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