ANNUAL REPORT 2005ccc.illinois.edu/s/2005_Presentations/05_JAoki... · 2007. 11. 20. · ANNUAL REPORT 2005 Meeting date: June 1, 2005 Jun Aoki (M.S ... Drag coefficient Lift force

1

ANNUAL REPORT 2005Meeting date: June 1, 2005

Jun Aoki (M.S. Student) &Brian G. Thomas

Department of Mechanical & Industrial EngineeringUniversity of Illinois at Urbana-Champaign

Ladle Mixing andInclusion Removal by Bubbles

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • J Aoki & BG Thomas 2

Acknowledgments

• The Continuous Casting Consortium• Dr. L. Zhang and Lab Members

• J. Peter and Dr. K. D. Peaslee, University of Missouri-Rolla

• Nucor Steel• Nucor Yamato Steel

• U.S. Department of Energy• National Science Foundation

• Fluent Inc., Lebanon, NH

2


BackgroundKey Phenomena in Ladle Refining

Slag entrainment

Re-oxidation

Inclusion collision & coarsening

Inclusion absorption into slag

Inclusion attachmentto bubble

Mixing

Alloy melting

Flow pattern

Slag-metal reactione.g.: Al+FeO Al2O3+Fe

Alloy addition

Gas injection

Slag layer

Inclusion

Bubble

Liq. steel


Outline

• Model 1: Multiphase ladle flow simulation

• Model 2: Alloy melting and mixing in ladle

• Model 3: Inclusion attachment to bubble

• Model 4: Inclusion removal by bubbles in ladle flow

• Model 5: Inclusion absorption at slag-metal interface

3


Model 1: Multiphase Ladle Flow Simulation


Model ApproachEulerian-Lagrangian Multiphase Model

Bubble

Liq. steel

Gas injection

Lagrangian:

Trajectories of Individual Bubbles

Eulerian:Molten steel flow pattern

Interaction:• Phase fraction• Momentum exchange• Source of turbulence

4


Model Configuration

Drag force

Buoyancy force

Virtual mass force

Pressure gradient force

Drag coefficient

Lift force

Bubble diameter

Bubble density

Source of turbulence from bubbles

Phase fraction

Momentum source

FLUENT UDF

Fluid velocityturbulence

phase fraction

Lagrangian bubble trajectory calculation

Eulerian fluid flow calculation

Local static pressure


Equations for Multiphase Turbulent Flowin Eulerian Frame of Reference

( ) ( ) 0=⋅∇+∂∂

lllll ut

ραρα

( ) ( ) ( )[ ] bltlllllllll Fupuuut

+∇+⋅∇+−∇=∇⋅+∂∂ µµαραρα

Continuity

Momentum conservation

Transport equation for turbulent kinetic energy

Transport equation for dissipation rate

Turbulent viscosity Generation of k

αl : Phase fraction of liquidul : Velocity of liquidρ l : Density of liquidp : Pressureµl : Viscosity of liquidµt : Turbulent viscosityC1, C2, Cµ, σk, σε :

Standard Empirical constants(=1.44, 1.92, 0.09, 1.0, 1.3)

Csk, Csε: Empirical constants(defined by matching withexperimental data0.1~0.7 suggested by (1))

ερµ µ

2kC lt =

kbsllt

llll Sk

Ck

CGk

Cut k

εεραεαεσµαεερα εε

+−+

∇⋅∇=

∇⋅+∂∂ 2

21

kbsklllk

tllll SCGkku

tk

k+−+

∇⋅∇=

∇⋅+∂∂ εραα

σµαρα

j

il

i

jl

j

iltk x

ux

uxu

G∂∂

∂

∂+

∂∂

= ,,,µ

Momentum source from bubbles

Turbulence source from bubbles

1. S. T. Johansen and F. Boysan, Met. Trans. B, Vol. 19B, 1988.

5


Equations of Motion of a Bubble(Lagrangian Approach)

