kamil wichterle vsb-technical university of ostrava czech republic modeling of gas bubble breakup in...
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Kamil Wichterle VSB-Technical University of Ostrava
Czech Republic
Modeling of gas bubble breakup in liquid steel
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contents
• Gas-liquid contacting in steel metallurgy• Bubbles in laboratory and in large-scale• Modelling of bubbles in liquid steel• Single bubble breakup kinetics• Cascade of bubble breakup• Sauter diameter decrease
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Gas – Liquid iron (steel)
Cort 1760 puddling
Liquid iron Fe-CSolid steel
Air C+1/2 O2 = CO
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Gas Liquid iron (steel)
Converter 1850 Bessemer (C )
1860 Thomas, Gilchrist (P,Si)
Liquid iron Fe-C Liquid steel Fe
Hot air C+1/2 O2 = CO
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Gas Liquid iron (steel)
Siemens, Martin 1880-1990
Liquid iron Fe-C-P-Si-S
Liquid steel Fe + slag: CaSiO3, Ca3(PO4)2, CaS
Hot air C+1/2 O2 = COFlue gas C+ CO2 = 2COLime CaO, iron ore FeO
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Gas Liquid iron (steel)
Durrer 1950
Liquid iron Fe-C-Si-P-S
Pure Fe + slag: CaSiO3, Ca3(PO4)2, CaS
Hot oxygen + lime C+1/2 O2 = CO
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Gases in steel
• Diluted gases CO, O, N, H…
• Solubility of gases in liquid steel HIGHER than in solid
• Solubility of gases in liquid metals INCREASES with increasing temperature
• DEGASSING IS ESSENTIAL !
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SECONDARY METALLURGY
• Desorption of diluted gases N, CO, H, O• Sedimentation - floating of slag particles• Addition of alloying metals• De-oxidation• Homogenization
• Removing of solid non-metal particles• Homogenization of temperature and
composition
ARGON – VACUUM LADLE
TUNDISH
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argon
Argon –vacuum degassing
vacuum
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ARGON –VACUUM TREATMENT• Argon gas-lift for agitation (10-300 W/m3) • Vacuum for desorption of soluble gases
(CO, O2, H2, N2)
Atmospheric pressure:1420 mm Fe
Superficial gas velocity: 0.001 m/s … bottom
> 1 m/s … level
DH Dortmund-Hoerde
RH Ruhrstaal - Heraeus
Actual size
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Scale problem of rising bubbles
• Laboratory – nearly constant bubble volume, short rising time;
• Metallurgy - large ferrostatic pressure,vacuum at the level,fast volume changes,moderate rising time;
• Deep wells, oceanography - large hydrostatic pressure,
slow volume changes, long rising time.
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Scale - up
Single bubble shape, bubble rising velocity and bubble breakup depends on:• The bubble volume • Liquid density• Liquid viscosity• Surface tension (and other surface
properties)• Gravity acceleration
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Dimensionless variables
Reynolds, Weber, Eötvös, Morton, Capillary, Laplace, …
… numbers
Here, three liquid properties μ, ρ, σ, can be everytimes grouped into two variables: μ/ρ (kinematic viscosity)
σ/ρ (kinematic surface tension)
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Similarity of bubbles in liquids
density dynamicviscosity
kinematic viscosity
surface tension
Laplace length
Laplace velocity
liquid Tempera ture ρ μ ν σ (σ/(ρg))1/2 (σg/ρ)1/4
oC kg/m3 Pas m2/s N/m m m/s
molten steel
1500 7200 5*10-3 0.7*10-6 1.4 4.5*10-3 0.21
water 25 1000 1.0*10-3 1.0*10-6 0.073 2.7*10-3 0.16
mercury 25 13500 1.5*10-3 1.1*10-6 0.46 1.8*10-3 0.14
Wood metal
80 10600 3*10-3 0.3*10-6 0.4 1.9*10-3 0.14
hexane 25 650 0.35*10-3 0.5*10-6 0.018 1.6*10-3 0.13
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STRATEGY
• Experimental study of motion and breakup of bubbles in water under common laboratory conditions
• Generalization of the results using dimensional analysis
• Introduction of the results into mathematical model of steelmaking process
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Experimental
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cooling coil
measuring section
rectangular columnwith conical channel
calming section
mirror
cooler
lamp
syringe system
rotating blade
drive
thermometer
vacuum
flowmeter
pump
Overall view
