Transcript Heat Transfer in Flux layers Using CON1D

TAPER PREDICTION IN SLAB
AND THIN SLAB CASTING
MOLDS
Claudio Ojeda
Department of Mechanical Engineering
University of Illinois at Urbana-Champaign
October 15, 2002
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
1
Introduction

Taper plays an important role to ensure good contact and heat
exchange between mold wall and shell surface.
– Shell growth uniformity

Problems
– Excessive taper causes:
 Narrow face wearing.
 Extra tensile stress causes transverse cracking.
 Buckling of the shell wide face, causes “gutter” and longitudinal
cracks.
– Insufficient taper causes:
 Breakouts in the steel shell.
 Bulging below mold causing subsurface longitudinal cracks.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
2
Objectives

Calculate ideal taper including the effects of:
–
–
–
–

Shell shrinkage
Mold distortion
Flux layer thickness
Funnel extra length (thin slabs)
Investigate the effect of heat flux profile on Ideal Taper in
conventional and thin slabs as affected by
–
–
–
–
–
Heat flux profile
Casting speed
Steel grade
Powder type
Mold length
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Claudio Ojeda
3
Model description




Finite difference heat transfer and solidification model
(CON1D).
2D Finite element elastic-viscoplastic thermal-stress
model (CON2D).
1D slice-domain representing the behavior of a
longitudinal slice through the centerline of the shell
moving down the mold.
Heat flux boundary condition is applied in the shell
surface.
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Claudio Ojeda
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Model description
Narrow face
Shell surface
liquid
steel
Constant u
Along this edge
Wide
face
Insulated
xx
q
F
t
Liquid
steel
y Solidifying
Shell
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Shell
Claudio Ojeda
5
Definition of ideal taper

Billet molds
IT= Shell shrinkage(z) – (Mold distortion(z) – Mold distortion meniscus)

Slab molds
IT= Shell shrinkage(z) – (Mold distortion(z) – Mold distortion meniscus)
– (flux thickness(z) – flux thickness meniscus)

Thin slab molds
IT= Shell shrinkage(z) – (Mold distortion(z) – Mold distortion meniscus)
– (flux thickness(z) – flux thickness meniscus)
– (funnel extra length meniscus – funnel extra length(z))
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Claudio Ojeda
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Billet Mold distortion
Billet casting operating
conditions
Elastic modulus
Poisson ratio
Thermal expansion coefficient
Density
Operating conditions
Pour temperature
Water slot heat transfer coefficient
Water temperature, Tw
Ambient temperature
Meniscus level (below top mold)
120 mm
120 mm
1100 mm
0.9
10.15 mm
0.8
360 W m-1 K-1
117 Gpa
0.343
16.0*10-6 K-1
-3
8940 kg m
1540 C
35 kW m-2 K-1
30 C
25 C
100 mm
0.7
|
DISPLACEMENT (mm)
Mold geometry
Slab width
Slab thickness
Mold height
Cu plate thickness
Copper properties
Thermal conductivity
Samarasekera, Brimacombe,
Ironmaking and Steel making, 1982,
Vol. 9, Issue 1, pp 1-15

|
|
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|
|
|
|
|
|
|
|
|
|
|
0.6
|
|
0.5
|
0.4
|
0.27%C, 1.0 m/min
|
0.3
0.2
Total shell shrinkage strain
Mold distortion
Ideal Taper
|
|
0.1
0|
-0.1
-0.2
-0.3
0
100
200
300
400
500
600
700
800
900 1000
DISTANCE BELOW MENISCUS (mm)
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Claudio Ojeda
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Slab Mold distortion
Mold distortion = Wide face expansion + Narrow face distortion
– Wide face expansion
 Transmitted
by clamping forces
 Linearized temperatures of hot and cold plate faces
 moldwidth Tcoldmen  Thotmen Tcold  Thot 
xWF   mold 



2
2
2



– Narrow face distortion
 Linearized
temperatures of hot and cold plate faces
 Water jacket stiffness
3 hot
x NF 
_
_