( )iblibib

Dldrag uu

dCF ,2

,,4Re3

−=ρµ

( )y

ib

libbuoyancy egF

,

,

ρρρ −

=

( ) liblib

lLlift uuuCF ×∇×−= ,

,ρρ

llib

lgradientpressure uuF ∇⋅=

,_ ρ

ρ

gradientpressureliftmassvirtualbuoyancydragib FFFFF

dtud

__, ++++=

( )iblib

lVMmassvirtual uu

dtdCF ,

,_ −=

ρρ

Forces acting on a bubble

Drag force

Buoyancy force

Virtual mass force

Lift force


ub,i : Velocity of ith bubbledb,i : Equiv diameter of ith bubbleρb,i : Density of ith bubbleCD : Drag coefficientCVM : Virtual mass coefficient (=0.5)CL : Lift coefficientxb,i : Position of ith bubbleζ :Normal Gaussian distributed

random number (σ=1)iR : Unit vector in random direction

Bubble position Turbulent effect

dtux ibib ∫= ,, Rll ikuu 32ς+=

78.000165.0 −= bLC α

1. S. W. Beyerlein et al., Int. J. Multiphase Flow, Vol.11, 1985.

(1)


Drag Coefficient and Terminal Velocity of Bubble

8We38

We1.2065Re

3We

Re100Re

3.6

100Re49.0Re

68.20

49.0ReRe16

6.2

385.0

643.0

>=

>=

<=

<<=

<=

D

D

D

D

D

C

C

C

C

C

l

iblibl uudµ

ρ ,,Re−

=

lb

iblibl uudσ

ρ2

,,We−

=

Drag coefficient(1)

Weber number

Reynolds number

0.01

0.1

1

0.1 1 10 100Volumetric equivalent diameter db (mm)

Term

inal

vel

ocity

uT (m

/s)

Clift et al. "Contaminated Water"Air in waterN2 in Wood's metalAr in liquid steel

sphere spheroid

spherical cap

db=6mm db=42mm

1. J. T. Kuo and G. B. Wallis, Int. J. Multiphase Flow, Vol. 14, 1998.2. R. Clift et al., Bubbles, Drops, and Particles, Academic Press, New York 1978.

(2)

(2)

6


Source of Fluid Momentum and Turbulencedue to Bubble Motion

Source of momentum

[ ]∑ ∆+++∆

−=cellbN

i

sibgradientpressureliftmassvirtualdrag

cellb tQFFFF

VF

,

,__1

Source of turbulence

Nb,cell : Number of bubbles in the computational cell

Qsb,i : Flow rate of the bubble

stream∆t : Bubble timestep∆Vcell : Cell volume

[ ] ( ) sib

N

iiblgradientpressureliftmassvirtualdrag

cellkb QuuFFFF

VS

cellb

,,__

,1 ∑ −⋅+++∆

−=


Bubble Density and Diameter

( )TT

pyHgp il

bib0

0

00,

−+=

ρρρ

TT

pgHp l

bbottomb

0

0

00

ρρρ +=

( )bottomb

il

lbottomb

ib

bottom

ib dyHgp

gHpdd b 3

0

03

,, −+

+==

ρρ

ρρ

Bubble Density

Bubble density at inlet nozzle (ladle bottom)

Bubble diameter (volumetric equivalent diameter)

ρb,i : Density of ith bubbleρ0b : Density of the gas in STPp0 : Standard pressure (101,325Pa)T0 : Standard temperature (273K)T : Liquid temperature in the vesselH : Bath depthyi : Vertical location of the ith bubble

7


Bubble Size Distribution

( ) ( )[ ]( )[ ]

−−= 2

2

ln2lnlnexp

sddPP

mbb

m

0007.004.02.02

+

=

gQd bm

b

Bubble number distribution(assumed logarithmic normal function)(1)

Diameter with the maximumnumber distribution

1. Y. Xie et al., ISIJ Int., Vol. 32, 1992.

0.01

0.1

1

10

100

1 10 100

Volumetric equivalnet diameter db (mm)

Prob

abili

ty (%

)

