Transient Thermo-fluid Model of Meniscus Behavior and

Xiaolu Yan

Department of Mechanical Science & Engineering

University of Illinois at Urbana-Champaign

CCC Annual ReportUIUC, August 19, 2015

Transient Thermo-fluid Model of

Meniscus Behavior and Oscillation

Mark Formation

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Xiaolu Yan • 2

Background

• Meniscus region controls many casting defects, such as:– Level fluctuations– Slag entrapment– Deep oscillation mark

• Many coupled phenomena occur,– melting powder, – oscillating mold, – steel flow with superheat, – re-solidified slag rim hitting

meniscus and pushing liquid slag into gap

– heat transfer through the gap and top slag layer,

– meniscus freezing,– overflow– Steel shell moving down Solidifying Steel

Shell

jet

entrainment

Coppermold

Resolidifiedslag

Oscillationmark

Slag rim

Slag powder

Liquid slag

Molten steel pool


Objectives

• Develop a transient thermo-fluid model of meniscus behavior and shell solidification

• Investigate mechanism of oscillation mark formation

• Predict during mold oscillation– Transient flow behavior of slag in meniscus region– Transient heat flux, temperature profile near

meniscus– Strand profile, shell thickness– Slag gap thickness, oscillation mark depth


MO

LD

MO

LD

MO

LD

MO

LDMeniscus freezing

Liquid Steel

Hook growth

Meniscus overflow

Liquid Steel

Liquid Steel

Liquid Steel

Hook tip fracture

Line of hook origin

New hook

Liquid flux

Shell growth

Liquid flux

Solid flux

Solid flux

Shell

Hook

Mechanisms of Hook & OM Formation –Overflow with hook

J. Sengupta, H. Shin, BG Thomas, et al, Met Trans B, 2006

Other mechanisms: “mini-sticker”; bending; overflow without hookthermal distortion


Hook – Overflow Animation Simulation result in current work

K. Thomas and BG Thomas, UIUC, 2010


Domain & modelling method

Slag

Steel

Mol

d

shell

Osc

illat

ion

• 2D simulation of a center slice through mold, gap, shell and liquid in the meniscus region

• K-ω SST turbulent CFD model to allow both turbulent flow in steel and laminar flow in slag and boundary layer

• Transient heat transfer• Solidification of slag rim by

increased specific heat and viscosity (temperature dependent functions)

• Solidification of steel by extracting latent heat and increasing viscosity and fixing shell velocity to casting speed

• VOF (volume of fluid) method to separate slag & steel phases


Equations

• � � �� : � ��

��

��Г�

� ��

� ��

� ��

��

��Г�

� ��

� ��

• VOFmethod:1�%

� &%�% � ' ∙ &%�%)% � �*+ � , -. /% � -. %/

0

/12• Solidification:

: � � � �;<=�=�% � �;<=


Boundary conditionsPressure Inlet, P=0 Gauge

Mold Wall ConvectionTamb=40 >? � 45272D/-FG

Pressure Outlet

P=4500Pa

Insulated wall

Insulated wall

Velocity Inlet (steel)Mass inflow rate =outflow rate at pressure outlet,inflow superheat=3.5>

Insulated wall

Fix Temp ZoneWidth=5mmSuperheat=3.5>

Slag Solidification Zone Width=3mm

Slag

Steel

Casting speed=1.39m/min

Mol

d


Material property & casting condition

Unit value

Density GJ/-K 7000Specific heat M/�J ∙ G 700Conductivity D/- ∙ G 30Latent heat M/�J 2.72 N 10O

Solidus temperature > 1528.85Liquidus temperature > 1529.85

Unit value

Density GJ/-K 2500

Slag property

Unit value

Stroke -- 5.89Oscillation frequency RS 2.9Casting speed -/-TU 1.39Negative strip time V 0.12Theoretical pitch -- 8.01

Casting condition Steel property (ULC)

Slag-steel interfacial tension coefficient:WXY/-Z � 1.3 � 8.38 N 10[\ N X1803 � �XGZZ

0 0.05 0.1 0.15 0.2 0.25 0.3-3

-2

-1

0

1

2

3

Mol

d po

sitio

n (m

/s)

0 0.05 0.1 0.15 0.2 0.25 0.3-0.06

-0.04

-0.02

0

0.02

0.04

Time in one cycle (s)

