Liquid metal free surfaces under AC magnetic fields Y. Fautrelle EPM 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 ! “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 gallium circular drop (ACLF=1.5 Hz) simple transition axisymmetric  azimuthal B = 0.15 T

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

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p = 3.54 A

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

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

 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