AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Introduction: continuous casting • Liquid steel is injected through the nozzles, and cools down along the mold • To prevent sticking, molten slag and mold oscillations (negative strip time) • Various defects are thought to be created at the meniscus A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Description of the meniscus area • •
• •
Mushy zone: latent heat release
•
Liquid and solid slag : conduction, radiation
•
Free surface movements, surface tension Solidified slag: glassy/crystalline structure
•
A. Moinet & A. W. Cramb
A static model for the meniscus
Heat input: hot metal Conduction through liquid metal: convection, diffusion, turbulence Conduction through solid metal: diffusion
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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 meniscus level, heat release • No certain explaination A. Moinet & A. W. Cramb
A static model for the meniscus
Withdrawal direction
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Theory for oscillation mark formation: meniscus overflow
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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, free surface, thermal radiative transfer) • Simplifications must be done, limit boundaries must be formulated • A preliminary static thermal model for the meniscus was designed
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Numerical methods • Heat transport:
• dT ⎛ ∂T ⎞ 2 ρ Cp = ρ Cp⎜ + V.∇T ⎟ = k ∇ T + Q dt ⎝ ∂t ⎠
– 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 •
Q = ρ HL ρ C p eff
∂f ∂T ∂T ∂f ∂f = ρ HL = C p latent heat ⇒ Clatent heat = ρ H L ∂t ∂T ∂t ∂t ∂T
• dT ⎞ ⎛ ∂T = ρ C peff ⎜ + V.∇T ⎟ = k ∇ 2T + Q dt ⎠ ⎝ ∂t
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Numerical methods: Issues with solidification modeling – 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
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
50 mm
10 mm
Description of the model
100 mm
A. Moinet & A. W. Cramb
A static model for the meniscus
50 mm
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Description of the model •
•
A. Moinet & A. W. Cramb
In an actual (transcient) conditions, the solidified steel is withdrawn. If not, solid steel accumulates and the calculated thickness of the shell will not be realistic. A flow that simulates steel withdrawal was calculated and applied to all calculations
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Temperature at boundaries: issues • Steel is injected in the mold at a temperature slightly superior to the liquidus temperature • From the exit of the nozzle to the surface of the mold, there exists a temperature gradient that is a function of the flow field and the conductivity of the metal • Both the flow field and the steel conductivity are not trivial A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Temperature at boundaries: dependance on flow field
Boundary conditions: Inlet (mass controlled) Outlet (free flow) k-ε for tubulence
Fluid flow (m/s) [Fluent simulation] A. Moinet & A. W. Cramb
k-ε model: Effective thermal conductivity (K/m/s) [Fluent simulation]
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Temperature at boundaries: dependance on flow field
Boundary conditions: T = Tsuperheat
Border 2
No solidification but T = Tliquidus
• • • •
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
A. Moinet & A. W. Cramb
A static model for the meniscus
Border 1
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Effective thermal conductivity in the meniscus area
k-ε model: Effective thermal conductivity (K/m/s) around the meniscus [Fluent simulation] A. Moinet & A. W. Cramb
• Effective thermal conductivity decreases linearly with the distance to the surface of the mold • Rather than calculating the turbulences at each step, effective thermal conductivity will be approximated by a linear function of the distance to the mold
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
To summarize
slag
Steel Solidus
1492 °C
Liquidus
1530 °C
Thermal conductivity in solid
40 W/m/K
Effective thermal conductivity in liquid
5,000 W/m/K
Latent heat of fusion
250,000 J/kg
Density
7000 kg/m3
Heat capacity
800 J/K/kg
Slag Thermal conductivity in solid Radiative heat transfer Density
1 W/m/K no 1000 kg/m3
casting parameters Withdrawal velocity Superheat water cooling convection coefficient
0.02 m/s 27 °C 20,000 W/K/m2
Copper mold
Steel (liquid) Steel (solid)
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Effects of superheat Superheat = 18°C Superheat = 27°C Superheat = 36 °C
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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 slag mold
steel
Heated area A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Heat input (1 MW/m2)
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Heat input (1 MW/m2)
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Heat input (100 MW/m2)
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Heat input (100 MW/m2)
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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 slag mold
steel
insulated area A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Insulating panel
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Insulating panel + heat input slag
mold
insulated area Heated area A. Moinet & A. W. Cramb
A static model for the meniscus
steel 30
AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Insulating panel + heat input: 10 MW/m2
A. Moinet & A. W. Cramb
A static model for the meniscus
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
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
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AISI/DOE TRP 0408 -Elimination or Minimization of Oscillation Marks
Thank you for your attention
A. Moinet & A. W. Cramb
A static model for the meniscus
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