Number distributionVolume distribution

N2 in Wood’s metalQb=204cm3/s (at nozzle)


Model Validation

Wood’s metal experiment by Xie and Oeters

N2

Magnet probefor local velocity measurements

h=370mm

d=400mm

nozzle diameter = 3mm

0.0042

µPas

70940012.512.52550

M.P.ºC

ρkg/m3

Cd%

Sn%

Pb%

Bi%

Wood’s metal properties

Bath temperature = 100 ºCGas flow rate = 100~800 Ncm3/s

Y. Xie and F. Oeters, Steel Research, Vol. 63, 1992

8


Model Validation – Flow Field

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

-0.2 -0.1 0 0.1 0.2x (m)

Ver

tical

vel

ocity

uy (

m/s

)

y=0.1m calc.y=0.2my=0.3my=0.1m exp.y=0.2my=0.3m

Time averaged velocity (m/s) Comparison of vertical velocity with experiment

Experimental points : Y. Xie and F. Oeters, Steel Research, Vol. 63, 1992

Qb = 200 cm3/s (STP)→ 204(bottom)~273(top) cm3/s

(actual temperature and pressure)Csk=0.25, Csε=0.25

5.00e-01

4.50e-01

4.00e-01

3.50e-01

3.00e-01

2.50e-01

2.00e-01

1.50e-01

1.00e-01

5.00e-02

0.00e+00ZY

X


Model Validation – Gas Volume Fraction

0

0.1

0.2

0.3

-0.1 -0.05 0 0.05 0.1x (m)

Bubb

le v

olum

e fra

ctio

n

y=0.1m calc.y=0.2my=0.3my=0.1m exp.y=0.2my=0.3m

Time averaged gas volume fraction Comparison of gas volume fraction with experiment

Experimental data: Y. Xie and F. Oeters, Steel Research, Vol. 63, 1992

Qb = 200 cm3/s (STP)→204(bottom)~273(top)cm3/s

(actual temperature and pressure)Csk=0.25, Csε=0.25

9


Model ImplementationThe LMF Ladle of Nucor Yamato Steel

2832mm

305mm

254mm

406mm

2680mm

1143mm

3581mm

300mm

464mm

652mm800mm

Alloy addition directly above porous plug(randomly distributed in 400mm diameter circle region)

Alloy addition

Porous plug(φ = 64mm)

Sampling location

xy

xz

725mm

110 m-tonne ladle


Flow Field and Bubble Distribution(FLUENT 6.1 output)

Flow field (m/s) Gas volume fraction (%)Gas Flow rate = 0.113 Nm3/min→ 0.254 (bottom) ~ 0.775 (top) m3/min Csk=0.10, Csε=0.08

10


Flow Field in 3D(FLUENT6.1 output)


Model 1 Summary

• An Eulerian-Lagrangian three-dimensional transient turbulent flow model is developed based on the commercial package FLUENT with extensive user defined subroutines.

• The calculated flow field and gas volume fraction match well with the experiments in Wood’s metal.

• Off-center Ar bubbling causes complex 3D swirling flow pattern in Nucor Yamato LMF ladle.

11


Model 2: Alloy Melting and Mixing in Ladle


Conditions of Alloy Addition in Nucor Yamato Steel(Experimental Heat 1)

Start alloy addition(t=0)

90secAlloy addition

37sec

Mixing 453sec

Plume

Operating Conditions

bal.0.070.0070.451.916.371.8

FeMoistureSPCSiMn

Chemical Composition of SiMn Alloy

Location of Alloy Addition

2m

0.4m

0 ~ 13mm : 5%13mm ~ 64mm : 90%~64mm : 5%

Size Distribution

Start bubbling Stop bubbling

12


Operating Conditions and Alloy Recoveriesin Nucor Yamato Steel

95.829735155215770.1708

94.724840153315770.1707

95.632734156415860.1136

95.133810156816050.1135

91.1231055152915660.1134

96.625415154115780.1133

93.030909155715900.1132

97.820380151615510.1701

FinalInitialFinalInitial

Mn recovery(%)