Mol

d ve

loci

ty (

m/s

)

NST


Slag properties – spatial and temperature variation

0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

Temperature (°C)

Sla

g C

on

du

ctiv

ity (

W/m

.k)

SolidifyingMelting

400 600 800 1000 1200 1400 160010

-1

100

101

102

103

104

105

Temperature (°C)

Sla

g v

isco

sity

(Pa.

s)

SolidifyingMelting

600 700 800 900 1000 11001000

1500

2000

2500

3000

3500

Temperature (°C)

Sla

g S

pe

cific

He

at,

Cp (

J/kg

.K)

Slag Solidification Zone

3mm


Fix solid steel shell velocity

• ADJUST UDF is used to fix steel shell velocity. It changes its value to casting speed at the beginning of each calculation iteration.

• When a cell satisfies:– Temperature <�;<=-0.1K– VOF fraction of steel > 0.8

Fix: ] _̂ � 0^̀ � 1.39-/-TU � abV�TUJVc

• Case 1: only adjust bottom of shell (y < 88mm)• Case 2: applied to whole domain (including shell

tip in meniscus region)


Steel shell viscosity

• Plasticity dominates solid steel mechanical behavior near solidus temperature

• Stress depends more on strain rate than strain

• Viscosity is appropriate to describe its mechanical behavior

• Current model only uses viscosity ~10Kdb ∙ V to avoid convergence issues with the real viscosity (that is 10\ Nhigher)

1480 1490 1500 1510 1520 1530 154010

-3

10-2

10-1

100

101

102

103

Temperature (°C)

Ste

el v

isco

sity

(P

a.s

)

(1489, 1e3) (1528.85,5e2)

(1529.85,6.3e-3)liquidus

solidus

• Case 1: Only has 10Kdb ∙ Vviscosity in meniscus region

• Case 2: In addition, uses Adjust function to fix velocity, effectively making viscosity infinite


Steel shell viscosity - theory

e̅.X1/VZ � 0.1gh0

gh � ijX�cbZkl ∙ �XGZ

300[O.OF

∙ 1 � 1000e̅ mkl � 13678 N ca�o [p.pOOq

U � 1.617 N 10[\ N � G � 0.06166 [2- � �9.4156 N 10[O N � G � 0.349501 Temperature

(K)

Pct Carbon

(%)

Von-Mises

Strain

Rate (1/s)

Viscosity

(Pa.s)

1800 0.001 0.01 4 N 10r

1800 0.001 0.1 6.8 N 10q

1800 0.001 1 1.15 N 10q

1800 0.01 0.01 3.5 N 10r

1800 0.1 0.01 3.1 N 10r

s � t_`e._`

� 23kl ∙ �XGZ

300[O.OF 1

e̅. 10u̅. 20

kl � 13678 N ca�o [p.pOOqU � 1.617 N 10[\ N � G � 0.06166 [2

Li C & BG Thomas, Met Trans B, 2004

Constitutive equations for delta-ferrite


Modeling Procedure

1. Initialize phase fraction distribution (slag vs steel) with Bikerman Eqn.

2. Flow-only transient simulation to smooth phase interface (meniscus shape)

3. Thermal-only steady state simulation to establish temperature field and form initial shell

4. Coupled flow-thermal transient simulation with no mold oscillation to establish flow field

5. Fully coupled transient simulation for 8 cycles (case 1) and 2 cycles (case 2)

1 cycle of simulation takes 1 day on 6 core PC


Viscosity Solution @7.25s

X (mm)Y

(m

m)Y (

mm

)

X axis elongated to show close up of gap


Velocity – case 1

• Domain at corner of NF• Flow entering domain is

form secondary recirculation zone, with velocityv 0.3-/V, carrrying 3.5> superheat

• Generates tertiary recirculation zone in corner

• Far-field flow pattern relatively stable (for 2.5s = 8 cycles)

• far-field surface waves

Video


Temperature – case 1

• Slag rim near meniscus represented by 1000C contour

• slow thermal response of mold

Video


Temperature in gap – case 1

• X axis expanded

• Note: solid layer on mold wall;

• nonlinear temperature gradient across gap due to fluid flow

• Slag gap grows, (from shell tip down)

