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