Oxygen (ppm)Temperature (ºC)

Ar flow rate

(Nm3/min)

Heat

Experiment: J. Peter and K. D. Peaslee, University of Missouri-Rolla


Concentration Histories duringHeat 1 Experiment

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-100 0 100 200 300 400 500

Time since start of alloy addition (s)

Mn

& 4

*Si c

once

ntra

tion

(wt%

)

0.05

0.06

0.07

0.08

0.09C

con

cent

ratio

n (w

t%)

% Mn% Si % C

1551 ºC

slag

SiMnaddition

1516ºC

slag


13


Concentration Histories duringHeat 2 Experiment

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

-100 0 100 200 300 400 500Time since start of alloy addition (s)

Mn

& 4

*Si c

once

ntra

tion

(wt%

)

0.05

0.06

0.07

0.08

C c

once

ntra

tion

(wt%

)

% Mn% Si % C

1590 ºC

slag

SiMnaddition

1557ºC

slag



Estimated Time before Alloy Release(Shell Solidification and Melting)

0

5

10

15

20

25

30

0 20 40 60 80 100Steel superheat (°C)

She

ll ex

iste

nce

time

arou

nd S

iMn

allo

y (s

) Solid alloy particle

Steel shell growth

Alloy melting inside

Steel shell melting

Steel shell disappearLiquid alloy release

d=30mm

14


Equations for Alloy Melting and Mixing

( ) MMt

tMMM SC

ScDCvC

t=

∇

+−⋅∇+

∂∂ µρρρ

2. t ≥ t1 for each particle : Turbulent diffusion of alloy element CM : Mass fraction of element M

DM : Diffusion coefficient of element M in liquid steel

Sct : Turbulent Schmidt number(=1)

SM : Source or element M

sM

sAApA

TTTT

hdC

t−−

= 01 π

ρ

Steel shell growth and melting model(1) t1 : Shell existence timeCpA : Specific heat of alloyρA : Density of alloyh : Heat transfer coefficientTs : Solidification temperature of

steelT0 : Initial temperature of alloyTM : Liquid steel temperature 1. t < t1 for each particle :

Alloy particle transport with no diffusion

1. L. Zhang and F. Oeters, Steel Research, Vol. 70, 1999.


Equations of Motion of Alloy Particle(Lagrangian Trajectory Calculation)

( )iplipip

Dldrag uu

dCF ,2

,,4Re3

−=ρµ

( )y

ip

lipbuoyancy egF

,

,

ρρρ −

= llip

lgradientpressure uuF ∇⋅=

,_ ρ

ρ

gradientpressuremassvirtualbuoyancydragip FFFF

dtud

__, +++=

( )iplip

lVMmassvirtual uu

dtdCF ,

,_ −=

ρρ

Forces acting on an alloy particle

Drag force

Buoyancy force

Virtual mass force


up,i : Velocity of ith particledp,i : Equiv diameter of ith particleρp,i : Density of ith particleCD : Drag coefficient

(Spherical model in FLUENT)CVM : Virtual mass coefficient (=0.5)xp,i : Position of ith particleζ :Normal Gaussian distributed

random number (σ=1)iR : Unit vector in random direction

Particle position Turbulent effect

dtux ipip ∫= ,, Rll ikuu 32ς+=

15


Alloy Position at the Slag-Metal Interface

( )θθπ 33 coscos3224

+−= pupper dV

( )θθπ 33 coscos3224

−+= plower dV

slag

molten steel

alloy

Vupper

Vlower

2θ

Volumes of upper and lower parts

Force balance at the interface

yloweralloy

steelliqalloyupper

alloy

slagalloybuoyancy egVVF

−+

−= −

ρρρ

ρρρ

θ= 65.3 º for SiMn particleρalloy = 6120 kg/m3, ρslag = 2700 kg/m3

ρliq-steel = 7000kg/m3

Balance position


Alloy Particle Distribution

Alloy addition

SiMn particle distribution 20 second after alloy addition start Colored by particle diameter (including shell thickness)

