mathematical modeling of thermal-fluid flow in the meniscus...

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • C. Ojeda 1

ANNUAL REPORT 2006Meeting date: June 15, 2006

Claudio Ojeda(Visiting Scholar from FUNDACION LABEIN-TECNALIA, Derio, Spain)

Joydeep Sengupta(Dofasco inc., Hamilton, Canada)

Brian G. Thomas

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

Mathematical Modeling of Thermal-Fluid Flow in the

Meniscus Region


PHENOMENA IN THE MOLDCONTINUOUS CASTING OF STEEL

INTRODUCTION

“Continuous casting consortium website” ccc.me.uiuc.edu


OSCILLATION MARK AND HOOK DESCRIPTION

J. Sengupta and B.G. Thomas “JOM-e(TMS)”, 2005


1 mm 0

Side view (of section)

Entrapped bubble

Curved hook

10 mm

Section cut through slab

OM pitch

( )Oscillation Marks OM

Front view (of slab)

Casting direction

Hook depth

OM

OM depth

J. Sengupta, H. Shin, BG Thomas, et al, Acta Mat., 2005

frequencyspeedcastingPitchOMlTheoretica =

OM

Hook

Frozen meniscus

Heat transfer to mold

Slab surface3D view of hooks & OM

HOOKS AND OSCILLATION MARKS


• Slag Inclusions

• Entrapped bubbles (eg. Pencil pipe)

• Segregation

• Cracks (oscillation mark root)

• Other problems (laps, blisters, bleeds, etc)

SURFACE DEFECTS ASSOCIATED WITH HOOKS AND OSCILLATION MARKS


• ~20-35% of hooks are straight • Curved hooks are ~ 1.5 times deeper• On both wide + narrow faces

OMOM

Curved hookStraight hook

ScarfingCasting directionHook depth

J.P. Birat et al., IRSID, Malzieres les Metz, France, in Mold Operation for Quality and

Productivity, ISS, 1991, p.8

J. Sengupta, H. Shin, BG Thomas, et al, Acta Mat., 2005

DEEP HOOKS TRAP INCLUSIONS & REQUIRE “SCARFING”


OMOM

OM

Ultra-low Peritectic Medium

10 mm

200

μ m

Badri et al., Met. Trans. B, 2005

Suzuki, CAMP-ISIJ, 1998

• Ultra-low carbon steels have deeper OMs and are more prone to form hooks• Higher solidus (1535 °C vs 1500 °C for high carbon steels)

thinner mushy zone (15 °C vs 50 °C for high carbon steels)

HOOKS AND OSCILLATION MARKS WORSE WITH LOWER %CARBON


HOW OSCILLATION MARKS AND MOLTENG SLAG CONSUMPTION AFFECT HEAT TRANSFER

X

Insulated (q=0)

Insulated (q=0)

conv

ectio

n h(

z,do

sc)

0 10 20 30

360

370

380

390

400

410

420

430

Z,t

Liquid Steel

Solid Shell

1531 Tliq

1508 Tsol

1400

1300

1250

1200

1150

1100

1050

1000

1522

A

B

X

Insulated (q=0)

Insulated (q=0)

conv

ectio

n h(

z,do

sc)

0 10 20 30

360

370

380

390

400

410

420

430

Z,t

Liquid Steel

Solid Shell

1531 Tliq

1508 Tsol

1400

1300

1250

1200

1150

1100

1050

1000

1522

A

B Effect on heat transfer with air filled depressions due to insufficient liquid slag flow into the gap between mold and steel shell (CON2D)

Transverse cracks and breakouts

K.-D. Schmidt, F. Fredel, K.-P. Imlau, W. Jager, and K. Muller, “Steel Research”, 2003


HOW OSCILLATION MARKS AFFECT HEAT TRANSFER

Distance Below Meniscus (mm)

Osc

illat

ion

Mar

kD

epth

(mm

)

She

llTh

ickn

ess

(mm

)

360 370 380 390 400-1

-0.5

0

0.5

1

1.5

2

2.5

11.5

12

12.5

13

13.5

14

14.5

15

Predicted Shell Thickness (CON2D)Predicted Shell Thickness without OM (CON2D)Measured Shell ThicknessOscillation Mark Depth


Osc

illat

ion

Mar

kD

epth

(mm

)

She

llTh

ickn

ess

(mm

)

360 370 380 390 400-1

-0.5

0

0.5

1

1.5

2

2.5

7

8

9

10

11

12

13

14

15


A

B


Osc

illat

ion

Mar

kD

epth

(mm

)

