IWASAKI Junya CCC2009 Calibration of Mold Heat Transfer

ANNUAL REPORT 2009ANNUAL REPORT 2009UIUC, August 5, 2009

Calibration of Mold Heat Transfer Modelswith Breakout Shell Measurements

Junya Iwasaki ( Visiting Scholar from NIPPON STEEL )( Visiting Scholar from NIPPON STEEL )

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 1

Department of Mechanical Science and Engineering

University of Illinois at Urbana-Champaign

Outline

1. The Circumstances of Breakout

2. Estimation of Flow Rate and Solidification timeand Solidification time

3. Heat Transfer Model C lib ti f G t Diff– Calibration for Geometry Differences

4. CON1D Model Verification with Plant

5. Conclusions



1600

1800

2000

2200in

)

80

-70

-60

-50

w m

old

Breakout(stop in flow at 0 (sec))

600

800

1000

1200

1400

1600

stin

g S

peed

(mm

/m

-130

-120

-110

-100

-90

-80

s le

vel-d

ista

nce

belo

wto

p (m

m)

Casting speed

Meniscus hight Vc = 1.4 (m/min)steady casting

0

200

400

600

-1500 -1400 -1300 -1200 -1100 -1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0 100

Casting Time (sec)

Cas

-160

-150

-140

-130

Men

iscu

sy g

Table 1. Casting ConditionFigure 1. History of recorded Casting Conditions

Casting speed 23 4 mm/s Steel Composition

Casting Time (sec)

Casting speed 23.4 mm/s Steel Composition

Strand thickness 252 mm 0.16 %C

Strand width 1360 mm 0.71 %Mn

SEN submergence depth 230 mm 0.016 %P

Pour temperature 1540 ℃ 0.006 %S


Meniscus dist. From mold top 96 mm 0.02 %Si

Mold conductivity ( WF ) 242 W/mK 0.039 %Al

( NF ) 355 W/mK


Top of the shell Top

Fixed Face

Breakout HoleBreakout Hole

Narrow Face(North)

Narrow Face(South)

1200mm below

Narrow Face (North)

Starting point

Fixed Face 50mm

the top of shellg p

of the breakout

Breakout PointFi d F N th id ff 30

CornerBottom

- Fixed Face, North side off corner 30mm

- 1200mm below the top of shell- 1200mm below the top of shell

- Hole size = 34107 mm2


Figure 2. Breakout shell and hole


90

100

1800

2000

-70

-60Stop in-flowat 0 (sec)

Start of Break Outat -22 (sec)

70

80

90

on (%

)

1400

1600

1800/m

in)

-90

-80

-70

mol

d to

p (m

m)at 0 (sec)at 22 (sec)

40

50

60

ng n

ozzl

e po

sitio

800

1000

1200

ng s

peed

(mm

/

-120

-110

-100

stan

ce b

elow

m

Error in Signal

10

20

30 Slid

in

200

400

600Cas

tin

150

-140

-130

enis

cus

leve

l-di

Casting speed

Meniscus level

Sliding nozzle position

( T >= -5 )

0

10

0

200

-60 -50 -40 -30 -20 -10 0 10 20 30Casting time (sec)

-160

-150 Me


Figure 3. History of recorded Casting Conditions during Breakout


2.0Stop in-flowStart of Break Out

~constant q:1.279MW/m2 (Fixed face)

1 2

1.4

1.6

1.8

m^2

)

at 0 (sec)at -22 (sec)

1.195MW/m2 (Loose face)

1.336MW/m2 (Nouth face)

1.294MW/m2 (South face)0.6

0.8

1.0

1.2

Hea

t flu

x (M

W/m

Fixed face

Loose face

(Average from -1000s to -23s; Vc = 1.4 m/min ~ constant)

0.0

0.2

0.4

0.6Nouth(Narrow) face

South(Narrow) face

Figure 4 History of recorded Heat Flux during Breakout

-60 -50 -40 -30 -20 -10 0 10 20 30Casting time (sec)


