Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •1 / 27University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 1

ANNUAL REPORT 2012UIUC, August 16, 2012

Bubble Formation, Breakup and Coalescence in Stopper-rod Nozzle Flow

and Effect on Multiphase Mold Flow

POSTECH: Seong-Mook Cho, Seon-Hyo Kim,

Hyoung-Jun Lee, Dae-Woo Yoon

UIUC: Brian G. Thomas

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •2 / 27

Research Scope Objectives:

- To gain insight of argon bubble behavior (bubble formation, breakup and coalescence) in stopper-rod nozzle and its effects on mold flow

- To evaluate Euler-Lagrange approach for predicting bubble behavior

Methodologies:

- 1/3 scale water model experiments for visualizing argon bubble behavior in nozzle and mold and measuring level fluctuation

- Computational modeling of argon behavior in moldwith Euler-Lagrange approach (Discrete Phase Model (DPM))

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •3 / 27

Free surface

Tundish

500mm75mm

Bore diameter of SEN: 25mm

1200mm

Submergence depth: 60mm

Water flow meter

Water flow meter

Stopper-rod

Dam

Weir

Pump

Pump Water bath

Ф 25*11 exit

423mm

Left Right

Port angle:

35 deg downward

Nozzle wall thickness: 10.5mm

Schematic of 1/3 Scale Water Model

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •4 / 27

Schematic of Stopper-rod

<Front View>

<Cross-sectional View>

6 holes for injecting argon gas

IR

OR

Right NF

Left NF

Tundish bottom

Stopper-rod

Nozzle

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •5 / 27

Liquid flow similarity between the 1/3 scale water model and the real caster conditions

Froude number (Ratio of Inertia force to gravitational force) = v / gL

Argon gas similarity between the 1/3 scale water model and the real caster conditions

Argon gas volume fraction (%)

=Argon gas volume flow rate (at 298K) X 100 Argon gas volume flow rate (at 1873K) X 100

Water volume flow rate + Argon gas volume flow rate (at 298K) Steel volume flow rate + Argon gas volume flow rate (at 1873K)

Process Conditions

1/3 scale water model Real process

Mold(width x

thickness)500mm x 75 mm 1500mm x 225 mm

Liquid flow rate 35.0, 40.0 LPM (Water) 545.6, 623.5 LPM (Steel)

Casting speed 0.93, 1.07 m/min 1.61, 1.85 m/min

Argon Gas Flow rate

0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6 SLPM (273K)0.2, 0.4, 0.6, 0.9, 1.1, 1.3, 1.5, 1.7 LPM (298K)

0.8, 1.7, 2.5, 3.3, 4.2, 5.0, 5.8, 6.7 SLPM (273K)3.3, 6.6, 9.9, 13.2, 16.4, 20.0, 23.0, 26.2 LPM (1873K)

Argon Gas Volume Fraction

0.6, 1.2, 1.8, 2.4, 3.0, 3.5, 4.0, 4.6 % (35.0 LPM)0.5, 1.0, 1.6, 2.1, 2.6, 3.1, 3.6, 4.0 % (40.0 LPM)

0.6, 1.2, 1.8, 2.4, 3.0, 3.5, 4.0, 4.6 % (545.6 LPM)0.5, 1.0, 1.6, 2.1, 2.6, 3.1, 3.6, 4.0 % (623.5 LPM)

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •6 / 27

Visualizing Bubble Behavior

Free surface

Tundish

500mm75mm

Bore diameter of SEN: 25mm

1200mm

Submergence depth: 60mm

Water flow meter

Water flow meter

Stopper-rod

Dam

Weir

Pump

Pump Water bath

Ф 25*11 exit

423mm

Left Right

Port angle:

35 deg downward

Nozzle wall thickness: 10.5mm

: ~ in the SEN

1

23456789

11

1 9

: , in the mold 1110

“Recording area”

~ 1 9

1110

: 1900fps, 512 x 384

, : 1200fps, 640 x 480

“Recording information”

