I
Mathematical and Physical Simulations of BOF Converters
Xiaobin Zhou
Doctoral Thesis
Stockholm 2015
Division of Applied Process Metallurgy
Department of Materials Science and Engineering
School of Industrial Engineering and Management
KTH Royal Institute of Technology
SE-100 44 Stockholm
Sweden
Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm,
framlägges för offentlig granskning för avläggande av Teknologie Doktorsexamen,
fredagen den 6 November, kl. 10.00 i M3, Brinellvägen 68, Materialvetenskap,
Kungliga Tekniska Högskolan, Stockholm
ISBN: 978-91-7595-714-2
II
Xiaobin Zhou Mathematical and Physical Simulations of BOF Converters
Division of Applied Process Metallurgy
Department of Materials Science and Engineering
School of Industrial Engineering and Management
KTH Royal Institute of Technology
SE-100 44 Stockholm
Sweden
ISBN: 978-91-7595-714-2
III
To my beloved parents
V
Abstract
The purpose of this study is to develop mathematical models to explore the mixing and its
related phenomena in converter bath. Specifically, first, a mathematical model of a physical
model converter, which was scaled down to 1/6th of a 30 t vessel, was developed in this study.
A number of parameters were studied and their effects on the mixing time were recorded in a
top blown converter. Second, a mathematical model for a combined top-bottom blown was
built to investigate the optimization process. Then, a side tuyere was introduced in the
combined top-bottom blown converter and its effects on the mixing and wall shear stress were
studied. Moreover, based on the above results, the kinetic energy transfer phenomena in a real
converter were investigated by applying the mathematical models.
A simplified model, in which the calculation region was reduced to save calculation compared
to simulations of the whole region of the converter, was used in the mathematical simulation.
In addition, this method was also used in the simulation of real converters. This approach makes
it possible to simulate the Laval nozzle flow jet and the cavity separately when using different
turbulence models.
In the top blown converter model, a comparison between the physical model and the
mathematical model showed a good relative difference of 2.5% and 6.1% for the cavity depth
and radius, respectively. In addition, the predicted mixing time showed a good relative
difference of 2.8% in comparison to the experimental data. In an optimization of a combined
top-bottom blown converter, a new bottom tuyere scheme with an asymmetrical configuration
was found to be one of the best cases with respect to a decreased mixing time in the bath. An
industrial investigation showed that the application effects of the new tuyere scheme yield a
better stirring condition in the bath compared to the original case. Furthermore, the results
indicated that the mixing time for a combined top-bottom-side blown converter was decreased
profoundly compared to a conventional combined top-bottom blown converter. It was found
that the side wall shear stress is increased by introducing side blowing, especially in the region
near the side blowing plume.
For a 100 t converter in real, the fundamental aspects of kinetic energy transfer from a top and
bottom gas to the bath were explored. The analyses revealed that the energy transfer is less
efficient when the top lance height is lowered or the flowrate is increased in the top blowing
operations. However, an inverse trend was found. Namely, that the kinetic energy transfer is
increased when the bottom flowrate is increased in the current bottom blowing operations. In
addition, the slag on top of the bath is found to dissipate 6.6%, 9.4% and 11.2% for the slag
masses 5, 9 and 15 t compared to the case without slag on top of the surface of the bath,
respectively.
Key words: mathematical model, physical model, converter, combined blown, cavity, mixing
time, optimized scheme, side tuyere, industrial experiment, kinetic energy transfer
VII
Acknowledgement
Though only my name appears on the cover of this dissertation, a great many people have
contributed to its production. I owe my gratitude to all those people who have made this
dissertation possible and because of whom my KTH experience has been one that I will cherish
forever.
I would like to express my deepest gratitude to my supervisor Pär Jönsson, for his caring,
patience, and providing me with an excellent atmosphere for doing research. I also would like
to thank my supervisor Mikael Ersson. I have been amazingly fortunate to have advisors who
gave me the freedom to explore on my own and at the same time the guidance to recover when
my steps faltered.
I also appreciate Professor Liangcai Zhong and Professor Jingkun Yu from Northeastern
University of China for their support and recommendation on my research in KTH.
I am thankful to the CFD meeting which was promoted by Mikael Ersson. I learned a lot of
useful numerical knowledge during the presentation and discussion with participants. I believe
this will lay a solid foundation for my future work.
Many friends in Sweden have helped me adjust to a new country. Their support and care helped
me overcome setbacks and stay focused on my study. I am grateful to my friends who gave me
many ideas and comments on my study. I greatly value their friendship and I deeply appreciate
their belief in me.
I would like to express my gratitude to China Scholarship Council for the financial support.
The scholarship from the Jernkontoret (The Swedish Steel Producers’ Association) is also
highly appreciated. I would like to extend my sincere gratitude to the Olle Eriksson Foundation
Scholarship and the Jubileumsanslaget Foundation in support of Conference trips.
Most importantly, none of this would have been possible without the love and patience of my
family. My immediate family, to whom this dissertation is dedicated to, has been a constant
source of love, concern, support and strength all the time. I warmly appreciate the generosity
and understanding of my extended family.
Stockholm, October 2015
IX
Supplements
The present thesis is based on the following supplements:
Supplement 1
Mathematical and Physical Simulation of a Top Blown Converter
Xiaobin ZHOU, Mikael ERSSON, Liangcai ZHONG, Jingkun YU, Pär JÖNSSON
Steel research int. 85 (2014) No.2, pp. 273-281.
Supplement 2
Optimization of the Combined Blown Converter Process
Xiaobin ZHOU, Mikael ERSSON, Liangcai ZHONG, Pär JÖNSSON
ISIJ Int. 54 (2014) No.10, pp. 2255-2262.
Supplement 3
Numerical and Physical Simulations of a Combined Top-Bottom-Side Blown Converter
Xiaobin ZHOU, Mikael ERSSON, Liangcai ZHONG, Pär JÖNSSON
Accepted for publication in Steel research int., DOI: 10.1002/srin.201400376
Supplement 4
Numerical simulations of the kinetic energy transfer in the bath of a BOF Converter
Xiaobin ZHOU, Mikael ERSSON, Liangcai ZHONG, Pär JÖNSSON
Accepted for publication in Metallurgical and Materials Transactions B, DOI:
10.1007/s11663-015-0465-0.
The contributions by the author to the supplements of the thesis:
Supplements 1-4
Literature survey, numerical simulation and major part of physical simulation and writing.
X
Part of the work have been presented at the following conference:
An analysis of a converter based on modelling, Xiaobin ZHOU, Mikael ERSSON, Pär
JÖNSSON, The 1st European Steel Technology and Application Days & 31st Join New
European Steel Industry Conference (1st ESTED & 31st JSI2014), Paris, France; April 7-8,
2014
Simulation of the influence of side-blowing on the stirring in the top-bottom-side blown
converter, Xiaobin ZHOU, Mikael ERSSON, Pär JÖNSSON, The 7th European Oxygen
Steelmaking Conference (EOSC2014), Třinec, Czech Republic, September 9-11, 2014
A numerical study of mixing behavior in the bath of a converter, Xiaobin ZHOU, Mikael
ERSSON, Liangcai ZHONG, Pär JÖNSSON, The 6th International Congress on the Science
and Technology of Steelmaking (ICS2015), Beijing, China, May 12-14, 2015.
XI
Contents
Abstract .............................................................................................................................................................. V
Acknowledgement ...................................................................................................................................... VII
Supplements ................................................................................................................................................... IX
Contents ............................................................................................................................................................ XI
Chapter 1 Overview ...................................................................................................................................... 1
1.1 Introduction ......................................................................................................................................... 1
1.2 Aim of this thesis ................................................................................................................................ 3
Chapter 2 Physical model........................................................................................................................... 7
Chapter 3 Mathematical model .............................................................................................................. 11
3.1 Assumption ................................................................................................................................... 11
3.2 VOF model ..................................................................................................................................... 11
3.3 DPM model .................................................................................................................................... 12
3.4 Turbulence equations ............................................................................................................... 14
3.5 User-Defined Scalar ................................................................................................................... 15
3.6 Boundary conditions and solution methods .................................................................... 15
3.6.1 The simulation of the physical model ........................................................................ 15
3.6.2 The simulation of the real converter .......................................................................... 16
Chapter 4 Industrial experiment ........................................................................................................... 19
Chapter 5 Results and discussion ......................................................................................................... 21
5.1 A physical model and a mathematical model of a pure top blown converter ..... 21
5.1.1 The cavity depth and radius .......................................................................................... 21
5.1.2 The calculation of mixing time ..................................................................................... 23
5.2 The optimization of combined top-bottom blown converter ................................... 26
5.2.1 Physical model results ..................................................................................................... 26
5.2.2 Mathematical model results .......................................................................................... 27
5.2.3 Industrial experimental results .................................................................................... 30
5.3 The combined top-bottom-side (TBS) blown converter ............................................. 30
5.3.1 The flow field in the bath ................................................................................................ 31
5.3.2 Mixing time ........................................................................................................................... 33
5.3.3 The shear stress on the wall .......................................................................................... 34
5.4 The kinetic energy transfer in a real converter .............................................................. 35
5.4.1 The top blowing process ................................................................................................. 35
5.4.2 The bottom blowing process ......................................................................................... 38
Chapter 6 Conclusions ............................................................................................................................... 43
Future work.................................................................................................................................................... 45
XII
Reference......................................................................................................................................................... 47
1
Chapter 1 Overview
1.1 Introduction
The liquid-motion, which results from the momentum transfer between the jet, bottom or side
plumes and the bath, represents a relatively complex physical phenomenon that occurs in the
bath of a steelmaking converter. The momentum of the gas injected from the top lance, bottom
and side tuyeres largely determines the agitation and mixing of the bath. In the combined blown
converter, the agitating and the mixing of the bath are forced by the top oxygen jets and the
bottom gas plumes. This combined stirring can result in a high mixing efficiency of the bath.
Previously, various numerical investigations of supersonic jets behavior from the Laval nozzle
have been reported in the literature [1-4].The top-lance height, the gas flow rates, bottom blowing
and side blowing are investigated to improve the steel making process in many studies [5-18].
Evidently, the bottom or side tuyere configuration in the combined blown converter is very
significant to the bath mixing, reaction of slag-metal, and splashing. There will be a high
chemical reaction rate, a calm smelting operation and a high efficiency if the stirring is intense
and well-distributed. Thus, it is necessary to investigate the interaction of gas and liquid in the
converter in order to provide a valuable reference to the steelmaking operation.
