1. Liquid metal free surfaces under AC magnetic fields
Y. Fautrelle
EPM lab./CNRS/Grenoble Polytechnic Institute
Outline:
introduction
static deformations
surface motions
conclusions

2. Context
Industrial :
In metallurgical applications the free surface is the key-point :
pollution (oxidation), inclusion entrapment
contact between melt and crucible
mass transfers and refining (degassing, alloying …)
Scientific :
full magnetohydrodynamic coupling

3. Static deformations
The electromagnetic pressure is responsible for a static free surface deformation :
 dome effect in induction furnaces  axisymmetric shaping
 levitation
but symmetry breaking may occur according to the aspect ratio  highly non-symmetric patterns

4. Static deformations (ACHF)
Domes are oftenly axisymmetric
static dome-shape deformation of an aluminium free surface under the effect of a AC magnetic field, f = 7.5 kHz, cold crucible melting

5. Static levitation of Al (ACHF=10 kHz)

6. Static levitation (ACHF=15 kHz)
titanium drop in a cold crucible (slighly unstable)

7. Static deformations (ACHF)
Axisymmetric shaping : not at all !
“Static dome” in a semi-levitation cold crucible; the liquid is a nickel-base alloy; pool diameter is 60 mm, electric current frequency is 30 kHz

8. Scheme of the apparatus
coil
liquid metal drop  60 mm
substrate

9. Static deformations of a flat gallium drop (ACHF)
The free surface may take complex static shapes R = 3cm, f = 14 kHz
B = mT

10. Static deformations of a flat gallium drop (ACHF 14 kHz + ACLF 0.5 Hz)

11. Free surface motions (ACLF)
Low frequency magnetic fields generate various types of surface waves
 Forced (axisymmetric) waves
Unstable (non-symmetric) resonant waves
symmetry breaking
digitation
emulsion

12. gallium circular drop (ACLF=1
gallium circular drop (ACLF=1.5 Hz) simple transition axisymmetric  azimuthal
B = 0.15 T

13. Stability diagram of a mercury drop
Inductor current (A)
Frequency (Hz)

14. gallium circular drop (ACLF + DC) the azimuthal instability is suppressed
BDC = T
BAC = % BDC

15. gallium elongated drop (ACLF = 2Hz) simple transition saussage type

16. gallium elongated drop (ACLF) simple transition snake-type

17. Oscillations of a gallium drop (ACLF) « big bang »

18. Emulsion of a gallium drop (ACLF) droplet formation

19. Increase of the 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p = 3.54 A

20. Evolution of the non-dimensional perimeter versus the coil current
log (p+)
2/3
log (I)

21. Energy balance A l Magnetic energy : Surface energy : thus :
with vol = h a2, A  p l
Surface energy :
thus : l A

22.  AC magnetic fields may be destabilizing even at high frequencies
conclusions
 AC magnetic fields may be destabilizing even at high frequencies
 It is possible to generate surface by resonant effects
by single frequency systems
by two frequency systems
 It is possible to create functions
stirring
emulsion
 DC magnetic field component is stabilizing