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Liquid metal free surfaces under AC magnetic fields

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 :

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Liquid metal free surfaces under AC magnetic fields

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

  9. 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

  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=1.5 Hz)simple transition axisymmetric  azimuthal B = 0.15 T

  13. Stability diagram of a mercury drop f4 f5 f6 f7 Inductor current (A) Frequency (Hz)

  14. gallium circular drop (ACLF + DC)the azimuthal instability is suppressed BDC = 1 - 2 T BAC = 1 - 15% 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. A l Energy balance Magnetic energy : with vol = h a2, A p l Surface energy : thus :

  22. 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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