Development of a Numerical Model for the Heat and Mass Transport in an Electric Arc Furnace ...

163 Pages·2016·12.1 MB·English

“Development of a Numerical Model for the Heat and Mass Transport in an Electric Arc Furnace
Freeboard”

From the Faculty of Georesources and Materials Engineering of the
RWTH Aachen University

Submitted by
Dipl- Ing. Jacqueline Christina Gruber

from Johannesburg, South Africa

in respect of the academic degree of
Doctor of Engineering
approved thesis

Advisors: Univ.-Prof. Dr.-Ing. Herbert Pfeifer
Prof. Dr.-Ing. Klaus Krüger
PD Dr. rer. nat. M. Kirschen

Date of the oral examination: 09.12.2015

This thesis is available in electronic format on the university library’s website
Jaqueline Christina Gruber
Development of a Numerical Model for the Heat and Mass Transport
in an Electric Arc Furnace Freeboard
ISBN: 978-3-95886-087-2
1. Auflage 2016
Bibliografische Information der Deutschen Bibliothek
Die Deutsche Bibliothek verzeichnet diese Publikation in der
Deutschen Nationalbibliografie; detaillierte bibliografische Da-
ten sind im Internet über http://dnb.ddb.de abrufbar.
Das Werk einschließlich seiner Teile ist urheberrechtlich geschützt. Jede Verwendung ist ohne die
Zustimmung des Herausgebers außerhalb der engen Grenzen des Urhebergesetzes unzulässig und
strafbar. Das gilt insbesondere für Vervielfältigungen, Übersetzungen, Mikroverfilmungen und die
Einspeicherung und Verarbeitung in elektronischen Systemen.
Vertrieb:
1. Auflage 2016
© Verlagshaus Mainz GmbH Aachen
Süsterfeldstr. 83, 52072 Aachen
Tel. [phone]
Fax [phone]
www.Verlag-Mainz.de
Herstellung:
Druck und Verlagshaus Mainz GmbH Aachen
Süsterfeldstraße 83
52072 Aachen
Tel. [phone]
Fax [phone]
www.DruckereiMainz.de
Satz: nach Druckvorlage des Autors
Umschlaggestaltung: Druckerei Mainz
printed in Germany
D 82 (Diss. RWTH Aachen University, 2015)
Acknowledgements
This thesis was created during my time as a research associate at the Department of Industrial
Furnaces and Heat Engineering (IOB) of the RWTH Aachen University in Germany.
I would especially like to thank University Professor Dr.-Ing. Herbert Pfeifer and Dr.-Ing. Thomas
Echterhof for giving me the opportunity to carry out the work concerning this dissertation and for
their patience, guidance, encouragement and advice. I greatly appreciate the invaluable input,
especially of Professor Pfeifer, during the phase when the results of the work done had to be
consolidated, explained and clearly presented, resulting in this thesis.
In addition, the constructive advice and correction suggestions made by both Prof. Dr.-Ing. Klaus
Krüger and PD Dr. rer. nat. Markus Kirschen should be mentioned. I would like to thank both my
advisors for their time and for their valuable input, giving me the benefit of advice based on many
years of in-depth experience concerning the topic of steel production in an EAF.
I would also like to thank all my colleagues at the IOB for their support. My special thanks goes to
those who have become good friends and whose inspiration, advice, good cheer and company
make working at the IOB a pleasure.
Last, but not least, I would like to thank my family, my children and especially my husband, for
their support and patience.