  cold  T hot  T cold t hot  t cold 


Lx  x 2
2
t cold K1

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
Claudio Ojeda
8
Validation of Thin-slab mold distortion
Heat flux profile
Thin Slab operating conditions
Mold geometry
Slab width
Slab thickness
Mold height
Cu plate thickness
Water slot depth – shallow slots
Water slot thickness
Distance between most slots
Copper properties
Thermal conductivity
Elastic modulus
Poisson ratio
Thermal expansion coefficient
Density
1260 mm
75 mm
1000 mm
60 mm
35 mm
5 mm
4.6 mm
-1
350 W m K
115 Gpa
0.34
-1
17.7*10-6 K -1
-3
8960 kg m
1.
Joong Kil Park, Brian G. Thomas,
Indira V. Samarasekera, and U. Sok
Yoon, Metallurgical and Materials
Transactions B, 2002, vol. 33B, pp
425-436.
Joong Kil Park, Brian G. Thomas,
Indira V. Samarasekera, and U. Sok
Yoon, Metallurgical and Materials
Transactions B, 2002, vol. 33B, pp
437-449.
Operating conditions
2.
-2
-1
Water slot heat transfer coefficient 38.45 kW m K
37.8 C
Water temperature, Tw
Ambient temperature
35 C
Meniscus level (below top mold) 100 mm
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Claudio Ojeda
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Validation of Thin-slab Mold distortion
Wide face temperature
Wide face expansion
600
TEMPERATURE (C)
500
400
y = -0.269x + 444.17
Thot
300
Tref
200
meniscus
y = -0.0495x + 116.57
100
Tcold
1.6
WIDE FACE EXPANSION (mm)
Hot face temperature
Cold face temperature
Hot face linearized temperature
Cold face linearized temperature
Wide face expansion from Con1d results
Wide face expansion from 3D simulation
1.4
1.2
1
0.8
meniscus
0.6
0.4
0.2
0
0
0
100
200
300
400
500
600
700
800
900 1000
DISTANCE BELOW TOP OF MOLD (mm)
0
100
200
300
400
500
600
700
800
900 1000
DISTANCE FROM TOP OF MOLD (mm)
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Claudio Ojeda
10
Validation conventional slab mold distortion
Conventional Slab operating cond.
Mold geometry
Slab width
Slab thickness
Mold height
Cu plate thickness
Water slot depth – shallow slots
Water slot thickness
Distance between most slots
Copper properties
Thermal conductivity
Elastic modulus
Poisson ratio
Thermal expansion coefficient
Density
914 mm
220 mm
700 mm
60 mm
25 mm
5 mm
35 mm
Heat flux profile
q  2.68  31.90.084 z 
q  2.68  2.58 z  0.084
-1
374 W m K
117 Gpa
0.343
-1
0.0<z<0.084m
0.084<z<0.7m
B.G.Thomas, G. Li, A. Moitra
and D. Habing: ISS
transactions, October 1998,
pp 125-143.
17.7*10-6 K-1
-3
8940 kg m
Operating conditions
Water slot heat transfer coefficient 35 kW m-2 K -1
15 C
Water temperature, Tw
Ambient temperature
35 C
Meniscus level (below top mold) 84 mm
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Claudio Ojeda
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Validation conventional slab mold distortion
Wide face temperature
Narrow face temperature
400
300
Hot face temperature
Cold face temperature
Linearized hot face temperature
Linearized cold face temperature
350
Hot face temperature
Cold face temperature
Linearized hot face temperature
Linearized cold face temperature
250
TEMPERATURE (C)
TEMPERATURE (C)
300
250
y = -0.2489x + 320.42
200
Thot
Tref
150
meniscus
200
Thot
y = -0.1678x + 220.98
150
meniscus
100
100
Tcold
Tcold
50
0
50
y = -0.032x + 59.535
y = -0.0769x + 95.16
0
100
200
300
400
500
600
DISTANCE BELOW TOP OF THE MOLD (mm)
700
0
0
100
200
300
400
500
600
700
DISTANCE BELOW TOP OF THE MOLD (mm)
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Claudio Ojeda
12
Validation conventional slab mold distortion
Wide face expansion + Narrow face distortion
4
MOLD DISTORTION (mm)
3.5
3
Narrow face distortion calculated in the 3D simulation
Analitical calculation of the mold distortion
2.5
2
1.5
meniscus
1
0.5
0
-0.5
-1
0
100
200
300
400
500
600
700
DISTANCE BELOW TOP OF THE MOLD (mm)
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Claudio Ojeda
13
Shell shrinkage

Heat flux profile
– Importance of changes in meniscus area

Casting speed
– Increasing casting speed increases instantaneous and average
heat flux but decreases time for shrinkage.

Mold length
– For the same conditions higher mold length causes higher
shrinkage

Steel grade
– Differences between low, peritectic and high carbon content
steels

Mold Powder composition
– Differences in solidification temperature
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Claudio Ojeda
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Effect of heat flux profile




Shell shrinkage controlled by heat flux profile.
Higher heat flux causes more shrinkage.
Shell shrinkage sensitive to minor changes specially near the
meniscus.
Mean heat flux determined with*:
QG  4.63 10 m
6
0.09
T
1.19
flow
0.47
C
V