Heat 1 (SH = 20 °C) Heat 2 (SH = 60 °C)

XY plane

16


Mixing Behavior: Mn Content(Heat 1, Qg=170Nm3/min, SH=60ºC)

XY plane YZ plane

15 second after alloy addition start


Mixing Behavior: Mn Content(Heat 2, Qg=113Nm3/min, SH=20ºC)

XY plane YZ plane

10 second after alloy addition start

17


Concentration Profiles at the Sampling Point

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 100 200 300 400

Time after alloy addition start (s)

Nor

mal

ized

con

cent

ratio

n

Heat 1 (calculated)Heat 1 (measured)Heat 2 (calculated)Heat 2 (measured)


Mixing Time at Various Monitoring Locations(Heat 1)

Z

Y

X

2

4

3

5

8

6

9

7

Porous plug

Plume

201

187

211

191

214

202

206

197

198

162

149

161

153

173

162

167

156

158

0 50 100 150 200 250

9

8

7

6

5

4

3

2

1

Mon

itorin

g lo

catio

n

Mixing time after alloy addition (sec)

±1% ±5%1: Sampling location

in industrial experiment

18


Model 2 Summary

• It takes 5~15 seconds for alloy particles to melt after they are added to molten steel.

• Alloy particles travel between slag and metal interface before they melt. Therefore, the place where alloy content starts to increase is different from where alloy particles are added.

• Using alloy particle transport and turbulent species diffusion model, the mixing behavior can be predicted.


Model 3: Inclusion Attachment to Bubble

19


Inclusions Captured by Bubbles in Steel

1. L. Zhang, B. Rietow and B. G. Thomas, Investigation of Ingot Inclusions Using Microscope and SEM, Univ. of Illionis at Urbana-Champaign, IMF project report, May. 04, 2004.

2. L. Kiriha et al., CAMP-ISIJ, Vol. 13, 2000.


Steps of Inclusion Attachment to Bubble

1.Collision-Particle trajectory

3.Slide- Sliding time ts- Film drainage time tf

2.Oscillation- Collision time tc

4.Attachment- Stability

ts=10-3~10-1sec

tc=10-7~10-5sec

tf=10-6~10-3sec

20


dC , SC

θC

ub

Bubble

Inclusion

Attachment Probability PA2

b

c

+==

pR

CA dd

dSSP

Inclusion Attachment Probability(Conventional Definition)

Assumption:Inclusion will be attached to bubble surface if sliding time ts is greater than film drainage time tf.The value of dc can be obtained by sliding time calculation.

L. Zhang and S. Taniguchi, Int. Mat. Reviews, Vol. 45, 2000.

SR

db dp


Example of Particle Trajectory Calculation(Conventional Method)

Particle Traces Colored by Particle Residence Time (ms)FLUENT 6.1 (axi, dp, segregated, ske)

May 01, 2004

6.95e+02

6.26e+02

5.56e+02

4.87e+02

4.17e+02

3.48e+02

2.78e+02

2.09e+02

1.39e+02

6.95e+01

0.00e+00

100µm silica inclusion trajectory toward 1mm Ar bubble

particle : SiO2 (spherical shape)

100db

yi

xy

attached if tf<ts

not attached

dc

Potential flow based trajectory calculation: C. M. Phan et al., Int. J. Miner. Process, Vol. 72, 2003.

• Assuming spherical bubble (db<1mm)• No consideration of turbulence

Particle trajectory calculation by computer simulation:L. Zhang, J. Aoki and Brian G. Thomas, MS&T 2004, New Orleans, LA. 2004.