She

llTh

ickn

ess

(mm

)

360 370 380 390 400-1

-0.5

0

0.5

1

1.5

2

2.5

7

8

9

10

11

12

13

14

15


A

B

Flux Filled Marks Air Filled Marks

B.G.Thomas, D. Lui, B. Ho, “Sensors and Modeling in Materials Processing: Techniques and Applications”, 1997


HOW OSCILLATION MARKS AFFECT HEAT TRANSFER

Distance Below meniscus (mm)

Hea

tFlu

x(M

W/m

2)

Tem

pera

ture

(C)

360 370 380 390 4000

0.5

1

1.5

2

2.5

3

3.5

900

1000

1100

1200

1300

1400

Heat FluxSteel Surface Temperature


Hea

tFlu

x(M

W/m

2)

Tem

pera

ture

(C)

360 370 380 390 4000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

880

900

920

940

960

980

1000

Heat Flux (MW/m2)Shell Temperature (C)

Flux Filled Marks Air Filled Marks


• Different meniscus (hook) shapes: (a) straight to (c) curved• Different shapes of overflow region

(a) (b) (c)

HJ Shin, G Lee, S. Kim, Postech, 2004

VARIATIONS IN HOOK AND OM SHAPE (CREATED DURING MENISCUS OVERFLOW)


• Random orientation of dendrites → Heterogeneous nucleation• Fine dendrite arms near origin line → Rapid solidification of under-cooled liquid• Large sudden change of growth direction → Movement of fractured hook tip

Solidification inward from frozen meniscus

Solidification within the liquid overflow region towards the mold wall

J. Sengupta, H. Shin, B. G. Thomas, et al., Acta Mat., 2006

DENDRITE GROWTH NEAR LINE OF HOOK ORIGINREVEALED BY SPECIAL ETCHING REAGENT


-0.06-0.05-0.04-0.03-0.02-0.01

00.010.020.030.040.050.06

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

time(s)

velo

city

(m/s

) s )

-0.004

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

disp

lace

men

t(m

) m

)

velocitycasting speedposition

NST

MOLD OSCILLATION PARAMETERS

NST = 0.14sStroke = 6mmFreq. = 155 cpm


PROPOSED OM AND HOOK FORMATION MECHANISM

J. Sengupta and B.G. Thomas JOM-e (TMS), 2006


Symmetry

P=1atm

P=1atm

Molten steel

Air

Molten Slag

Variable Steel LevelSymmetry

P=1atm

P=1atm

Molten steel

Air

Molten Slag

Variable Steel Level

MODEL DESCRIPTION

Twall = 1073K

h=100w/m2K

T=300K Predict meniscusPhenomena:- fluid flow, - Interface motion,- Heat transport

2-D FDM + VOF model

•Velocity & P Navier-Stokes Eq.

•Phase fract Volume Of Fluid

•Surf. Tens.=1.3N/m

•Temperature Heat Conduction Eq.Steel Shell (CON1D)

Oscillating Mold Wall

0.5mm interfacial gap (solid and liquid mold flux)


Computational Model Governing Equations (CFD + VOF + Energy)

Continuity Equation, Volume Fraction Equation

Properties

Momentum

Energy


INTERFACIAL TENSION

γsteel(l)-slag = steel(l)-gas+ slag-gas-2 ( steel(l)-gas slag-gas)0.5 [*]

steel(l)-gas = 1.89 N/m [*]

slag-gas = 0.4 N/m [*]

= 0.55 (between 0 and1, increases with the attraction between phases) [*]

Fe(s)-gas = 2.15N/m [*]

steel(s)-slag = 1.02 N/m (calculated considering slag-Fe(s) = 40 [*])

Fe(l)-Fe(s) = 0.26N/m (Sulfur is not interface active at the liquid/solid metal interface) [**]

= contact angle = 46

steel(l)-slag = 1.33 N/m

[*]A.W. Cramb and I. Jimbo, “W.O. Philbrook Memorial Symposium Conference Proceedings”, 1988

[**]G. Kaptay, “Metallurgical and Materials Transactions A”, 2002

Liquid steel

Solid steel

Molten powder

γsteel(l)-slag

steel(s)-slagsteel(s)-steel(l)

Liquid steel

Solid steel

Molten powder

steel(l)-slag

θ γ steel(s)-slagγsteel(s)-steel(l)

γsteel(l)-slag = γ steel(l)-gas+ γ slag-gas-2Φ(γ steel(l)-gas γ slag-gas)0.5 [*]