10

Recording high speed videos

Analyzing videos and snap shots

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •7 / 27

62.5mm

< Measuring positions of surface level>

Ultrasonic displacement

sensor

Response time

20Hz

Collecting data

frequency1Hz

Collecting data time

1000sec

Sensor head

dimension

Measuringdirection

Vertical direction to sensor head

Specifications

30mm

10mm

- Measure surface level with ultrasonic displacement 3

sensors

- Compare level profiles on 1/8, 1/4, 3/8 points between

right and left NF

- Calculate average level, standard deviation of level

- Transfer level fluctuation profiles to power spectrum by

FFT( Fast Fourier Transform) analysis

Measuring Surface Level Fluctuation

w1

w4

1w

8

3w

8

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •8 / 27

Mechanism of Argon Bubble Formation

<Snap Shot of Initial Behavior of Bubbles>Argon Gas

Stopper-rod Head

Sometimes, small bubble remains

Pressure by liquid

Pressure by gas

<Expansion> <Elongation> <Detachment><Initiation>

Tundish

Hole

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •9 / 27

Effect of Liquid and Argon Flow Rate on Active Holes

- Argon gas flow rate affect on the number of activated gas holes

- There is the threshold of argon gas flow rate for activating gas hole

- Minimum argon gas flow rate could be between 1.4 and 1.6 SLPM for activating all gas holes

Based on observations of video of 1/3 water model

Unstable 2 activated; sometimes, just 1 hole is activated

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80

1

2

3

4

5

6

7

Water flow rate 35 LPM 40 LPM

Th

e n

um

ber

of

acti

vate

d G

as H

ole

s (#

)

Argon gas flow rate (SLPM)

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •10 / 27

Total Bubbling Frequency & Argon Bubble Size

- Total bubbling frequency get higher with higher argon gas injection

- Averaged bubble size get bigger with higher argon gas injection

Qmain : total argon flow rate (mm3/sec)Vbubble : averaged bubble volume (mm3)f : total bubbling frequency in the six holes measured

from video (#/sec)dcal: calculated average bubble diameter (mm)

3

main calbubble

Q d4V = = π

f 3 2

1

3main

cal

24Qd =

4πf

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8100

200

300

400

500

600

700

800

35.0 LPM 40.0 LPM

Tot

al f

req

ue

ncy

(#/s

ec)

Argon gas volume flow rate (SLPM)0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

3.0

3.5

4.0

4.5

5.0

35.0 LPM 40.0 LPM

Ave

rag

ed d

iam

eter

of

arg

on

bu

bb

le (

mm

)

Argon gas volume flow rate (SLPM)

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •11 / 27

Predicted:4.3mm

Validation of Bai’s Model Prediction of Argon Bubble Size

- Measured bubble size (from video):5 mm

- Calculated with bubbling frequency: 4.5mm

- Predicted with Hua Bai’s analytical model: 4.3mm

Vertical red line == measured water velocity from small bubbles in video= 0.6m/s

Argon flow rate = 4.4 ml/s

Bai’s model can be applied to predict the initial bubble size in the gas hole at stopper-rod

Bai and Thomas, MTB, Vol. 32B, 2001, p. 1143-1159

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •12 / 27

1 2

Average bubble diameter: ~ 4.5 mm

- Bubbles from the gas holes break up at the region between 1st

and 2nd region (between tundish bottom and SEN inlet)

Argon Bubble Breakup near Stopper-rod tip

pp

1

2

a

b

~40mm from stopper-rod head tip

Maximum bubble diameter: < 1 mm

a

b

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •13 / 27

3 4

Argon Bubble Distribution through the Nozzle

c

d5

e

6

f

- Bubbles look bigger down through the nozzle

- Perhaps: larger bubbles accumulate with time ; or else bubbles coalesce

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •14 / 27

Argon Bubble Size Change near Nozzle Exit

8

9 Bubble break up?

- Bubbles smaller at nozzle bottom

- Bubbles coalesce at the top region of nozzle port (stagnant flow region)

Bubble coalescence

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •15 / 27

( )2

w ar−

1/3

w M Arc

w

ρ u d ρWe =

σ ρ

( )2 2/3w-Ar 1 Mu = C (Ed )