Video


Initial solidification & OM formation – case 1

• During 8-cycle (2.5s) simulation: two occurrences of overflow happen at 7.5s and 7.9s

• As the simulation goes on meniscus cool down and freeze, changes to bending behavior

• Bending is due to viscosity 10\ times smaller and ADJUST function not in use at meniscus Video


Initial solidification & OM formation – case 2

• Duration 2 cycles• Shell is rigid after

solidification (turning blue)• Overflow happens when

mold has maximum speed upward

• Small hook forms (even with no undercooling)

• Smaller slag gap compared to bending mechanism

Video


1 mm 0

Side view (of section)

Entrapped bubble

Curved hook

Oscillation Marks and Hooks

Hook depth

OM

OM depth

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


Shell & slag gap profile – case 1

X (mm)

Y(m

m)

20 22 240

20

40

60

80

100

X (mm)

Y(m

m)

20 22 240

20

40

60

80

100

Time: 10.135 sX (mm)

Y(m

m)

20 22 240

20

40

60

80

100

X (mm)

Y(m

m)

20 22 240

20

40

60

80

100

X (mm)

Y(m

m)

20 22 240

20

40

60

80

100

Video

• X axis expanded• The ADJUST

function is capable of keeping OM shape, but still allows too much movement

• Slag gap gets wider as simulation goes on


Predicted strand surface profile along the strand

0 10 20 30 40 50 60 70 80 90 100 110 120

-2

0

2M

old

Pos

ition

(m

m)

0 10 20 30 40 50 60 70 80 90 100 110 1200.6

0.8

1

1.2

1.4

1.6

1.8

2

Ys: Distance along the shell (strand) (mm)

Gap

thic

knes

s (m

m)

@10.13 s (9.79s + 1 cycle)@ 9.79 s@ 9.44 s (9.79s - 1 cycle)

Theoretical pitch: 8.01mmPredicted pitch average: 7.82mmStandard deviation: 0.94mm

All lines at same position along shell surface (i.e. in shell frame of reference) �; � 0 means far field meniscus @ 9.79s

Difference between 3 lines shows the non-physical movement of the shell due to viscosity being 10\ times smaller


Heat flux at mold hot face


Thermocouple locations

• Due to insufficient heat in meniscus region, mold temperature is constantly dropping during simulation

• In order to extract the temperature fluctuation due to oscillation, the TC temperature history is fitted to a cubic function, which captures the cooling trend.

• A modified temperature is then acquired by subtracting the cubic function

#1 #2

#3 #4

#5 #6

#7 #8

#9 #10

#11 #12

7

0

-6

-12

-18

-25

Distance (mm) above meniscus


Thermocouple #1temperature fluctuations

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

110

112

114

116TC#1, x=15

Y L

oca

tion

(m

m)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10110

110.05

110.1

110.15

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

100

105

110

Time (s)

Ra

wT

emp

era

ture

( °C

)


Thermocouple #2temperature fluctuation

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

110

112

114

116TC#2, x=18.5

Y L

oca

tion

(m

m)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

116.7

116.8

116.9

117

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

105

110

115

Time (s)

Ra

wT

emp

era

ture

( °C

)



8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

104

106

108

110TC#3, x=15

Y L

oca

tion

(m

m)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10129.3

129.4

129.5

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

115

120

125

Time (s)

Ra

wT

emp

era

ture

( °C

)


Thermocouple #4~0.3C temperature fluctuations

Near Hot face; at far field meniscus

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

104

106

108

110TC#4, x=18.5

Y L

oca

tion

(mm

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10138.5

138.6

138.7

138.8

Mod

ifie

dT

em

per

atu

re ( °

C)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10120

125

130

135

Time (s)

Raw

Te

mp

erat

ure

( °C)

NST

NST

NST

NST

NST

NST



8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 1096

98

100

102

TC#5, x=15

Y L

oca

tion

(m

m)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10155.25

155.3

155.35

155.4

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

135

140

145

150

155

Time (s)

Ra

wT

emp

era

ture

( °C

)



8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 1096

98

100

102

TC#6, x=18.5

Y L

oca

tion

(m

m)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10171.2

171.4

171.6

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

150

160

170

Time (s)

Ra

wT

emp

era

ture

( °C

)