In recent years, more and more physical and chemical phenomena in metallurgical vessels have
been studied along with the development of computer technology. In Solórzano-López’s
study[5], the agreement between the 3D-mathematical model predictions and experimental
measurements were found to be excellent for both the velocity component of the liquid and the
cavity size. Also, Ersson et al. developed a 2D-mathematical model to study the interaction
between top-gas and liquid[6]. The predicted penetration depth was found to agree well with
measured surface deformations and predictions using analytical equations. Asai et al.[ 7 ]
developed a model to describe the penetration behavior of a liquid jet into a liquid bath by
using the MPS (moving particle demi-implicit) model. A two-dimensional simulation of the
impingement was performed for a slag–metal system, and the interfacial area between a slag
and a metal was estimated. The result showed that the penetration depth agreed well with the
reported empirical equations. Vikas et al. [8] carried out a water model study of a combined
blown converter in order to optimize the locations of the bottom blown nozzles with respect to
the mixing time. A mathematical model was also used to simulate the bottom blowing in the
converter. Overall, their computational results showed a good agreement with the experimental
observations in some of the cases. Also, Shiv et al. [9] used a cold model and thermodynamic
analysis to evaluate the bottom stirring of a converter. They found that the dolomite lining life
of the vessel increases and the total Fe content of the slag decreases with an increased bottom
stirring. However, there are few reports [10,11,12] on mathematical simulation of a combined
blowing. Wei et al. [10, 11] developed a mathematical model of a combined top-side blown AOD
converter. The changes and the number of the tuyere in the AOD were investigated. The results
showed that the fluid flow in the bath can reliably be predicted. In the research of Odenthal et
al. [12], a combined VOF and DPM model was used to describe the 3D, transient and non-
isothermal flow of the melt, slag, and oxygen for a 335 t combined blown converter. Moreover,
some researchers [13-16] put efforts in the investigation of the decarburization process in BOF.
The side blown technology is commonly utilized in steel making vessels such as the Argon
Oxygen Decarburization (AOD) process. Many investigations [17-20] on this process have been
performed for this process to study the effect of side blowing on the kinetics and
2
thermodynamics, using both the physical and mathematical modellings. Studies of an AOD
converter have been carried out by Odenthal et al. [17], when they applied a water model and a
mathematical model to investigate the bath stirring and the oscillation. The oscillation and the
vibration amplitudes were investigated for both the water and CFD model for different filling
levels of the bath and for several side flow rates. It was found that the CFD simulation was an
effective tool to make the AOD process more transparent. A numerical model coupling the
fluid dynamics and the vessel oscillation has been developed and tested successfully in
Wuppermann et al.’s work[18]. The oscillation of the bath was studied and a comparison of the
results with plant trail data proved that the model is capable to predict the oscillation
frequencies for the AOD process. The numerical model can be used to design the vessel shape
and structure, to ensure a reliable and stable process. The flow field of the side blowing in a
Peirce-Smith-converter was solved using the commercial CFD-code PHOENICS by Vaarno et
al. [19]. The results demonstrated that the side blown gas flowrate has a decisive role on the gas
stirring and liquid flow pattern in the bath. The gas jet from the top lance can enhance the gas
stirring and bath turbulence. The gas stirring and fluid flow characteristics in a combined top
and side blown AOD were investigated using a water model in Wei et al.’s work[20]. The results
demonstrated that the side blown gas flowrate has a decisive role on the gas stirring and liquid
flow pattern in the bath. More specifically, the gas jet from the top lance can enhance the gas
stirring and bath turbulence.
Overall, the side blowing technology has been shown to be useful in other metallurgical
operations. Despite this, only a few researchers used the side blowing technology in the Basic
Oxygen Furnace (BOF) studies. The combined stirring effects were studied by Hirata et al. [21]
in a 10 ton test converter using top oxygen injection from the top and side and nitrogen injection
from the bottom. It was found that oxygen blown from the side blowing oxygen stirs the slag
without creating an excessive amount of metal droplets. Moreover, that the heat transfer
efficiency increased without a decreased post combustion ratio. Also, Liangcai Zhong et al. [22]
applied a side blown tuyere in a 30 t converter to form a top-bottom-side (TBS) blowing
converter. It was found that the formation of a mushroom at the end of the side tuyere is more
favourable to protect the side tuyere and the ambient lining near it. The metallurgical results
showed that the consumption of ferrous alloys as well as lime could be reduced when using a
TBS converter.
For the real metallurgical vessels, quite a few mathematical models [1-4, 12-16, 23-25] have been
developed to describe the process kinetics of the furnace. One of the great advantages of
mathematical models is that they give researchers opportunities to have insights into this
complex system. Previously, a transient three-dimensional mathematical model was developed
to analyze the three-phase flow in a 150 t EAF (electric arc furnace).[ 23 ] The numerical
simulation provided an explanation to the serious erosion of the lining that took place next to
the oxygen lance in actual production. Also, Nakazono et al. [24] used numerical analysis to
describe a supersonic O2-jet impingement on to a liquid iron bath. The surface reaction on O2-
C and O-C were included in the model and the results showed that the effects of surface
reactions on the cavity geometry are very small. The effects of different densities of slag had
on the cavity in a BOF were studied in a mathematical model built by Lv et al. [25].
So many researchers already made efforts to study the impinging gas jets on a liquid surface,
bottom blowing or side blowing in the bath. Here, the cavity shapes and the mixing times were
mainly studied. However, only a few people considered the energy transferred from top jets
and bottom blowing gases to the bath. Specifically, Hwang et al. [ 26 ] developed a 2D
mathematical model to study top-blowing operations. The kinetic energy transferred from the
3
top-blowing gas to the bath was calculated without considering the effects of the physical
properties of the slag, the top- blowing parameters, and the surface roughness. Also, Dipak et
al. [27, 28] carried out a physical modelling to study the energy dissipation phenomena with and
without an overlying second phase liquid. The results showed that the overlying liquid is found
to dissipate about 10 percent of the input energy.
1.2 Aim of this thesis
Due to the importance of the liquid-motion in improving the steel making process of the
converter, a mathematical model was built based on the geometry of a physical model. Then
the mixing phenomena of the bath was studied by this mathematical model. Thereafter, the
mathematical model was used to simulate the optimization of a combined top-bottom and top-
bottom-side blown converter. Furthermore, the kinetic energy transfer phenomena in a real
converter were explored by applying the mathematical model. The main work of this study can
be summarized as shown in Figure 1.1.
Supplement 1
The first part is focused on the development of a mathematical model of a top blown converter
which is based on a scaled down physical model of a 30t converter. In this work, a 3D
mathematical model was built. The results of the mathematical model were compared to the
experimental measurements of the cavity shape and the mixing time. Then, the predicted
differences of the mixing time of the bath for different simulation times were compared to the
results from the physical model.
Supplement 2
Based on the model built in previous work (Supplement 1), the mathematical model was
executed to include a description of the optimization process of a converter equipped with three
bottom tuyeres and top blowing. The fluid flow characteristics in the bath of the original and
the optimized tuyere schemes was studied by analyzing the mixing times and turbulent
parameters. A new calculation method for mixing time of the bath was applied in this study.
The whole region of the bath can be considered with respect to the change of the tracer
concentration to avoid the defects brought by the discrete-point method. More details about the
methodology will be presented in Chapter 5. Moreover, to further verify the impact of the new
tuyere setup, an industrial investigation was carried out to study the differences in species
concentrations between the original scheme and the optimized scheme at tapping.
Supplement 3
A side tuyere was introduced to investigate how it is possible to enhance the bath agitation and
to avoid problems of a reduced stirring when using the application of a slag splashing process
in the combined top-bottom blown converter. The effects of the side blowing on the mixing of
the bath was investigated by both physical and mathematical models. Furthermore, with the
help of the mathematical model, the shear stress at the wall in the TBS converter was
considered since the furnace lining is important when side blowing is used in the converter.
Supplement 4
The mathematical results in the previous study showed that some phenomena, which are
difficult to investigate in the physical model, were possible to explore by using a mathematical
model. The work in this part focuses on the fundamental aspects of the kinetic energy transfer
4
from the top and bottom gases injection to the bath of a converter by applying mathematical
modelling. The aim of this research is to contribute to the understanding of the energy transfer
from the top jets and bottom blowing plumes to the bath in a full-scale BOF converter. In the
study, the effects of the top lance heights and gas flowrates on the energy transfer efficiency
were investigated. The distribution of bottom tuyeres and tuyeres number were also concerned
in the model. Furthermore, a slag with different physical properties was added on top of the
bath to investigate its effects on the kinetic energy transfer. In addition, the formation of a
foaming slag in the steelmaking process was also considered when exploring the energy
transfer in the bath.
5
Fig
ure
1.1
Ou
tlin
e o
f th
e p
rese
nt
wo
rk
7
Chapter 2 Physical model
The study was performed by using a 1:6 scaled model of a 30t converter. The physical model
apparatus can be seen in Figure 2.1. The experimental conditions are listed in Table 2.1. The
experimental testing methods were the same as used by Lai et al.[29].
Figure 2.1. Schematic of the experimental setup
Table 2.1. Physical experiment conditions
Parameters Model Prototype
Geometry Top lance flowrate, Nm3/h
Number of top lance nozzles
Nozzle’s angle Height of top lance, mm
Height of liquid in bath, mm
Density of water, kg/m³ Density of gas, kg/m³
Diameter of model bath, mm
Number of bottom tuyeres Bottom gas flowrate, Nm3/h
Side tuyere radial angle
Side tuyere diameter, mm Bottom gas flowrate, Nm3/h
1:6
34.66 3
10.5°
158
150
1000 1.293
417/492
3 50, 90, 180, 270
25°
- 96, 287
1
7600 3
10.5°
950
900
7800 1.429
2500/2950
3 0.21, 0.47, 0.94, 1.21
25°
1.4 0.5, 1.5
The temperature effects were not considered since, the impact of the temperature on the
dynamic pressure of the jets is relatively small [30,31]. Water and compressed air were used to
simulate the molten steel and the gas used in the top, bottom and side blowing, respectively.
The top lance was a three-hole lance, which is the same as is used in industry. The Modified
Froude Number, which is defined as the ratio of the inertial force to the buoyancy force
(equation 1), was applied to make the model dynamically similar to the actual converter:
Flowmeter Valve
Air compressor
Data collector Tracer
8
𝐹𝑟′ =𝜌𝑙
𝜌𝑙−𝜌𝑔∙𝑣2
𝑔𝐻 (1)
where Fr´ is the Modified Froude Number, ρl and ρg are the densities of water and air
respectively, v is the velocity, g is the acceleration of gravity, and H is the characteristic length.
To optimize the combined blown converter, a number of bottom-tuyere configurations were
tested in order to optimize the dynamic conditions of the bath [32]. Several schemes were found
to be effective in improving the mixing effects. The bottom blown converter was also studied
to find an appropriate flow rate of the blown gas.
In this study, an optimized scheme with a bottom-tuyere configured asymmetrically was chosen
to show the optimized results and it was also used as the reference scheme of the mathematical
simulation. Figure 2.2 shows the distribution of bottom tuyeres in the original and the
optimized scheme. To eliminate other influencing factors, the top blown gas flow rate was kept
constant in both cases.
(a) Original scheme (b) Optimized scheme
Figure 2.2. The bottom tuyere distribution of the converter (mm). The three blown directions of the top lance can also be seen in the figure
Figure 2.3 shows the distribution of the side blown tuyeres, as well as the bottom tuyeres and
the cavity resulted from the top blowing jets. In the experiment, an asymmetric distribution of
the bottom tuyeres was used. The flow rates for the bottom and top blowing are kept constant
in order to study the side blowing effects in different locations of the bath. The radial angle of
the side tuyere was set to 25o. Four cases with different side tuyere installations were studied
in the physical model. Two different heights (tuyere A and B) of vertically positioned the side
blown tuyeres were investigated to study the effects of tuyere the vertical height on the flow in
the bath. Three side blown tuyeres (tuyere B, C and D), which were located in the circle of the
bath with the same height, were used to study the flow interaction between the bottom and
different side plumes with the top blowing.
In the mixing time testing, 3 probes (point A, B and C) were set at different locations to monitor
the concentration of the tracer element in the bath. A volume of 150 ml NaCl solution was used
as tracer to enable measurement of the water’s electronic conductivity in different locations of
the bath. In this work, the mixing time is defined as a time when the tracer concentration at the
monitor points reach 99% of the mean tracer concentration in the bath. The mixing times
100
83
50
116
83
50
116
9
obtained from points A, B and C are defined as TA, TB and TC, respectively. The mean mixing
time (Tm) is calculated as an arithmetical mean value using equation 2:
𝑇𝑚 =𝑇𝐴+𝑇𝐵+𝑇𝐶
3 (2)
The cavity shape images were recorded by a video camera. Thereafter, the cavity depth was
measured from the recordings.
Figure 2.3. The distribution of side and bottom tuyeres of the physical model (mm)
10
100
150
492
417
A
B, C, D
116
83
50
116
25o C
D
A, B
11
Chapter 3 Mathematical model
To describe the interface formation in the simulation, the volume of fluid (VOF) [33] method
was applied to describe the interface between gas and liquid. In addition the bottom or the side
blowing plumes in the combined blown converter was described by a discrete phase model
(DPM) [34]. Also, the UDS (user defined scalar) model was used to calculate the mixing time
in the bath of the converter[34].
3.1 Assumption
Since the phenomena in the bath of the converter are very complex, the mathematical model
for the fluid flow and bubbles from the bottom blowing in the converter are based on the
following assumptions:
For the simulation of the physical model:
a) Air and water are regarded as Newtonian fluids.
b) The flow in the model is isothermal.
c) The air and water are incompressible
d) The coalescence and break-up of bubbles resulting from the bottom and side blowing
are ignored.
e) The effects of pressure change on the volume of bubbles are ignored.
For the simulation of the real converter:
a) Oxygen, foam, slag, molten steel, and bottom blowing gas are regarded as Newtonian
fluids.
b) The flow in the model is isothermal.
c) No mass sources are taken into account in the calculations.
d) The molten steel, slag and foam are incompressible and the top jets and bottom blowing
gases are compressible.
e) The foam is simplified to have a uniform density and viscosity.
f) The effects of chemical reaction on the cavity and the flow are ignored.
g) The coalescence and break-up of bubbles resulting from the bottom blowing are ignored.
3.2 VOF model
A coupled level-set and VOF model was used in the simulation. The level-set method is used
for producing accurate estimates of interface curvature and surface tension force. The tracking
of the interface between gas and liquid is accomplished by the solution of a continuity equation
for the volume of gas or liquid phase. For the qth phase, the equation has the following form:
𝜕𝛼𝑞𝜌𝑞
𝜕𝑡+ �⃗� ∙ ∇𝛼𝑞𝜌𝑞 = 0 (3)
where αq is the fraction of phase, ρq is the density of phase and v is the velocity.
The primary-phase volume fraction is computed based on the following constraint:
∑ 𝛼𝑞𝑛𝑞=1 = 1 (4)
12
The momentum equation, shown as below, is dependent on the volume fractions of the gas
and the water phases through the properties ρ and µ:
𝜕
𝜕𝑡(𝜌 �⃗�) + ∇(𝜌 �⃗��⃗�) = −∇𝑝 + ∇ ∙ [𝜇(∇ �⃗� + ∇�⃗�𝑇)] + 𝜌�⃗� + �⃗� (5)
where p is the static pressure, ρg is the gravitational force, F is the external body force and
model-dependent source terms, ρ and µ are shown as below:
𝜌 = 𝜌gas𝛼gas + (1 − 𝛼gas)𝜌liquid (6)
𝜇 = 𝜇gas𝛼gas + (1 − 𝛼gas)𝜇liquid (7)
3.3 DPM model
The liquid and top blowing gas phases in the simulation were treated as continuous phases by
solving the Navier-Stokes equations. However, the bubbles used in the bottom and side
blowing were described by DPM model. A user defined function (UDF) was used to delete the
discrete phase bubbles when they reached the liquid/gas interface. Thus, it was assumed that
the bubbles would escape to the gas above the interface in this case.
The trajectory of the bubbles was predicted by integrating the force balance on the bubbles.
This force balance equates the bubbles inertia with the forces acting on the bubbles, and can be
shown as follows:
𝑑𝑣𝑏
𝑑𝑡= 𝐹𝐷(�⃗� − 𝑣𝑏⃗⃗⃗⃗⃗) +
�⃗⃗�(𝜌𝑏−𝜌)
𝜌𝑏+ �⃗� (8)
where v is the water velocity in the bath, vb is the velocity of the bubbles, ρb is the density of
bubble, ρ is the density of liquid, F is an additional acceleration term, 𝐹D(�⃗� − 𝑣b⃗⃗⃗⃗⃗) is the drag
force per unit bubble mass and
𝐹D =18𝜇
𝜌b𝑑𝑏2
𝐶D𝑅𝑒
24 (9)
where, µ is the molecular viscosity of the liquid; CD is the drag coefficient of the bubbles.
In the real bath of the 100 t converter, several double-pipe nozzles were applied in the bottom
blowing process. When the gas is injected into the bath through a bottom tuyere, a mushroom
will be formed on top of the nozzle, as molten steel comes in contact with the blowing gas. The
mushroom contains a great number of small pores, which originates from the outlet of
individual pipes of the nozzle [35]. The diameter for each pore is about 0.3 mm. The temperature
near the mushroom is above 1200℃. As the gas in the blowing process is heated, the volume
is increased and the density is decreased. All the factors mentioned above together with the
coalescence and break-up of bubbles on top of the mushroom make it difficult to estimate the
diameters of bubbles and the diameter distribution. Iguchi et al. [36] carried out an experiment
to study the bubble characteristics in a molten iron bath at 1600℃. The results show that the diameter of the bubbles is in the region of 20 to 40 mm at a flowrate of 100 cm3/s. Consequently, the diameters used in this mathematical model were estimated roughly to have
values ranging from 20 to 40 mm and having a mean value of 30 mm. The volume growth and
13
the density change of the bubbles during the rise process were calculated by a UDF. The
equations used in the UDF are shown as follows:
𝜌𝑏 = 𝑃b ×𝜌𝑏_𝑖𝑛
𝑃0 (10)
𝑃𝑏 = (𝑃0 − 𝜌𝑠𝑔𝑧 +2𝜎
𝑑𝑏) (11)
where Pb is the inner pressure of bubbles, P0 is the pressure at the surface of molten steel, ρs is
molten steel density, g is the gravity acceleration, z is the bath depth, db is bubble diameter, σ
is the surface tension of molten steel, ρb_in and ρb are the densities of bubbles at the inlet and
the rising process, respectively.
The temperature of the molten steel is not taken into account in the mathematical model. So
the effect of the temperature on the volume growth of the bubbles was considered by injecting
a gas which is heated by the molten steel. The density of the blowing bubbles is computed by
the equation as follow:
𝜌𝑏_𝑖𝑛 =𝑃𝑠
𝑃0×𝑇0
𝑇s× 𝜌0 (12)
where Ps is the pressure at the bottom inlet, T0 and Ts are standard and molten steel temperature,
respectively. The parameter ρ0 is the density of the bubble at standard temperature.
Another UDF for the DPM model was used to describe the drag force of bubbles in the liquid.
The shape of the bottom blowing bubbles is irregular in the bath, especially when the diameters
of the bubbles are large and the flow rate is high. As a result, the rigid sphere drag force
coefficient is not suitable to describe all the bubbles mathematically. In the physical model, the
ellipsoidal-shaped and cap-shaped bubbles are in majority and the bubble shape will affect the
bubble drag force. Therefore, the liquid flow in the bath was roughly divided into four turbulent
regions based on the relative Reynolds number. This is due to that the shape of the bubbles in
the liquid is affected by the relative Reynolds number. The drag force coefficient is defined as
follows[37]:
𝐶𝐷 =
{
64
𝜋𝑅𝑒∙ (1 +
𝑅𝑒
2𝜋), (0 < 𝑅𝑒 ≤ 0.01)
64
𝜋𝑅𝑒∙ (1 + 10−0.883+0.906 log10 𝑅𝑒−0.025(log10 𝑅𝑒)
2), (0.01 < 𝑅𝑒 ≤ 1.5)
64
𝜋𝑅𝑒∙ (1 + 0.138𝑅𝑒0.792), (1.5 < 𝑅𝑒 ≤ 133)
1.17, (133 > 𝑅𝑒)
(13)
where Re is the relative Reynolds number, which is defined as
𝑅𝑒 ≡𝜌𝑑𝑏|�⃗⃗�−𝑣𝑏⃗⃗ ⃗⃗ ⃗|
𝜇 (14)
where ρ is the density of liquid, db is the bubble diameter, µ is the molecular viscosity of the
liquid.
The additional acceleration F includes the “virtual mass” force [34, 38] and the “pressure gradient”
force [34]. Because the bubble density used in the model is much smaller than that of molten
steel and slag, the virtual mass force need to be considered in the calculation. Virtual mass is
14
the inertia added to a system because an accelerating or decelerating body must move some
volume of surrounding fluid as it moves through it. Virtual mass is a common issue because
the object and surrounding fluid cannot occupy the same physical space simultaneously. And
an uncoupled contribution from ‘’pressure gradient’’ force was also considered. The coupled
forces can be written as equation 15 and equation 16, respectively:
𝐹𝑣𝑖𝑟𝑡𝑢𝑎𝑙 =1
2
𝜌
𝜌𝑏
𝑑
𝑑𝑡(�⃗� − 𝑣𝑏⃗⃗⃗⃗⃗) (15)
𝐹𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =𝜌
𝜌𝑏𝑣𝑏∇𝑣 (16)
In the DPM model, the node-based averaging method was applied to distribute the bubble’s
effects to neighbouring mesh nodes. The grid dependency of the bubble simulation can be
reduced since the bubbles effects [34] on the flow solver are distribute more smoothly across the
neighbouring cells.
