Liquid metal free surfaces under AC magnetic fields

Y. FautrelleEPM lab./CNRS/Grenoble Polytechnic Institute

Outline: introduction static deformations surface motions conclusions

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

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

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

Static levitation of Al (ACHF=10 kHz)

Static levitation (ACHF=15 kHz)

titanium drop in a cold crucible (slighly unstable)

Static deformations (ACHF)

Axisymmetric shaping : not at all !

coil

cold cruciblesemi-levitatedliquid blob

“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

Scheme of the apparatus

coil

liquid metal drop 60 mm

substrate

Static deformations of a flat gallium drop (ACHF)

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

B = 0 - 40 mT

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

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

gallium circular drop (ACLF=1.5 Hz)simple transition axisymmetric azimuthal

B = 0.15 T

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

gallium circular drop (ACLF + DC)the azimuthal instability is suppressed

BDC = 1 - 2 T BAC = 1 - 15% BDC

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

gallium elongated drop (ACLF)simple transition snake-type

Oscillations of a gallium drop (ACLF)

« big bang »

Emulsion of a gallium drop (ACLF)droplet formation

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= 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

log (I)

log

(p+)

2/3

Energy balance

Magnetic energy : with vol = h a2, A p l

Surface energy :

thus :

vol220 lBEm

AhpEs

3/20

3/1320/ B

aBApp

l

A

conclusions

It is possible to generate surface by

resonant effectsby single frequency systemsby two frequency systems

It is possible to create functions

stirring emulsion

DC magnetic field component is

stabilizing

AC magnetic fields may be destabilizing

even at high frequencies