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Liquid metal free surfaces under AC magnetic fields
Y. Fautrelle EPM lab./CNRS/Grenoble Polytechnic Institute Outline: introduction static deformations surface motions conclusions
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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
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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
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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
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Static levitation of Al (ACHF=10 kHz)
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Static levitation (ACHF=15 kHz)
titanium drop in a cold crucible (slighly unstable)
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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
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Scheme of the apparatus
coil liquid metal drop 60 mm substrate
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Static deformations of a flat gallium drop (ACHF)
The free surface may take complex static shapes R = 3cm, f = 14 kHz B = mT
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Static deformations of a flat gallium drop (ACHF 14 kHz + ACLF 0.5 Hz)
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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
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gallium circular drop (ACLF=1
gallium circular drop (ACLF=1.5 Hz) simple transition axisymmetric azimuthal B = 0.15 T
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Stability diagram of a mercury drop
Inductor current (A) Frequency (Hz)
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gallium circular drop (ACLF + DC) the azimuthal instability is suppressed
BDC = T BAC = % BDC
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gallium elongated drop (ACLF = 2Hz) simple transition saussage type
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gallium elongated drop (ACLF) simple transition snake-type
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Oscillations of a gallium drop (ACLF) « big bang »
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Emulsion of a gallium drop (ACLF) droplet formation
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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+ = 2p = 3.54 A
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Evolution of the non-dimensional perimeter versus the coil current
log (p+) 2/3 log (I)
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Energy balance A l Magnetic energy : Surface energy : thus :
with vol = h a2, A p l Surface energy : thus : l A
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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
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