CCC Annual ReportUIUC, August 14, 2013

Rui Liu and Seong-Mook Cho

Department of Mechanical Science & EngineeringUniversity of Illinois at Urbana-Champaign

Gas Flow Through Upper Tundish

Nozzle Refractory and Bubble Size

Evolution Inside SEN

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 2

OUTLINE

• PART 1: UTN porous gas flow model– Review of previous model– Model updates:

• Realistic pressure distribution on UTN inner surface• Bubble formation threshold for gas pressure• One-way passing pressure boundary condition

– Effects of back pressure effects– Effects of gas leakage at UTN bottom

• PART 2: Bubble size study in a water model– Bubble size distributions in SEN– Evolution of gas volume fraction down the SEN

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 3

Development and Validation of Gas Porous Flow Models – Review

( )

210

10

D

D

KT PP P

r T K P

rTr

′′ ′′′ ′+ − + + =

′′ =

( ) ( )D D

RT pK p K p

p RT∇ ⋅ ∇ = − ∇ ⋅ ∇

R1 (m) R2 (m) P1 (Pa) T1 (K) T2 (K) V (m/s)0.0375 0.0725 100000 1800 1000 0.0073

1-D Simplified Eqns.:

3-D Coupled Eqns.:( ) 0k T∇⋅ ∇ =

R. Liu and B.G. Thomas, Proc. AISTech2012 Conf. (Atlanta, GA), p2235, (2012)

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 4

Schematic and Parameters for the Base Case

Inlet pressure Pin 200 kPa (abs.)

Pressure at nozzle inside

wall & ambient

P∞

101 kPa (abs.)

Specific permeability

Kp 10.1 nPm = 10.1 x10-7 mm²

Dynamic Viscosity*

µ 7.42 x10-5 Pa.s(at 1280C)

Permeability (K p/ µ)

KD 1.36x10-8 m²/(Pa.s) (at 1280C)

Thermal conductivity

k 18 W/mK

Heat transfer coefficient

(nozzle exterior)

h 40 W/m2K

Pin

P∞

P∞

*Ref:

*R. Dawe and E. Smith. Viscosity of Argon at High

Temperatures. Science, Vol. 163, pp 675~676, 1969.

( ) ( )20.63842lg 6.9365/ 3374.72/ 1.51196

0 10T T T

Tµ µ − − −= ∗5

0 2.228 10 Pa sµ −= × ⋅ Room temperature (20 C)

argon viscosity

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 5

Scenarios for the Base Case

• Further Factors to consider:– Hydrostatic pressure profile with steel

velocity (Bernoulli’s eqn.)

– Bubble formation pressure threshold at pore (due to surface tension)

• Scenarios:1. Base case parameters, with porous flow

model, constant gas viscosity, constant pressure

2. Base case parameters, but with temperature-dependent gas viscosity

3. Consider liquid steel pressure distribution at UTN inner surface (using Bernoulli’s Eqn)

4. Same with case 3, but consider bubbling pressure threshold due to surface tension

Radial Distance (m)

UT

Nhe

ight

(m)

0 0.05 0.1 0.15

0

0.05

0.1

0.15

0.2

0.25

1815179617761756173717171698167816581639161916001580

Temperature (K)

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 6

Pressure Threshold for Bubble Formation

• In order for gas to intrude into the liquid and for m bubbles, surface tension effects have to be considered:

Bubble expanding stage (assume bubbles expand slowl y in equilibrium):

g lp p σκ− =

1 2

3 2

r r

r r

>>

2

rκ =

2g l

p pr

σ= + 2 1

2 3

g g

g g

p p

p p

>>

Pressure threshold for bubble formation:

pg pl pg pl pg pl

1 2 3step step step

r1 r2 r3

r2 = rpore

2

2 2g l l

pore

p p pr r

σ σ= + = +

Parameters used in current study: 1.2 , 200poreN r mmσ µ= =

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 7

Radial Distance (m)

UT

NH

eigh

t(m

)

0 0.05 0.1 0.15

0

0.05

0.1

0.15

0.2

0.25

9500085000750006500055000450003500025000150005000

Pressure (Pa)

Pressure Distributions – Base Case Scenarios

Radial Distance (m)

UT

NH

eigh

t(m

)

0 0.05 0.1 0.150

0.05

0.1

0.15

0.2

0.25

9500085000750006500055000450003500025000150005000

Pressure (Pa)