γsteel(l)-gas = 1.89 N/m [*]

γslag-gas = 0.4 N/m [*]

Φ = 0.55 (between 0 and1, increases with the attraction between phases) [*]

γFe(s)-gas = 2.15N/m [*]

γ steel(s)-slag = 1.02 N/m (calculated considering θ slag-Fe(s) = 40˚ [*])γ Fe(l)-Fe(s) = 0.26N/m (Sulfur is not interface active at the liquid/solid metal interface) [**]

θ = contact angle = 46˚

γ steel(l)-slag = 1.33 N/m

[*]A.W. Cramb and I. Jimbo, “W.O. Philbrook Memorial Symposium Conference Proceedings”, 1988

[**]G. Kaptay, “Metallurgical and Materials Transactions A”, 2002


Meniscus shape analytical solution (Bikerman Eq)


0

1

2

3

4

5

6

7

8

9

10

11

12

130 5 10 15 20 25 30 35 40

Distance from wall(mm)

Z (m

m)

Bikerman equation+8.5mm+10mm+11mm

VALIDATION OF CFD+VOF MODEL


SLAG PROPERTIES

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Temeprature (K)

Visc

osity

(Pa.

s)

SolidifyingMelting

0

0.5

1

1.5

2

2.5

3

3.5

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Temperature(K)

Con

duct

ivity

(W/m

K)

solidifyingmelting

Viscosity Conductivity

R. McDavid and B.G. Thomas, “Metallurgical and Materials Transactions B”, 1996

Y.Meng, B.G.Thomas, A.A. Polycarpou, A.Prasad and H. Henein, “Cnadian Metallurgical Quarterly”, 2006


TEMPERATURE AND VISCOSITY CONTOURS

TEMPERATURE CONTOURS VISCOSITY

Molten Steel

Molten Slag

Solid Rim

Powder

Molten slag pool thickness = 13mm

Molten Slag Pool thickness = 13mm ≈15 mm measured by H.-J. Shin (PhD Thesis)


MODEL RESULTS


-0.06-0.05-0.04-0.03-0.02-0.01

00.010.020.030.040.050.06

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

time(s)

v(m

/s) Beginning

overflow

End overflow

NST

MODEL RESULTS


COMPARISON OF MODEL RESULTS WITH EXPERIMENTAL DATA

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

0 0.5 1 1.5 2 2.5mm

mm

Measured lines: J. Sengupta, B.G. Thomas and H-J Shin “Metallurgical and Materials Transactions A”, 2005

J. Sengupta, B.G. Thomas and H-J Shin, G. G. Lee and S-H Kim “Metallurgical and Materials Transactions A”, 2005


THERMAL-STRAIN CALCULATIONS

With overflow

Without overflow

Difference

Deformations x10Fractured hook tip entrapped in

the shell

Truncated hook Un-melted fractured tip travels to the surface

J. Sengupta, H. Shin, B. G. Thomas, et al., Acta Mat., 2006

Reheating due to overflow

Line of hook origin

Overflow region(melted back

mold flux layer

Scale0 1 mm

Original position of hook tip

Oscillation mark

Fractured hook tip

hook


-0.06-0.05-0.04-0.03-0.02-0.01

00.010.020.030.040.05

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4time(s)

Slag

con

sum

ptio

n(kg

/s m

)

Mean QSolid+LiquidLiquid


Mean consumption (liquid) = 0.0062Kg/ms ≈0.0058Kg/ms Experimental mean consumption (Shin et al. 2005)

overflow

NST



K. Tsutsumi, J.-I. Ohtake and M. Hino, “ISIJ International”, 2000

Velocity Components Close to Gap Inlet

time (s)

m/s

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

NST

overflow


NST

overflow

PRESSURE CHANGES DURING OSCILLATION


HEAT FLUX AT MOLD WALL

Heat Flux in Meniscus region Heat Flux at Shell Tip

Peak Heat Flux at NST

overflow

NST


A.Badri, T.T.Natarajan, C.C.Snyder, K.D.Powders, F.J.Mannion and A.W.Cramb, Met. and Mat. Trans. B, 2005

AVERAGE HEAT FLUX AT MOLD WALL IN THE MENISCUS REGION

-500000

0

500000

1000000

1500000

2000000

2500000

3000000

0 1 2 3 4 5 6

Time (s)

Hea

t flu

x (W

/m2 )

T/C1 (5.25")T/C2 (5.50")T/C3 (5.75")15.8mm down from meniscus (Lab frame)9.5mm down from meniscus (Lab frame)

D.Li, “Heat transfer during continuous casting of steel”

NST

overflow


STEEP RIM MODEL DESCRIPTION

AIR

SLAG

MOLTEN STEEL

Unknown interface location

Steel shell (CON1D)

Gap between mold and steel

0.2mm

Symmetry

Pressure outlet = 1atm

Pressure inlet = 1 atm

Oscillating mold wall2-D FDM + VOF model

•Velocity & P Navier-Stokes Eq.

