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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