3.4 Turbulence equations
For the simulation of the physical model, the Standard k-ε model [39] was used to describe
turbulence, which solves equations to obtain the eddy viscosity field:
𝜇t = 𝜌𝐶μ𝑘2 𝜀⁄ (17)
For the Standard k-ε model, the turbulence kinetic energy, k, and its rate of dissipation, ε, are
calculated from the following transport equations:
𝜕
𝜕𝑡(𝜌𝑘) +
𝜕
𝜕𝑥𝑖(𝜌𝑢𝑖𝑘) =
𝜕
𝜕𝑥𝑗((𝜇 +
𝜇𝑡
𝜎𝑘)𝜕𝑘
𝜕𝑥𝑗) + 𝐺𝑘 − 𝜌𝜀 (18)
and
𝜕
𝜕𝑡(𝜌𝜀) +
𝜕
𝜕𝑥𝑖(𝜌𝑢𝑖𝜀) =
𝜕
𝜕𝑥𝑗((𝜇 +
𝜇𝑡
𝜎𝜀)𝜕𝜀
𝜕𝑥𝑗) + 𝐶1𝜀(𝐺𝑘 + 𝐶3𝜀𝐺𝑏)
𝜀
𝑘− 𝐶2𝜀
𝜀2
𝑘𝜌 (19)
in the equations, Gk represents the generation of turbulence kinetic energy due to the mean
velocity gradient, calculated as described as follows:
𝐺𝑘 = −𝜌𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ 𝜕𝑢𝑗
𝜕𝑥𝑖 (20)
where C1ε,C2ε,σk,σε and Cμ are constant and have the following default values [39],
C1ε=1.44,C2ε=1.92,Cμ=0.09,σk=1.0,σε=1.3.
For the simulation of the real converter, two turbulence models were applied in the
mathematical simulation. The Standard k-ε model was applied to calculate the domain for the
lower part of the converter. For the supersonic jet flow, the standard k-ω model was used, as
described below.
15
The gas jet from the top lance was calculated by the standard k-ω model [40,41] based on the
Wilcox turbulence model which incorporates modifications for compressibility and shear flow
spreading. The transport equations for the turbulence kinetic energy, k, and its dissipation rate,
ω, can be expressed as follows:
𝜕
𝜕𝑡(𝜌𝑘) +
𝜕
𝜕𝑥𝑖(𝜌𝑢𝑖𝑘) =
𝜕
𝜕𝑥𝑗((𝜇 +
𝜇𝑡
𝜎𝑘)𝜕𝑘
𝜕𝑥𝑗) − 𝜌𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ 𝜕𝑢𝑗
𝜕𝑥𝑖− 𝑌𝑘 (21)
and
𝜕
𝜕𝑡(𝜌𝜔) +
𝜕
𝜕𝑥𝑖(𝜌𝑢𝑖𝜔) =
𝜕
𝜕𝑥𝑗((𝜇 +
𝜇𝑡
𝜎𝜔)𝜕𝜔
𝜕𝑥𝑗) − 𝜌𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ 𝜕𝑢𝑗
𝜕𝑥𝑖
𝜔
𝑘− 𝑌𝜔 (22)
In these equations. σk and σω are the turbulent Prandtl numbers for k and ω, Yk and Yω represent
the dissipation of k and ω due to turbulence. The turbulent viscosity, μt, is computed by
combining k and ω as follows:
𝜇𝑡 = 𝜌𝑘 𝜔⁄ (23)
3.5 User-Defined Scalar
The mixing time of the bath is the main parameter used to study the stirring effects in both the
physical model and the mathematical model. The simulation of the mixing time uses a User-
Defined Scalar model, which solves the following equation [34]:
𝜕
𝜕𝑡(𝜌∅) +
∂
∂𝑥𝑖(𝜌𝑢𝑖∅ − Γ
𝜕𝜙
𝜕𝑥𝑖) = 0 (24)
where Γ is the diffusion coefficient in turbulent flows, which is computed in the following form:
𝛤 = 𝜌𝐷𝑚 +𝜇𝑡
𝑆𝐶𝑡 (25)
here, Dm is the mass diffusion coefficient, SCt is the turbulent Schmidt number (µt /ρDt where
µt is the turbulent viscosity and Dt is the turbulent diffusivity).
3.6 Boundary conditions and solution methods
3.6.1 The simulation of the physical model
The simulations were performed in a transient state. When comparing the mixing time results
between the physical and the mathematical model, long-time simulation results are needed in
order to get a relatively steady state solution. As a result, the mathematical model was
simplified to make long-time simulations possible. As shown in Figure 3.1a, the initial
calculation region is the lower part of the converter model (model A). When the cavity formed
in the bath was relatively steady, the data, which includes velocity, pressure, turbulent kinetic
energy and turbulent dissipation rate of data-exporting-face, were exported and imported to a
simplified model (Figure 3.1b) as an inlet boundary condition. Thereafter, this simplified
model (model B) was used to calculate the long-time conditions.
16
(a) Model A (b) Model B
Figure 3.1. Schematic of mathematical model simplification
All mathematic simulation boundary conditions were chosen to correspond to the experimental
process parameters (Table 2.1). In the physical model, the velocity of gas at the top lance
nozzle exit was less than 130 m/s (i.e. 2/5 the speed of sound). In the mathematical model, a
velocity-inlet boundary condition was used to describe the gas supplied from the top through
the lance. Also, a pressure condition equal to atmospheric pressure was used at the converter
mouth. In addition, different mass flow rates inlet boundary conditions of bottom and side
blowing gas were used with the DPM model.
3.6.2 The simulation of the real converter
The top blowing and the bottom blowing operations were calculated separately using different
models in order to investigate the energy transfer specifically. The flow phenomena, input
energy and the average kinetic energy of motion within the bath were investigated as a function
of top lance gas flowrates, top lance heights and bottom blowing flowrates. The slag and the
foam with different physical properties were poured on top of the molten steel so as to study
the effects of different slag and foam on the flow of the molten steel in the bath. The main
parameters and physical properties of the fluid used in the model are shown in Table 3.1 and
Table 3.2.
Table 3.1. Dimensions of the 100t converter and the main parameters used in the model
Parameter Values
Top lance height, mm 1000, 1300, 1600
Top gas flowrate, Nm3/h 20000, 22000, 25000 Number of top lance nozzles 4
Nozzles angle 12o
Nozzle diameter, mm inlet throat outlet
60 36 44
Bath diameter, mm 4471/3876
Bath depth, mm 1256
Number of the bottom tuyere 4, 6 Bottom gas flowrate, Nm3/h 216, 432, 648
Melt charge weight, t 100 Slag charge weight, t 5, 9, 13
Inlet
Data exporting faceData importing face
Calculative region
17
Table 3.2. Physical properties of the fluid
Physical properties Density, kg/m3 Viscosity, µ Pa·s
Molten steel 7000 600
Oxygen 1.29 15.9 Argon 1.61 14.0
Slag 3500 0.025, 0.05, 0.2 Foam 350, 875, 1400 0.136, 0.145, 0.154
The jets from the top lance reached a supersonic velocity, which influences the density of the
oxygen gas flow significantly. Therefore, the density-based solver was applied to calculate the
compressible gas flow. Because the VOF model is not available with the density-based solver,
the supersonic jet flow and the impinging of the jet on the surface of the molten steel were
calculated in the density-based and the pressure-based solver, respectively. The simplification
method of the mathematical model described in Figure 3.1 were applied to make it possible to
calculate the top blowing phenomena during modellings using different solvers. More
calculation information is shown in Table 3.3.
Table 3.3. Main information of mathematical simulation for different operations
Operation Solver Turbulence model Compressibility of fluid Phase
Laval jet Density-based k-ω Compressible Single Phase
Top blowing Pressure-based k-ɛ Incompressible VOF
Bottom blowing Pressure-based k-ɛ Molten steel, slag, foam Incompressible VOF
Bubbles Compressible DPM
A fine mesh at the liquid/gas interface and high velocity-gradient regions together with the
Geo-reconstruct algorithm was used to track the free surface deformation due to top-, bottom-
and side-blowing. Pressure-velocity coupling was solved using the PISO algorithm. The
second upwind scheme was chosen for momentum and turbulence in the spatial discretization.
For the simulation of the physical model, the time steps used in the fluid simulations were
2×10-4 s. However, a frozen flow field was used for the mixing time calculations. In this case,
the time-step could be increased to 0.1 s in those simulations. The simulations were run during
a long enough time to obtain a fully developed flow. This flow field was acquired by
monitoring the velocity of the fluid in the bath. For the simulation of real converter, the
developed transient solutions were obtained using a velocity-monitor method with time steps
of 1×10-6 s for the top blowing and 1×10-2 s for the bottom blowing operations, respectively.
19
Chapter 4 Industrial experiment
Some industrial experiments were performed in a 30 t combined converter. This was done to
verify the new tuyere configuration found using the physical and the mathematical models. The
study method in the industrial experiment was a bit different from that of the physical and the
mathematical modelling due to the high temperature, which makes the mixing effects of the
bath difficult to measure directly. However, the flow field, which is affected by the gas flow
rates, can partly be reflected by the C, O and P content in the liquid steel. As a result, the
original and the optimized converter experiment results were compared by studying the content
of these elements in the liquid steel at tapping. Table 4.1 shows the raw material and gas supply
in the industrial experiment.
Table 4.1. The industrial experiment conditions
Parameter
Hot metal, t 23-25
C/wt% 4.0-4.5
P/wt% 0.067-0.138
T/℃ 1271-1312
Scrap, t 3-4
Pig iron, t 5-6
Top gas oxygen flow rate, Nm3/h 7600-7800
Top-lance height, m 0.8-1.2
Bottom gas flow rate, Nm3/h 0.046-0.05
As can be seen in Table 4.1, the elements’ content in the hot metal, as well as the mass of raw
material and gas, do not have constant values, since it is difficult to control all the parameters
accurately in the industrial experiments.
21
Chapter 5 Results and discussion
5.1 A physical model and a mathematical model of a top blown converter
Initially, a verification of the possibility and feasibility of using the simplified model (model
B) was done. More specifically, the predicted cavity depth using the simplified model was
monitored and compared to the results from the more complex model (model A). Figure 5.1
shows the cavity depth versus time for the complex model (model A) and the simplified model
(model B) during the initial blowing stage of the process. As shown in the figure, both the
cavity depths of model A and model B fluctuate intensively during the first 0.5 s. Thereafter,
the cavity depth gradually reaches a steady state. The cavity depths of both models have
reached similar values after about 1.2 s and onwards. This suggests that it is possible to use the
simplified model B to predict an accurate cavity depth.
Figure 5.1. Comparison of variation of cavity depth against time for model A and model B
5.1.1 The cavity depth and radius
The predicted cavity formed under the jet of the top blown converter is shown in Figure 5.2.
The calculation was performed for more than 38 s. The results shown that cavity fluctuated
intensively during the initial state of the simulation and then reached a stable shape. Figure 5.3
shows the oscillation of the cavity depth with time by setting a line monitor at the central axis
of the cavity. At the semi steady-state, the bottom of the cavity fluctuates between values from
0.114 m to 0.108 m with a center at 0.111 m. This means that the cavity depth is between 0.036
m and 0.042 m (mean 0.039 m). The cavity radius values in the calculation are also relatively
steady as they have reached values around 0.080±0.002 m.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
Time, s
Surf
ace
hei
ght
of
cavit
y , m
Model A
Model B
22
Figure 5.2. The cavity and flow field in the bath of the top blown converter
Figure 5.3. Predicted surface height of cavity as a function of time using the mathematical model
The cavity depth was also determined from the physical model experiments to compare with
the simulation results. The experimentally determined cavities fluctuated more intensely than
that of a simulation. Thereafter, it was difficult to measure in cavities. However, images (as
Figure 5.4) were captured from the movie to estimate the cavity shape. The semi-steady cavity
depth region was found to be 0.040±0.010 m for the current experimental conditions. However,
some deeper cavity depths could sometimes be captured. The cavity radius, which was quite
unstable, varied between 0.07 to 0.10 m.