  0.107  %C  2  


 
1  0.152exp 

  0.027   


QG is the mean heat flux (MW/m2), m is the powder viscosity at 1300 oC, (Pa-s),
Tflow is the melting temperature of the mold flux (oC), Vc is the casting speed
(m/min), and %C is the carbon content
–
*C. Cicutti, M. Valdez and T. Perez, "Mould Thermal Evaluation in a Slab Continuous Casting Machine,"
85th Steelmaking Conference, (Nashville, TE, USA), Iron and Steel Society, Inc. (USA), Vol. 85, 2002,
97-107.
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Claudio Ojeda
15
Effect of heat flux
6
5
Higher Meniscus heat flux
Higher mold exit heat flux
4
SHELL SHRINKAGE (mm)
HEAT FLUX (MW/m2)
5
Heat flux average = 1.466 MW/m2
0.08%C, 1.5 m/min
3
2
3
Higher meniscus heat flux
Higher mold exit heat flux
2
Heat Flux Average=1.466 MW/m2
0.08%C, 1.5 m/min
1
1
0
4
0
100
200
300
400
500
600
700
DISTANCE BELOW MENISCUS (mm)
800
0
0
100
200
300
400
500
600
700
800
DISTANCE BELOW MENISCUS (mm)
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Claudio Ojeda
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Effect of casting speed
– Higher casting speed causes higher heat flux (more
shrinkage) but less dwell time (less shrinkage).
Net effect: less shrinkage
SHELL SURFACE TEMPERATURE(C)
7
HEAT FLUX (MW/m2)
6
5
High heat flux q=6.5(t+1)
-0.5
4
3
2
1
0
0
10
20
30
40
50
TIME BELOW MENISCUS (mm)
60
1500
Width: 200 mm
1400
0.07%C, Flux E
1.1 m/min
1.5 m/min
1.9 m/min
1300
1200
1100
1000
0
100
200
300
400
500
600
700
800
DISTANCE-BELOW-MENISCUS(mm)
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Claudio Ojeda
17
Effect of casting speed
18
TOTAL SHELL SHRINKAGE STRAIN (%)
1.5
SHELL THICKNESS (mm)
16
14
12
10
8
6
Width: 200 mm
0.07%C, Flux E
1.1 m/min
1.5 m/min
1.9 m/min
4
2
0
0
100
200
300
400
500
600
700
DISTANCE BELOW MENISCUS (mm)
800
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
Width: 200 mm
0.6
0.5
0.07%C, Flux E
0.4
1.1 m/min
1.5 m/min
1.9 m/min
0.3
0.2
0.1
0
0
100
200
300
400
500
600
700
800
DISTANCE-BELOW-MENISCUS(mm)
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Claudio Ojeda
18
Effect of casting speed

Effect of casting speed on Ideal taper
1.5
1.4
Width: 200 mm
1.3
0.07%C, Flux E
1.1 m/min
1.5 m/min
1.9 m/min
1.2
IDEAL TAPER (%)
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
0
100
200
300
400
500
600
700
800
DISTANCE BELOW MENISCUS (mm)
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19
Effect of casting speed
Peritectic steels
High carbon steels
1.5
1.5
1.4
1.4
1.2
IDEAL TAPER (%)
1.1
|
%
%
%
%
Carbon Content, 1.2 m/min Casting Speed
Carbon Content, 1.5 m/min Casting Speed
Carbon Content, 1.18 m/min Casting Speed
Carbon Content, 1.5 m/min Casting Speed
1
|
Width: 200 mm
0.9
|
|
0.8
|
0.7
|
|
0.6
|
0.5
0.4
|
|
|
|
|
|
|
|
0.3
0|
0
1.1
|
1
0.9
%
%
%
%
Carbon Content, 1.2 m/min Casting Speed
Carbon Content, 1.5 m/min Casting Speed
Carbon Content, 1.04 m/min Casting Speed
Carbon Content, 1.3 m/min Casting Speed
Width: 200 mm
0.8
|
|
|
0.7
|
0.6
|
|
0.5
|
0.4
|
|
|
|
|
|
|
|
|
|
0.2
|
|
0.1
0.27
0.27
0.47
0.47
1.2
0.3
|
0.2
-0.1
|
|
1.3
IDEAL TAPER (%)
0.13
0.13
0.16
0.16
1.3
0.1
|
0|
100
200
300
400
500
600
700
DISTANCE BELOW MENISCUS (mm)
800
-0.1
0
|
100
200
300
400
500
600
700
800
DISTANCE BELOW MENISCUS (mm)
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Claudio Ojeda
20
Effect of casting speed
Cases
0B
1B
2B
Grade
low carbon
Tliquidus
1527
Carbon content
0.07%
%Mn, %Si
.3%, .03%
%P, %S
.01%, .007%
Powder type
E (220)
Viscosity (Pa-s)
0.083
sol. Temp ( C )
1120
Casting Speed (m/min)
1.1 1.5
1.9
Tundish temp (C)
1567
Heat Flux (MW/m2)
Heat Average (MW/m2)
1.70 1.94 2.13
Surf Temp (exit (C)
1016 1032 1044
Shrinkage (mm) CON1D
13.18 12.36 11.74
Shrinkage 50mm CON2D
2.40
1.84 1.41
Shrinkage (mm) CON2D
6.80
6.29 5.92
Taper (%/mold) CON2D
1.36
1.26 1.18
Flux layer (mm)
1.47
1.25 1.14
Mold distortion+expansion (mm) -0.43 -0.55 -0.65
Ideal NF (mm)
5.70
5.60 5.45
Ideal NF (%)
1.14
1.12 1.09
3B
4B
peritectic
1527
0.08%
0.42%, 0.01%
.07%, .07%
E (220)
0.083
1120
1.3
1.45
1555
1.83
1005
8.98
2.47
6.98
1.40
1.39
-0.49
6.05
1.21
1.94
1010
8.68
2.27
6.81
1.36
1.33
-0.55
6.05
1.21
5B
6B
medium carbon
1521
0.13%
.57%, .22%
.07%, .07%
C (666)
0.192
1215
1.2
1.5
1555
1.77
1001
8.30
2.87
7.42
1.48
2.34
-0.46
5.55
1.11
1.94
1012
7.84
2.47
7.08
1.42
2.07
-0.55
5.55
1.11
7B
8B
medium carbon
1517
0.16%
.87%, .14%
.007%, .005%
C (666)
0.192
1215
1.18
1.5
1559
1.76
1006
11.03
2.36
6.79
1.36
2.23
-0.46
5.00
1.00
1.94
1018
10.47
1.96
6.44
1.29
1.91
-0.55
5.10
1.02
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9B
10B
high carbon
0.27%
E(220)
0.083
1120
1.2
1559
1.77
1006
8.64
1.94
6.29
1.26
1.99
-0.46
4.75
0.95
1.5
1.94
1018
8.16
1.56
5.96
1.19
1.76
-0.55
4.75
0.95
11B
12B
high carbon
1490
0.47%
.75%, .22%
.018%, .007%
E (220)
0.083
1120
1.04
1.3
1542
1.67
972
8.09
1.81
6.05
1.21
1.99
-0.41
4.50
0.90
Claudio Ojeda
1.83
984
7.17
1.46
5.73
1.15
1.76
-0.49
4.45
0.89
21
Effect of casting speed
Higher casting speed causes higher heat flux (more shrinkage) but less dwell time
(less shrinkage).
Measured data of heat flux*
Net effect: no change in shrinkage
8
Flux E
Slab width: 1000 mm
Slab thickness: 200 mm
Working mold length: 800 mm
o
Pouring temperature: 1567 C
HEAT FLUX (MW/m2)
|
6
X
|
|
X
X
|
3
X
|
X
|
2
X
|
X|
X|
100
200
X|
X|
X|
X|
X|
X|
X|
X|
X|
300
400
500
600
700
DISTANCE BELOW MENISCUS (mm)