Figure 4. History of recorded Heat Flux during Breakout

2. Estimation of Flow Rate and Solidification time

2.1. Estimation of Flow RateQd

… (1)in drop out drainQ Q Q Q+ = +

draint < -22 : Q = 0 Q

Qdrop

inQ : Input from sliding nozzle gate

drain

in

Q

t > 0 : Q = 0Qin

in

drop

out

Q : Flow rate of Drop in level

Q : Output by casting speed Qdrain

drainQ : Drainage from breakout hole

t : Casting time (sec)

Figure 5 Schematic of

Qout


(Use Eulerian reference frame based on steady-meniscus position)

Figure 5. Schematic ofMass Balance

2.1. Estimation of Flow Rate

Second order approximation

Qin ; Input from Sliding Nozzle Gate4.0Second order approximation

20.0002 0.0368in t tQ X X= + … (2)

X : SN position at time t (%)y = 0.0002x2 + 0.0368x

2.5

3.0

3.5

4.0

on/m

in)

Q ; Output by Casting Speed 0 5

1.0

1.5

2.0

Flow

rat

e (t

o

Qout ; Output by Casting Speed

out C tQ W Y Vρ −= × × × … (3)

3l d i ( / ) 7 4

0.0

0.5

0 10 20 30 40 50 60 70 80 90

Sliding nozzle position (%)

Figure 6. Real date of Flow Rate from Sliding Nozzle

3 : steel density (ton/m ) = 7.4

W : slab width (m)

Y : slab tickness (m)

V ti d t ti t ( / i )

ρ


C-tV : casting speed at time t (m/min)


t < -5

1( )

( ( 1))t t

drop

z zQ W Y

t tρ −−

= × × ×− −

… (4)

Qdrop ; Flow Rate of Drop in Level

( ( 1))t t

( )drain out in dropQ Q Q Q= − + … (1)’

Qdrain ; Drainage from Breakout Hole

3 : steel density (ton/m ) = 7.4

W : slab width (m)

Y : slab tickness (m)

z : distance below steady state meniscus to liquid level at time t (m)

ρ

( )drain out in dropQ Q Q Q

draint

t

QS

vρ=

×… (5)

t

hole-t-1

z : distance below steady state meniscus to liquid level at time t (m)

z : distance below steady state meniscus to breako

2t

ut hole at time t-1sec (m)

t : casting time (min)

S : hole size at time t (m )

v : speed of running fluid from breakout hole at time t (m/sec)

12t tv gh −= … (6)

1 1 1t hole t th z z− − − −= − … (7)


t

2

t-1

v : speed of running fluid from breakout hole at time t (m/sec)

g : gravitational acceleration (m/sec ) = 9.8

h : liquid height from liquid level to breakout hole at time t-1sec (m)


t >= -5

Exponential approximation0.21193713 7 tS e= … (8)

Qdrain ; Drainage from Breakout Hole

30000

35000

40000

Measured points

3713.7tS e= ( )

drain t tQ S vρ= × × … (5)’

2v gh= … (6)

y = 3713.7e0.2119x

15000

20000

25000

Hol

e si

ze (m

m^2

)

Calculated hole size

Estimated hole sizeas exponential curve

12t tv gh −= ( )

1 1 1t hole t th z z− − − −= − … (7)

Qd ; Flow Rate of Drop in Level0

5000

10000

-60 -50 -40 -30 -20 -10 0 10 20 30

C ti g ti ( )

from mass balance

Figure 7. Estimated Hole sizedrop out drain inQ Q Q Q= + − … (1)’’

( ( 1))dropQz z t t= + − − … (4)’

Qdrop ; Flow Rate of Drop in Level Casting time (sec)


1 ( ( 1))t tz z t tW Yρ−= + − −

× ×… (4)


30

20

25m

in)

Input from sliding nozzle gate

Flow rate due to Drop in level

output by casting speed

Drainage from breakout hole

15

w r

ate

(ton

ne/m

Top of breakout shellcasting point = -4(sec)

5

10

Flow

g p ( )Meniscul lelel drop in (m/s) > casting speed (m/s)

0

-60 -50 -40 -30 -20 -10 0 10 20 30

Casting time (sec)


Figure 8. Estimated Flow Rate

Casting time (sec)

