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)