•Phase fract Volume Of Fluid

•Surf. Tens.=1.3N/m

•Temperature Heat Conduction Eq.

Predict meniscusPhenomena:- fluid flow, - Interface motion,- Heat transport

Takeuchi et al. “Steelmaking Conference Proceedings”, 1991, pp 73-77


MODEL RESULTS

Interface evolution (phases fraction contour)

Interface evolution (velocity vectors)


-0.06-0.05-0.04-0.03-0.02-0.01

00.010.020.030.040.050.06

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

time(s)

v(m

/s) Beginning overflow

End overflow

NST

MODEL RESULTS


EFFECT OF FAR FIELD STEEL LEVEL ON STAGNANT MENISCUS SHAPE

0.000 0.005 0.010 0.015 0.020 0.025 0.0300.0700

0.0750

0.0800

0.0850

0.0900

0.0950

0.1000

+11mm

+8.7mm

+5mm

+2mm

+12mm

Dis

tanc

e ab

ove

shel

l tip

(m)

Distance from mold wall (m)

Shell tip


Deeper level drops cause more shell distortion

0 1 2

z(m

m)

0

5

10

15

20

25

30

0 1 20 1 20 1 2 0 1 20 1 2

2mm level drop

5 mm level drop

8 mm level drop

10 mm level drop

16 mm level drop

- 0.09 mm - 0.09 mm

No level fluctuation

Shell thickness = 1.74 mm

- 0.02 mm - 0.02 mm +0.07 mm +0.07 mm +0.23 mm +0.23 mm +0.36 mm +0.36 mm +0.46 mm +0.46 mm

15001450140013501300125012001150110010501000

Temperature (oC)

Jog

Shell

Jog

Shell

Fredriksson and Elfsberg, Scandinavian J. of Met., 2002

J. Sengupta and B.G. Thomas, “Modeling of Casting, Welding and Advanced Solidification Processes XI”, 2006


STRAIGHT HOOKS CAN FORM BY SHELL DISTORTION FOLLOWED BY OVERFLOW CREATING OM

-24

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

40 2 4 6 8Distance across slab width (mm)

Dist

ance

alo

ng m

old

leng

th (m

m)

SOLIDSLAG

MOLD

LIQUID SLAG

LIQUID STEEL

MENISCUS(equilibrium)

MENISCUS(after overflow)

STEELSHELL

-24

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

40 2 4 6 8Distance across slab width (mm)

Dist

ance

alo

ng m

old

leng

th (m

m)

SOLIDSLAG

MOLD

LIQUID SLAG

LIQUID STEEL



STEELSHELL

Distance across slab width (mm)

Dist

ance

alo

ng m

old

leng

th (m

m)

SOLIDSLAG

MOLD

LIQUID SLAG

LIQUID STEEL



STEELSHELL

HOOK

OM

Solidification after overflow

0.48 mm

0.46 mm distortion for a 16 mm level drop

MECHANISM:• Shell distortion during negative strip causes

shell bending away from mold (hook):e.g. sudden level drop

• Meniscus overflows over hook

• Solidification in overflowed region creates OM

Effect of pressure & friction cannot be ignored!

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

10

20

30

40

50

60

70

80

90

100

POSCO 2004 resultsNarrow face + 1/4 wide face(Mean value: 66 ~ 82 hooks)

(# o

f hoo

k ty

pe) /

(# o

f exa

min

ed O

Ms)

Level fluctuation during sampling (mm)

Curved type Surface type

HJ Shin, Postech, PhD Thesis, 2006J. Sengupta and B.G. Thomas, “Modeling of Casting, Welding and Advanced Solidification Processes XI”, 2006


Thermal distortion due to level fluctuation depends on steel grade

z(m

m)

0

5

10

15

20

0 1 2 0 1 2 0 1 2

16mm level drop

16 mm level drop

16mm level drop

Temperature (oC)