2.2. Estimated Solidification Time

Note: Eulerian frame of reference (based on steady-meniscus position)Time when slice started at meniscus (s)Time when slice started at meniscus (s)

1500

2000

us (m

m)

Estim a te d liq u id le v e l

t= 30

t= -40

t= -50

t= -59

1000

tead

y-st

ate

men

isc

Mo ld Ex it

B o tto m o f b r e a lo u t ho le

t= -4

t= -10

t= -20

t= -30

B o tto m o f b r e ako u t ho le casting p o in t = -5 9 (se c)

ts 1ts 0

500

Dis

tanc

e be

low

st

Me asu r e d liq u id le ve l

To p o f b r e ako u t she ll

t= -4

L

L

Figure 9 Distance traveled by different points on

0

-60 -50 -40 -30 -20 -10 0 10 20 30

Casting time (sec)To p o f b r e a ko u t she ll casting p o in t = -4 (se c)


Figure 9. Distance traveled by different points onthe shell surface relative to the dropping

2.2. Estimated Solidification Time

0 1s s st t t= + … (9) 70

80

ts

ts0

4

0s

t

CtV dt L

− =∫1st dz

∫

… (10)

(11)30

40

50

60

ifica

tion

time

(sec

)

ts1

Poly. (ts1)

1

4

( )s

Ct

dzV dt L

dt−

− =∫ … (11)

Cubic curve approximation

y = 15.778x3 - 34.956x2 + 30.803x

0

10

20

0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1 1 2

Solid

Figure 10. Solidification time

3 21 15.778 34.956 30.803st L L L= − +

st : solidification time at L (sec)… (12)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Distance below the top of shell (m)

s

s0

s1

C

( )

t : solidification time at L before -4 (sec)

t : solidification time at L after -4 (sec)

V : casting speed (m/min)


C g p ( )

z : distance below steady state maniscus to liquid level(m)

L : distance from the top of shell (m)

3. Heat Transfer Model –Calibration for Geometry DifferencesCalibration for Geometry Differences

3. 1. Mold Geometry Simplification with CON1D

Wide Face

80

Water channels

(Original)

25

11

R2.5

80

30o

Water ChannelsThermocoupleHot Face 12

13

2.46

Water channels

(for CON1D)

Fi 12 Wid f

2

20

13

5

6φ

20 20 10

9.8φ

12

5

Figure 11. Wide face mold geometry

Figure12 . Wide faceWater channel &

CON1D Simplification


p

3. 1. Mold Geometry Simplification with CON1D

Narrow Face

11

129

Water ChannelsThermocouple

Hot Face

Center Water channels

(Original)

50

15

37

5

5

R2.5

12φ

6φ30o

22

15

4.46

Water channels

(for CON1D)

Fi 14 N f

16 16 21 21 21 10.5

21

111

16o33.5

14

5

Figure 13. Narrow face mold geometry Figure 14. Narrow faceWater channel &

CON1D Simplification


p

3. 2. CON1D Model Offset Determinationwith ABAQUS

3. 2. 1. Procedure of Offset

CON1D• Heat Flux

•Cooling water Temperature

• Hot Face and Cold Face Temperatures

ABAQUS (2D)

• Influence of Heat Transfer Coefficient differenceCON1D Offset - 1

• Influence of Heat Transfer Coefficient difference

between CON1D and ABAQUS-2D model

ABAQUS (3D)

• Influence of Thermocouple Hole geometry


CON1D Offset - 2p g y

3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -

Heat Transfer Coefficient Formula

Q

1d⎛ ⎞

CON1D

Wch

Water channelsCold faceHot face

11/ scale

waterscale fin

dh

k h

⎛ ⎞= +⎜ ⎟⎜ ⎟

⎝ ⎠

( ) 22 2tanhw mold ch chw ch w ch

h k L wh w h dh

−+

… (13)

solid mold

( )tanhw ch w ch

finch ch mold ch ch

hL L k L w

= +−

… (14)2

waterh : heat transfer coefficient using CON1D (W/m K)

d l hi k f l ld ld f ( )

fin Lch

Figure15 Water channel

scale

scale

w

d : scale thickness of water scale at mold cold face (m)

k : conductivity of water scale at mold cold face (W/mK)

h : heat transfer coeff 2icient between water and sides of water channels (W/m K)