i

Content
Nomenclature ................................................................................................................................ iii
Abstract ....................................................................................................................................... viii
Kurzfassung ................................................................................................................................... x
1 Introduction ............................................................................................................................. 1
1.1 EAF-Steelmaking ................................................................................................................ 1
1.1.1 Relevance of the EAF steel production route ............................................................... 1
1.1.2 Types of electric arc furnaces....................................................................................... 2
1.1.3 Description of the EAF steelmaking process ................................................................ 3
1.2 Problem definition, objectives and approach ...................................................................... 5
2 Current state of research ..................................................................................................... 10
2.1 Numerical models of the heat and mass transport in an EAF freeboard ........................... 10
2.2 Electric arc models............................................................................................................ 27
2.2.1 Magneto- fluid dynamic models .................................................................................. 27
2.2.2 Channel Arc Model (CAM) ......................................................................................... 36
2.2.3 Black-box models ....................................................................................................... 39
2.3 Experimental investigations .............................................................................................. 40
3 EAF model description ......................................................................................................... 45
3.1 Basic characteristics ......................................................................................................... 45
3.2 Arc model .......................................................................................................................... 46
3.3 Electrode model ................................................................................................................ 47
3.4 Thermal radiation model ................................................................................................... 48
3.5 Modelling of chemical reactions ........................................................................................ 52
3.6 Conservation equations and turbulence modelling ........................................................... 56
3.6.1 Mass, momentum and energy conservation ............................................................... 56
3.6.2 Turbulence ................................................................................................................. 58
3.6.3 Wall functions and wall surface roughness ................................................................ 61
4 Model implementation .......................................................................................................... 64
4.1 Geometry .......................................................................................................................... 64
4.2 Discretisation .................................................................................................................... 67
4.2.1 Influence of boundary conditions on convergence of simulations .............................. 67
4.2.2 Mesh sensitivity study ................................................................................................ 70
4.3 Material properties ............................................................................................................ 72
ii

4.3.1 Fluids .......................................................................................................................... 72
4.3.2 Solids ......................................................................................................................... 75
4.4 Boundary conditions ......................................................................................................... 76
4.4.1 Inflows, outflows and sources..................................................................................... 76
4.4.2 Electrodes .................................................................................................................. 79
4.4.3 Electric arc region ....................................................................................................... 79
4.4.4 Surfaces ..................................................................................................................... 81
5 Results ................................................................................................................................... 83
5.1 Overview of simulations .................................................................................................... 83
5.2 Arc region modelling ......................................................................................................... 85
5.2.1 Flow field .................................................................................................................... 85
5.2.2 Temperature distributions ........................................................................................... 91
5.2.3 Mass transfer and post-combustion ........................................................................... 96
5.2.4 Residence time ........................................................................................................... 99
5.2.5 Energy flows ............................................................................................................. 102
5.3 Slag layer height ............................................................................................................. 105
5.3.1 Flow field .................................................................................................................. 105
5.3.2 Temperature distributions ......................................................................................... 109
5.3.3 Mass transfer and post-combustion ......................................................................... 113
5.3.4 Energy flows ............................................................................................................. 114
5.4 Validation of Results ....................................................................................................... 116
5.4.1 Electrode temperature profile ................................................................................... 116
5.4.2 Energy Flows............................................................................................................ 117
6 Conclusions and Recommendations ................................................................................ 119
7 Summary ............................................................................................................................. 122
8 References .......................................................................................................................... 126
9 Appendix ............................................................................................................................. 131
9.1 User subroutine - Energy source/sink due to electrode consumption ............................. 131
9.2 Overview of simulation results ........................................................................................ 136
Nomenclature iii