( ) ( )

3/5

-2/5-1/5cM Ar w

σWed = ρ ρ E

2

3

w

SEN

2f(u )E =

D

( )-1/4

wf = 0.079 Re

w w SENw

w

ρ u DRe =

μ

Calculation of Maximum Bubble Diameter in the Nozzle

Water density 998.2 kg/m3

Argon gas density 1.623 kg/m3

Water absolute viscosity

0.001 kg/m,sec

surface tension 0.0122 N/m

SEN inner diameter 0.025 m

Water velocity 1.19 m/sec

Water Reynolds number

2.97e+04

friction factor 0.006

average energy dissipation rate /

unit mass

0.808 m2 / sec3

critical Weber number

1.2

maximum diameter 0.00326 m

(3.26 mm)

wρ

Md

wμ

σ

wu

wRe

f

cWe

SEND

Evans et.al., Chemical Engineering Sicience, Vol. 54, 1999, p.4861-4867

≈1C 2.0 (by Batchelor)

Critical Weber number:

Kolmogoroff energy distribution law:

- Maximum bubble size in the stopper-rod nozzle can be predicted well by Evans’s model

E

Arρ

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •16 / 27

Geometry, Mesh and Boundary Conditions (Nozzle Flow)

- Hexa meshes - The number of total meshes: 0.24 million

Nozzle inlet

Nozzle port outlet

Stopper-rod

Water

(inlet)

: 1.057 m/sec

: 1e-05 m2/sec2

: 1e-05 m2/sec3

Port outlet

: 1e-05 m2/sec2

: 1e-05 m2/sec3

wu

k

k

ε

ε

Water: 35.0 LPM

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •17 / 27

“Velocity magnitude” “Turbulent kinetic energy”“Turbulent kinetic energy

Dissipation rate”

Stopper-rod Nozzle Flow

a

b

c

d

e

f

a

b

a

b

a

b

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •18 / 27

Bubble breakup ?

Bubble breakup

Calculated Turbulent Kinetic Energy Dissipation Rate & Argon Bubble Breakup

a

b

- Nozzle flow with high turbulent kinetic energy dissipation rate breaks bubbles up

Bubble coalescence

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •19 / 27

Stopper-rod

SEN

Mold

Geometry, Mesh for Lagrange Model

Tundish bottom Domain The number of Meshes

¼ domain 0.14 million

2 folds symmetry with stopper-rod

system

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •20 / 27

Transport of Argon Bubbles: Lagrange Discrete Phase Model (DPM)

i

Ar ArD Ar Ar Ar

Ar Ar Ar i

du (ρ - ρ) 1 ρ d ρ u= F (u - u ) + g + (u - u ) + u

dt ρ 2 ρ dt ρ x

∂

∂

DD 2

Ar Ar

C Re18μF =

ρ d 24Ar Arρd u - u

Re =μ

Force balance on argon bubble

Drag forceGravity force Virtual

mass force

Pressure gradient force

The model assumption: low (<10%) volume fraction of the dispersed phase (argon)

Ar

Ar

Ar

u : water velocity

u : argon velocity

μ : molecular viscosity of water

ρ : water density

ρ : argon density

d : argon bubble diameter

- Virtual mass force: the force required to accelerate the fluid surrounding the particle

Numerical method: Two-way turbulence coupling

Continuous phase (Water) flow field calculation

Discrete phase (Argon bubble) trajectory calculation

continuous phase source terms calculation( )

•

pmom,Ar D G V PS = F + F + F + F m Δt

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •21 / 27

Argon Size Distribution for Input: Rosin-Rammler Diameter Distribution

Rosin-Rammler Diameter Distribution

( )n- d/d

dY = e dY : Mass fraction of particles with diameter greater than d

d : Mean diameter

n : spread parameter

Total flow rate 1.082e-05 kg/sec

Min diameter 0.1 mm

Max diameter 2 mm

Mean diameter 1 mm

Spread parameter 3.5

Number of diameters 20

Argon: 1.6 SLPM

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

, - Rosin-Rammler Diameter Distribution

Mas

s fr

acti

on

of

arg

on

bu

bb

les

(>d

)