(using ABAQUS 2D and 3D model shown in formura 3 on next slide)

k d i i f ld ( / )

dchXmold

dml


Figure15 . Water channel in the mold

moldk : conductivity of mold (W/mK)

Lch, wch, dch : geometry parameters shown in Figure 5 (m)


ABAQUS (2D and 3D)k

Q

( )1 25 0.015Re Prc cwatermw waterf waterw

kh

D= + … (15)

2 ch chW dD

W d= … (16)

0.59 0.001waterm waterk T= + … (21)

0.59 0.001t ldk T= + … (22)ch chW d+

( )1 0.88 0.24 / 4 Prwaterwc = − + … (17)

0.6Pr2 0.333 0.5 waterwc e−= + … (18)

0.59 0.001waterw coldk T+ ( )

792.42

273.1592.062*10 *10 filmT

waterf waterμ ρ⎛ ⎞⎜ ⎟⎜ ⎟+− ⎝ ⎠= … (23)

792.42

273 159* * T

⎛ ⎞⎜ ⎟

+⎝ ⎠ (24)2 0.333 0.5c e+ ( )

Re water waterwaterf

waterf

v Dρμ

= … (19)

273.1592.062*10 *10 coldTwaterw waterμ ρ +− ⎝ ⎠= … (24)

0.5( )film water coldT T T= + … (25)

k : conductivity of water (W/mK)

Pr waterw waterwaterw

waterw

Cp

k

μ= … (20)

water

water

water

3water

k : conductivity of water (W/mK)

μ : water viscosity (Pa s)

v : cooling water velosity (m/s)

ρ : water density (kg/m ) = 995.6

Cp : water heat capacity (J/kg) = 4179


water

water

Cp : water heat capacity (J/kg) = 4179

T : cooli o

ocold

ng water temperature ( C)

T : cold face temperature ( C)

[C. A. Sleicher and M. W. Rouse, Int. J. Heat Mass Transf. V. 18, pp. 677-683, 1975]


ABAQUS 2D modelWide Face

Q

- Boundary conditions and properties

Q

Parameter Value Units

1.443 MW/m2

37 31 kW/m2 K

Q

h

moldk

37.31 kW/m K

33.71 oC

242 W/m K

wh

waterT

moldk

Narrow Face

ThParameter Value Units

2Q , Tw waterh 1.443 MW/m2

50.73 kW/m2 K

37.86 oC

355 W/ K

Q

wh

waterT

k


Figure 16. boundary conditions and properties355 W/m Kmoldk


Temperature profiles Path-1Path-2

Q

180

Wide Face

120

140

160

ture

(C)

ohotΔT = 8.0 ( C)

Figure 17. Calibration results

80

100

Tem

pera

t

ABAQUS Path-1

ABAQUS Path-2

CON1D

( )1 2

12hot path hot path

hot hot CON D

T TT T

− −−

−Δ = −

… (26)

40

60

0 5 10 15 20 25 30Distance from Hot Face (mm)

hot

o

ohot

T : Hot Face temperature difference

between CON1D and ABAQUS ( C)

T : Hot Face temperature ( C)

Δ


Distance from Hot Face (mm)

Figure 18. Temperature profiles in Wide face


Determination of Offset-1

id

Q

… (27)

Wide Face1offset hot

dxd T

dT− = Δ

160

180

ABAQUS Path 1

offset-1

hot

o

d : offset-1 distance (mm)



Δ

100

120

140

160

ture

(C)

ABAQUS Path-1

ABAQUS Path-2

CON1D

o

dx/dt : inverse of the temperature

gradient from CON1D (mm/ C)

40

60

80

Tem

pera

1 34mm

ohotΔT = 8.0 ( C)

0

20

0 2 4 6 8 10 12 14


1.34mmOffset-1


Figure 19. Determination of Offset-1 in Wide FaceDistance from Hot Face (mm)


Path-1Path-2Temperature profiles

Q

180

oΔT = 5 6 ( C)