Figure 5.4. Cavity shape determined in the physical model
0 5 10 15 20 25 30 35 40
0.107
0.108
0.109
0.110
0.111
0.112
0.113
0.114
0.115
Su
rfa
ce
he
igh
t o
f ca
vity, [ m
]
Time, [ s ]
23
The cavity depth of a liquid caused by a single-hole nozzle jet can according to Banks and
Chandrasekhara be written as follow: [42, 43]
𝑀
𝜌𝐿𝑔ℎ3=
π
𝛽∙𝐿
ℎ∙ (1 +
𝐿
ℎ)2
(26)
where M is the momentum of the jet, ρL is the density of the liquid, g is the acceleration of
gravity, h is the top lance height, and L is the cavity depth. The constant β is recommended to
have a value of 125[42,43]. According to Asahara et al. [43] the measured data of the cavity depth
formed by the jets from the single-hole, the 3-hole and the 4-hole nozzles were found to be in
a good agreement with the estimated cavity depth calculated from equation 26 [43]. Based on
the conditons of this study, the cavity depth is 0.048 m according to equation 26.
Table 5.1 shows a comparison of the cavity shape values determined by mathematical
simulations, physical modeling, and analytical equations. It is clear that the results from
analytical equations, simulations and experiments all agree well, with regard to the cavity depth
caused by the impinging jets. As presented previously, the predicted cavity depth was 0.039±
0.003 m, which agrees well with the experimental data of 0.040±0.010 m when the mean
values are considered. However, the amplitude of the bath oscillation in the experiment is more
than three times as large as that of the simulation values. More specifically, if the mean values
are used, the relative difference between the mathematically and experimentally determined
cavity depth data is 2.5%. However, the prediction using an analytical equation (26) gives a
slightly higher value of 0.048 m, which is 20% larger than the experimental value. The cavity
radius value in the simulation was predicted as 0.080±0.002 m, which showed a relative
difference of 6.1% compared to the experimental values of 0.085±0.015 m.
Table 5.1. Comparison of cavity shape determined though simulations, experiments and analytical solutions.
Simulation Experiment Analytical
Cavity depth 0.039±0.003 m 0.040±0.010 m 0.048 m [12,13]
Cavity radius 0.080±0.002 m 0.085±0.015 m *
* There were no literatures inputs with multi-hole nozzles theory for cavity radius found by the author.
5.1.2 Calculations of the mixing time
As presented in 3.6, model B was used to calculate the long-time unsteady behavior in the
converter. Three points at different locations were set in the bath of the converter to monitor
the velocity change in the liquid in order to estimate the flow field conditions (Figure 5.5).
Point-1 has the highest mean velocity of the three points, followed by point-2 and point-3. The
velocity in point-1, which is close to the bottom of the cavity, fluctuates sharply over time. As
can be seen from Figure 5.5, the trend for the velocity in point-1 is that it increases between
0.5 to 12 s. During the same period, a similar trend can be seen for point-2. For the velocity in
point-3, less fluctuations over the whole period can be seen compared to the other data. These
results show that a steady state does not exist in the system, at least not within the simulated
time range. However, the fluctuations in each point are centered around a relatively stable mean
value, which is reached after approximately 25 s of the simulation. From the results, it is clear
that at least 25 s of simulation time is needed before the simulation of a tracer can be started
(where a frozen flow field is used).
24
Figure 5.5. Simulative velocity change in three different measurement positions, which are illustrated in
the upper part of the figure
By estimating whether the flow field reaches a steady-state or not in the simulation, several
points in the simulations were chosen to calculate the mixing time according to the velocity
change curves. Figure 5.6 shows the mixing time calculation curves at three different times:
1.1 s (a), 10.8 s (b) and 35.0 s (c). As can be seen, the liquid fluctuates sharply in the beginning
of the simulation. The intense oscillation in the bath increases the stirring effect and decreases
the mixing time. The average mixing time is 21.3 s, when a frozen flow field from 1.1 s of
blowing is used.
(a) (b)
(c)
Figure 5.6. Mixing time curves at different points in time (Mean time =21.3, 98.0, 54.7 s for a, b, c respectively)
0 10 20 30 40 50 60 70 80 90 1000.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
Co
nce
ntr
atio
n o
f tr
ace
r [ C
/C0 ]
Time [ s ]
1.07s
35s11s
18s
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 1500.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
Co
nce
ntr
atio
n o
f tr
ace
r [ C
/C0 ]
Time [ s ]
10.79s
78s
96s
120s
0 10 20 30 40 50 60 70 80 90 1000.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
Co
nce
ntr
atio
n o
f tr
ace
r [ C
/C0 ]
Time [ s ]
35.04s
70s
52s42s
0 5 10 15 20 25 30 35 40 450.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
Point-3
Point-2
Ve
locity [ m
/s ]
Time [ s ]
Point-1
25
The bath oscillation magnitude was reduced as the blowing progressed, as shown in Figure
5.6. As a result, the mixing time for this period was longer than at shorter blowing times. With
a frozen field from 10.8 s of blowing, the average mixing time is 98.0 s. In the case of a frozen
flow field taking after 35.0 s of blowing, the mean mixing time is decreased to 55.0 s.
A summary of the results of the mixing time simulation is illustrated in Figure 5.7. More
specifically, it illustrates how the mixing time changes for different blowing times when using
a frozen flow field in the mixing time calculations. The mixing times are very short at the
beginning of the simulation. Thereafter, as the blowing time is increased the mixing times
increase rapidly up to about 20 s of blowing. Then, the values begin to decrease parabolically
to reach a more stable value.
Figure 5.7. Mean mixing time calculated at discrete points for the blowing time
Several points in blowing time were chosen to calculate the mixing time in this stable region.
The minimum and maximum values were 54 s and 67 s, respectively. Although the mixing
time fluctuates in a 13 s time interval with a mean mixing time of 62 s, it shows some
regularities. The mixing time decreases after about 25 s and thereafter it stays within a relatively
stable time interval. This means that the flow fields are close to a fully developed state. This
also corresponds well to the results of the velocity fluctuations seen in Figure 5.5. Overall, it
is clear that using a frozen field, where the flow is not developed, gives very large errors.
However, it is also seen that it is possible to use a frozen flow field after the point where the
flow has developed in order to reduce the computational time. This is something that usually
limits calculation performed for metallurgical systems.
Figure 5.8 shows the mixing time curves in the bath from the physical model experiments. The
mixing times in the three different points are 57、64 and 60 s,respectively, and 60.3 s on
average. The mathematical result, which is 62 s on average, agreed well with that of the
physical model. More specifically, the predicted average value is 2.8% higher than the
measured average value.
0 5 10 15 20 25 30 35 40
10
20
30
40
50
60
70
80
90
100
Mix
ing
tim
e, T
m [ s
]
Blowing time [ s ]
26
Figure 5.8. Mixing curves of the bath determined though physical modeling (The mean mixing time is
60.3 s.)
One important thing which should be considered further is the difference of mixing curves
between the physical model and the mathematical model. In the physical model, the mixing
times of the different probe points are closer to each other compared to the data of the
mathematical model. Some investigators [44] used the longest mixing time of several probes as
the mixing time of the bath in their experiments. In the physical study of this work, the mean
mixing time of three probes was used in order to avoid the errors coming from every probe. In
the mathematical model, the gap between the longest and the shortest mixing time is sometimes
more than 20 s. Under this circumstance, there are still some differences even if the mean
mixing time is close between the physical and the mathematical model. To overcome the
drawbacks from the mathematical model, the locations of probe monitoring the tracer
concentration should be paid more attention since there may be some so called “dead zone”
regions. The results will be more acceptable if the concentration changes in the whole bath are
monitored. A suitable method to realize this function will be described in the next section. In
addition, the mean mixing time value of more probe points may decrease the errors arising
from each probe. Since the current work aimed to compare the prediction results with physical
model results (3 probes), this method was not carried out in this study. However, the physical
model has its limitations resulting from the equipment or human beings’ operations. So trying
to advance the reliability of the physical model is a precondition for an improved comparison
to the predictions.
Overall, the above results show that it is possible to use this velocity monitoring method to
estimate an unsteady flow field of a converter bath. Furthermore, to choose a few blowing time
points to calculate the mixing time of the bath. This considerably reduces the simulation time
compared to carrying out a complete mathematical simulation.
5.2 The optimization of a combined top-bottom blown converter
5.2.1 Physical model results
The mixing times at elevated gas flow rates for the bath are indicated in Figure 5.9. Generally,
the mixing time decreases with an increased bottom gas flow rate, as can be seen from the
figure. However, several inverse trends are also achieved in the experiments. Some critical
flow rates are also observed from the experimental results in which an extra gas supply lead to
unobvious changes or opposite effects with respect to mixing time. This indicates that higher
0 10 20 30 40 50 60 70 80 900.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
C/C
0
Time, s
57 64
60
27
bottom flow rates of bottom blown may not always give positive effects to the stirring of the
bath. As shown in Figure 5.9, the mixing time increases with increasing bottom flow rates that
are higher than 0.47 Nm3/h, when the original scheme is employed with a 158 mm top-lance
height. Some similar tendencies can be found when a 133 mm lance height is used in both the
original and the optimized schemes.
Figure 5.9. Mixing time in the combined blown converter versus the flow rates from the bottom tuyeres
It may be seen that a lower top-lance height shows significantly shorter mixing times than that
of the higher one for both the original and the optimized schemes. This indicates that a lower
top-lance height is better for the mixing effects in the bath, at least for the current span of flow
rates. However, the collision between the top jet and the bottom plume on the surface of the
bath shall also be considered more during the change of the lance height.
The mixing times with the optimized scheme are shorter than those of the original scheme, for
all the top-lance heights and corresponding bottom blowing rates. This means that the
optimized converter scheme leads to a better stirring in the bath than that of the original one.
The mixing times have been decreased by 13.6 %, 21.2 % and 27.1 % for top-lance heights of
133, 158 and 183 mm at a bottom blowing rate of 0.47 Nm3/h, respectively. Therefore, it is
reasonable to believe that better stirring effects can be achieved in practice, when the height of
the top lance is adjusted during the process.
In the plant, the bottom blowing rates are from 50 Nm3/h to 270 Nm3/h, which corresponds to
0.21 to 1.21 Nm3/h in the experiment. According to the experimental results, a bottom blowing
rate above 0.94 Nm3/h (180 Nm3/h in the plant) is not recommended.
