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 O2 = 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 O2 = CO

Gas  Liquid iron (steel) Siemens, Martin 1880-1990 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

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

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

ARGON –VACUUM TREATMENT Argon gas-lift for agitation (10-300 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

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 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

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 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

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 front view BUBBLE side view lamp bubble feed syringe bubble injection burette water syringe

Bubble generation

Breakup record of levitating bubble Liquid flow

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

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-0.04 (R2 = 0,93) (R2 = 0,88)

Bubble half-life as a function of the bubble size

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).

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

Average (Sauter) bubble volume VS

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 No breakup Bubble size increases Bubble breakup Bubble number increases Decreasing pressure Increasing volume

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

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

Volume of bubbles after a cascade of breakup Rising velocity Local pressure Bubbles approaching the level: 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

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