Narrow Face

120

140

160

ture

(C)

ABAQUS Path-1

hotΔT = 5.6 ( C)


80

100

Tem

pera

t

ABAQUS Path-2

CON1D( )1 2

12hot path hot path

hot hot CON D

T TT T

− −−

−Δ = −

… (26)

40

60

0 5 10 15 20 25 30 35 40Distance from Hot Face (mm)

hot

o

ohot



T : Hot Face temperature ( C)

Δ


Figure 21. Temperature profiles in Narrow face



dx

Q

… (27)Narrow Face

1offset hot

dxd T

dT− = Δ

160

180

ABAQUS Path-1offset-1

hot

o

d : distance of offset-1 (mm)




Δ

100

120

140

160

atur

e (C

)

Q

ABAQUS Path-2

CON1D

o

p

gradient from CON1D (mm/ C)

20

40

60

80

Tem

pera

1.38mm

ohotΔT = 5.6 ( C)

0

20

0 2 4 6 8 10 12 14 16 18 20 22 24


Offset-1


Figure 22. Determination of Offset-1 in Narrow Face

( )


Temperature profiles with Offset-1

Q

Narrow FaceWide Face

160

180

ABAQUS Path-1 160

180

100

120

140

160

pera

ture

(C)

ABAQUS Path-1

ABAQUS Path-2

CON1D-Offset-1

100

120

140

160

pera

ture

(C

)

ABAQUS Path-1

ABAQUS Path-2

40

60

80

100

Tem

p

40

60

80

100

Tem

p

CON1D-Offset-1

Figure 23. Temperature profiles with Offset-1

40

0 5 10 15 20 25 30Distance from Hot Face (mm)

40

0 5 10 15 20 25 30 35 40




Generalization of Offset-1 by water channel geometry

Q

240 240

Wide Face geometry Narrow Face geometry

12.4

6

25

5

Lch

14.4

6

37

5

180

200

220

240

ratu

re (

o C)

hotTΔ

180

200

220

240

ratu

re (

o C)

hotTΔ

Lch

140

160

180

Hot

Fac

e Te

mpe

r

ABAQUS-2D Q=2.0MW/m^2CON1D Q 2 0MW/ ^2

hotTΔ

140

160

180

Hot

Fac

e Te

mpe

r

ABAQUS-2D Q=1.9MW/m^2CON1D Q 1 9MW/ ^2

hotTΔ

100

120

5 10 15 20 25 30

Distance between water channels Lch (mm)

CON1D Q=2.0MW/m^2ABAQUS-2D Q=1.4MW/m^2CON1D Q=1.4MW/m^2

100

120

5 10 15 20 25 30

Distance between water channels Lch (mm)

CON1D Q=1.9MW/m^2ABAQUS-2D Q=1.4MW/m^2CON1D Q=1.4MW/m^2


Figure 24. Relation of distance between water channelto Hot Face temperature with CON1D and ABAQUS-2D


Generalization of Offset-1 by water channel geometry

… (27)

Q

1offset hot

dxd T

dT− = Δ2.5

ch

DX

L= … (28)

( )1offset hot dT

1.5

2.0

mm

)

WF z=250WF z=80NF z=220NF z=80Power (Offset-1)

2 ch ch

ch ch

W dD

W d=

+ … (16)

2.00831 0.1659ff td X −= … (29)

Power approximationy = 0.1659x-2.0083

R2 = 0.99120 5

1.0

1.5

Offs

et-1

(m

1 0.1659offsetd X− ( )

offset-1

mold

h t


k : conductivity of mold (W/mK)

ΔT : Hot Face temperature difference

0.0

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

D/ Lch

Figure 25. Relation of water channel geometry parameter X to Offset-1

hot

o

ch

ΔT : Hot Face temperature difference


X : water channel geometry parameter

d : water channel depth (mm)


ch

ch

L : distance between water channel (mm)

W : water channel width (mm)


Error of generalized Offset-1

Q

5

2

3

4e

deffe

renc

e A

BA

QU

S-2

D WF z=250

WF z=80NF z=220NF z=80

-1

0

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

ce te

mpe

ratu

reD

-offs

et-1

and

(oC

)