8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 1090

92

94

96

TC#7, x=15

Y L

oca

tion

(m

m)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10176.45

176.5

176.55

176.6

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10150

160

170

Time (s)

Ra

wT

emp

era

ture

( °C

)



8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 1090

92

94

96

TC#8, x=18.5Y

Lo

catio

n (

mm

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

197.1

197.2

197.3

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

170

180

190

Time (s)

Ra

wT

emp

era

ture

( °C

)Near Hot face; 12 mm below field meniscus



8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 1084

86

88

90

TC#9, x=15

Y L

oca

tion

(m

m)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10193.35

193.4

193.45

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

170

180

190

Time (s)

Ra

wT

emp

era

ture

( °C

)



8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 1084

86

88

90

TC#10, x=18.5

Y L

oca

tion

(m

m)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10216.9

217

217.1

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10180

190

200

210

Time (s)

Ra

wT

emp

era

ture

( °C

)



8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

78

80

82

84TC#11, x=15

Y L

oca

tion

(m

m)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10207.45

207.5

207.55

207.6

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

180

190

200

Time (s)

Ra

wT

emp

era

ture

( °C

)



8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

78

80

82

84TC#12, x=18.5

Y L

oca

tion

(m

m)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

233.2

233.3

233.4

Mod

ifie

dT

emp

era

ture

( °C

)

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10

200

210

220

230

Time (s)

Ra

wT

emp

era

ture

( °C

)


Slag temperature near meniscusat x=21mm, y=106mm

X (mm)20.9999 20.9999 21 21 21

106

106

106

106

106

106

106

106

106

2602402202001801601401201008060

TemperatureMold (C)

X (mm)20.9999 20.9999 21 21 21

106

106

106

106

106

106

106

106

106

X (mm)20.9999 20.9999 21 21 21

106

106

106

106

106

106

106

106

106

X (mm)20.9999 20.9999 21 21 21

106

106

106

106

106

106

106

106

106

X (mm)20.9999 20.9999 21 21 21

106

106

106

106

106

106

106

106

106

1531.851530.851529.851528.85150014001300120011001000900

TemperatureSteel&Slag (C)

Steel Solidus1528.85 C

Time: 6.774715 sSolution Time (s)

Tem

pera

ture

(C)

7 7.5 8 8.5 9 9.5 10

600

700

800

900

1000


Shear stress at mold hot face


Slag consumption for 7 cycles

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35-0.1

-0.05

0

0.05

0.1

Time in one cycle (s)

Sla

g flo

w (

kg/m

.s)

InstantaneousConsumptionMeanConsumption

Cycle # 1 2 3 4 5 6 7 Average

Mean Consumption Xw m∙;⁄ Z 2.3 4.6 2.2 2.3 3.8 3.8 5.3 3.5

NST

Average consumption 3.5 g/ms


Conclusion - modelling

• New thermal-fluid VOF model of mold, slag, powder, solidifying steel shell, and gap has been developed to investigate initial solidification

• Model can predict oscillation mark formation, with different mechanisms (both bending and overflow) according to different material property (steel viscosity)


Conclusion – OM mechanism

• Low viscosity steel (nonphysical) - Bending mechanism– OM forms when mold at lowest position– Wider meniscus gap, causing lower meniscus heat flux and less mold TC

temperature variations– Very wide contoured OM shape – Slag consumption profile similar to previous work, but average consumption is

low– Nonphysical because frozen meniscus would break under so much bending

• Rigid steel viscosity - Overflow mechanism– Rigid shell (moving downward) combined with meniscus movement exceeds – Occurs when mold has maximum speed going up– OM shape is shallower than that from bending mechanism– Seems physically reasonable– We expect higher meniscus heat flux, larger TC temperature fluctuation.


Future work

• Eliminate the cooling trend by improving powder surface inlet boundary condition

• Improve realism of shell behavior at meniscus by increasing viscosity (if possible) or fine tune the ADJUST function zone

• Validate with more measurements• Parametric studies


Acknowledgments

• Continuous Casting Consortium Members(ABB, AK Steel, ArcelorMittal, Baosteel, JFE Steel Corp., Magnesita Refractories, Nippon Steel and Sumitomo Metal Corp., Nucor Steel, Postech/ Posco, SSAB, ANSYS/ Fluent)

Documents

Transient Thermo-fluid Model of Meniscus Behavior and