Nomenclature
Latin characters
Symbol Description Unit
a Absorption coeff. of a fluid for thermal radiation 1/m
A Area of arc inlet m2
arc,inlet
A Pre-exp. factor for Arrhenius reaction rate 1/s
r
C Molar concentration of species j kmol/m3
j,r
c Specific heat J/(kg·K)
p
C Roughness constant -
S
d Diameter m
d Electrode diameter m
electrode
d Diameter of upper vessel of EAF m
uppervessel
e Electron charge C
E Internal energy J/kg
(cid:40) Energy inflow of air W
(cid:68)(cid:76)(cid:85)
(cid:40) Energy outflow due to inflow into arc columns W
(cid:68)(cid:85)(cid:70)(cid:15)(cid:76)(cid:81)(cid:73)(cid:79)(cid:82)(cid:90)
(cid:40) Energy input due to outflow of arc columns W
(cid:68)(cid:85)(cid:70)(cid:15)(cid:82)(cid:88)(cid:87)(cid:73)(cid:79)(cid:82)(cid:90)
(cid:40) Energy flow due to convection W
(cid:70)(cid:82)(cid:81)(cid:89)
(cid:39)(cid:40) Sum of heat of reaction W
(cid:70)(cid:75)(cid:72)(cid:80)(cid:17)(cid:85)(cid:72)(cid:68)(cid:70)(cid:17)
(cid:40) Net energy input due to thermal radiation exchange W
(cid:70)(cid:92)(cid:79)(cid:17)(cid:86)(cid:88)(cid:85)(cid:73)(cid:68)(cid:70)(cid:72)
and convection at the cylindrical surface
(cid:40) Energy outflow of off-gas W
(cid:82)(cid:73)(cid:73)(cid:16)(cid:74)(cid:68)(cid:86)
E Activation energy for Arrhenius reaction rate J/kmol
r
(cid:40) Net energy input due to CO sources and O2 sink W
(cid:86)(cid:82)(cid:88)(cid:85)(cid:70)(cid:72)(cid:86)
(cid:40) Energy inflow of steam W
(cid:86)(cid:87)(cid:72)(cid:68)(cid:80)
f Frequency 1/s
(cid:41) External body force vector N/m3
g Gravitational acceleration m/s2
G Generation of k due to buoyancy W/m3
b
G Generation of k due to mean velocity gradients W/m3
k
h Specific enthalpy J/kg
h Arc specific enthalpy J/kg
arc
h Surrounding fluid specific enthalpy J/kg
F
h Height of foaming slag layer m
slag
I Electric arc current A
arc,elec
I Electric current A
elec
I Electric current flowing through the electrodes A
electrode
I Thermal radiation intensity W/m2
rad
j Electric current density A/m2
j Mean electric arc current density (CAM) kA/cm2
arc,CAM
iv Nomenclature

JJ Diffusion flux of species j kg/(s·m2)
j
j Average electric current density at the cathode A/m2
cathode
J Maximum electric current density A/m2
max
k Turbulent kinetic energy m2/s2
k Boltzmann’s constant J/K
B
k Effective conductivity W/(m·K)
eff
k Arrhenius forward rate constant for reaction r 1/s
f,r
K Surface roughness height m
S
Arc length from electrode tip to bath (CAM) m
arc,CAM
Characteristic length m
ch
Electrode length m
electrode
mm Mass flow rate kg/s
mm Mass flow rate in arc channel (CAM) kg/s
aarrcc,CCAAMM
mm Defined mass flow rate into arc channel kg/s
aarrcc,iinnffllooww
m EAF capacity tons
tap
m Mass flow rate of ingress air into EAF kg/s
ingress_air
m Mass flow rate of air at post-combustion gap kg/s
post_combustion_air
m Total mass flow rate of off-gas kg/s
total,off(cid:16)gas
M Molecular weight of species i kg/mol
w,i
n Coordinate normal to a wall m
n Refractive index -
O Work function for the anode V
an
P Operating power W
p Pressure Pa
P Electric arc power due to Joule heating W
arc,Joule
P Energy dissipation at the electric arcs due to W
conv,CAM
convection
P Energy dissipation at the electric arcs due to electron W
e,CAM
flow
P Electrical power input W
in,electric
p Operating pressure Pa
op
P Energy dissipation at the electric arcs due to radiation W
r,CAM
p Static pressure of surroundings Pa
s
QQ Energy input from arc region W
arcregiion
QQ Energy input at plasma/electrode interface W
arc//ellecttrodde
QQ Energy input at plasma/melt interface W
arc//melltt
QQ Energy outflow due to cooling by water cooled panels W
coolliing
QQ Net energy outflow at bottom surface W
bbatthh
QQ Energy outflow by conduction at top surface of W
condduc.ellecttr.
electrodes
QQ Heat source in the electrodes due to Joule heating W
ellecttrodde
q(cid:99)(cid:99)(cid:99)(cid:99)(cid:99)(cid:99) Volumetric electrode heat source due to Joule heating W/m3
electrode
Nomenclature v