-4

-3

-2

Err

or o

f hot

fabe

twee

n C

ON

1

owithin 1.0 C±

Figure 26 Error of hot face temperature

-5

D/ Lch

b


Figure 26. Error of hot face temperature between CON1D-generalized offset-1 to ABAQUS-2D

3. 2. 3 Offset - 2 - Influence of Thermocouple Hole geometry -

ABAQUS 3D model - Boundary conditions and properties

Wide Face

Q


1.443 MW/m2

37 31 kW/m2 K

Q

hk 37.31 kW/m K

33.71 oC

242 W/m K

wh

waterT

moldk

moldk

Number of elements : 196598 ( hexahedrons, tetrahedrons )

, Tw waterh



Figure 27. Wide face boundary conditions and properties


Temperature profiles

id P th 2

Path-3Path-4

200

Wide Face Path-1Path-2

120

140

160

180

re (o C

)


60

80

100

Tem

pera

tur

Path1Path2P th3


0

20

40

0 5 10 15 20 25 30

Path3Path4CON1D Offset-1



Figure 29. Temperature profiles in Wide face



Wide Face

( )2offset TC hf TC

dxd T T d

dT− = − −

Wide Face

180

200

offset-2

TC


T : thermocouple temperature

… (30)

1

120

140

160

ture

(o C)

TC

o

hf

o

from ABAQUS ( C)


from CON1D ( C)

d /dt i f th t t40

60

80

100

Tem

pera

t

ABAQUS Path-1

CON1D Offset-1dx/dt : inverse of the temperature

gradient f o

TC

rom CON1D (mm/ C)

d : actual depth of the thermocouple

from Hot Face (mm)

0

20

40

0 2 4 6 8 10 12 14

1.61mmOffset-2


Figure 30. Determination of Offset-2 in Wide Face



ABAQUS 3D model - Boundary conditions and properties

Narrow FaceNarrow Face

Q


1.443 MW/m2

50 73 kW/m2 K

Q

whmoldk50.73 kW/m K

37.86 oC

355 W/m K

w

waterT

moldk


, Tw waterh


Figure 31. Narrow face boundary conditions and properties


Temperature profiles Path-1Path-2

Path-3Path-4

180

200

Narrow FacePath 1

120

140

160

180

re (o C

)


60

80

100

Tem

pera

tur

Path-1Path-2Path-3


0

20

40

0 5 10 15 20 25 30 35 40

Path-4CON1D Offset-1



Figure 33. Temperature profiles in Narrow face



Narrow Face

( )2offset TC hf TC

dxd T T d

dT− = − −

Narrow Face

160

180

offset-2

TC



… (30)

100

120

140

atur

e (C

)

TC

o

hf

o

from ABAQUS ( C)


from CON1D ( C)

d /dt i f th t t40

60

80

Tem

pera

ABAQUS Path-1

1.65mmOffset-2


gradient f o

TC

rom CON1D (mm/ C)

d : actual depth of the thermocouple

from Hot Face (mm)

0

20

0 2 4 6 8 10 12 14 16 18 20 22 24Distance from Hot Face (mm)

QCON1D Offset-1


Figure 34. Determination of Offset-2 in Wide Face



Table 2. CON1D Fitting ConditionFixed face Narrow face

Simulation shell Fixed faceCasting speed 23.4 mm/sSEN submergence depth 230 mmPour temperature 1540 ℃

Meniscus dist. From mold top 96 mmFraction solid for shell thickness location 0.35Treatment of superheat - 1 : default

Mean heat flux in mold - measured 1.279 MW/m2 1.294 MW/m2

Fitting Parameters - Solid flux conductivity 1.00 W/mK - Liquid flux conductivity 1.00 W/mK - Location of peak heat flux - 0.03 mp - Slag rim thickness at metal level - 2.20 mm - Slag rim thickness at heat flux peak - 0.75 mm - Cold face scale thickness - 0.002mm - Constant ratio of solid flux velocity

t ti k 0 085 0 084


to casting speek 0.085 0.084CON1D prediction

- Mean heat flux in mold 1.279 MW/m2 1.293 MW/m2


Fixed face

Solidification History with CON1D (steady state 1.4m/min)Solidification time (min)