Argon bubble diameter (mm)0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.00

0.05

0.10

0.15

Mass fraction The number of bubbles

Argon bubble diameter (mm)

Mas

s fr

acti

on

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

Th

e n

um

ber

of

bu

bb

les

(#/s

ec)

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •22 / 27

Argon Distribution in the Mold

Water model Computational model

250mm

Gas area

144 mm

200mm

- With Lagrange model (DPM), argon distribution in the mold is well predicted; argon floating region at the surface and argon penetration depth into mold inner region

Water: 35.0 LPM, Argon: 1.6 SLPM

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •23 / 27

Mold Flow Pattern with Argon Injection

- After argon injection, classic double roll pattern is changed to complex flow pattern; By buoyancy force induced by argon bubbles

- Surface flow near SEN goes up to the surface; this could induces more severe level fluctuation

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •24 / 27

Argon Effect on Surface Level & Fluctuation: Measurement

With more argon gas injecting

- Greater surface level difference between SEN and NF

- Severe level fluctuation at the region near SEN, but Smaller level fluctuation at the others

SEN

NF

NF

0 50 100 150 200 250-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Ave

rag

ed s

urf

ace

leve

l &

flu

ctu

atio

n (

mm

)

Distance from SEN center (mm)

No gas 0.8 SLPM (2.5%) 1.6 SLPM (4.6%)

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •25 / 27

Argon Effect on Surface Level Power Spectrum

3W/8 (near SEN) W/4 W/8 (near NF)

Ar_1.6 SLPM (4.6%)

- Level fluctuation near SEN show more power than other regions

- With 1.6 SLPM of gas flow rate, power difference between nozzle and NF is quite severe in the frequency range bigger than 0.05Hz

1E-3 0.01 0.11E-6

1E-5

1E-4

1E-3

0.01

0.1

1

Po

wer

sp

ectr

um

(m

m^

2)

Frequency (Hz)

No gas 0.8 SLPM (2.5%) 1.6 SLPM (4.6%)

1E-3 0.01 0.11E-6

1E-5

1E-4

1E-3

0.01

0.1

1

Po

wer

sp

ectr

um

(m

m^

2)

Frequency (Hz)

No-gas 0.8 SLPM (2.5%) 1.6 SLPM (4.6%)

1E-3 0.01 0.11E-6

1E-5

1E-4

1E-3

0.01

0.1

1

Po

wer

sp

ectr

um

(m

m^

2)

Frequency (Hz)

No gas 0.8 SLPM (2.5%) 1.6 SLPM (4.6%)

1E-3 0.01 0.11E-6

1E-5

1E-4

1E-3

0.01

0.1

1

Po

wer

sp

ectr

um

(m

m^

2)

Frequency (Hz)

3W/8 region W/4 region W/8 region

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •26 / 27

Summary

Bubble behavior in the nozzle

- Initial bubble is expanded, elongated and detached from stopper-rod tip

- Bubbles breakup due to shear in region of high velocity gradient / turbulent dissipation in stopper/nozzle gap and perhaps also in nozzle well bottom

- Bubble size distribution entering mold is smaller than initial size at stopper

- Bubbles coalesce in recirculation regions, such as top of nozzle port

Bubble behavior in the mold

- Argon bubble floating up affect the flow pattern, resulting in complex double roll pattern

- These bubbles disrupt surface where they exit near SEN, and thus more surface level fluctuations with higher gas injection

Euler-Lagrange coupled multiphase flow model can simulate the mold flow pattern, bubble distribution, and the surface level fluctuation effects.

Pohang University of Science and Technology •Materials Science and Engineering •Seong-Mook Cho •27 / 27

Acknowledgements

• Continuous Casting Consortium Members(ABB, ArcelorMittal, Baosteel, Tata Steel, Goodrich, Magnesita Refractories, Nucor Steel, Nippon Steel, Postech/ Posco, SSAB, ANSYS-Fluent)

• POSCO (Grant No. 4.0007764.01)