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Sino-German Workshop on Electromagnetic Processing of Materials, 11.10 – 13.10.2004 Shanghai, PR China Use of magnetic fields during solidification under microgravity conditions J.Dagner, M.Hainke, J.Friedrich, G.M ü ller Outline:

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Sino german workshop on electromagnetic processing of materials

Sino-German Workshop on Electromagnetic Processing of Materials,

11.10 – 13.10.2004 Shanghai, PR China

Use of magnetic fields during solidification under microgravity conditions

J.Dagner, M.Hainke, J.Friedrich, G.Müller

Outline:

  • The conservation equations utilizing the volume averaging technique

  • Models for time dependent magnetic fields

  • Influence of forced flows on the solidification process

Contract no. 14347/00/NL/SH

Contract no. 50WM0042


Sino german workshop on electromagnetic processing of materials

Microgravity – Is it necessary?

Objectives of MICAST (The effect of magnetically controlled fluid flow on microstructure evolution in cast technical Al-alloys):

Systematic analysis of the influence of convection on

  • the evolution of the mushy zone

  • micro- and macro segregation

  • morphology of dendrites

    in binary AlSi, ternary AlSiMg and technical A357 alloys.

Diffusive and controlled convective conditions are achieved by using microgravity environment and time-dependent magnetic fields, i.e. rotating magnetic fields (RMF).

Schematic of dendrites solidifying under the influence of convection

MICAST - MAP Project No. AO-99-031


Directional solidification with time dependent magnetic fields applied

G=4K/mm

T

Directional solidification with time dependent magnetic fields applied

  • Modeling of (global) heat transfer and macrosegregation

  • Solidification of binary AlSi7 and ternary AlSi7Mg0.6 cast alloys

  • Influence of rotating and traveling magnetic fields on the solidification process

Heat flux

z

AlSi7

Melt flow

Bulk liquid

Mushy zone

Vg= 0,1mm/s

Solid

d=8mm

The software package CrysVUn

Condition for directional solidification


The volume averaging technique 1

solid

mush

liquid

The volume averaging technique1

For a quantity  in the phase k (k= solid

or liquid) the volume average is defined:

The fraction of phase k is:

The intrinsic volume average:

Mixture concentration within the REV:

Macrosegregation:

solid

liquid

Representative elementary

volume (REV) 0 ; Ts=Tl=T;

REV

Solidifying alloy sample with one

of the REV inside the mushy zone (marked)

[1] Poirier et al. Met. Trans. B. 22 889-900 (1991)


Interdendritic convection is causing macrosegregation

z

z

l

T

Interdendritic convection is causing macrosegregation

As Pr<<Sc the concentration field is changed

at much smaller flow velocities than the temperature field.

Phase diagram

z

Local solute enrichment due to upwards

directed flow.

flow

MZ

Convective parameter

C

<0 negative macrosegregation

0<<1positive macrosegregation

>1 remelting

Axial temperature, liquid concentration

and liquid volume fraction during directional

solidification.


Model 2 for directional alloy solidification

Model2 for directional alloy solidification

Energy conservation

Convective term causing

macrosegregation

Species conservation

For ternary systems: Plain liquidus surface for primary solidification with isothermal binary valleys

Phase diagram relation

Momentum conservation

Lorentz – force vector

Mass conservation

[2] Poirier et al. Met. Trans. B. 22 889-900 (1991)


Time dependent magnetic fields

Time dependent magnetic fields

Rotating Magnetic Field [3]:

Principal action of the Lorentz-force generated by a magnetic field rotating around the axis of a cylindrical melt volume

Lorentz-force:

Taylornumber :

Lorentz-force

Secondary flows in meridonal plane occur on bottom and top in a finite cylinder geometry

Flow field (r: azimuthal, l: meridonal)

[3] B. Fischer et al., Proc. EPM 2000, 497-502 (2000)


Time dependent magnetic fields1

t+t

t

z

Bz

r

Br

Time dependent magnetic fields

Traveling Magnetic Field [4]:

A single axisymmetric harmonic

magnetic wave traveling in z

direction

Lorentz –force:

Taylor number:

z

r

Flow field with fl pointing downward

Lorentz-force

[4] K. Mazuruk, Adv. Space Res. 29,4,541-548 (2002)


Directional solidification of alsi7 applying rmf

Mushy zone

Directional solidification of AlSi7 applying RMF

B0=2mT

vg=0.1mm/s,

Gl=4K/mm

Vmax = 3.2x10-4 m/s

Cmix=8.28wt.%

Symmetry axis

Channel

formation

Te=850K

Mixture

concentration

Streamlines for

meridonal flow

Azimuthal

flow

Liquid fraction

Experimental result from DLR, Cologne

Hainke, Friedrich, Müller; J. Mat. Sci., 2004


Rmf applied to the solidification of a ternary alloy

RMF applied to the solidification of a ternary alloy

Comparison between the macrosegregation caused by the

forced fluid flow for a binary (AlSi7) and a ternary

(AlSi7Mg0.6) Aluminum alloy.

Extension of mushy

zone AlSi7: 37 K

AlSi7Mg0.6: 60 K


Comparison of the macrosegregation due to tmf and rmf for alsi7

Comparison of the macrosegregation due to TMF and RMF for AlSi7

Resulting macrosegregation for RMF or TMF

applied to the solidification of a binary AlSi7

alloy.

Left part: stream function; right part: liquid fraction (d=0.05).

The arrow indicates the direction of the Lorentz-force.

Dagner, Hainke, Friedrich, Müller; EPM, 2003


Conclusions

Conclusions

  • Depending on field configuration and strength, macrosegregation is observed in calculations and experiment even in small samples for AlSi7 and AlSi7Mg0.6 Alloys

  • The differences in the resulting macrosegregation between AlSi7 and AlSi7Mg0.6 within the used model are negligible. Thus AlSi7Mg0.6 can be treated as a binary mixture

  • The calculations suggested that using TMF will lead to a more pronounced effect than in the case of RMF

  • When TMF is used, the direction of the Lorentz-force represents a additional process parameter influencing macrosegregation


Acknowledgements

Acknowledgements

Prof. Dr. L. Ratke and S. Steinbach (Institute for Space Simulation, DLR, Cologne) for the experimental results obtained with the ARTEMIS and the ARTEX facilities.

This work was financially supported by the DLR under contract no. 50WM0042 and by ESA under contract no. 14347/00/NL/SH within the framework of the

European research project MICAST (ESA MAP AO-99-031).

http://www.cgl-erlangen.com


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