5.2.2 Mathematical model results
As presented in the physical model, too high bottom blowing rates may give negative results
and are not recommended to use in plants. Therefore, to make the simulations representative,
a blowing rate of 0.47 Nm3/h and a 158 mm top-lance height are chosen as a reference in both
the original scheme and the optimized scheme.
The stirring effects of the bath were investigated by calculating the mixing time of the bath at
different simulation times where the flow field is considered to be a developed flow. Five points
in time were chosen from the fully-developed flow both in the original and the optimized
schemes; the mixing times are shown in Figure 5.10. As can be seen from the figure, the total
mixing times over the selecting time points revealed a general trend of fluctuations. The bath
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.620
30
40
50
60
70
80
90
100
110
120
Mix
ing
tim
e (
s)
Flow rate (Nm3/h)
Original, top lance height 133mm
Original, top lance height 158mm
Original, top lance height 183mm
Optimized, top lance height 133mm
Optimized, top lance height 158mm
Optimized, top lance height 183mm
28
of the original scheme is in the range of mixing times from 54.1 to 64.2 s, where the mean
value is 59.6 s. The mixing time in the optimized scheme varies between 49.0 and 55.0 s, with
a mean value of 52.0 s. It is clear that the mixing time is decreased by 12.8% in the optimized
bath compared to the original scheme. Note, that the mathematical results are slightly higher
than the physical model results in which the corresponding mixing times are 54.3 and 47 s,
respectively.
Figure 5.10. The mixing times in the original and the optimized scheme for different blowing times
The turbulence in the bath is very important to the mixing of the bath. Therefore, the total
turbulent kinetic energy of the liquid in the bath has been evaluated to check when the flow is
developed. As shown in Figure 5.11, fluctuation of turbulent kinetic energy happened both in
the original and the optimized bath schemes. However, the fluctuation in the optimized bath
gave a higher mean value of 0.14 m2/s2, which is 7.4% higher than that of 0.13 m2/s2 found in
the original bath. This indicates that the rearrangement of the bottom tuyeres in the bath
changes the turbulence, as well as the mixing conditions in the bath.
Figure 5.11. Comparison of variation of turbulent kinetic energy with time in the bath
As we know that there are some zones in which the flow field is not active enough with respect
to the stirring or some metallurgical vessels where it hard to obtain a suitable stirring; we call
this kind of zone a “dead zone”. However, this kind of zone is very difficult to realize and to
locate since the situation can be changed with operating parameters, size of vessels, etc. In this
physical model, three probes were used to measure the concentration change of the tracer. But
it is very difficult to measure the concentration in the dead zone because too many probes may
affect the flow field in the bath. Furthermore, sometimes it is impossible to confirm the location
0 1 2 3 4 5 640
45
50
55
60
65
70
Mix
ing
tim
e, s
Mixing times in different blowing time
Original scheme
Optimized scheme
100.0 100.5 101.0 101.5 102.0 102.5 103.00.120
0.125
0.130
0.135
0.140
0.145
0.150
Tu
rbu
len
t kin
etic e
ne
rgy, m
2/s
2
Optimized
100.0 100.5 101.0 101.5 102.0 102.5 103.00.120
0.125
0.130
0.135
0.140
0.145
0.150
Time, s
Original
29
of the dead zone. Therefore, the measured results using probes usually lacks information from
the dead zone. Fortunately, numerical tools give investigators chances to consider all regions
as small as the mesh size in the studied domain.
The definition of the mixing time using the probe method is similar to that used in the physical
model. To consider the concentration change of all the regions in the bath, a new mixing time
method was applied in this study. The mixing time is calculated based on the volume of 99% -
101% homogenization of the scalar over the entire bath volume. Figure 5.12 shows the
differences in the mixing time calculations by different methods. The mixing times based on a
discrete point monitor in Figure 5.12 (a) are 38.7, 54.5, and 61.5 s, with a mean value of 51.6
s. By considering the whole region of the bath, it took 62.0 s, which is 20.1% longer than that
of the discrete point monitor result, to achieve the same homogenous requirement for the bath.
Figure 5.12. The comparison of different mixing time calculations
As a consequence, the volumetric monitor method was used in the optimized case to calculate
the mixing time in the chosen time-point; the results are shown in Figure 5.13. Noticeably, all
the results calculated by the volumetric method revealed a trend of a higher mixing time than
those of the discrete point monitor method. This means that some regions in the bath may not
reach homogeneousness when the measured points get homogeneous. The differences between
the two methods vary from a minimum value of 12.7% to a maximum value of 44.9%, which
indicates that the location of the point monitor may greatly affect the results in the calculation.
The mean value of mixing time in the volumetric calculation is 64.0 s, which is 23.1% higher
than the mean value of 52.0 s determined by the discrete point method. This suggests that the
mixing time acquired from the discrete point method is representative to a certain extent.
However, the volumetric method should be executed in the mixing time calculation if the dead
zones in the bath or vessels are of concern.
Figure 5.13. The mixing time differences in different monitor-type
0 10 20 30 40 50 60 70 800.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
C/C
0
Time, s
(a)
0 10 20 30 40 50 60 70 80
0.0
0.2
0.4
0.6
0.8
1.0
V/V
0
Time, s
(b)
1 2 3 4 50
10
20
30
40
50
60
70
80
90
Mix
ing
tim
e, s
Mixing times in different blowing time
Points monitor
Volumetric monitor
30
5.2.3 Industrial experimental results
Figure 5.14 presents the comparison of C, O and P contents at tapping using both the original
and the optimized schemes. As can be seen from the statistics, the O content fluctuates sharply
between 0.05% and 0.09% in both the original and the optimized schemes. The O content in
the optimized schemes is decreased but sometimes higher in the optimized scheme than that of
the original scheme. As a whole, the O content is decreased by 6.0% from 0.067% (original
scheme) to 0.063% (optimized scheme) by considering the mean values of all heats in the
experiment. However, an obvious C content change has not been found in these results. There
is not a great difference between the original and the optimized schemes with respect to the C
contents, which are 0.051% and 0.048%, respectively.
A low P content is one of the main metallurgical requirements in the steel making process using
the BOF for most of the steel grades. This is due to that a high P content of the steel will cause
a tempering embrittlement, a low ductility and a low strength. A good stirring of the bath can
enhance the removing rate of P during the process of the dephosphorization. With the original
scheme, the P content is relatively high with a mean value of 0.031%. A favorable result of the
optimized scheme can be seen where the P content is significantly decreased; it is 33% lower
than for the original scheme.
All the results from the experiments indicate that the BOF has been optimized successfully and
that the stirring effect of the optimized scheme gives a favorable result in practice based on the
analyses of elements content at tapping.
Figure 5.14. Industrial experiments comparing the original tuyere scheme to the optimized tuyere
scheme
5.3 The combined top-bottom-side (TBS) blown converter
A side tuyere was introduced to the model to form a combined top-bottom-side blown converter
to study the effects of the side blowing plume on the stirring of the bath. This was one base on
the combined top-bottom blown converter model used in the previous section. The mixing
times of the converter with different schemes of the side tuyeres were measured by using the
physical model. In the mathematical model, the flow fields and the wall shear stresses, as well
as the mixing time, were investigated.
0 1 2 3 4 5 6 7 8 9 10
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
Ma
ss%
Heat number
Coriginal
Ooriginal
Poriginal
Coptimized
Ooptimized
Poptimized
31
5.3.1 The flow field in the bath
Figure 5.15 shows a typical simulation result of the TBS blown converter. The cavity was
formed in the bath due to the momentum from the top jets. The plumes resulting from the side
and the bottom blowing can also be seen from the figure. The plumes showed in the figure
represent the bubble-water two phase zones formed during the blowing process.
The original idea to distribute the bottom tuyeres in an asymmetric way is to form an
asymmetric flow, which can stir the bath more efficiently, compared to the symmetric tuyeres
distribution. The latter result in several independent stirring regions in the bath and the mixing
between each region is not strong. The design of the side blowing is to produce a horizontal
flow to stir the regions separated by the bottom blowing. The stream line of the horizontal flow
resulting from the side blowing in the bath can be seen in Figure 5.15.
A comparison of the flow field in different blowing operations is shown in Figure 5.16, for a
horizontal cut at 100 mm. Figure 5.16 (a) shows that the velocity is very low except in the
regions near the plumes in the pure bottom blown bath. This reveals that the mixing between
the regions is not efficient enough in the bath. With a side flow rate of 0.5 Nm3/h, shown in
Figure 5.16 (b), the velocity is higher than that of pure bottom blown bath. However, there are
still some regions with a low velocity. This means that the side blowing does contribute to the
stirring of the bath, but it has the potential to be improved. When increasing the flow rate to
1.5 Nm3/h, the horizontal flow becomes clearly visible in the bath, as shown in Figure 5.16 (c).
The horizontal flow caused by side blowing breaks the flow pattern formed by the bottom
blowing plumes. This means that the separated flow regions formed by the bottom blowing can
be mixed by the horizontal flow. Furthermore, including the top blowing in the combined
bottom-side blown case, the flow field is not affected too much by the flow near the cavity
region. This shows that the horizontal flow will also be available in a TBS blown converter, as
shown in Figure 5.16 (d). In the physical model, the horizontal flow in a water TBS model
were also observed by using some particles as tracer elements.
Figure 5.15. Typical phase interface of the TBS blown converter
32
(a) (b)
(c) (d)
Figure 5.16. The flow field of the bath in different operations. (a) Pure bottom blown. (b) Bottom-side blown with side flow gas of 0.5 Nm3/h. (c) Bottom-side blown with side flow gas of 1.5 Nm3/h. (d) Top-
bottom-side blown with side flow gas of 1.5 Nm3/h.
In the mathematical model, a vertical monitor region was placed in the bath to monitor the
horizontal flow caused by the side blown plume, as shown in Figure 5.17. The region monitor
results in a developed flow are shown in Figure 5.18. With a side flow rate of 0.5 Nm3/h, the
water flow rate in the monitor region changes between 0.1 and 0.2 kg/s. The level location of
tuyere B is 90 mm higher than that of tuyere A. The flow rates in the monitor region increases
with an increased side blown flow rates and it reaches 1.4 kg/s as the side flow rate increases
to a value of 1.5 Nm3/h. By taking the average value of the flow rate in the monitor region, it
is seen that tuyeres A and B produce similar results. However, the flow across the monitor
region produced by tuyere B causes a more intensive oscillation compared to the case of tuyere
A. It is found that the velocity changes periodically in the monitor region and that this
contributes to the vibration of the flow in the bath. The change of flow rates is periodic in a
region from 0.6 to 2.0 kg/s.
Some similar situations were seen when using the tuyere types C and D, but with different
intensities. The oscillation period in the monitor region is approximately 1.5 s for a side flow
rate of 1.5 Nm3/h. When increasing the height of the side tuyere, the side plume is closer to the
surface of the bath. Therefore, the surface movement becomes more intensive. Thereby, the
intensive horizontal flow near the surface interacts with the flow near the cavity formed due to
the top blowing. The interaction between these two flow streams was accelerated compared to
the case with a lower side blown location.
