Transcript Bl - vsb.cz
Modeling of gas bubble breakup in liquid steel
Kamil Wichterle VSB-Technical University of Ostrava Czech Republic
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 Air C+ 1 / 2 O 2 = CO Liquid iron Fe-C Solid steel
Gas
Liquid iron (steel)
Converter 1850 Bessemer (C ) 1860 Thomas, Gilchrist (P,Si) Liquid steel Fe Liquid iron Fe-C Hot air C+ 1 / 2 O 2 = CO
Gas
Liquid iron (steel)
Siemens, Martin 1880-1990 Hot air C+ 1 / 2 O 2 Flue gas C+ CO 2 = CO = 2CO Lime CaO, iron ore FeO Liquid iron Fe-C-P-Si-S Liquid steel Fe + slag: CaSiO 3 , Ca 3 (PO 4 ) 2 , CaS
Gas
Liquid iron (steel)
Durrer 1950 Hot oxygen + lime C+ 1 / 2 O 2 = CO Liquid iron Fe-C-Si-P-S Pure Fe + slag: CaSiO 3 , Ca 3 (PO 4 ) 2 , CaS
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
• • • • •
ARGON – VACUUM LADLE Desorption of diluted gases N, CO, H, O Sedimentation - floating of slag particles Addition of alloying metals De-oxidation Homogenization
• •
TUNDISH Removing of solid non-metal particles Homogenization of temperature and composition
Argon –vacuum degassing
vacuum argon
ARGON –VACUUM TREATMENT
• •
Argon gas-lift for agitation (10-300 W/m 3 ) Vacuum for desorption of soluble gases Superficial gas velocity: 0.001 m/s … bottom > 1 m/s … level (CO, O 2 , H 2 , N 2 ) Atmospheric pressure: 1420 mm Fe RH Ruhrstaal - Heraeus DH Dortmund-Hoerde
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
liquid molten steel water mercury Wood metal hexane Tempera ture o C 1500 25 25 80 25
ρ
kg/m 3 7200 1000 13500 10600 650 density dynamic viscosity
μ
Pas 5*10 -3 kinematic viscosity
ν
m 2 /s 0.7*10 -6 1.0*10 -3 1.5*10 -3 3*10 -3 0.35*10 3 1.0*10 -6 1.1*10 -6 0.3*10 -6 0.5*10 -6 surface tension
σ
N/m 1.4
0.073
0.46
0.4
0.018
Laplace length ( σ/(ρg)) 1/ 2 m 4.5*10 -3 2.7*10 -3 1.8*10 -3 1.9*10 -3 1.6*10 -3 Laplace velocity ( σg/ρ) 1/4 m/s 0.21
0.16
0.14
0.14
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
Overall view
vacuum cooling coil calming section measuring section rectangular column with conical channel mirror cooler drive thermometer rotating blade lamp flowmeter syringe system pump
upper projection of the measuring section conical measuring section in a rectangular vessel Mirror Bubble to the camera
100 mm
Detailed view of the measuring section mirror rectangular column PMMA 100 ×100 mm conical channel Ø 35-65 mm flowmeter
BUBBLE side view BUBBLE front view
lamp bubble injection burette bubble feed syringe water syringe
Bubble generation
Breakup record of levitating bubble
Fraction of non-broken mother bubbles
1 smaller bubbles
N/N
0 0.1
0.01
0
V B
= 450 mm 3 700 mm 3 600 mm 3 20 40 60 500 mm 3 80
t
[s] 100 120
Time
N
(
t
)
N
(0) exp ln(2)
t t
1
/
2
Dimensionless
half- life
1
/
2
t
1
/
2 1
/
1
/
4 4
g
3
/
4
Eötvös
Bubble size
Eo
d B
2
g M
Morton
viscosity 4 3
g
Experimental (M=10 -11 -10 -7 ; Eo =10-20)
Θ
1/2 = 1.66×10 10
Eo
-6.05
M
-0.04 1 / 2 5900
Eo
10 6 (
R
2 = 0,93) (
R
2 = 0,88)
Bubble half-life as a function of the bubble size
10000
1/2
Water Glycerol 56% Glycerol 76% 1000 100 10 15
Eo
20
The half-life (in seconds) for air bubbles in water is
t
1/2 = 0.7 V
B
-4 (when volume is measured in cubic centimeters).
The half-life for gas bubbles in liquid steel should be
t
1/2 = 410 V
B
-4 (according to dimensional analysis).
Fraction of bubble generations Mother bubble
1 0 .8
0 .6
m i
0 .4
Daugthers Grand daughters…
i=0 1 2 3 4 5 6 0 .2
0 -3 -2 -1 0 1 2
lo g
3 4 5 Modified dimensionless time (logarithmic) 6 7
V S /V 0
1 0 , 1 0 , 0 1 Average (Sauter) bubble volume
V S V S
(
k
0 .
64
t
) 1 /
a
0 , 1 1 1 0
Q
(
t
)
Q
( 0 )
t
1
t
0
Q
(
s Q
( 0 ) )
a
d
s
1
a
1 0 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 Bubble size increases Bubble number increases No breakup Bubble breakup
Dimensionless time of breakup of growing bubbles
k V a
0 0
t
Q
(
s Q
( 0 ) )
a
d
s a
d ln(
t
1 / 2 d ln(
V
) )
k
ln( 2
V a t
1 / 2 )
Q
= variable gas volume
Q
(
t
)
Q
( 0 )
p
0
p
0
g
H g
H
g v t
External pressure Hydrostatic pressure bottom Hydrostatic pressure at the moving bubble
Delay coefficient in bubble breakup
( 1
X
B
(
a
X
1 ) ) 1 1
B X
1
a
1 1
a B
p
0
g H B
p
0
g H
5 4 3 2 1 0
B
= 0 .0 0 0 0 1 0 .1
1
Steelmaking Pachuca leaching Laboratory experiments
0 . 2 0 . 4 0 . 6
X
0 . 8 1
X
t H v
Vacuum treatment in metallurgy – some delay
Volume of bubbles after a cascade of breakup
V S
0 .
64 ( 1 )
k
p g v
1
a
Rising velocity Local pressure
Bubbles approaching the level: External pressure,
p
0 [Pa] 100 000 10 000 1 000 Sauter diameter,
d S
[mm] water 9.1
11.0
13.3
liquid steel 17.8
21.6
26.1
100 16.1
31.7
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