame can usually be obtained. The
mathematical model was established on the basis of the above description [6].
Basic assumptions
(1) It is assumed that the gases belong to the continuous medium when the degree of
vacuum is below 133 Pa, i.e. there are enough gases in the small chosen volume.
outlet gases from the molten steel in the vacuum chamber follow the pattern
of the normal distribution, taking the up-leg as the symmetrical center axis:
Where a,,a,are x-axis and y-axis coordinates of the up-leg; b,,b2 are x-axis
and y-axis intensity values of the Gaussian distribution; Q is the circulation flow
of the gas; A is cross sectional area of RH vacuum chamber.
The combustion of CO in the vacuum chamber is assumed to be turbulent
diffision combustion.
The trace amounts of H2and N2 in the gases are not taken into consideration.
Mathematical Modeling of the Vacuum Chamber of RH-KTB Process
(ii) Mathematical model
The k - c two-equation turbulent model was used to perform the numerical
calculations of the fluid field. The model includes the continuity equation, momentum
equations in x, y and z directions, turbulent kinetic energy k equation, and turbulent
kinetic dissipation E equation. In the vacuum chamber, the post combustion of CO is
turbulent diffusion combustion and the quick reaction model is applied to the simple
chemical reaction system in the turbulent diffision combustion. It is presented as
Mixture fraction is defined:
Pulse dissipation of mixture fraction is defined:
Where 4 is the conservation value in the system; and subscripts A, F and A4
represent oxygen, CO and the product stream respectively; P v) is the PDF of the
mixture fraction.
After the mixture fraction and the pulse dissipation were defined, then their
control equation (similar to that in the turbulent kinetic energy equation) can also be
obtained. After incorporating the energy-T equation and the concentration-Mi
equation, the mathematical model is available. The universal equation for all these
components is:
a(r am) +ax # a x
r,-a4) +-a ( r am) +s,
* az
The parameters defining each equation are given in Table 1.
(iii) Boundary conditions
( I ) Velocity$eld
At the molten steel plane on the bottom of the vacuum chamber where u = 0, v
then w is the same as given by Equation ( 1 ) .
At the top and on the walls of the vacuum chamber, then:
%=o, i=1,2,3,j=1,2,3,
i# j
Zong-Ze Huang, Yi-Sheng Chen and You-Duo He
(2) Temperaturefield
On the molten steel surface in the vacuum chamber, then:
q = a x (TI - Tg)
At the top of the flow and on the walls, then:
q, = o (i=l, 2, 3 )
(3) Concentrationfield
On the molten steel surface in the vacuum chamber, then:
m, = m,, (i=CO, H2, N2, 0 2 , A d
At the top of the flow and on the walls, then:
m, = o (i=CO,H2, N2,Oz, Ar)
Table 1. Parameters of the general equations.
r+ s,
Turbulent kinetic
energy equation
Turbulent kinetic
dissipation equation
Momentum equation
Momentum equation
Momentum equation
Mixture fraction
G, - P&
i(clGk -C*PE)
- r
Where subscript i represents CO, CO2 and Ojorespectively: Q k is heat released by combustion:
r is the rate of chemical reaction.
Mathematical Modeling of the Vacuum Chamber of RH-KTB Process
(iv) Numerical solution method to the equations
The equations in Table 1 were discretized and transformed into difference equation
groups by using a control volume method. The numerical solutions to the variables
were obtained by using the SIMPLE calculation method.
Calculated Results and Discussion
(i) Velocityfield
When the flow rate of the carrying gas (Ar) is 1.608 Nm’/min and the degree of
vacuum is 10532 Pa, then the velocity field of the gas in RH chamber is generally
characterized as follows. The horizontal branch velocity of the gases escaping from
the vacuum chamber is low compared with that in the vertical direction. The velocity
of the gas along the up-leg is very high, and it is uniformly distributed on all the
intersections of the RH chamber with increasing altitude. If an oxygen stream is
present, it will give rise to a vigorous agitation zone. The gas flow fields on the cross
section of the vacuum chamber are shown in Figure 1 .
Figure 1. The velociqjeld in RH chamber for diTerent positions of the top lance;
(a) no top lance; (6) I m; (c) 2 m; (4 3 m.
Zong-Ze Huang, Yi-Sheng Chen and You-Duo He
After comparison of the velocity fields shown in Figure 1 (a) to (d), the influence
of different positions of the top lance on the flow field at the bottom of the vacuum
chamber is obvious. The oxygen stream has a strong impulsive force that causes a
compression zone 3-4 m tall in the environment of the rising gases. Comparing
Figure I(b) with (c) and (d), for situation (b) when the position ofthe lance is at Im to
the molten steel surface, the high-speed jet descends too quickly to diffuse before
reaching the surface of the molten steel in the vacuum chamber. This creates many
steel drops and excess oxidization of the molten steel,
In Figure I(d), the position of the lance of RH-KTB is 3 m from the molten steel
surface, the compressive kinetic energy of the oxygen jet has dissipated without
reaching the molten steel surface, and the oxygen stream rises because the gases flow
in the reverse direction. Although excess oxidization may not take place at this time, it
is very difficult to heat the molten steel surface by means of the combustion of CO
because the oxidizing zone is away from the surface region of the molten steel under
this condition. If the position of the top lance is at 2 m to the molten steel surface,
then it is relatively easy to heat the molten steel by combustion of CO, and the molten
steel can also avoid becoming excessively oxidized by the oxygen stream.