X
Y
Z
0.1 m/s
X
Y
Z
0.1 m/s
X
Y
Z
0.2 m/s
X
Y
Z
0.2 m/s
33
Figure 5.17. The schematic of the flow monitor face in the bath.
Figure 5.18. The mass flow rate of the flow in the bath using different tuyere positions and gas flow rates
(Nm3/h)
5.3.2 Mixing time
The mixing behaviour of the bath in the converter is an important criterion which should be
considered when using a side blown tuyere. The mixing times of the bath with four different
side blown tuyeres were investigated in the mathematical model and the predictions were
compared with the physical modelling results. Figure 5.19 shows the mixing times comparison
between the physical model and the mathematical model for different side blown flow rates,
when using the side tuyere type A. As shown in the figure, the mixing times in the bath decrease
with increasing side blowing flow rates. In the physical model results, the mixing time with a
side flow rate of 0.5 Nm3/h is decreased by 62% compared to the case without using side
blowing. As the side flow rate is increased to 1.5 Nm3/h, the mixing time is 10 s. Thus, it is
decreased by 44% compare to the case when using a side flow rate of 0.5 Nm3/h. The results
from the mathematical model show a similar trend and a good agreement with that of the
physical model. However, the mixing times for all the cases are longer than those of the
physical model. One of the possible reasons here is that the oscillation in the bath is higher than
that of the physical model due to the assumption of bubbles size for the side blowing case. The
oscillation in the bath can give some negative effects on the calculation of the mixing times.
Figure 5.20 shows the mixing time results with the side blown tuyeres located at the same level
at different circumference positions. The results do not show an apparent regularity in mixing
times at a side flow rate of 1.5 Nm3/h in both the physical and the mathematical model. The
0.00
0.50
1.00
1.50
2.00
2.50
3.00
346 348 350 352 354
Flo
w r
ate,
kg/
s
Time, s
Tuyere A 1.5 Tuyere B 1.5 Tuyere A 0.5
Monitor face
34
mixing times changed in a range from 10 to 15 s for the physical model and in a range from 15
to 17 s for the mathematical model. This indicates that the location of the side blown tuyeres
does not affect the mixing of the bath much when using the current model parameters. Instead,
the flow rate seems to be much more important.
Figure 5.19. Mixing times for different side blown flow rates
Figure 5.20. Mixing times for a flow rate of 1.5 Nm3/h and for different side tuyere geometries in the
physical model and the mathematical model
5.3.3 The shear stress on the wall
With the side blowing process in the metallurgical vessels, the wear of the lining near the side
blown plume is a concerned problem. The high wall shear stress corresponds to the wear of
lining on the side wall in reality.
Figure 5.21 shows the fluctuation of the integral shear stress on the whole side wall for a
transient simulation. The mean values for the shear stress were calculated after the flow was
developed. It can be seen from the figure that the shear stress is higher when a side tuyere is
used compared to when no side tuyere is used. The fluctuation when using tuyere A is much
lower compared to the other 3 tuyere configurations, which locations are higher than for tuyere
A. The wall shear stress when using tuyere D is much higher than that of the other
configurations for a side flow rate of 1.5 Nm3/h. This indicates that the location of the side
tuyere can change the flow in the bath. Moreover, it can affect the shear stress on the side wall
although the mixing times are largely unaffected. The simulation results suggest that the shear
stress is not increased too much by introducing tuyeres A, B or C compare to the case without
0
10
20
30
40
50
60
0 1.5
Mix
ing
tim
e, s
Side flow rate, Nm3/h
Physical model
Mathematical model
0.5
B C D0
5
10
15
20
25
30
Mix
ing
tim
e, s
Side tuyere
Physical model
Mathematical mdoel
35
side blowing. However, the results also shows the possibility that the shear stress on the side
wall can be increased dramatically when the side blown location is not appropriate.
Figure 5.21. The integral wall shear stress comparison on the side wall by using different side tuyeres in
the flow rate of 1.5 Nm3/h
5.4 The kinetic energy transfer in a real converter
For investigating the effects of the blowing gas on the molten flow of the bath, the flow was
calculated separately for the top blowing and the bottom blowing operations.
5.4.1 The top blowing process
To study the energy transfer behaviour from top gas to the bath of the converter, the energy
transfer index was defined as a ratio between the specific kinetic energy of the molten steel and
the specific kinetic energy input rate. The specific kinetic energy is calculated by using the
following equation:
𝐸𝑘 =∫𝜌𝑠𝑢
2𝑑𝑉
𝑊 (27)
where ρs is the density of the molten steel, u and V are the velocity and volume for each cell,
respectively. Furthermore, W is the mass of the molten steel.
The specific kinetic energy input rate for top blowing operation was defined as the following
equation [45]:
𝜀𝑖𝑛_𝑡 = 8.5 × 10−3𝐾3𝜌𝑜𝑄𝑑0𝑢2 cos2 𝜃 𝑊ℎ⁄ (28)
where K is the turbulent jet parameter (7.81) and Q is the top gas flowrate, d0 is the diameter
of the Laval nozzle outlet, ρo is the density of oxygen, u is the velocity, θ is the nozzle angle
and h is the height of the top lance. The specific kinetic energy determined by the equation is
shown in Table 5.2. The kinetic energy input rate was found to increase with an increased inlet
flowrate of the top lance. Specifically, it rises from 2.83 to 4.84 W/kg when the inlet flowrate
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
No side tuyere Tuyere A Tuyere B Tuyere C Tuyere D
Wal
l sh
ear
stre
ss,
Pa·
m2
Side tuyere
Mean value
Maximum
Minimum
36
is increased from 20000 to 25000 Nm3/h at a top lance height of 1600 mm. When keeping the
inlet flowrate at a constant value of 22000 Nm3/h, the specific kinetic energy input rate can be
increased when the top lance height is decreased.
Table 5.2. The specific kinetic energy input rate with different top lance heights and inlet flowrates
Lance height,
mm
Inlet flowrate,
Nm3/h
Specific kinetic energy
input rate, W/kg
1600 20000 2.83
1600 22000 3.62
1600 25000 4.84
1300 22000 6.75
1000 22000 9.41
The calculation time to achieve a developed flow is more than 20 s for the mathematical model
of the top blowing converter used in this simulation. The results applied in the analyses were
from the developed state. Figure 5.22 shows the specific kinetic energy of the molten steel in
the bath with different top lance flowrates. It can be seen from the figure that as the flowrate is
increased, the specific kinetic energy of the molten steel increases.
Figure 5.22. The specific kinetic energy of molten steel with different top lance blowing input flowrates
in the transient simulation
Figure 5.23 shows the influence of the top lance height on the kinetic energy transfer from top
blowing gas to the molten steel at a top lance input flowrate of 22000 Nm3/h. Comparing the
specific kinetic energies of 0.037 J/kg at the top lance height of 1600 mm, the specific kinetic
energy are increased by 47% and 66% for top lance value of 1300 and 1000 mm, respectively.
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
20000 22000 25000
Sp
ecif
ic k
inet
ic e
ner
gy,
J/k
g
Top lance input flow rate, Nm3/h
37
Figure 5.23. The specific kinetic energy of molten steel with different top lance heights in the transient
simulation
Figure 5.24. The energy transfer index from top blowing gas to the bath with different operations
The energy transfer index from the top blowing gas to the molten steel in the bath is shown in
Figure 5.24. Here, the specific kinetic energy input rates represent the situation in different
operations, as is shown in Table 5.2. It is remarkable that the energy transfer is less effective
when the specific kinetic energy input rate is increased. Specifically, in the conditions of
operation, the energy transfer index is a decreasing function of the top lance kinetic energy
input rate (or gas flowrate) when the top lance is fixed at a height of 1600 mm. By comparing
the energy transfer index when the flowrate is increased, the energy transfer index decreases
27% with an increased flowrate of 25% higher. Specifically, it is increased from 20000 Nm3/h
to 25000 Nm3/h. This means that the energy transfer is more efficient when the top lance
flowrate is lower at a fixed top lance height. If the flowrate is kept constant at a 22000 Nm3/h
rate, as is shown in the figure, the energy transfer index reveals a decreasing trend with a
lowered top lance. A 36% decrease rate of the energy transfer index due to decrease of the top
lance height from 1600 to 1100 mm indicates that the energy transfer from top lance to the bath
can be less efficient when the top lance is lowered.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
1000 1300 1600
Sp
ecif
ic k
inet
ic e
ner
gy,
J/k
g
Top lance height, m
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
2.84 3.62 4.84 6.75 9.41
En
ergy t
ran
sfer
in
dex
Specific kinetic energy input rate, W/kg
38
5.4.2 The bottom blowing process
In the real bottom blowing operation, 4-tuyere and 6-tuyere configuration are very commonly
used. As a result, in the bottom blowing simulation, three different bottom tuyere distributions
were performed to study the effects of the bottom tuyere number, bottom tuyere distribution
and the bottom blowing flowrates on the kinetic energy transfer. This is shown in Figure 5.25.
These variables must evidently affect the dynamics of the flow and the efficiencies of the
blowing process as well as the mixing behaviour in the bath. The specific kinetic energy input
rate for bottom blowing operation was defined as follows:
𝜀𝑖𝑛_𝑏 =𝜌𝑠𝑔𝑄𝐿
𝑊 (29)
where ρs is the density of the molten steel, Q is the bottom blowing flowrate, L is the depth of
the bath and W is the total mass of the molten steel in the bath.
(a) (b) (c)
Figure 5.25. The bottom tuyeres distribution
To estimate the extent of the kinetic energy transfer from the bottom blowing gas to the molten
steel, a volumetric monitor method was performed to calculate the specific kinetic energy of
the molten steel as a function of the bottom blowing time. Different specific kinetic energy
input rates were used in the transient simulation. A typical result is shown in Figure 5.26. It
should be noted that the specific kinetic energy increases during the blowing process and that
it is stable with slight fluctuations after a period of time for all three different blowing
operations. The flow field in these stable periods is formed because the energy dissipation rate
is in balance with the energy input from the bottom blowing gas. Therefore, the flow is
developed. Remarkably, higher specific kinetic energy input rate reveals more intense
fluctuations for both the undeveloped and developed flows.
Figure 5.27 shows the kinetic energy transfer indexes for the bottom blowing process and
using scheme (a). It is noticeable that the energy transfer indexes in the bottom blowing process
are much higher (twenty times or even more) than that of top blowing process, if these results
are compared to the results shown in Figure 5.24. This means that the bottom blowing is more
efficient than the top blowing to create a bath stirring. For the current bottom blowing flowrates,
the energy transfer index is an increasing function of the specific kinetic energy input rate.
Remarkably, this trend is the opposite of the situation found for the top blowing process.
30°
0.5D
30° 30°
0.5D
30° 30°
0.5D
0.6D
39
Figure 5.26. The specific kinetic energy of molten steel with different specific energy input rates (W/kg)
calculated using transient simulations
Figure 5.27. The energy transfer index for bottom blowing of gas into the bath
Figure 5.28 shows that different bottom tuyeres configurations can affect the kinetic energy
transfer from the bottom blowing gas to the molten steel in the bath of the converter. Generally,
the specific energy of the molten steel in the bath is increased but not linearly proportional to
the specific energy input rate. The specific kinetic energy in the bath with scheme (a) is much
higher than that of scheme (b). However, it is close to the result from scheme (c) for all three
kinetic energy input rates.
