1. Modeling of gas bubble breakup in liquid steel
Kamil Wichterle
VSB-Technical University of Ostrava
Czech Republic

2. 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

3. Gas – Liquid iron (steel)
Cort 1760 puddling
Air
C+1/2 O2 = CO
Liquid iron Fe-C
Solid steel

4. 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 O2 = CO

5. Gas  Liquid iron (steel)
Siemens, Martin
Hot air C+1/2 O2 = CO Flue gas C+ CO2 = 2CO Lime CaO, iron ore FeO
Liquid iron Fe-C-P-Si-S
 Liquid steel Fe slag: CaSiO3, Ca3(PO4)2, CaS

6. Gas  Liquid iron (steel)
Durrer 1950
Hot oxygen + lime C+1/2 O2 = CO
Liquid iron Fe-C-Si-P-S
 Pure Fe slag: CaSiO3, Ca3(PO4)2, CaS

7. 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 !

8. 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

9. Argon –vacuum degassing

10. ARGON –VACUUM TREATMENT
Argon gas-lift for agitation ( W/m3)
Vacuum for desorption of soluble gases (CO, O2, H2, N2)
Superficial gas velocity:
0.001 m/s … bottom > 1 m/s … level
Atmospheric pressure:
1420 mm Fe RH
Ruhrstaal - Heraeus
Actual size DH
Dortmund-Hoerde

11. 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.

12. 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

13. 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)

14. Similarity of bubbles in liquids
density
dynamic
viscosity
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
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
hexane
650
0.35*10-3
0.5*10-6
0.018
1.6*10-3
0.13

15. 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

16. Experimental

17. Overall view drive vacuum thermometer cooling coil rotating blade
measuring section
rectangular column
with conical channel
calming section
mirror
cooler
lamp
syringe system
rotating blade
drive
thermometer
vacuum
flowmeter
pump
Overall view

18. upper projection of the measuring section
conical measuring section
in a rectangular vessel
Mirror
Bubble
to the camera
100 mm

19. Detailed view of the measuring section
mirror
rectangular column
PMMA 100×100 mm
conical channel
Ø mm
flowmeter
BUBBLE
front view
BUBBLE
side view
lamp
bubble feed syringe
bubble injection
burette
water
syringe

20. Bubble generation

21. Breakup record of levitating bubble
Liquid flow

22. Fraction of non-broken mother bubbles
smaller bubbles
Log scale
larger bubbles
Time

23. Dimensionless half- life
viscosity
Morton
Bubble size
Eötvös
Experimental (M=10‑11‑10‑7 ; Eo =10-20)
Θ1/2 = 1.66×1010 Eo-6.05 M (R2 = 0,93)
(R2 = 0,88)

24. Bubble half-life as a function of the bubble size

25. The half-life (in seconds) for air bubbles in water is t1/2 = 0
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).

26. Fraction of bubble generations
Mother bubble
Daugthers
Grand daughters…
Modified dimensionless time (logarithmic)

27. Average (Sauter) bubble volume VS

28. 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

29. Gas volume increase in hydrostatic column
No breakup
Bubble size increases
Bubble breakup
Bubble number increases
Decreasing pressure
Increasing volume

30. Dimensionless time of breakup of growing bubbles
Q = variable gas volume
External pressure
Hydrostatic pressure bottom
Hydrostatic pressure
at the moving bubble

31. Delay coefficient in bubble breakup
Steelmaking
Pachuca leaching
Laboratory experiments
Vacuum treatment in metallurgy – some delay

32. Volume of bubbles after a cascade of breakup
Rising velocity
Local pressure
Bubbles approaching the level:
External pressure, p0 [Pa]
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

33. 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

34. 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

35. Thank you for the attention