OK for small bubbles and low turbulence (mold)Not applicable in steelmaking ladle condition

21


Bubble Morphology forSpheroidal or Spherical Cap Bubble

1

2

3

4

5

0.1 1 10 100

dp (mm)

e

0.7571/ 2 1 0.163e r r Eo= = +

Spherical cap

Sphere Spheroid

Spheroidal bubble(1)

( )σ

ρρ bbgdEo −=

2Eotvos number

db (mm)

Spherical cap bubble

r1r2

2θR

R = 9/8db (constant CD = 8/3)

θ=50.59°(volume matching)experiment: θ=46°~64°

1. R. M. Wellek et al., A. I. Ch. E. Journal, Vol. 12, 1966.

volumetric equivalent diameter

aspe

ct ra

tio


Inclusion Trajectories near Bubble in Various Global Turbulent Flow Fields

k = 10-6m2/s2 k = 10-4m2/s2

k = 10-2m2/s2 k = 10-1m2/s2

db = 100mm, dp = 100µm

22


Re-definition of Inclusion Attachment Probabilityfor Strongly Turbulent Flow Fields

( )4

2pbS

p

ap

A ddC

NP

+=

π

2

b

c

+=

pA dd

dP

Injecting surface (must include all inclusions which eventually attach)

bubble

Inclusion trajectory

Attachment probabilitynumber attached (#)

inclusion concentration on the injecting surface (#/m2)

reference surface area (m2)(conventional definition)

db

dp

Conventional method2

4 cSp

ap dCN π=

Number of inclusions attached is counted out of 40,000~400,000 injected inclusions per case

lCC Vp

Sp ∆=

CpV : Volumetric inclusion concentration (#/m3)

∆l : Bubble path length (arbitrary) (m)


Attachment and Entrapment

( )4

2pbS

p

ap

A ddC

NP

+=

π

Attachment probability

( )4

2pbS

p

ep

E ddC

NP

+=

π

Entrapment probability

Total removal probability by a bubble

EATR PPP +=

Nep : number of entrapped inclusions in the

wake for more than bubble floatationtime (3sec)

k=10-2m2/s2

0

10

20

30

0 20 40 60 80 100 120

Volumetric equivalent diameter db (mm)

Pro

babi

lity

(%)

k=10-6m2/s2

0

10

20

30

0 20 40 60 80 100 120

Pro

babi

lity

(%)

Attached to the bubbleTrapped in the wakeTotal

23


Effect of Turbulence

0

5

10

15

20

25

1E-08 1E-06 1E-04 1E-02 1E+00

k (m2/s2)

Pro

babi

lity

(%)

attachmententrapmenttotalconventional method

db=100mm, dp=100µm

0

20

40

60

80

100

120

1E-08 1E-06 1E-04 1E-02 1E+00

k (m2/s2)

Pro

babi

lity

(%)

attachmentconventional method

db=1mm, dp=100µm


Inclusion Removal Probabilitywith Turbulent Motion

Turbulence greatly increases inclusion attachment probability (especially at large bubble diameter and high turbulence levels)

0.1

1

10

100

1000

1 10 100Volumetric equivalent diameter db (mm)

Atta

chm

ent p

roba

bilit

y P

A (%

)

Conventional methodk = 10-6m²/s²k = 10-4m²/s²k = 10-2m²/s²k = 10-1m²/s²

0.2 0.3 0.4 0.5 0.6 0.7Bubble rising velocity (m/s)

Particle diameter dp=100µm

Tota

l rem

oval

pro

babi

lity

PTR

(%)

24


Model 3 Summary

• The model for predicting inclusion attachment probability to a large distorted bubble in a turbulent flow field is developed for the first time.

• Inclusion entrapment in the recirculation zone behind large bubble at low turbulence level is also important.

• Probability of Inclusion removal by bubbles considering turbulence is 10 to 100 times higher than that of the conventional model.