Radial Distance (m)

UT

NH

eigh

t(m

)

0 0.05 0.1 0.15

0

0.05

0.1

0.15

0.2

0.25

9500085000750006500055000450003500025000150005000

Pressure (Pa)

bottom sealed ,Bernoulli-based pressure

bottom leakage,constant liquid pressure

bottom sealed ,Bernoulli-based pressure, and bubbling threshold

center axis

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 8

Radial Distance (m)

UT

NH

eig

ht

(m)

0 0.05 0.1 0.15

0

0.05

0.1

0.15

0.2

0.25

0.1m/s

center axis

Velocity Distributions – Base Case Scenarios

Radial Distance (m)

UT

NH

eigh

t(m

)

0 0.05 0.1 0.15

0

0.05

0.1

0.15

0.2

0.25

0.02 m/s

Radial Distance (m)

UT

NH

eig

ht

(m)

0 0.05 0.1 0.15

0

0.05

0.1

0.15

0.2

0.25

0.1 m/s

bottom sealed ,Bernouli-based pressure

bottom leakage,constant liquid pressure

bottom sealed ,Bernouli-based pressure, and bubbling threshold

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 9

Radial Velocity Distributions

0.00 0.05 0.10 0.15 0.20 0.250.00

0.02

0.04

0.06 open bottom, no hydrostatic pressure, constant gas viscosity open bottom, no hydrostatic pressure, varying gas viscosity wall bottom, with hydrostatic pressure, no bubbling threshold wall bottom, with hydrostatic pressure and bubbling threshold

Rad

ial V

eloc

ity (

m/s

)

Distance from UTN Bottom (m)

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 10

Gas Velocity (m/s)Without the one-way

passing B.C.With the one-way

passing B.C.

Reversed flow from the steel side, results not physical

Using One-Way Passing B.C. is NECESSARY!

Gas Velocity (m/s)

Effect of One-Way Passing Pressure B.C.

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 11

Model Validation with Static Bubbling Test

0.00270.00220.00180.00150.00130.00100.00080.00070.00060.0005

Gas Normal Velocity (m/s)

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 12

Pressure Distribution – Bottom Leakage vs. Sealed

Radial Distance (m)

UT

NH

eigh

t(m

)

0 0.05 0.1 0.150

0.05

0.1

0.15

0.2

0.25

9500085000750006500055000450003500025000150005000

Pressure (Pa)

Radial Distance (m)

UT

NH

eig

ht

(m)

0 0.05 0.1 0.15

0

0.05

0.1

0.15

0.2

0.25

9500085000750006500055000450003500025000150005000

Pressure (Pa)

Radial Distance (m)

UT

NH

eigh

t(m

)

0.04 0.05 0.06 0.07 0.08 0.09 0.1-0.01

0

0.01

0.02

0.03

0.04

9500085000750006500055000450003500025000150005000

0.05 m/s

Pressure(Pa)

Radial Distance (m)

UT

NH

eig

ht

(m)

0.04 0.05 0.06 0.07 0.08 0.09 0.1

0

0.01

0.02

0.03

0.04

0.05

94737942119368493158926329210591579910539052690000

0.005

Pressure (Pa)

m/s Bottom SealedBottom Leakage

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 13

Radial Distance (m)

UT

NH

eigh

t(m

)

0 0.05 0.1

0

0.05

0.1

0.15

0.2

0.25

0.01 m/s

Radial Distance (m)

UT

NH

eig

ht

(m)

0 0.05 0.1

0

0.05

0.1

0.15

0.2

0.25

0.01 m/s

Radial Distance (m)

UT

NH

eigh

t(m

)

0.04 0.05 0.06 0.07 0.08 0.09 0.1-0.01

0

0.01

0.02

0.03

0.04

0.05

0.05 m/s

Radial Distance (m)U

TN

Hei

ght(

m)

0.04 0.05 0.06 0.07 0.08 0.09 0.1-0.01

0

0.01

0.02

0.03

0.04

0.05

0.005m/s

Velocity Distributions –Bottom Leakage vs. Sealed

Bottom SealedBottom Leakage

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 14

0.00 0.05 0.10 0.15 0.20 0.250.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Rad

ial V

eloc

ity (

m/s

)

Distance from UTN Bottom (m)

Open Bottom Case Perfectly Sealed Case

Evaluation of UTN Gas Injection – Bottom Leakage vs. Sealed

DEFINE:

