Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at...
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Transcript of Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at...
![Page 1: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/1.jpg)
Heat Transfer with Change of Phase in Continuous Casting
Ernesto Gutierrez-MiraveteRensselaer at Hartford
ANSYS Users Group MeetingSeptember 28, 2010
![Page 2: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/2.jpg)
Outline
• Continuous Casting Processes• Physics and Mathematics of Heat
Conduction with Change of Phase and Mass Transport• Finite Element Formulations• Illustrative Examples
![Page 3: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/3.jpg)
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)
![Page 4: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/4.jpg)
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
![Page 5: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/5.jpg)
Latent Heat of Phase Change
Enthalpy (H)
Temperature (T)
Hf
Tf
∂H/∂T = Cp
![Page 6: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/6.jpg)
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) t T(x,t) • Interface Motion driven by Physics,
unrelated to Position of Mesh Nodest = f(t)
• Grid Peclet Number ConstraintV L Cp/2k < 1
![Page 7: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/7.jpg)
Finite Element Formulation of Heat Conduction with Change of Phase Problems in CC
• Variational Statement of the Problem• Galerkin’s Method • Time Stepping• Handling of the Stefan Condition– Enthalpy Method– Effective Specific Heat Method
• Effect of Mass Transport
![Page 8: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/8.jpg)
Illustrative Examples
• Continuous Casting in 2D (a Useful Toy Model)• Direct Chill Continuous Casting Model• Thin Slab Continuous Casting Model
![Page 9: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/9.jpg)
Continuous Casting in 2D
![Page 10: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/10.jpg)
Effect of M (kg/min) and q (W/m2) on T-z Curve along Slab Centerline
![Page 11: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/11.jpg)
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
![Page 12: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/12.jpg)
Direct Chill Continuous Casting
![Page 13: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/13.jpg)
2D DC CC Model (Slab Detail)
![Page 14: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/14.jpg)
2D DC CC Model (Mold Detail)
![Page 15: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/15.jpg)
3D DC CC Square Bar Model (Slab and Mold Temperatures)
![Page 16: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/16.jpg)
3D DC CC Model (Slab CL Detail)
![Page 17: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/17.jpg)
3D DC CC Model (Full Slab View from CL)
![Page 18: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/18.jpg)
3D DC CC Model (Full Slab View from Narrow Face)
![Page 19: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/19.jpg)
Thin Slab Continuous Casting
![Page 20: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/20.jpg)
Thin Slab Continuous Casting Mold
![Page 21: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/21.jpg)
This Slab CC Mold Heat Flux(Measured)
![Page 22: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/22.jpg)
Thin Slab CC Mold Model (Mesh)
![Page 23: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/23.jpg)
Thin Slab CC Mold Model(Predicted Temperature and Displacements)
![Page 24: Heat Transfer with Change of Phase in Continuous Casting Ernesto Gutierrez-Miravete Rensselaer at Hartford ANSYS Users Group Meeting September 28, 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062712/56649c895503460f94941c40/html5/thumbnails/24.jpg)
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