X|
X|
X|
1400
Flux E, 0.07%C, 1.1 m/min
Flux E, 0.07%C, 1.5 m/min
Flux E, 0.07%C, 1.9 m/min
Flux E, 0.08%C, 1.3 m/min
Flux E, 0.08%C, 1.45 m/min
X|
X|
X|
1350
|
X|
X
X|
1300
X|
X|
1250
X|
X|
X|
X|
X|
X|
X|
1150
X|
1100
0
X|
1200
X|
1
0
1450
0.07%C, 1.1 m/min, avg q: 1.39 MW/m2
0.07%C, 1.5 m/min, avg q: 1.61 MW/m2
0.07%C, 1.9 m/min, avg q: 1.8 MW/m2
2
0.08%C, 1.3 m/min, avg q: 1.48 MW/m
0.08%C, 1.45 m/min, avg q: 1.56 MW/m2
X
|
4
1500
TEMPERATURE(C)
7
800
TOTAL SHELL SHRINKAGE STRAIN (%)
X
5
1.3
X
1550 X|
0
100
200
300
X|
X|
400
X|
X|
500
X|
X|
X|
600
X|
X|
700
X|
800
1.2
1.1
1
X|
X|
X|
X|
X|
X|
X|
X|
0.7
X|
0.6
X|
|
X
X|
0.5
0.4
X|
X|
X|
|
X|
0.1 X|
X||
X
|
X
X
|
0
X|
X|
X|
0.8
0.2
X|
X|
X|
0.9
0.3
X|
X|
X|
X|
0
DISTANCE-BELOW-MENISCUS(mm)
X
100
200
300
Flux E, 0.07, 1.1 m/min
Flux E, 0.07, 1.5 m/min
Flux E, 0.07, 1.9 m/min
Flux E, 0.08, 1.3 m/min
Flux E, 0.08, 1.45 m/min
400
500
600
700
800
DISTANCE-BELOW-MENISCUS(mm)
*C. Cicutti, M. Valdez and T. Perez, "Mould Thermal Evaluation in a Slab Continuous Casting
Machine," 85th Steelmaking Conference, (Nashville, TE, USA), Iron and Steel Society, Inc. (USA), Vol.
85, 2002, 97-107.
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Claudio Ojeda
22
Effect of mold length