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to the camera
Bubble
Mirror
conical measuring sectionin a rectangular vessel
upper projection of the measuring section
100 mm
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bubble injection
conical channelØ 35-65 mm
mirror
lamp
bubble feed syringe
flowmeter
rectangular column PMMA 100×100 mm
burette
watersyringe
BUBBLEfront viewBUBBLE
side view
Detailed view of the measuring section
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Bubble generation
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Breakup record of levitating bubble
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Fraction of non-broken mother bubbles
0.01
0.1
1
0 20 40 60 80 100 120
t [s]
N/N 0
800 mm3 700 mm
3 500 mm
3 600 mm
3
450 mm3 VB =
Time
smaller bubbles
larger bubbles
21
ln(2)exp(0)
)(
/t
t
N
tN
Lo
g scale
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Dimensionless half- life
41
434121
21 /
///
/ gt
Θ1/2 = 1.66×1010 Eo-6.05 M-0.04 (R2 = 0,93)
(R2 = 0,88) 6
2/1 105900
Eo
gd
Eo B2
Bubble size
Eötvös
3
4 gM
viscosity
Morton
Experimental (M=10‑11‑10‑7 ; Eo =10-20)
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Bubble half-lifeas a function of the bubble size
100
1000
10000
10 15 20Eo
1/2
Water
Glycerol 56%
Glycerol 76%
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The half-life (in seconds) for air bubbles in water is
t1/2 = 0.7 VB-4
(when volume is measured in cubic centimeters).
The half-life for gas bubbles in liquid steel should be
t1/2 = 410 VB-4
(according to dimensional analysis).
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Fraction of bubble generations
0
0.2
0.4
0.6
0.8
1
-3 -2 -1 0 1 2 3 4 5 6 7
log
m i
i=0 1 2 3 4 5 6
Modified dimensionless time (logarithmic)
Mother bubble
Daugthers Grand daughters…
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Average (Sauter) bubble volume VS
0,1
1
0,01 0,1 1 10 100
V S /V 0
aS
tkV
/1)(
64.0
aat
sQ
sQ
tQ
tQ
1
0d
)0(
)(1
)0(
)(
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This is valid for any case of increasing bubbles :
•Hydrostatic pressure decrease
•Other ways of external pressure change
•Production of bubbles by phase change (boiling, desorption)
•Production of bubbles by chemical reactions
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Gas volume increase in hydrostatic column
Dec
reas
ing
pres
sure
In
crea
sin
g v
olu
me
No breakup
Bubble size increases
Bubble breakup
Bubble number increases
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Dimensionless time of breakup of growing bubbles
sQ
sQVk
at
a d)0(
)(
00
)ln(d
)ln(d 2/1
V
ta
2/1
)2ln(
tVk
a
Q = variable gas volume
tvgHgp
Hgp
Q
tQ
0
0
)0(
)(
External pressure
Hydrostatic pressure bottom
Hydrostatic pressure at the moving bubble
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Delay coefficient in bubble breakup
Hg
pB
0
Hg
pB
0
H
vtX
a
a
B
X
aX
XB11
111
)1(
)1(
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1X
0.000010.11
B =
Steelmaking
Pachuca leaching
Laboratory experiments
Vacuum treatment in metallurgy – some delay
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Volume of bubbles after a cascade of breakup
a
S pk
vgaV
1
)1(64.0
Local pressure
Rising velocity
External pressure, p0 [Pa] 100 000 10 000 1 000 100
Sauter diameter,
dS [mm]water 9.1 11.0 13.3 16.1
liquid steel 17.8 21.6 26.1 31.7
Bubbles approaching the level:
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Conclusions
• Size of bubbles rising in a large column can be determined from the developed model using breakup probability data for a single bubble under constant pressure conditions
• Average size of bubbles depends on the actual local pressure and rising velocity
• Dimensional analysis can be used to estimate the process in liquid metals
• Air-water is a better laboratory model of two phase flow in liquid steel than mercury or Wood metal
• Further research: The effect of bubble interactions will be considered
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Lenka Kulhánková Pavel Raška Jana Wichterlová
Marek C. Ruzicka Jiří Drahoš
Financial support by the Grant Agency of the Czech Republic
(grant No.104/04/0827) is greatly appreciated
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Thank you for the attention
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