Model 4: Inclusion Removal by Bubblesin Ladle Flow

25


Modeled ProcessThe LMF Ladle of Nucor Yamato Steel

2832mm

305mm

254mm

406mm

2680mm

1143mm

3581mm

Porous plug(φ = 64mm)

xy

xz

725mm

110 m-tonne ladle


Flow Field and Bubble Distribution(FLUENT 6.1 output)

Flow field (m/s) Turbulent kinetic energy (m2/s2)Gas Flow rate = 0.170 Nm3/min→ 0.379 (bottom) ~ 1.166 (top) m3/min Csk=0.10, Csε=0.08

26


Equations for Inclusion Transport in Ladle Flow(Eulerian Approach)

( ) ( ) ( ) ( ) ( )p

Mp

tlMpll

z

MpllT

py

Mpll

xMpll SC

SczC

uyC

uuxC

uCt

−∇

∇=

∂∂

+∂

∂++

∂∂

+∂∂ µαραραρα

ρα

( ) ( )∑

−

+

∆=

cellbN

iibl

Mpll

pibRbpiTR

cellp uuC

ddSkddP

VS ,

2,

, 4,,1 ρα

π

2

2

,2

4b

pipb

R d

dNd

Sπ

ππ −

=

Inclusion transport in turbulent flow

Inclusion removal rate by attaching to bubbles

Surface area correction factorCp

M : Inclusion number concentration per unit liquid mass (#/kg)

ux, uy, uz: Liquid velocityup

T : Terminal velocity of inclusionSc : Turbulent Schmidt number (=1)PTR : Total inclusion removal probability (Model 4)

(function of db, dp, and k)dp = 100µm, k=0.1m2/s2 (assumed constant)


Initial and Boundary Conditions

Boundary ConditionsCASE 1. Cp

M at top surface = 0(All inclusions reached to the interface will be absorbed into slag)

Bubble attachment(All inslusions attached to bubbles will be removed)

CASE 2. Bubble attachment only

CASE 3. Top surface removal only

Absorption into top slag

Attachment to bubble

Initial ConditionsInitial [O] = 50 ppm (75,156 inclusions/kg)Uniform distribution in the ladleinclusion diameter = 100 µm

27


Change of Oxygen Content

Case 1Bubble and Top surface

Case 2Bubble only

Case 3Top surface only

Snapshots at 60 seconds after bubbling start


Calculated Oxygen Content andDeoxidization Rate Constant

0

10

20

30

40

50

60

0 100 200 300 400 500 600Bubbling time (s)

Oxy

gen

Con

tent

(%)

Case 1 (bubble + top surface)Case 2 (bubble only)Case 3 (top surface only)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 100 200 300 400 500 600Bubbling time (s)

Deo

xidi

zatio

n ra

te c

onst

ant K

o (1

/min

) Case 1 (bubble + top surface)Case 2 (bubble only)Case 3 (top surface only)

[ ] [ ]OOOK

dtd

−=Rate Constant

28


Comparison of KO with Various Processes

100 101 102 103 10410-3

10-2

10-1

100

KO (min - 1)

d[O]/dt=Ko [O][O]: ppmt: min

KO: min - 1

Ar gas bubbling ASEA-SKF (I) ASEA-SKF (II) VOD (NK-PERM) VOD (Convent.) RH (NK-PERM) RH (Convent.)

ε (Watt/ton)

bubble

L. Zhang and B. G. Thomas, 7th European Steelmaking Conference, Milano, 2002

bubble + top surface

top surface


Model 4 Summary

• Inclusion removal model in ladle flow considering absorption into top slag-metal surface and attachment to bubbles is developed.

• Assuming all inclusions will be absorbed into top slag, the rate constant is much higher than actual steelmaking processes. Thus, correct estimation of inclusion absorption at the slag-metal interface is very important.

• To predict the deoxidization rate more accurately, further modeling is necessary which includes:1. Inclusion absorption at the slag-metal interface.2. Re-oxidation from slag.3. Size distribution of inclusions.