Mold length
– For the same conditions (including heat flux), shell
shrinkage strains for different mold lengths can be
approximated with the same curve
– Shell shrinkage for different mold lengths can be
obtained truncating the curves at the desired working
mold length
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Claudio Ojeda
23
Effect of mold length
7
TOTAL SHELL SHRINKAGE STRAIN (%)
1.5
HEAT FLUX (MW/m2)
6
5
q=6.5(t+1)
-0.5
4
3
2
1
0
0
10
20
30
40
TIME BELOW MENISCUS (s)
50
60
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.07%C, Flux E
0.4
1.1 m/min
1.5 m/min
1.9 m/min
0.3
0.2
0.1
0
0
100
200
300
400
500
600
700
800
DISTANCE-BELOW-MENISCUS(mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
24
Effect of steel grade


Steel grade effect
– Higher plastic strain
– Higher thermal expansion
Thermal Linear Expansion (m/m)
0.02

0.01
0.005
0
Reference Temperature = Solidus

-0.005
-0.01
-0.015
-0.02
800
1000
1200
Temperature (oC)
Peritectic steels (0.1%)
– Deeper oscillation marks
causes lower heat flux
– Higher thermal expansion
– Final result the smallest shell
shrinkages
0.003%C
0.044%C
0.1%C
0.27%C
0.44%C
0.015
Low carbon steels (>0.08%C)
1400
1600
High carbon steels (>0.2%)
– Shallow oscillation marks
Higher heat flux
– Small inelastic strain
Thermal strain
– Heat flux and shell shrinkage
similar to low carbon steels
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
25
Effect of steel grade
5X
5
X|
|
X
X
HEAT FLUX (MW/m2)
4
|
X
3
0.07%C, Flux E
0.08%C, Flux E
0.13%C, Flux C
0.16%C, Flux C
0.47%C, Flux E
X
|
|
|
X
X
X
|
2
X
|
X
|
X
|
|
X
|
X
|
1
0
0
3
X
|
2
4
Casting speed: 1.5 m/min
100
200
300
X
|
X
|
400
X
|
X
|
500
X
|
X
|
600
X
|
X
|
700
DISTANCE BELOW MENISCUS (mm)
|
X
1
0
800
SHELL SURFACE TEMPERATURE (C)
1550
|
X
Casting speed: 1.5 m/min
0.07%C, Flux E
0.08%C, Flux E
0.13%C, Flux C
|
0.16%C, Flux C
X
0.47%C, Flux E
1500 X|
X|
1450 X|
X
|
1400
|
X
X|
1350
X|
X |
1300
|
X
|
|
X
1250
|
|
X
|
|
|
|
X
1200
|
|
|
|
|
|
|
|
|
X
X
X
X
X
X
X
X
X
X
1150
X
X
X
X
X
X
X
X
1100
0
100
200
300
400
500
600
700
800
DISTANCE-BELOW-MENISCUS(mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
26
Effect of steel grade
14
13
SHELL THICKNESS (mm)
12
11
10
9
|X
8
|X
|X
|X
|X
|X
|X
|X
|X
|X
|X
|X
7
|X
|X
6
|X
|X
5
|X
4
1
0 X|
0
Casting speed: 1.5 m/min
0.07%C, Flux E
0.08%C, Flux E
0.13%C, Flux C
|
0.16%C, Flux C
X
0.47%C, Flux E
|X
|X
|X
3
2
|X
|X
|X
|X
|X
|X
100
200
300
400
500
600
700
DISTANCE BELOW MENISCUS (mm)
800
TOTAL SHELL SHRINKAGE STRAIN (%)
1.4
1.3
1.2
1.1
1
0.9
0.8
X
0.7
X
X
X
X
X
0.6
X
X
0.5
|
X
X |
0.1 X |
X| |
|
0 XX|
0
|
|
|
|
100
200
|
|
X
X
X
|
|
|
|
X
X
X
X
|
|
|
|
Casting speed: 1.5 m/min
0.07%C, Flux E
0.08%C, Flux E
0.13%C, Flux C
|
0.16%C, Flux C
X
0.47%C, Flux E
|
X
X
0.3
|
|
|
X
0.4
0.2
X
X
X
300
400
500
600
700
800
DISTANCE-BELOW-MENISCUS(mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
27
Effect of steel grade
1.3
1.4
1.2
Powder E, meniscus to mold exit
Powder C, meniscus to mold exit
Powder E, 50 mm to mold exit
Powder C, 50 mm to mold exit
1.3
1.2
1.1
1
1
0.9
0.8
0.7
0.6
0.5
0.9
0.8
0.7
X
0.6
X
X
0.5
X
X
0.4
0.4
0.3
0.3
0.2
0.2
0.1
X
X
|
X
|
|
X
|
X
|
X
|
X
|
X
|
X
|
X
|
X
|
X
|
X
X
|
X
|
|
|
|
|
|
|
0 X|
0.1
0
Casting speed: 1.5 m/min
0.07 %C, Flux E
0.08 %C, Flux E
0.13 %C, Flux C
|
0.16 %C, Flux C
X
0.47 %C, Flux E
1.1
IDEAL TAPER (%)
TOTAL SHELL SHRINKAGE STRAIN (%)
1.5
0
0.1
0.2
0.3
CARBON CONTENT (%)
0.4
0.5
-0.1
0
100
200
300
400
500
600
700
800
DISTANCE BELOW MENISCUS (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
28
Effect of steel grade
Grade
Tliquidus
Carbon content
%Mn, %Si
%P, %S
Powder type
viscosity (Pa-s)
sol. Temp (C)
Flux comsumption rate (kg/t)
Solid flux velocity ratio (V/Vc)
Oscilation mark depth (mm)
Casting Speed (m/min)
Tundish temp (C)
Heat flux average (MW/m 2)
Surf Temp (exit (C)
Shrinkage (mm) CON1D
Shrinkage 50mm CON2D
Shrinkage (mm) CON2D
Taper (%/mold) CON2D
Flux layer (mm)
Narrow face distortion (mm)
Wide face expansion (mm)
Ideal NF (mm)
Ideal NF (%)
low carbon
1527
0.07%
.3%, .03%
.01%, .007%
E (220)
0.083
1120
0.245
0.02
0.24
1.5
1567
peritectic
1527
0.08%
0.42%, 0.01%
.07%, .07%
E (220)
0.083
1120
0.245
0.0185
0.24
1.5
1567
medium carbon
1521
0.13%
.57%, .22%
.07%, .07%
C (666)
0.192
1215
0.245
0.0026
0.34
1.5
1567
1.61
1126.7
9.40
2.73
6.21
1.24
1.30
-1.54
1.07
5.37
1.0737
1.59
1134.3
5.96
2.62
6.04
1.21
1.31
-1.51
1.06
5.19
1.037
1.29
1250.2
3.12
1.43
3.72
0.74
1.98
-1.32
0.96
2.09
0.418
medium carbon
1517
0.16%
.87%, .14%
.007%, .005%
C (666)
0.192
1215
0.245
0.0091
0.34
1.5
1567
1.37
1218
6.52
1.33
3.74
0.75
1.97
-1.35
1.01
2.11
0.421
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
high carbon
1490
0.47%
.75%, .22%
.018%, .007%
E (220)
0.083
1120
0.05
0.009
0.05
1.5
1567
1.64
1114.7
4.96
2.31
4.61
0.92
1.51
-1.71
1.45
3.36
0.672
Claudio Ojeda
29
Effect of mold flux composition

