Control of liquid metal by AC magnetic fields :

examples of free surfaces and solidification

Y. FautrelleEPM lab./CNRS/Grenoble Polytechnic

Institute

Outline

introduction

action on free surfaces

action on solidification

conclusions

Context

Free surface is a key-factor for - pollution, inclusion entrapment

- mass transfers

Many defects occurs during solidification due to fluid flows, both in the liquid and mushy zone : segregations, structures

Both topics are strongly influenced by AC magnetic fields

1 : Action on free surfaces :

static deformations

The electromagnetic forces are responsible for two kinds of effects :

static free surface deformation :

dome effect, levitation

free surface agitation :

surface stirring, emulsion …

Example of non-symmetric static free surface

coil

liquid metal drop 60 mm

substrate

Scheme of the apparatus

Static deformations of a flat gallium drop

The free surface may take complex static shapes R = 3cm, f = 14 kHz

B = 0 - 40 mT

Example of static deformations (ACHF)

Axisymmetric shaping may not be always possible!

coil

cold cruciblesemi-levitatedliquid blob

1 : Action on free surfaces :

agitation

Free surface motions (ACLF)

Low frequency magnetic fields generate various types of surface waves

Forced (symmetric) waves

Unstable (non-symmetric) waves

symmetry breaking

digitation

emulsion

gallium circular drop (ACLF=1.5 Hz)

simple transition axisymmetric forced waves azimuthal unstable waves

gallium elongated drop (ACLF)

simple transition snake-type

gallium elongated drop (ACLF + DC)

the symmetry breaking is suppressedBAC = 1 - 15% BDC

BDC= 2.2 T

BAC = 0.3 T

Emulsion of a gallium drop (ACLF = 6

Hz)

droplet formation

Increase of the area / perimeter

A being almost constant, increase of the surface area occurs through an increase of the drop perimeter p

thus let us consider the non-dimensional perimeter

NB : for a circle p+ = 2= 3.54

App /

A

Evolution of the non-dimensional perimeter versus

the coil current

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,4 1,6 1,8 2 2,2

coil current log (I)

drop

per

imet

er lo

g (p

+)

2/3

emulsion threshold

theoretical minimum

3/20

3/1320/ B

aBApp

two-frequency system : bulk + surface stirring

-400

-300

-200

-100

0

100

200

300

400

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

time (s)

coil

inte

nsity

(A

)

main frequency f1 = 14 kHzmodulation frequency f2 = 1- 10 Hz

Enhancement of mass transfer through liquid-liquid interfaces

G allium pool

Single turn coil

= 84 m mmolten salt +Zr

liquidAl-Cu

The surface stirring promotes the transfer of Zirconium from the salt to the liquid metal

Sans modulation Avec modulationWithout surface agitation with surface agitation

after 40 mn after 10 mn

Al-Cu

Fluoride salt

Al-Cu

dark layer containingZirconium

2 : Action on solidification :

segregation control by

moderate AC fields

Modèle FHPStirring in the mushy zone

Laminar flow regime

Darcy approximation in the mushy zone

Hypotheses :

Columnar solidification

Two-phase statistical model + envelope model

Some effects of AC fields on solidification can be understood by numerical modelling

Case of rotating magnetic fields

2 cm

1 cm

Alloy : Pb-Sn10%wtCooling rate : 1K/min

rotary stirrer

mushy zone

liquid zone

10 mm

heat extraction

z

gravity

Résultats CmResults in the pure-natural convection

mixing concentration maps [ Cm min = 4,7 % ; Cm max = 19,3 %]

Time : 1350 seconds

horizontal cross-section at h = 5 mm.

channels

ContexteSarrazin – Hellawell experiment 88 (Pb-Sn)

FrecklesDark channels

Cartes Cm

h = 0 mm.

h = 5 mm.

h = 15 mm.

h = 10 mm.

h = 20 mm.

Cm min = 5,13% ; Cm max = 25%

Centralchannel

Effect of a moderate rotating e.m.s.

Appearance of a central segregation

Pompage d’EckmanInterpretation : stirring in the mushy zone

The solute is drained from the wall toward the centre

The mushy zone is « washed » by the fluid flow

High pressure

Low pressure

Rotationof the liquid

Flow in the mushy zone

+ + + +

Effect of moderate travelling fields on the segregations during solidification

Two kinds of electromagnetic forces :

force of constant amplitude F0

force with a sinusoidal amplitude

F0 sin(2t/p)

F0

10 5 mm 2D-ingot

e.m. stirrers

Extracted heat flux

BrassageEffect of steady electromagnetic forces

Pb-10wt%Sn, F0 = 1000 N.m-3

Evolution of the averaged solute concentration (Medina et al. 2004)

Natural convection electromagnetic stirring

(b)

Mushy zone

Liquid zone

Segregated

channels

Heat flux

TMF effectB = 0 B = 0,35 T B = 0,07 T

Experimental evidence : Zaidat et al. (2004)

Al-Ni3.5wt.%

Travelling magnetic fieldCylindrical rod R =5mmB = 30 mT

1mm

Central channel segregate

Al-7wt%Si, 10 5 mm 2D-ingot, GT = 1000 K/m, Cooling rate = 24 K/min

constant e.m. force modulated force (period = 10 s)

averaged solute concentration

Freckle suppression by modulated electromagnetic forces

Time evolution of the solidification of a Al-Si 7%wt ingot under modulated e.m. stirring

Initial fluid motion liquid fraction

Conclusions

1. Free surfaces

AC magnetic fields may be destabilizing even at high

frequencies

It is possible to create various functions : stirring, emulsion

2. Segregations during solidification

The liquid pattern has a significant influence on the

segregation

stirring in the mushy zone is able to control (partly) the

segregations

interpretation by energy balance

Magnetic energy :

with vol = h a2, A p l

Surface energy :

thus :

Emulsion occurs when : l < lc

vol220 lBEm

AhpEs

3/20

3/1320/ B

aBApp

l

A

2/1

g

lc

Stability diagram of a mercury drop

50

100

150

200

250

1 1,2 1,4 1,6 1,8 2 2,2 2,4

fréquence (Hz)

inte

nsité

du

cour

ant i

nduc

teur

(A

)

mode 4mode 5mode 6mode 7In

duct

or c

urre

nt (

A)

Frequency (Hz)

f5 f6f4 f7

unstable region

stable region

gallium elongated drop (ACLF = 2Hz)

simple transition saussage type