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
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
Gas – Liquid iron (steel)
Cort 1760 puddling
Liquid iron Fe-CSolid steel
Air C+1/2 O2 = CO
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
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
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
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 !
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
argon
Argon –vacuum degassing
vacuum
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
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.
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
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)
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
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
Experimental
cooling coil
measuring section
rectangular columnwith conical channel
calming section
mirror
cooler
lamp
syringe system
rotating blade
drive
thermometer
vacuum
flowmeter
pump
Overall view
to the camera
Bubble
Mirror
conical measuring sectionin a rectangular vessel
upper projection of the measuring section
100 mm
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
Bubble generation
Breakup record of levitating bubble
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
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)
Bubble half-lifeas a function of the bubble size
100
1000
10000
10 15 20Eo
1/2
Water
Glycerol 56%
Glycerol 76%
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).
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…
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(
)(
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
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
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
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
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:
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
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
Thank you for the attention