0.554.763 1.9306t sol solS t t= +0.04st ≤

0.04st >… (26)

Fixed face

16

18

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.525.244 3.0216t solS t= − … (27)

0S0.01st ≤

(28)

Narrow face10

12

14

16

ickn

ess

(mm

)

0tS =

0.520.604 2.1854t solS t= −0.01st >

… (28)

… (29)

2

4

6

8

Shel

l thi

Fixed Face

Narrow Face

s

t

t : Solidification time (min)

S : Shell thickness (mm)0

2

0 200 400 600 800 1000Distance below meniscus (mm)


Figure 35. CON1D calculated thickness profile


Analyzed Breakout Shell Thickness

30 Fixed Face Center Mesured

22

24

26

28

30

)

Fixed Face CON1D (BO conditions)Fixed Face CON1D (steady casting Vc=1.4 (m/min)Narrow Face Center Mesured"Narrow Face CON1D (BO conditions)Narrow Face CON1D (steady casting Vc=1.4 (m/min)

12

14

16

18

20

Thi

ckne

ss (m

m)

4

6

8

10

12

Shel

l

0

2

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Distance below top of shell (mm)


Figure 36. Comparison between CON1D calculatedprofile and measurements from BO shell


Wide Face

Analyzed Thermocouple Temperatures

d d d+ (30)Wide Face

140

160C

) CON1D with Offset

1 2offset offset offsetd d d− −= + … (30)

80

100

120

tem

pera

ture

s (C Measured (Ave.)

20

40

60

Ther

moc

oupl

e t

0

20

-100 0 100 200 300 400 500 600 700 800

Distance below meniscus (mm)


Figure 37. Thermocouple temperatures comparisonbetween CON1D and Measured data


Narrow Face d d d+ (30)Narrow Face

160

180

200

)

CON1D with Offset

Measured (Ave )

1 2offset offset offsetd d d− −= + … (30)

100

120

140

160

Then

pera

ture

(C

Measured (Ave.)

40

60

80

Term

ocou

ples

T

0

20

-100 0 100 200 300 400 500 600 700 800

Distance below meniscus (mm)


Figure 38. Thermocouple temperatures comparisonbetween CON1D and Measured data


Table 3. Thermocouple Temperature Comparisonp

Distance below Measured (Ave.) CON1D with offset

Meniscus Temperature Temperature Difference

mm oC oC oC

Wide Face 151.5 110.9 115.43 4.5254 0 95 1 102 61 7 5

10.0

15.0

20.0

erat

ure

Wide Face

Narrow Face

254.0 95.1 102.61 7.5Narrow Face -56 43.9 42.21 -1.6

-16.0 55.2 56.08 0.84.0 75.5 81.65 6.124.0 127.8 122.66 -5.244 0 178 1 169 86 8 2

-10.0

-5.0

0.0

5.0

-100 -50 0 50 100 150 200 250 300

moc

oupl

e Te

mpe

Diff

eren

ce (o

C)44.0 178.1 169.86 -8.2

64.0 176.7 175.35 -1.3104.0 159.7 165.46 5.7151.5 156.4 152.75 -3.6219.0 142.8 139.57 -3.2

Figure 39 Thermocouple Temperature

-20.0

-15.0

10.0

Distance below Meniscus (mm)Th

erm


Figure 39. Thermocouple TemperatureDifference

5. Conclusions

• Mass balance equation for deriving solidification time and flow-rate history of breakout shell is developed and applied to

• General Offset formula established and applied:

rate history of breakout shell is developed, and applied to understand a real breakout.

General Offset formula established and applied:• 2D ABAQUS heat transfer model to CON1D for hotface• 3D ABAQUS heat transfer model to CON1D for TC.

• Analyzed shell thickness with CON1D agreed well with the measured shell thickness from the breakout shell.

• Analyzed thermocouple temperature with CON1D with offset agree well with the measurement thermocouple temperature within 8.2 oC.


8. C.

Documents

IWASAKI Junya CCC2009 Calibration of Mold Heat Transfer