Study of the effect of Powder composition in
shell shrinkage
– Mold powder viscosity
 Slight
changes in shell shrinkage
– Mold powder Solidification temperature
 Higher
solidification temperature causes a lower heat flux
and consequently lower shell shrinkage
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
30
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1
1
0.9
0.9
0.8
0.7
|
|
|
|
|
|
|
|
|
|
|
|
IDEAL TAPER (%)
TOTAL SHELL SHRINKAGE STRAIN (%)
Effect of mold flux composition
|
|
|
0.6
|
|
0.5
|
0.4
|
0.3
|
|
0.1
|
|
|| |
0
|
0.07%C, 1.5 m/min
0.8
0.7
|
|
0.6
|
|
0.5
|
0.4
0.3
|
o
Flux solidification temperature: 1040 C
o
Flux solidification temperature: 1120 C
Flux solidification temperature: 1160 oC
Flux solidification temperature: 1215 oC
|
0.2
0
0.07%C, 1.5 m/min
o
100
200
300
400
500
600
700
DISTANCE-BELOW-MENISCUS(mm)
Flux solidification temperature: 1040 C
Flux solidification temperature: 1120 oC
Flux solidification temperature: 1160 oC
Flux solidification temperature: 1215 oC
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.2
0.1
0|
800
-0.1
0
100
200
300
400
500
600
700
800
DISTANCE BELOW MENISCUS (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
31
Effect of mold flux composition
Grade
Tliquidus
Carbon content
%Mn, %Si
%P, %S
Powder type
viscosity (Pa-s)
sol. Temp (C)
Flux comsumption rate (kg/t)
Solid flux velocity ratio (V/Vc)
Oscillation mark depth (mm)
Casting Speed (m/min)
Tundish temp (C)
Heat Flux average (MW/m 2)
Surf Temp (exit (C)
Shrinkage (mm) CON1D
Shrinkage 50 mm CON2D
Shrinkage (mm) CON2D
Taper (%/mold) CON2D
Flux layer (mm)
Narrow face distortion (mm)
Wide face expansion (mm)
Ideal NF (mm)
Ideal NF (%)
low carbon
1527
0.07%
.3%, .03%
.01%, .007%
A (RB1 - B)
0.225
1160
0.25
0.008
0.24
1.5
1567
1.41
1202.1
7.72
2.12
4.98
1.00
1.59
-1.36
0.94
3.81
0.76
C (666)
0.192
1215
0.25
0.015
0.24
1.5
1567
D (155)
0.115
1040
0.25
0.011
0.24
1.5
1567
E (220)
0.083
1120
0.25
0.020
0.24
1.5
1567
1.36
1220
7.24
1.88
4.64
0.93
1.73
-1.29
0.88
3.32
0.66
1.71
1090
10.36
3.08
6.82
1.36
1.12
-1.65
1.17
6.15
1.23
1.61
1126.7
9.40
2.73
6.21
1.24
1.30
-1.54
1.07
5.37
1.07
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
32
Conclusions