When O2 is blown in by the top lance of RH-KTB, at first the low temperature center
is formed around the top lance, then the temperature rises gradually toward the
peripheral section and reaches the highest value in the combustion and diffusion zone
of CO and 02,and then the gas temperature continuously declines approaching the
furthest peripheral region. The post combustion region in the vacuum chamber is a
high-speed flame in turbulent motion and with diffusion to create an irregular
curve-like interface.
Figure 2 displays three temperature fields corresponding to the three flow fields
having the same position of the top lance. Comparing the results of the three
temperature fields shows that there is no obvious change in temperature near the
molten steel surface after lowing the position of the lance from 2 m to 1 m. This is
because when the lance position is too low there is insufficient time for the oxygen jet
to filly contact the up-rising CO and, hence, generate the required combustion. In this
case, post combustion takes place mostly in the upper part of the vacuum chamber.
Comparing the temperature field of the lance position at 2 m with that at 3 m, then the
lower is the position of the lance, the higher is the temperature next to the surface of
the liquid steel. Therefore, the preferred position of the top lance is at 2 m for heating
the molten steel by means of post combustion.
(iii) Concentrationfleld
In the vacuum chamber of RH-KTB process, the gases mainly consisted of CO, C 0 2
and O2 whose distributions are characterized as follows. The CO is concentrated
mostly on the molten steel surface, especially on the area round the up-leg, and
disappearing quickly with an increase in distance away from the surface. The
concentration of C 0 2 increases with the increase of height, and there is a
comparatively low concentration region near the head of the oxygen lance. The 02 is
Mathematical Modeling of the Vacuum Chamber of RH-KTB Process
distributed in an asymmetrical curve-like zone with the head as its center, and the
oxygen concentration reducing from the center to the peripheral region. The
distributions of the gases CO, COz and O2at the three lance positions (at 1 m, 2 m and
3 m) are shown in Figure 3 and Figure 4, corresponding to the velocity fields at the
same positions o f the top lance in Figure 1.
Analysis of the results presented in Figures 1 to 4 indicates that when the lance
position is at 1 m, the oxidized zone extends to the liquid steel surface and causes
direct oxidization of the liquid steel by the oxygen stream. Therefore, more deoxidizer
was consumed and more deoxidized products were produced. For the lance at 3 m, the
oxidized zone is far away from the molten steel surface and there is failure in the
heating and insulation of the liquid steel. For the lance at 2 m, the peripheral part of
the oxidized zone lies on the liquid steel surface, which can protects the liquid steel
from excess oxidization and also means that there is good heating of the molten steel
from post combustion.
8.1 -
2. I
2.3 1.6
0 2.3 1.6
0 2 . 3 1.6
Figure 2. Temperature field in the RH vacuum chamber for diflerent positions of the
top lance; (a) I m; (b) 2 m; (c) 3 m.
Zong-Ze Huang, Yi-Sheng Chen and You-Duo He
L. L
I I I'
. -..."l
Figure 3. Concentrationsfields of CO (a-c) and CO2 (d-fl in RH vacuum chamber:
(a) and (d) I m position of top lance; (b) and (e) 2 m position of top lance; (c) and fl
3 m position of top lance.
Mathematical Modeling of the Vacuum Chamber of RH-KTB Process
. ..
2. 1
0. 1
0 2.3 1.6
0 2.3 1.6
0.8 0
Figure 4. O2 concentration field in RH vacuum chamber: (a) I m position of lance;
(b) 2 m position of oxygen lance; (c) 3 m position of oxygen lance.
1. An oxygen jet in post combustion can create vigorous agitation of the fluid field at
the bottom of the vacuum chamber of the RH-KTB process, and the agitation
contributes significantly to the uniform distribution of gases at the cross-sections
of the vacuum chamber.
2. The optimum position of the top lance of the RH-KTB to ensure heating and
insulation of the molten steel is at an altitude of 2m in the vacuum chamber.
1. Kuwabara, T., Harada, S., Furusaki, T., et al. 1986. The development of RH-Injection technology.
Proceedings of the 6VhSfeelmakingConference, ISSIAIME, 293-297.
2. Kazuro, S., and Julian, S. 1983. A mathematical model of fluid flow and inclusion coalescence in the
RH vacuum degassing system. Trans.BIJ, 23(3), 465-473.
3. Wei, J.H., Zhu, S.J., and Yu,N.W. 1998. Kinetics of powder top blowing desulfurization in RH refining
Acta Metal. Sinica, 34(5), 497-505.
45 7
Zong-Ze ffuang, Yi-Sheng Chen and You-Duo He
4. Huang, Z.Z., Zheng, J.Z., and Gu, W.B. 2003. Development and optimization of secondary refining
and future work at Baosteel. China Metallurgv (in Chinese), l3(7), 17-20.
5 . Hanna, R.K., Jones, T., Blake, R.1.,et at. 1994. Water modeling to aid improvement of degasser
performance for production of ultra low carbon interstitial free steels. Ironmaking & Steelmuking, 21( I),
6. Nakanishi, K., Szekely, J., and Chang, C.W. 1975.Experimental and theoretical investigation of mixing
phenomena in the RH vacuum process. Ironmaking & Steehnaking, 2(2), 115-124.
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