Specifically, with the bottom tuyeres located in the similar radial positions but having different
tuyere numbers, the results from scheme (a) reveal 26.7%, 39.2% and 21.6% higher specific
energies compared to the results from scheme (b). The comparison between the results from
scheme (b) and (c) show that different configurations of the bottom tuyeres give significantly
different kinetic energy transfer efficiencies. The specific kinetic energies with scheme (c) are
19.5%, 28.2% and 21.1% higher than those of scheme (b) if the specific kinetic energies input
rates are 0.18, 0.27 and 0.37 W/kg, respectively.
Overall, the above results suggest that both the radial position and the configuration of the
bottom tuyeres should be considered during the design and the operation of the converter.
0
0.02
0.04
0.06
0.08
0.1
0.12
0 20 40 60 80 100
Sp
ecif
ic k
inet
ic e
ner
gy,
J/k
g
Time, s
0.18 0.27 0.36 W/kg
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.18 0.27 0.37
En
ergy t
ran
sfer
in
dex
Specific kinetic energy input rate, W/kg
40
Figure 5.28. The specific kinetic energy of molten steel for different bottom tuyeres configurations
In the steel making process of the converter, the slag mass is a variable during the blowing
process. To investigate how the mass change of the slag affects the energy transfer of the
bottom blowing gas, the effects of the slag on the kinetic transfer efficiency of the bath were
also investigated by using scheme (c) and using a specific kinetic energy input rate of 0.27
W/kg. Figure 5.29 shows the comparison of the specific kinetic energy of the molten steel in
the bath with the slag masses 0, 5, 9 and 13 t. It is clear that the slag on top of the surface of
molten steel decreases the efficiency of energy transfer from the bottom blowing gas to the
bath. The data in the figure show that the specific kinetic energies drop by 6.6%, 9.4% and
11.2% for the slag masses 5, 9 and 15 t compared to the case without a slag on top of the surface
in the bath, respectively.
Figure 5.29. The specific kinetic energy of molten steel for different masses of slag
In the blowing period, the component of the slag, such as CaO, SiO2, FeO and MnO, is a
variable during the different stages of the blowing process. Consequently, the physical
properties of the slag changes with a change of the slag components, as well as with changed
temperatures. Figure 5.30 shows the effects of the viscosity on the energy transfer with the
specific energy input rate of 0.27 W/kg in the bath. The viscosities in the region from 0.025 to
0.2 Pa•s in the figure represent the viscosity of the slag with different component. As is
indicated in the figure, the specific kinetic energy reveals a decreasing trend when the viscosity
of the slag is increased. By comparing the results in Figure 5.29 to the case without the slag
0
0.02
0.04
0.06
0.08
0.1
0.12
0.18 0.27 0.37
Sp
ecif
ic k
inet
ic e
ner
gy,
J/k
g
Specific kinetic energy input rate, W/kg
(a)
(b)
(c)
0.0580
0.0600
0.0620
0.0640
0.0660
0.0680
0.0700
0.0720
0.0740
0 5 9 13
Sp
ecif
ic k
inet
ic e
ner
gy,
J/k
g
Slag mass, t
41
on top of the surface in the bath, the specific kinetic energy drop 7.75 %, 8.65% and 8.73% for
the slag viscosity of 0.025, 0.05 and 0.2 Pa•s. These results also indicate that the kinetic energy
transfer is not largely influenced by the viscosity of the upper slag phase. The specific kinetic
energy decreased by only 10.7% when the slag viscosity increases eight fold.
Figure 5.30. The effects of different slag viscosity on the specific kinetic energy of molten steel
In the blowing process of the BOF converter, the process generates a large quantity of gas
which, in turn, causes a considerable slag formation. The falling metal droplets and rising gas
bubbles have finite residence times in the foam. The three phase mixture of slag, metal droplets
and gas bubbles is simplified as a uniform flow liquid in this work. During the middle blowing
period, the gas fraction in the slag foam may range from 0.6 to 0.95. At such high gas fractions
the viscosity of the gas-slag foam at different gas void fractions can be estimated as follow [46]:
𝜇𝑓 =2𝜇𝑠(1−𝜑𝑔)
3(1−𝜑𝑔
13)
(30)
where μs is the viscosity of slag and φg is the gas void fraction in the foam.
Figure 5.31 shows the specific kinetic energy transfer with the upper foam layer on top of the
slag surface. By comparing the case without a foam layer in the bath, the specific kinetic energy
for molten steel has been decreased with an increased thickness of the foam. The specific
kinetic energies decreases by 0.82%, 1.72% and 2.38% for the corresponding foam thicknesses
of 1.0, 1.5 and 2.0 m, respectively. It clearly shows that the influence of the foam on the energy
transfer due to the bottom blowing gas to the bath is lower than that of the slag. The effects of
the gas fractions of the foam were also investigated in the mathematical model and the results
are shown in Figure 5.32. Here, only the viscosity result from the gas fraction was considered.
As shown in the figure, the specific kinetic energy decreases with an increased gas fraction of
the foam. The comparison between the gas fractions of 0.6 and 0.9 shows that the difference
between the specific kinetic energies is only 0.15%. This means that the viscosity of the foam
does not give noticeable effects on the kinetic energy, due to the injection of the gas from the
bottom of the converter.
0.0650
0.0652
0.0654
0.0656
0.0658
0.0660
0.0662
0.025 0.05 0.2
Sp
ecif
ic k
inet
ic e
ner
gy,
J/k
g
Slag viscosity, Pa•s
42
Figure 5.31. The specific kinetic energy of molten steel for different thicknesses of the foam which is
formed on top of the slag
Figure 5.32. The specific kinetic energy of molten steel for different gas fractions of foam on top of the slag
0.0630
0.0635
0.0640
0.0645
0.0650
0.0655
0.0660
0 1 1.5 2
Sp
ecif
ic k
inet
ic e
ner
gy,
J/k
g
Foam thickness, m
Slag mass = 9 t
Foam gas fraction = 0.75
Specific energy input rate = 0.27 W
0.0642
0.0643
0.0643
0.0643
0.0643
0.0643
0.0644
0.0644
0.0644
0.0644
0.6 0.75 0.9
Sp
ecif
ic k
inet
ic e
ner
gy,
J/k
g
Gas fraction
Slag mass = 9 t
Foam thickness = 1.5 m
Specific energy input rate = 0.27 W
43
Chapter 6 Conclusions
In this study, a modified converter model was developed based on the physical model. It was
used to simulate the jet impingement on the liquid surface as well as the mixing time. Also, a
velocity-monitor method was used in the simulation to estimate the flow condition of the liquid
in the bath. Based on this mathematical model, an optimization process of combined top-
bottom blown converter was investigated in the mathematical model and the results were
compared with the physical modelling results. The flow phenomena in a combined top-bottom-
side blown converter was also investigated by applying the mathematical model. Furthermore,
the kinetic energy transfer between the blowing gas and bath for a real converter was simulated.
The specific findings from this study may be summarized as follows:
In the top blown converter simulation,
1) The simulated cavity depth is 0.039±0.003 m, which agrees well with that of the
experimental data with a relative difference of 2.5%. The cavity radius value in the
simulation was predicted as 0.080±0.002 m, which is in a relative difference of 6.1%
compared to the experimental results.
2) A relatively developed flow field can be recorded by monitoring the velocity change
of the liquid over time. This analysis is very important if a reliable mixing time
calculation is to be performed, using a frozen flow field approach.
3) The mean mixing time in the mathematical model is 62 s. This gives a good relative
difference of 2.8% compared to the result of the physical model, which has a mean
mixing time of 60.3 s.
For the combined blown converter, the following specific conclusions can be yielded:
1) In the optimized scheme, the mixing times have been decreased 13.6%, 21.2% and
27.1% using top-lance heights of 133, 158 and 183 mm and at bottom blowing rate
of 0.47 Nm3/h, respectively. The calculated mixing time decreased by 12.8% in the
optimized bath compared to an original stirring scheme. However, the simulation
results are slightly higher than the physical model results.
2) The volumetric method can calculate concentration changes of the tracer in all the
regions of the bath. It revealed a trend of 23.1% higher mixing time than that of the
(standard) discrete point mixing time calculations.
3) Good industrial results were achieved by using the optimized scheme instead of the
original scheme. The C, O and P content were decreased by 5.8%, 6.0% and 33%,
respectively.
4) A horizontal flow in the converter bath can be formed when using an appropriate
flow rate of the side blown gas. The bath stirring can be enhanced with increasing
side blowing flow rates. In the physical results, the mixing time with a side flow rate
of 0.5 Nm3/h is decreased by 62.1% compared to the case without side blowing.
When increasing the side flow rate to 1.5 Nm3/h, the mixing time is 10.2 s. This value
corresponds to a decrease of 43.6% compared to the case of a side flow rate of 0.5
Nm3/h.
5) The side wall shear stress is increased by introducing side blowing, especially in the
region near the side blowing plume. The fluctuations with a side tuyere positioned at
44
a lower height is less than that of the other vertical positions. This location of the side
tuyere can affect the shear stress on the side wall.
For the simulation of the real converter:
1) A 36% decreased rate of the energy transfer index from the lowering of the top
lance height of 1600to 1100 mm indicates that the energy transfer from the top
blowing gas to the bath is less efficient when the top lance is lowered for the
current conditions. When the top lance height is fixed at a 1600 mm height, the
energy transfer index decreases by 27% when the flowrate increased from 20000
to 25000 Nm3/h. However, for the current conditions, an inverse trend was found
for the bottom blowing process, namely that the kinetic energy transfer is increased
when the bottom flowrate is increased.
2) In the bottom blowing operations, the specific kinetic energies with scheme (c) are
19.5%, 28.2% and 21.1% higher than those of scheme (b) for the specific kinetic
energy input rates of 0.18, 0.27 and 0.37 W/kg, respectively. This suggests that
both the radial position and the configuration of the bottom tuyeres should be
considered during the design and the operation of the converter.
3) The present study shows that the specific kinetic energies drop by 6.6%, 9.4% and
11.2% for slag mass values of 5, 9 and 15 t compared to the case without a slag on
top of the surface in the bath, respectively.
45
Future work
Based on the previous study, future work should be done to study the kinetic energy distribution
and mixing behavior of the bath with different blowing scheme. e.g. The effects of asymmetric
blowing gas of tuyeres or intermittent blowing on the kinetic energy transfer from blowing gas
to the bath.
In addition, it is very interesting in the reaction-percentage of oxygen reacted in the vicinity
of the cavity. The understanding of this would give researchers or engineers an insight to the
oxygen reaction behavior in the BOF process. As a result, the next step should focus on the
reaction between the oxygen blowing from the Laval nozzle and the molten steel in the vicinity
of the cavity resulting from the top blowing.
47
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