Heat Transfer with Change of Phase in Continuous Casting - PowerPoint PPT Presentation

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Heat Transfer with Change of Phase in Continuous Casting

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Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010 – PowerPoint PPT presentation

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Title: Heat Transfer with Change of Phase in Continuous Casting


1
Heat Transfer with Change of Phase in Continuous
Casting
  • Ernesto Gutierrez-Miravete
  • Rensselaer at Hartford
  • ANSYS Users Group Meeting
  • September 28, 2010

2
Outline
  • Continuous Casting Processes
  • Physics and Mathematics of Heat Conduction with
    Change of Phase and Mass Transport
  • Finite Element Formulations
  • Illustrative Examples

3
Continuous Casting Processes
  • Metal Processing often involves Molten Metals
  • Molten Metals must be Solidified to produce Bulk
    Solid Specimens
  • Metal Solidification for the Production of Bulk
    Specimens is carried out in Practice either in
    Batches (Ingot or Shape Casting) or Continuosly
    (Continuous Casting)

4
Mathematical Formulation of Heat Conduction
with Change of Phase Problems
  • Differential Thermal Energy Balance Equation
    Inside the Bulk Phases (Energy Conservation)
  • Heat Flux-Temperature Gradient Relationships
    Inside the Bulk Phases (Fourier Law)
  • Differential Thermal Energy Balance Equation at
    the Interface between Phases accounting for the
    Latent Heat of Phase Change (Stefan Condition)
  • Boundary Conditions on External Boundaries

5
Latent Heat of Phase Change
Enthalpy (H)
Hf
?H/?T Cp
DTf
Temperature (T)
6
Critical Issues in Numerical Solution ofHeat
Conduction problems with Change of Phase in CC
  • Stefan Condition makes problem Non-Linear even
    for Constant Properties
  • T(x,t) ? x(t) ? T(x,t)
  • Interface Motion driven by Physics, unrelated to
    Position of Mesh Nodes
  • x(t) f(t)
  • Grid Peclet Number Constraint
  • V L r Cp/2k lt 1

7
Finite Element Formulation of Heat Conduction
with Change of Phase Problems in CC
  • Variational Statement of the Problem
  • Galerkins Method
  • Time Stepping
  • Handling of the Stefan Condition
  • Enthalpy Method
  • Effective Specific Heat Method
  • Effect of Mass Transport

8
Illustrative Examples
  • Continuous Casting in 2D (a Useful Toy Model)
  • Direct Chill Continuous Casting Model
  • Thin Slab Continuous Casting Model

9
Continuous Casting in 2D
10
Effect of M (kg/min) and q (W/m2) on T-z Curve
along Slab Centerline
11
Predicted Metallurgical Length zm 2D Model
M (kg/min) Zm (m)
24 0.52
27 0.63
30 0.72
33 0.83
36 0.98
Q (W/m2) Zm (m)
-0.8e5 1.10
-0.9e5 0.84
-1.0e5 0.72
-1.1e5 0.66
-1.2e5 0.57
12
Direct Chill Continuous Casting
13
2D DC CC Model (Slab Detail)
14
2D DC CC Model (Mold Detail)
15
3D DC CC Square Bar Model (Slab and Mold
Temperatures)
16
3D DC CC Model (Slab CL Detail)
17
3D DC CC Model (Full Slab View from CL)
18
3D DC CC Model (Full Slab View from Narrow Face)
19
Thin Slab Continuous Casting
20
Thin Slab Continuous Casting Mold
21
This Slab CC Mold Heat Flux(Measured)
22
Thin Slab CC Mold Model (Mesh)
23
Thin Slab CC Mold Model(Predicted Temperature
and Displacements)
24
In Closing
  • Heat Conduction with Change of Phase is the
    Simplest Model of a Solidifying System
  • Additional Important Issues and Future Goals
  • Thermo-Mechanical Effects
  • Liquid Metal Flow Effects
  • Solidified Microstructure Development
  • Solid State Phase Changes
  • Optimal Heat Extraction Practices
  • Comprehensive, Push-Button Models
  • Partial support from CCAT for the performance and
    presentation of this work is gratefully
    acknowledged
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