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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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 2
1. The Circumstances of Breakout
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 3
Meniscus dist. From mold top 96 mm 0.02 %Si
Mold conductivity ( WF ) 242 W/mK 0.039 %Al
( NF ) 355 W/mK
1. The Circumstances of Breakout
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 4
Figure 2. Breakout shell and hole
1. The Circumstances of Breakout
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 5
Figure 3. History of recorded Casting Conditions during Breakout
1. The Circumstances of 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)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 6
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 7
(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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 8
C-tV : casting speed at time t (m/min)
2.1. Estimation of Flow Rate
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)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 9
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)
2.1. Estimation of Flow Rate
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)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 10
1 ( ( 1))t tz z t tW Yρ−= + − −
× ×… (4)
2.1. Estimation of Flow Rate
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)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 11
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)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 12
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)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 13
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 14
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 15
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 16
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 17
Figure15 . Water channel in the mold
moldk : conductivity of mold (W/mK)
Lch, wch, dch : geometry parameters shown in Figure 5 (m)
3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 18
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]
3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 19
Figure 16. boundary conditions and properties355 W/m Kmoldk
3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 20
Distance from Hot Face (mm)
Figure 18. Temperature profiles in Wide face
3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -
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)
T : Hot Face temperature difference
between CON1D and ABAQUS ( C)
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
Distance from Hot Face (mm)
1.34mmOffset-1
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 21
Figure 19. Determination of Offset-1 in Wide FaceDistance from Hot Face (mm)
3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -
Path-1Path-2Temperature profiles
Q
180
oΔT = 5 6 ( C)
Narrow Face
120
140
160
ture
(C)
ABAQUS Path-1
hotΔT = 5.6 ( C)
Figure 20. Calibration results
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 difference
between CON1D and ABAQUS ( C)
T : Hot Face temperature ( C)
Δ
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 22
Figure 21. Temperature profiles in Narrow face
3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -
Determination of Offset-1
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)
T : Hot Face temperature difference
between CON1D and ABAQUS ( C)
dx/dt : inverse of the temperature
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
Distance from Hot Face (mm)
Offset-1
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 23
Figure 22. Determination of Offset-1 in Narrow Face
( )
3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -
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
Distance from Hot Face (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 24
3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 25
Figure 24. Relation of distance between water channelto Hot Face temperature with CON1D and ABAQUS-2D
3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -
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
d : distance of offset-1 (mm)
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
between CON1D and ABAQUS ( C)
X : water channel geometry parameter
d : water channel depth (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 26
ch
ch
L : distance between water channel (mm)
W : water channel width (mm)
3. 2. 2. Offset - 1 - Influence of Mold Heat Transfer differencebetween CON1D and ABAQUS-2D model -
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 27
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
Parameter Value Units
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 28
Number of elements : 196598 ( hexahedrons, tetrahedrons )
Figure 27. Wide face boundary conditions and properties
3. 2. 3 Offset - 2 - Influence of Thermocouple Hole geometry -
Temperature profiles
id P th 2
Path-3Path-4
200
Wide Face Path-1Path-2
120
140
160
180
re (o C
)
Figure 28. Calibration results
60
80
100
Tem
pera
tur
Path1Path2P th3
Figure 28. Calibration results
0
20
40
0 5 10 15 20 25 30
Path3Path4CON1D Offset-1
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 29
Distance from Hot Face (mm)
Figure 29. Temperature profiles in Wide face
3. 2. 3 Offset - 2 - Influence of Thermocouple Hole geometry -
Determination of Offset-2
Wide Face
( )2offset TC hf TC
dxd T T d
dT− = − −
Wide Face
180
200
offset-2
TC
d : distance of offset-2 (mm)
T : thermocouple temperature
… (30)
1
120
140
160
ture
(o C)
TC
o
hf
o
from ABAQUS ( C)
T : thermocouple temperature
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 30
Figure 30. Determination of Offset-2 in Wide Face
Distance from Hot Face (mm)
3. 2. 3 Offset - 2 - Influence of Thermocouple Hole geometry -
ABAQUS 3D model - Boundary conditions and properties
Narrow FaceNarrow Face
Q
Parameter Value Units
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
Number of elements : 481590 ( hexahedrons, tetrahedrons )
, Tw waterh
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 31
Figure 31. Narrow face boundary conditions and properties
3. 2. 3 Offset - 2 - Influence of Thermocouple Hole geometry -
Temperature profiles Path-1Path-2
Path-3Path-4
180
200
Narrow FacePath 1
120
140
160
180
re (o C
)
Figure 32. Calibration results
60
80
100
Tem
pera
tur
Path-1Path-2Path-3
Figure 32. Calibration results
0
20
40
0 5 10 15 20 25 30 35 40
Path-4CON1D Offset-1
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 32
Distance from Hot Face (mm)
Figure 33. Temperature profiles in Narrow face
3. 2. 3 Offset - 2 - Influence of Thermocouple Hole geometry -
Determination of Offset-2
Narrow Face
( )2offset TC hf TC
dxd T T d
dT− = − −
Narrow Face
160
180
offset-2
TC
d : distance of offset-2 (mm)
T : thermocouple temperature
… (30)
100
120
140
atur
e (C
)
TC
o
hf
o
from ABAQUS ( C)
T : thermocouple temperature
from CON1D ( C)
d /dt i f th t t40
60
80
Tem
pera
ABAQUS Path-1
1.65mmOffset-2
dx/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
0 2 4 6 8 10 12 14 16 18 20 22 24Distance from Hot Face (mm)
QCON1D Offset-1
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 33
Figure 34. Determination of Offset-2 in Wide Face
Distance from Hot Face (mm)
4. CON1D Model Verification with Plant
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 34
to casting speek 0.085 0.084CON1D prediction
- Mean heat flux in mold 1.279 MW/m2 1.293 MW/m2
4. CON1D Model Verification with Plant
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)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 35
Figure 35. CON1D calculated thickness profile
4. CON1D Model Verification with Plant
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)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 36
Figure 36. Comparison between CON1D calculatedprofile and measurements from BO shell
4. CON1D Model Verification with Plant
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)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 37
Figure 37. Thermocouple temperatures comparisonbetween CON1D and Measured data
4. CON1D Model Verification with Plant
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)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 38
Figure 38. Thermocouple temperatures comparisonbetween CON1D and Measured data
4. CON1D Model Verification with Plant
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
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 39
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.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Junya Iwasaki • 40
8. C.