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:o The conservation equations utilizing the volume averaging

techniqueo Models for time dependent magnetic fieldso Influence of forced flows on the solidification process

Contract no. 50WM0042Contract no. 14347/00/NL/SH

Microgravity – Is it necessary? Microgravity – Is it necessary?

Systematic analysis of the influence of convection on● the evolution of the mushy zone● micro- and macro segregation● morphology of dendritesin binary AlSi, ternary AlSiMg and technical A357 alloys.

Schematic of dendrites solidifying under the influence of convection

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

Objectives of MICAST (The effect of magnetically controlled fluid flow on

microstructure evolution in cast technical Al-alloys):

MICAST - MAP Project No. AO-99-031

Directional solidification with time dependent magnetic Directional solidification with time dependent magnetic fields appliedfields 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

Bulk liquid

Mushy zone

Solid

Melt flowAlSi7

z

TG=4K/mm

Vg=

0,1

mm

/s

d=8mm

Condition for directional solidification The software package CrysVUn

The volume averaging techniqueThe volume averaging technique11

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 mush liquid

Representative elementary volume (REV) 0 ; Ts=Tl=T;

solid

liquid

Solidifying alloy sample with oneof the REV inside the mushy zone (marked)

0

d1

0kkk X

0

Ωin1 kkX

0

kk

kk

kkk

k

k X

1d

1

0

1 sklk

REV

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

l

lll

s

sss CCC mix

0mix CC

Interdendritic convection is causing macrosegregationInterdendritic convection is causing macrosegregation

Tl

lC

l

lvC

Tl

lC

ll '

z

T

MZ

z

C

z

l

Gv

0mix CC

Axial temperature, liquid concentrationand liquid volume fraction during directionalsolidification.

T

C

0C

)1(

mixC

Phase diagram

Local solute enrichment due to upwardsdirected flow.

As Pr<<Sc the concentration field is changed at much smaller flow velocities than the temperature field.

G

l

v

vConvective parameter

flow

<0 negative macrosegregation0<<1 positive macrosegregation>1 remelting

ModelModel22 for directional alloy solidification for directional alloy solidification

Energy conservation

t

LTTvcTct

ls

l

llpllp

,

Species conservation

li

lllml

l

l

lilll

imix CDvCC

t ,*

Phase diagram relation

l

i

il

ipure CmTT

Momentum conservation

bvK

Mpvvvt l

l

lll

ll

l

l

l

lll

l

lll

2

Li

irefl

lil

iCrefTl fCCTTgb

,

Mass conservation

0 l

lll v

Convective term causing macrosegregation

Lorentz – force vector

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

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

Time dependent magnetic fieldsTime dependent magnetic fields

Lorentz-force:

Taylor number :

Lorentz-force:

Taylor number :

Rotating Magnetic Field [3]:Principal action of the Lorentz-force generated by a magnetic field rotating around the axis of a cylindrical melt volume

Secondary flows in meridonal plane

occur on bottom and top in a finite

cylinder geometry

Lorentz-force

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

Flow field (r: azimuthal, l: meridonal)

p

LBTa RMFm 2

42

2

efrBf 22

1 20

Time dependent magnetic fieldsTime dependent magnetic fields

Traveling Magnetic Field [4]:A single axisymmetric harmonic magnetic wave traveling in zdirection

Lorentz-force

r

z

Br

Bz

tt+t

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

Lorentz –force:

Taylor number:

Lorentz –force:

Taylor number:

r

z

Flow field with fl pointing downward

aRIBa

RTa TMFm

21

202

3

2

arIa

Bf z

21

20

2

Directional solidification of AlSi7 applying RMFDirectional solidification of AlSi7 applying RMFS

ymm

etry

axi

s

Mus

hy z

one

Azimuthalflow

Streamlines for meridonal flow

Mixture concentration

Liquid fraction

Channelformation

Experimental result from DLR, Cologne

B0=2mTvg=0.1mm/s,

Gl=4K/mmVmax = 3.2x10-4 m/s

Cmix=8.28wt.%

B0=2mTvg=0.1mm/s,

Gl=4K/mmVmax = 3.2x10-4 m/s

Cmix=8.28wt.%

Te=850K

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 KAlSi7Mg0.6: 60 K

Comparison of the macrosegregation due to TMF and Comparison of the macrosegregation due to TMF and RMF for AlSi7RMF for AlSi7

Resulting macrosegregation for RMF or TMFapplied 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

ConclusionsConclusions

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

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