Gas Leakage Rate

1 inL

total

m

mθ = −

&

&

0Lθ =

0.86Lθ =

• Possible gas leakage through UTN bottom does not affect much gas deliver through the upper slit

• An 86% gas leakage is found in current case with the complete open-bottom case

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 15

Radial Distance (m)

UT

NH

eigh

t(m

)

0 0.05 0.1 0.15

0

0.05

0.1

0.15

0.2

0.25

1360001320001280001240001200001160001120001080001040001000009600092000

0.02m/s

Pressure (Pa)

Effects of Back Pressure on Gas Velocity Distributions in Refractory

Radial Distance (m)

UT

NH

eigh

t(m

)

0 0.05 0.1 0.15

0

0.05

0.1

0.15

0.2

0.25

980009700096000950009400093000920009100090000

0.002m/s

Pressure (Pa)

99 kPa

Radial Distance (m)

UT

NH

eigh

t(m

)

0 0.05 0.1 0.15

0

0.05

0.1

0.15

0.2

0.25

899808994089900898608982089780897408970089660896208958089540

0.001m/s

Pressure (Pa)

90 kPa 140 kPa

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 16

Effects of Back Pressure and Sealing on Gas Radial Velocity Distributions

0.00 0.05 0.10 0.15 0.20 0.25

0.000

0.004

0.008

0.012

0.016

0.020

0.024

Rad

ial V

eloc

ity (

m/s

)

Distance from UTN Bottom (m)

90 kPa, perfectly sealed 90 kPa, open bottom 99 kPa, perfectly sealed 99 kPa, open bottom

120 kPa, perfectly sealed 120 kPa, open bottom 140 kPa, perfectly sealed 140 kPa, open bottom

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 17

Effects of Back Pressure on Gas Mass Flow Rate and Leakage Ratio

90 100 110 120 130 14010-7

10-6

10-5

10-4

10-3

Total/entering gas flow rate, perfectly sealed Total gas flow rate, open bottom Gas entering flow rate, open bottom

Gas

Mas

s F

low

Rat

e (k

g/s)

Back Pressure (k Pa)90 100 110 120 130 140

0.0

0.2

0.4

0.6

0.8

1.0

Gas leakage Ratio of gas entering rate,

open bottom / perfectly sealed

Rat

io

Back Pressure (k Pa)

• For both open-bottom and perfectly-sealed cases, ga s mass flow rates increase with increasing back pressure

• For open-bottom cases, with different back pressure s in this work, gas leakage ratio decreases with increasing back pressu re, but all above 70%, with ratio of gas entering rate also remaining 70% between open-bottom and perfectly sealed cases

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 18

Part 1 : Conclusion – UTN Porous Gas Flow Model

• UTN porous gas flow model has been improved to incorporate realistic conditions, including:– Liquid steel pressure distribution on UTN inner sur face– Bubble formation gas pressure threshold – One-way passing pressure boundary condition to elim inate

unphysical reversed gas flow on UTN surface

• Parametric studies on gas injection back pressure reveal:– For both open-bottom and perfectly sealed cases, ga s flow

rates increases with increasing back pressure;– Open-bottom cases leaks more than 70% of the gas un der

normal pressure conditions (14~21 psi)– Upper slit in open-bottom cases maintains a gas ent ering

ratio of ~70% compared with the perfectly sealed ca se

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seong-Mook Cho • 19

35 LPM (Water)_0.8 SLPM (Argon)

35 LPM (Water)_1.6 SLPM (Argon)

- Bubbles look bigger with distance down the nozzle

- Perhaps: bubbles coalesce; or else larger bubbles a ccumulate with time

Bubbles Moving Down in the SEN

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seong-Mook Cho • 20

Bubble Size Change Near Nozzle Exit

- Bubbles smaller at the nozzle bottom

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

“35LPM (Water)_1.6SLPM (Argon)”

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seong-Mook Cho • 21

0 1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

80

100

120

140

160

180

200

220

240

The number of bubbles (#) Ratio of bubbles (%)

Row Numbers

The

num

ber

of b

ubbl

es (

#)

05101520253035404550556065707580859095100

Rat

io o

f bub

bles

(%

)

0 1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

80

100

120

140

160

180

200

220

240

The number of bubbles (#) Ratio of bubbles (%)

The

num

ber

of b

ubbl

es (

#)

