A. Moinet & A. W. Cramb A static model for the meniscus AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks 1 Elimination or minization of oscillation marks – A path to improved cast surface quality static model of the meniscus for continuous casting A. Moinet & A.W. Cramb 9th AISI / DOE TRP Industry briefing session
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A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
1
Elimination or minization of oscillation marks – A path to improved cast surface quality
static model of the meniscus for continuous casting
A. Moinet & A.W. Cramb
9th AISI / DOE TRP Industry briefing session
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
2
Outline• Introduction
– Continuous casting– The meniscus area– Oscillation marks
• Model– Numerics– Description of the problem– Simplifications:
• Limits• Turbulence• Shell removal
• Results– Determination of key parameters for this simulation– Effect of heat input and/or insulating panel on oscillation marks
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
3
Introduction: continuous casting• Liquid steel is injected
through the nozzles, and cools down alongthe mold
• To prevent sticking, molten slag and moldoscillations (negativestrip time)
• Various defects are thought to be created atthe meniscus
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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Description of the meniscus area• Heat input: hot metal• Conduction through
liquid metal: convection, diffusion, turbulence
• Conduction throughsolid metal: diffusion
• Mushy zone: latent heat release
• Liquid and solid slag : conduction, radiation
• Free surface movements, surface tension
• Solidified slag: glassy/crystallinestructure
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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Oscillation marks• Perpendicular to the
withdrawal direction• Typically, one mark per
oscillation of the mold• Up to a few millimeters
deep• Source of other defects
(inclusions, cracks), necessity of hot rolling
• Observations: formation happen at the meniscuslevel, heat release
• No certain explaination
Withdrawal direction
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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Theory for oscillation mark formation: meniscus overflow
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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Goal of the project• The partial solidification of the meniscus is likely to be
responsible for oscillation marks• We need to better understand what’s going on near the
meniscus• Eventually, the meniscus area will be modelled, including
all the phenomena aforementionned (heat, flow, freesurface, thermal radiative transfer)
• Simplifications must be done, limit boundaries must beformulated
• A preliminary static thermal model for the meniscus wasdesigned
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
8
Numerical methods• Heat transport:
– Governed by Fourier’s law:– Continuous second order differential equations can be solved by
finite element methods
• Solidification modeling– Latent heat release in regions where:
• Tsolidus< T < Tliquidus
– Use of effective heat capacity
•
+∇=⎟⎠⎞
⎜⎝⎛ ∇+∂∂
= QTkTtTC
dtdTC pp
2.Vρρ
TfHC
tTC
tT
TfH
tfHQ LheatlatentheatlatentpLL ∂
∂=⇒
∂∂
=∂∂
∂∂
=∂∂
=•
ρρρ
•
+∇=⎟⎠⎞
⎜⎝⎛ ∇+∂∂
= QTkTtTC
dtdTC peffeffp
2.Vρρ
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
– The effective heat capacity is not continuous and it can be much larger than the actual heat capacity
• Ex: δ-ferrite: Cp = 800 J/K/kg, Cpeff = 9000 J/K/kg – The area where to use Cpeff instead of Cp moves: the
mesh cannot be easily adapted– Various methods:
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
10
Description of the model
100 mm 50 mm
50 m
m10
mm
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
11
Description of the model• In an actual (transcient)
conditions, the solidified steelis withdrawn. If not, solid steelaccumulates and thecalculated thickness of theshell will not be realistic.
• A flow that simulates steelwithdrawal was calculated andapplied to all calculations
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
12
Temperature at boundaries: issues• Steel is injected in the mold at a
temperature slightly superior to theliquidus temperature
• From the exit of the nozzle to the surface of the mold, there exists a temperaturegradient that is a function of the flow fieldand the conductivity of the metal
• Both the flow field and the steelconductivity are not trivial
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
13
Temperature at boundaries: dependance on flow field
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
14
Temperature at boundaries: dependance on flow field
• Temperature drop is not linear or uniform within the mold• It is stronger around the meniscus• Horizontal gradient is smaller on border 1• Temperature has to be set on border 2
Border 1
Bor
der 2
Boundary conditions:
T = Tsuperheat
No solidification but
T = Tliquidus
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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Effective thermal conductivity in themeniscus area
• Effective thermal conductivity decreaseslinearly with the distance to the surface of the mold
• Rather than calculating theturbulences at each step, effective thermal conductivitywill be approximated by a linear function of thedistance to the mold
k-ε model: Effective thermal conductivity(K/m/s) around the meniscus [Fluent simulation]
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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To summarize
• The mold is 100 mm thick, the slag layer is 1-2 mm thick and the 50 mm around the meniscus are investigated
• The heat input: fixed temperature before the meniscus• The heat release: water cooling, forced convection, function of h
(convection coefficient)• Heat conduction in the liquid metal: proportional to the distance to the
border• We want to see how various parameters affect the meniscus
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
17
To summarize
20,000 W/K/m2water cooling convection coefficient
27 °CSuperheat
0.02 m/sWithdrawal velocity
casting parameters
1000 kg/m3Density
noRadiative heat transfer
1 W/m/KThermal conductivity in solid
Slag
800 J/K/kgHeat capacity
7000 kg/m3Density
250,000 J/kgLatent heat of fusion
5,000 W/m/KEffective thermal conductivity in liquid
40 W/m/KThermal conductivity in solid
1530 °CLiquidus
1492 °CSolidus
Steel
Steel (liquid)Steel (solid)
slag
Copper mold
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
18
Effects of superheat
Superheat = 27°C
Superheat = 18°C
Superheat = 36 °C
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
19
Effects of water cooling convection coefficient
h = 20,000 W/K/m2
h = 40,000 W/K/m2
h = 10,000 W/K/m2
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
20
Effects of effective conductivity in the liquid steel
Keff max = 5,000 W/m/K
Keff max = 6,000 W/m/K
Keff max = 4,000 W/m/K
No effective conductivity
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
21
Effects of radiative heat transfer in the slag layer
No radiative heat transfer
Absorption coefficient = 5000 m-1
Absorption coefficient = 2000 m-1
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
22
Effects of the slag layer conductivity
k = 0.5 W/M/K
k = 1 W/m/K
k = 2 W/m/K
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
23
Heat input• Heat input could reduce heat transfer, in order to prevent
freezing of the meniscus• The effect of heat input at the meniscus level (a quantity
similar to the heat flux, 1 MW/m2) was monitored
steel
slag
mold
Heated area
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
24
Heat input (1 MW/m2)
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
25
Heat input (1 MW/m2)
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
26
Heat input (100 MW/m2)
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
27
Heat input (100 MW/m2)
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
28
Insulating panel• An insulating material is inserted between the slag layer
and the mold, at the meniscus level• The effect of heat input at the meniscus level (a quantity
similar to the heat flux, 1 MW/m2) was monitored
steelmold
insulated area
slag
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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Insulating panel
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
30
Insulating panel + heat input
mold
insulated area
slag
Heated areasteel
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
31
Insulating panel + heat input: 10 MW/m2
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
32
Conclusions• A model for studying the meniscus at steady state was
designed• When focusing on the meniscus area, some parameters
can be neglected or simplified: turbulent heat transport, mold water cooling
• Superheat is a sensitive parameter but can be evaluated• The slag properties are very sensitive• Inputting heat transfer in the mold can hinder
solidification of the steel shell. However, energy input rates are very high to have any effect
• Inserting an insulating board can be effective• The heat needs to be brought directly on the steel
A. Moinet & A. W. Cramb A static model for the meniscus
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks