Numerical and experimental studies on solidification control by alternating magnetic fields

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Numerical and experimental studies on
solidification control by alternating magnetic
fields

• P. Nikrityuk1, K.Eckert1 , B. Willers2, S.
  Eckert2,
• U. Michel3, G. Zouhar3
• 1 Institute of Aerospace Engineering, Dresden
  University of Technology,
• D-01062 Dresden, Germany
• 2Forschungszentrum Rossendorf (FZR), D-01314
  Dresden, Germany
• 3Institute of Material Science, Dresden
  University of Technology
• Sino-German Workshop on Electromagnetic
  Processing of Materials
• October 11-12, 2004, Shanghai, China

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Solidification control by alternating magnetic
fields
Rotary stirring and mixing liquid metals during
solidification homogenization of the liquid
phase
The modification of thermosolutal and
shrinkage-driven flows
Applications of alternating magnetic fields to
control of a metal solidification
Affect the microstructure, e.g. modification of
the grain structure
Control of Columnar-Equiaxed Transition (CET)
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Classification of rotating magnetic fields (RMF)
Magnetic Taylor number
Hartmann number
Reynolds number corresponding to the magnetic
field rotation
Angular frequency of the magnetic field
Relative frequency of the magnetic field
metals and semiconductors stirring
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Experimental set-up

• Alloy Pb-85wtSn
• Cylindrical mold made from stainless steel
• Ingot dimensions
• R 25 mm, H 60 mm
• Superheat 90K
• RMF six coils
• B 0...25mT, f 10...400Hz
• (Ta 1105 ... 3108)

• Sketch of the experimental facility
• (FZ Rossendorf)

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Numerical formulation

• Continuum based model (Incropera, 1987) of a
  binary metal alloy solidification
• Mixture viscosity model (Roplekar Dantzig,
  2001)
• The energy equation is written for mixture
  enthalpy
• Volume fraction of liquid

• Lorentz force - low-frequency and low induction
  approximation has been used (Gorbachev et al.
  1974)

Time averaged azimuthal Lorentz force (Ta
5.8?104, finite cylinder R 25 mm H 63 mm)
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Basic equations of the mixture model

• Mass Conservation Equation
• Momentum Conservation Equation
• Mixture viscosity approach usul.
  Permeability approach us0.
• Energy Conservation Equation
• Species Mass Conservation Equation

0 (usul)
0 (usul)
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Mixture quantities

• Mass Fraction of Liquid and Solid
• Mixture Density
• Mixture Enthalpy
• Mixture Mass Fraction of Sn
• Mixture thermal conductivity

Dynamic viscosity of the mixture. (Roplekar
J.K., and Dantzig J.A. 2001) Int. J. Cast. Metals
Research. Vol. 14, No. 2, pp. 79-98.
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Numerical simulation of hypereutectic Pb85wtSn
alloy solidification

• Mixture viscosity approach is used
• to model fluid flow within mushy zone
• Solidification front velocity is about 0.2
  mm/sec
• Volume fraction of liquid is calculated
• from relation

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Results I Fluid flow during solidification
UDV measurements, Ta 5.8106, r 22 mm
Numerical simulation

• Two-phase problem
• Modification of the geometry (aspect ratio!)
• Modification of the effective Lorentz force
• Modification of the material properties
• Free surface

Ta2106, Sn-15MPb
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Results II Curvature of the solidification front
Azimuthal velocity
Volume fraction of liquid

Pb85wtSn, Ta2 106
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Results III Modification of heat transfer
Experiment
Numeric

• RMF driven convection enhances the heat transfer
  between liquid and solid phases
• Temperature gradient is reduced by the forced
  convection
• Increase of Ta number leads to the convective
  transport of Latent heat

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Results IV The distribution of mass fraction of
Sn after solidification with stirring, B1mT,
Ta2.3 105. Numerical results.
Permeability constant model Us0
Mixture viscosity model UsUl
Zero gravity
Zero gravity
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Results V Columnar-to-equiaxed transition (CET)

Ta 0
Ta 1.4108

• Convection promotes the CET
• Vertical CET position depends on the Taylor
  number
• Columnar crystallites are inclined towards the
  flow direction

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Results VI Columnar-to-equiaxed transition (CET)

B 10 mT, f 50 Hz, Ta 2107, Longitudinal
section
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Outlook / Further steps

• Variations of the alloy composition, alloy
  systems
• Quantitative analysis of microstructure
  parameters
• Coupling of microscale and macroscale models
• Optimisation of the electromagnetic stirring

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Conclusions

• Modification of a columnar into an equiaxed
  micro-structure of a directionally solidified
  Sn15wtPb alloy was achieved using a RMF
• Forced convection modifies distribution of
  temperature and concentration
• Significant effects of the flow on the convection
  in the mushy zone and on the shape of the
  interface solid/liquid can be observed
• The flow structure is considerably more complex
  as compared with the steady-state flow structures
  

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Acknowledgement

• The research is supported
• by the Deutsche Forschungsgemeinschaft (DFG) in
  the frame of the SFB 609 Electromagnetic Flow
  Control in Metallurgy, Crystal Growth and
  Electrochemistry.
• This support is gratefully acknowledged by the
  authors.

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