05101520253035404550556065707580859095100

Rat

io o

f bub

bles

(%

)

0 1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

80

100

120

140

160

180

200

220

240 The number of bubbles (#) Ratio of bubbles (%)

The

num

ber

of b

ubbl

es (

#)

05101520253035404550556065707580859095100

Rat

io o

f bub

bles

(%

)

0 1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

80

100

120

140

160

180

200

220

240

The number of bubbles (#) Ratio of bubbles (%)

The

num

ber

of b

ubbl

es (

#)

05101520253035404550556065707580859095100

Rat

io o

f bub

bles

(%

)

davg = 0.77 mm davg = 0.91 mm davg = 1.29 mm

( )∑d

n3

k3k=1

avg

4π r

3= 2nπ

2nd 3rd 4th

davg = 1.30 mm5th

0 1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

80

100

120

140

160

180

200

220

240

The number of bubbles (#) Ratio of bubbles (%)

The

num

ber

of b

ubbl

es (

#)

05101520253035404550556065707580859095100

Rat

io o

f bub

bles

(%

)

6th

davg = 1.19 mm

0 1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

80

100

120

140

160

180

200

220

240

The number of bubbles (#) Ratio of bubbles (%)

The

num

ber

of b

ubbl

es (

#)

05101520253035404550556065707580859095100

Rat

io o

f bub

bles

(%

)

7th

davg = 1.81 mm

0 1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

80

100

120

140

160

180

200

220

240

The number of bubbles (#) Ratio of bubbles (%)

The

num

ber

of b

ubbl

es (

#)

05101520253035404550556065707580859095100

Rat

io o

f bub

bles

(%

)

8th

davg = 2.20 mm

0 1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

80

100

120

140

160

180

200

220

240

The number of bubbles (#) Ratio of bubbles (%)

The

num

ber

of b

ubbl

es (

#)

05101520253035404550556065707580859095100

Rat

io o

f bub

bles

(%

)

9th

davg = 2.06 mm

0~ 0.6~ 1.2~ 1.8~2.4~ 3.0~3.6~ 4.2~ 4.8~ 5.4~ 6.0~

0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6v

0~ 0.6~ 1.2~ 1.8~2.4~ 3.0~3.6~ 4.2~ 4.8~ 5.4~ 6.0~

0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6

0~ 0.6~ 1.2~ 1.8~2.4~ 3.0~3.6~ 4.2~ 4.8~ 5.4~ 6.0~

0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6

0~ 0.6~ 1.2~ 1.8~2.4~ 3.0~3.6~ 4.2~ 4.8~ 5.4~ 6.0~

0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6

0~ 0.6~ 1.2~ 1.8~2.4~ 3.0~3.6~ 4.2~ 4.8~ 5.4~ 6.0~

0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6

0~ 0.6~ 1.2~ 1.8~2.4~ 3.0~3.6~ 4.2~ 4.8~ 5.4~ 6.0~

0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6

0~ 0.6~ 1.2~ 1.8~2.4~ 3.0~3.6~ 4.2~ 4.8~ 5.4~ 6.0~

0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6

Argon Bubble Size Distribution through the Nozzle 35 LPM (Water)_0.8 SLPM (Argon)

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seong-Mook Cho • 22

Gas Volume Fraction Evolution

2 3 4 5 6 7 8 90.0

0.5

1.0

1.5

2.0

2.5

3.0

Arg

on g

as v

olum

e fr

actio

n (%

)

Region

Injected gas volume fraction: 2.4%

- Bubble accumulation ?- Calculating drift flux of bubble is needed to obtai n gas void fraction

considering argon and water superficial velocities, and bubble size.

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Seong-Mook Cho • 23

Part 2 : Conclusion – Bubble Size Distribution in SEN

• Average bubble size is smaller in SEN upper regions, but larger in lower SEN regions

• Small gas bubbles appear at SEN bottom, but large bubbles are found close to SEN port upper region

• Measured gas volume fraction increases in general along the downward SEN direction, but still smaller than the superficial gas volume fraction

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 24

Acknowledgments

• Continuous Casting Consortium Members(ABB, ArcelorMittal, Baosteel, MagnesitaRefractories, Nippon Steel, Nucor Steel, Postech/ Posco, Severstal, SSAB, Tata Steel, ANSYS/ Fluent)

• Rob Nunnington at Magnesita