static model of the meniscus for continuous casting

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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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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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



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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



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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



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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



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Theory for oscillation mark formation: meniscus overflow



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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



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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



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Numerical methods: Issues withsolidification 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:



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Description of the model

100 mm 50 mm

50 m

m10

mm



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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



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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



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Temperature at boundaries: dependance on flow field

Fluid flow (m/s) [Fluent simulation]

k-ε model: Effective thermal conductivity (K/m/s) [Fluent

simulation]

Boundary conditions:

Inlet (mass controlled)

Outlet (free flow)

k-ε for tubulence



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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



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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]



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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



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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



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Effects of superheat

Superheat = 27°C

Superheat = 18°C

Superheat = 36 °C



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Effects of water cooling convection coefficient

h = 20,000 W/K/m2

h = 40,000 W/K/m2

h = 10,000 W/K/m2



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Effects of effective conductivity in the liquid steel

Keff max = 5,000 W/m/K



No effective conductivity



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Effects of radiative heat transfer in the slag layer

No radiative heat transfer

Absorption coefficient = 5000 m-1

Absorption coefficient = 2000 m-1



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Effects of the slag layer conductivity

k = 0.5 W/M/K

k = 1 W/m/K

k = 2 W/m/K



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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



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Heat input (1 MW/m2)



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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



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Insulating panel



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Insulating panel + heat input

mold

insulated area

slag

Heated areasteel



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Insulating panel + heat input: 10 MW/m2



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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



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Thank you for your attention

static model of the meniscus for continuous casting

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