QQ Energy outflow due to heat losses at the uncooled W
hheattlloss
walls made of refractory material
QQ Joule heating of the electrodes W
JJoullehheattiing
QQ Energy loss due to thermal radiation out of all gaps and W
radd.,gaps
the slag door
QQ Energy flow due to thermal radiation W
tthhermallraddiiattion
QQ Total heat transferred at the anode surface W
ttottall,anodde
R Universal gas constant J/(K·mol)
r Radius m
rr Point position m
r Radius of electric arc (CAM) m
arc,CAM
R Electrical resistance V/A = (cid:58)(cid:3)
arc
r Cathode spot radius m
cathode
R Electric resistance (cid:58)(cid:3)
electrode
Rˆ Molar rate of creation or destruction of species i during kmol/(m3·
i,r
reaction r(cid:3)(cid:3)(cid:3) s)
R Net rate of production of species i due to reaction r kg/(m3·s)
i,r
ss Vector direction m
S User defined source term W/m3·s
(cid:72)
S Energy sources W/m3
h
S User defined source term W/m3
k
S Mass sources kg/(s·m3)
m
T Temperature K
t Time s
T Arc temperature (CAM) K
arc
T Temperature of surroundings Pa
S
u* Dimensionless velocity -
U , U , U AC phase voltages V
1 2 3
U , U , U Phase to phase voltages V
12 23 31
U Anode drop voltage V
an
U Electric potential of the electric arc V
arc
u, u Velocity components in i- or j- direction m/s
i j
u Mean velocity of the fluid at the near-wall node P m/s
P
u Arc radiation density W/m3
rad,arc
V Volume m3
VV Volumetric flow rate m3/s
V , V , V AC phase voltages without transformer voltage drop V
1 2 3
V Electrode volume m3
electrode
V Neutral point potential V
m
v Average gas velocity of arc (CAM) m/s
arc,CAM
v Velocity defined at arc inlets m/s
arc,inflow
vv Velocity vector m/s
v Tangential velocity component at a wall m/s
t
v ,v ,v Velocity components in x-, y-, z-direction m/s
x y z
vi Nomenclature

x Mole fraction of species i -
n,i
Y Contribution of fluctuating dilation in compr. turbulence W/m3
m
to the overall dissipation rate
x, y, z Cylindrical coordinates m
y Distance of near-wall node P from the wall m
P
Z Transformer and reactor impedance (cid:58)
tr
Z Line impedance (cid:58)
line
Z Arc impedance (cid:58)
arc
Z Media impedance (cid:58)
media

Greek characters
Symbol Description Unit
(cid:69) Temperature exponent for Arrhenius reaction rate -
r
(cid:71) Kronecker delta ((cid:71) = 0 if i (cid:122)(cid:3)j and (cid:71) = 1 if i = j) -
i,j ij ij
d(cid:58)(cid:3) Solid angle m2/m2
(cid:72)(cid:3) Emissivity -
(cid:72)(cid:3) Turbulent dissipation rate m2/s3
(cid:73) Electric potential V
elec
(cid:73)(cid:3) Scalar (e.g. velocity, pressure, shear stress,…) -
(cid:78)(cid:3) Isentropic exponent -
(cid:79) Thermal conductivity W/(m·K)
(cid:79) Air-fuel equivalence ratio -
(cid:80) Magnetic field constant H/m
0
(cid:80)(cid:3) Dynamic viscosity kg/(s·m)
(cid:80) Turbulent viscosity kg/(s·m)
t
(cid:75)(cid:99) Reactant rate exp. of species j for reaction r -
j,r
(cid:75)(cid:99)(cid:99) Product rate exp. of species j for reaction r -
j,r
(cid:81)(cid:99) (cid:3) Reactant stoichiometric coeff. of species j for reaction r -
j,r
(cid:81)(cid:99)(cid:99) Product stoichiometric coeff. of species j for reaction r -
j,r
(cid:85)(cid:3) Density kg/m3
(cid:85) Density of a DC arc kg/m3
DC
(cid:85) Specific electrical resistance (cid:58)·m
elec,arc
(cid:86)(cid:3) Stefan-Boltzmann constant J/K
(cid:86) Electrical conductivity A/(V·m)
elec
(cid:86) (cid:86) Turbulent Prandtl numbers -
k, (cid:72)(cid:3)
(cid:86) Scattering coefficient 1/m
s
(cid:87)(cid:3) Shear stress N/m2
(cid:87)(cid:3) Space-time s
(cid:90)(cid:3) Pulsation of the power supply voltage 1/s
(cid:91) Mass fraction of species i kg/kg
i
Y Mass fraction of species i kg/kg
i

Abbreviations
Abbreviation Meaning
AC Alternating current