More taper is needed near the top of the mold to
compensate the more shrinkage of the steel shell.
As casting speed increases, shrinkage decreases.
Shell shrinkage depends mainly of the heat flux profile
which depends of the casting speed and interface
conditions.
Peritectic steels generally requires smaller taper (due to
the lower heat flux caused by bigger oscillation marks).
Mold powders with higher solidification temperatures
require less taper (due to lower heat flux).
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
33
Extra length in Funnel

In thin slab casting there is a taper induced by
the change in perimeter of the wide face,
because of the funnel shape.
 a 2  b 2

 2ab 
EL  2
sin 1  2

a

2 
2
b
a

b





University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
34
Extra length in funnel
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
35
Thin slab casting ideal taper


Higher casting speeds than conventional
slab casting.
Funnel shape effect.
IT= Shell shrinkage(z) – (Mold distortion(z) – Mold distortion meniscus)
– (flux thickness(z) – flux thickness meniscus)
– (funnel extra length meniscus – funnel extra length(z))
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
36
Thin slab casting conditions

Operating Conditions.
Mold geometry
Slab thickness
Mold Heigth
Cu plate thickness
Funnel
Funnel width: a
Funnel depth at top: b
Funnel heigth
Description
Difficult to cast low carbon
Low Carbon
Approximately Peritectic
High Carbon
Carbon Content
0.04%
0.06%
0.074%
0.83%
49.78 mm
1100 mm
121 mm
1020 mm
60 mm
750 mm
Casting Speed
4.5 m/min
4.7 m/min
3.9 m/min
4 m/min
Mold Width
1280 mm
1100 mm
1020 mm
1020 mm
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Meniscus level
83 mm
83 mm
83 mm
58 mm
Claudio Ojeda
37
Thin slab casting ideal taper
Heat flux and surface temperatures

1550
|
4.5
4
|
2
HEAT FLUX (MW/m )
|
3.5
|
|
3
|
|
|
2.5
|
|
|
2
|
|
|
|
|
1.5
0
|
0
|
|
|
|
|
0.04% C, 4.5 m/min Casting speed, 1280 mm Mold Width
0.055% C, 4.7 m/min Casting speed, 1105 mm Mold Width
0.074% C, 3.9 m/min Casting speed, 1020 mm Mold Width
0.83% C, 3.7 m/min Casting Speed, 1021 mm Mold Width
1
0.5
|
100
200
300
400
500
600
700
800
900 1000
DISTANCE BELOW MENISCUS (mm)
SHELL SURFACE TEMPERATURE(C)
5
1500
1450
|
|
0.04% C, 4.5 m/min Casting Speed, 1020 mm Mold Width
0.055% C, 4.7 m/min Casting Speed, 1105 mm Mold Width
0.074% C, 3.9 m/min Casting Speed, 1020 mm Mold Width
0.83% C, 3.7 m/min Casting Speed, 1021 mm Mold Width
|
|
1400
|
1350
|
|
1300
|
|
1250
|
|
1200
|
|
|
1150
|
|
1100
|
|
|
|
|
|
|
1050
1000
0
100
200
300
400
500
600
700
800
|
|
900 1000
DISTANCE-BELOW-MENISCUS(mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
38
Thin slab casting ideal taper

Solidified steel shell thickness
10
0.04% C, 4.5 m/min, 1280 mm Mold Length
0.055% C, 4.7 m/min, 1105 mm Mold Length
0.074% C, 3.9 m/min, 1020 mm Mold Length
0.83% C, 4.0 m/min, 1021 mm Mold Length
SHELL THICKNESS (mm)
9
8
|
7
6
|
|
|
|
|
|
5
|
|
|
4
|
|
|
3
|
|
|
2
|
|
|
1
|
|
0|
0
|
100
200
300
400
500
600
700
800
900 1000
DISTANCE BELOW MENISCUS (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
39
Thin slab casting ideal taper

Difficult to cast low carbon
6
0.04% Carbon Content, 4.5 m/min Casting Speed
1280 mm Mold Width
5.5
5
Steel shell shrinkage
Mold narrow face distortion
Mold flux layer thickness
Funnel extra length
Ideal Taper
4.5
4
|
DISTANCE (mm)
3.5
3
2.5
2
|
|
1.5
|
|
1
|
|
0.5
|
0|
|
-0.5
|
-1
|
|
|
|
|
|
|
|
|
|
|
-1.5
-2
0
100
200
300
400
500
600
700
800
900 1000
DISTANCE BELOW MENISCUS (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
40
Thin slab casting ideal taper