29


Model 5: Inclusion Absorption at theSlag-Metal Interface


Inclusion (Alumina) Behavior at theSlag-Metal-Bubble Interface

contact angle in steel θ=130°

contact angle in slag θ=40°~60°

Alumina inclusion will detach from the bubble at the interface

molten steel

slag

bubble

inclusion

30


Inclusion Pile-up at the Slag-Metal Interface(Dissolution Rate < Transfer Rate)

Alumina dissolution into slag can be the rate-controlling process

molten steel

slag


Alumina Particle Dissolution in Slag

( )t

RCCMk

RR slag

OAlsat

OAlmt

0

)()(

0

32321ρ

−−=

Mass transfer (diffusion) control model

R : Particle radius (m)R0 : Particle initial radius (m)kmt : Mass transfer coefficient (m/s)M : Molecular weight of alumina

(=0.102kg/mol)C(sat)

Al2O3 : Saturation concentration of alumina (mol/m3)

C(slag)Al2O3 : Slag bulk concentration of

alumina (mol/m3)ρ : Density of alumina (kg/m3)t : Time (s)

W. D. Cho and P. Fan, ISIJ Int., Vol. 44, 2004.

Al

CaO

Si

31


Controlling Factors of Dissolution Rate

W. D. Cho and P. Fan, ISIJ Int., Vol. 44, 2004.

Temperature SiO2 content in slag Al2O3 content in slag

T SiO2 Al2O3

Time (s) Time (s)Time (s)

Par

ticle

Siz

e (µ

m)

Par

ticle

Siz

e (µ

m)

Par

ticle

Siz

e (µ

m)

Alumina dissolution rate increases with•Higher temperature•Lower SiO2 content in slag•Lower Al2O3 content in slag


Conversion from Dissolution Rate toAbsorption Rate per Unit Surface Area

( )0

)()(3232

RCCMk

dtdRR

slagOAl

satOAlmt

ρ−

−==&

dtAVd

dtA

Wd pOAl

A

−=

−=ρ

β 32

Rf

fNR

NR

AV

p

p

343

4

2

3

==π

π

Rf ppOAl

A&ρβ

34

32 −=

Dissolution rate (m/s)

Absorption rate (kg/m2s)

Top view of the slag-metal interface

R : Radius of particleW : Total mass of particlesA : Surface area occupied by particlesV : Total volume of particlesN : Number of particlesfp : Packing factor

(=0.907 for close packed spheres on a plane)

32


Deoxidization Rate Assuming Interface Control

(m/s)10128.1 6−×−=R&

1045451500

SiO2Al2O3CaO

Slag composition (wt%)Temp.(°C)

Experimental dissolution rate(1)

1. W. D. Cho and P. Fan, ISIJ Int., Vol. 44, 2004.

Absorption rate at the interface

Deoxidization rate in steel

s)(kg/m0048.0 332 =OAlAβ

[ ] (ppm/min)3.13 32

32

−=−=Steel

OAlA

OAl

O

WA

MM

dtOd β

0

10

20

30

40

50

60

0 100 200 300 400 500 600

Bubbling time (s)

Oxy

gen

Con

tent

(%)

Model 4: Case 1 Case 2 Case 3Interface control


Comparison of Deoxidization Rate Constantwith Various Processes

100 101 102 103 10410-3

10-2

10-1

100

KO (min - 1)

d[O]/dt=Ko [O][O]: ppmt: min

KO: min - 1

Ar gas bubbling ASEA-SKF (I) ASEA-SKF (II) VOD (NK-PERM) VOD (Convent.) RH (NK-PERM) RH (Convent.)

ε (Watt/ton)

Interface control

Model 4

33


Model 5 Summary

• Alumina inclusion particles carried by bubbles are considered to detach at the slag-metal interface.

• Alumina dissolution rate is strongly affected by temperature and slag composition.

• Interface absorption of inclusions may be one of the rate controlling process for deoxidization of steel ladle.


Conclusion

• Ladle refining model is developed including multiphase turbulent flow simulation, alloy mixing, and inclusion removal.

• This model is ready to use to help optimize the operating conditions in actual steel plants, and to design the future continuous steelmaking process.

34


Future Work

• Combine the interface rate control model (model 5) with the ladle deoxidization model (model 4).

• Consider the effect of re-oxidization.• Consider the effect of wall attachment.• Include the effect of inclusion size distribution using the

inclusion collision model by L. Zhang and B. G. Thomas.

• Develop surface reaction model (e.g. de-S) using the ladle flow model together with a chemical reaction model.

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