15001450140013501300125012001150110010501000

Ultra-low carbon steel0.003% C

Low carbon steel0.04% C

Peritectic steel0.13% C

+0.46 mm +0.46 mm +0.38 mm +0.38 mm +0.64 mm +0.64 mm

z(m

m)

0

5

10

15

20

0 1 2 0 1 2 0 1 2

16mm level drop

16 mm level drop

16mm level drop

Temperature (oC)

15001450140013501300125012001150110010501000

Ultra-low carbon steel0.003% C

Low carbon steel0.04% C

Peritectic steel0.13% C

+0.46 mm +0.46 mm +0.38 mm +0.38 mm +0.64 mm +0.64 mm

J. Sengupta and B.G. Thomas, “Modeling of Casting, Welding and Advanced Solidification Processes XI”, 2006


-800-600-400-200

0200400600800

1000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4time(s)

Pres

sure

(Pa)

NST

overflow

-800-600-400-200

0200400600800

1000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4time(s)

Pres

sure

(Pa)

NST

overflow

-800-600-400-200

0200400600800

1000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4time(s)

Pres

sure

(Pa)

NST

overflow

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

time(s)

Slag

con

sum

ptio

n(kg

/s m

)

NST

Overflow

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

time(s)

Slag

con

sum

ptio

n(kg

/s m

)

NST

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

time(s)

Slag

con

sum

ptio

n(kg

/s m

)

NST

Overflow

MODEL RESULTS

Pressure changes during oscillation

Liquid slag consumption varies during oscillation.

Mean consumption = 0.0053Kg/ms ≈

0.0058Kg/ms Experimental mean consumption (Shin et al. 2005)

Larger flux rim causes overflow to occur earlier


0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

0 0.5 1 1.5 2 2.5


Measured lines: J. Sengupta, B.G. Thomas and H-J Shin “Metallurgical and Materials Transactions A”, 2005

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

0 0.5 1 1.5 2 2.5mm

mm

Steep Rim Calculated Rim


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

time(s)

Vel

ocity

(m/s

)

x-componenty-component

NST

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

time(s)

Vel

ocity

(m/s

)

x-componenty-component

NST

-0.07-0.06-0.05-0.04-0.03-0.02-0.01

0

0.010.020.030.040.050.060.070.08

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

time(s)

Velo

city

(m/s

)

x-component

y-component

NST

-0.07-0.06-0.05-0.04-0.03-0.02-0.01

0

0.010.020.030.040.050.060.070.08

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

time(s)

Velo

city

(m/s

)

x-component

y-component

NST


Point near gap inlet

Point far from gap inlet

K. Tsutsumi, J.-I. Ohtake and M. Hino, “ISIJ International”, 2000


Gap steel-moldRim Gap steel-moldRim

MODEL RESULTS

Note: excessive slag rim (below 4mm) melts back slightly during each cycle


CONCLUSIONS

• The oscillating solidified slag rim controls the flow pattern in the meniscus region.

• Pressure in the gap between the shell and mold oscillates.

• Overflow event starts earlier with a more severe solid slag rim.

• Computations and experimental data both show that the overflow event can start at different times during the oscillation cycle, but often starts ~beginning of negative strip time.

• Liquid flux consumption varies continuously during the oscillation cycle, but is consumed intothe gap only during negative strip time.

• The heat flux peak occurs several mm below the meniscus level, owing to meniscus curvature.

• The range of meniscus shapes predicted during the oscillation cycle matches well with the range of shapes of measured hooks.

• The slight extra curvature appearing in hook measurements might be due to thermal strainand requires further study.

• The meniscus sometimes drops below the shell tip, exposing it to slag, and creating relatively straight hooks with associated surface defects


FACTORS CONTROLLING HOOKS AND OSCILLATION MARKS

• Steel grade (shrinkage stress & strength)

• Meniscus heat flow (mold flux composition)– Resolidified flux rim shape; – Liquid flux consumption rate into meniscus gap

• Fluid flow pattern

• Level fluctuations (both rapid & gradual)

• Superheat of molten steel

• Oscillation practice (stroke, frequency, asymmetry ratio, negative strip time, etc.)


ACKNOWLEDGMENTS

• FUNDACION LABEIN-TECNALIA (DERIO, SPAIN)

• National Science Foundation (Grant DMI 05-28668)

• Continuous Casting Consortium Members at University of Illinois at Urbana-Champaign

• Fluent Inc.

• Ho Jung Shin, Go Gi Lee, Jose Luis Arana, Jon Barco.

mathematical modeling of thermal-fluid flow in the meniscus...

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