Common low carbon steel
6
0.055 % Carbon Content, 4.7 m/min Casting Speed
1100 mm Mold Width
5.5
5
Steel shell shrinkage
mold narrow face distortion
Mold flux layer thickness
Funnel extra length
Ideal Taper
4.5
DISTANCE (mm)
4
|
3.5
3
2.5
2
1.5
1
0.5
0|
|
-0.5
|
-1
|
|
|
-1.5
-2
0
100
200
|
|
300
|
400
|
|
500
|
|
600
|
|
700
|
|
800
|
|
|
900 1000
DISTANCE BELOW MENISCUS (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
41
Thin slab casting ideal taper

Approximately peritectic steel
6
0.074% Carbon Content, 3.9 m/min Casting Speed
1020 mm Mold Width
5.5
5
Steel shell shrinkage
Mold narrow face distortion
Mold flux layer thickness
Funnel extra length
Ideal Taper
4.5
DISTANCE (mm)
4
|
3.5
3
2.5
2
1.5
1
0.5
0|
|
-0.5
|
|
|
-1
|
|
|
|
-1.5
-2
0
100
200
300
400
|
|
500
|
600
|
|
700
|
|
800
|
|
|
900 1000
DISTANCE BELOW MENISCUS (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
42
Thin slab casting ideal taper

High carbon steel
DISTANCE (mm)
6
5.5 0.83% Carbon Content, 3.7 m/min Casting Speed
1020 mm Mold Width
5
Steel shell shrinkage
4.5
Mold distortion
Mold flux layer thickness
4
Enter-XY Data
3.5
|
Ideal Taper
3
2.5
2
1.5
1
0.5
0|
-0.5 |
-1
|
-1.5
|
|
-2
|
|
-2.5
|
|
|
|
|
|
-3
|
|
|
-3.5
0
100 200 300 400 500 600 700 800
|
|
|
900 1000
DISTANCE BELOW MENISCUS (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
43
Thin slab casting ideal taper
0.3
0.2
0.04%C, 4.5 m/min
0.055%C, 4.7 m/min
0.074%C, 3.9 m/min
0.83%C, 3.7 m/min
0.1
IDEAL TAPER (%)
|
0|
|
-0.1
|
|
-0.2
|
|
-0.3
|
-0.4
|
|
|
|
|
-0.5
|
|
|
|
|
-0.6
-0.7
0
100
200
300
400
|
|
|
|
500
|
600
|
|
700
800
900 1000
DISTANCE BELOW MENISCUS (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
44
Thin slab casting ideal taper

Results
Case
(carbon
content %)
Recorded
T (°C)
Recorded
Heat Flux
(kW/m2)
Computed
T (°C)
Computed
Heat Flux
(kW/m2)
Suggested
Taper used
Taper from
currently
Calculations (%/mould)
(%/mold)
0.04
11.66
2732.48
9.44
2346
0.23
0.85
0.055
8.33
2310
9.79
2355
0.0
0.95
0.074
7.22
2177
8.67
2152
-0.01
0.95
0.83
7.88
2310
7.98
2149
-0.42
1.2
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
45
Thin slab casting ideal taper

Results
– The shell shrinks more on the top of the mold than in
the bottom of the mold, so it is difficult to match the
shrinkage of the shell shell with a linear Taper.
– Mold distortion, flux layer thickness and extra length
of funnel significantly affect the Ideal taper.
– The Ideal Taper predicted is for all cases smaller
than the taper used currently.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
46
Effect of ferrostatic pressure
TOTAL SHELL SHRINKAGE STRAIN (%)
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
Without ferrostatic pressure
Width: 120 mm with Ferrostatic pressure
Width: 200 mm with ferrostatic pressure
0.3
0.2
0.1
0
0
100
200
300
400
500
600
700
800
900 1000
DISTANCE-BELOW-MENISCUS(mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
47
Conclusions
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More taper is needed near the top of the mold, such as achieved using
parabolic taper.
As casting speed increases, shrinkage decreases (for same conditions
and heat flux profile).
Mold length affects the taper only by extending the nonlinear curve (for the
same conditions and heat flux profile).
Mold taper depends mainly on the heat flux profile, which in turn depends
on the casting speed and interface conditions (powder, steel grade, etc.).
Peritectic steels generally require slightly less taper than either low or high
carbon steels, owing to their lower heat flux.
Mold powders with higher solidification temperature have lower heat flux
(compared with both oil lubrication or low solidification temperature
powders) and consequently have less shrinkage and less ideal taper
(other conditions staying the same).
Flux layer thickness, mold distortion and extra length of funnel (thin slabs)
make important contributions to Ideal Taper.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab •
Claudio Ojeda
48