Control of liquid metal by AC magnetic fields : examples of free surfaces and solidification Y. Fautrelle EPM lab./CNRS/Grenoble Polytechnic Institute

Outline  introduction  action on free surfaces  action on solidification  conclusions

Context  Free surface is a key-factor for - pollution, inclusion entrapment - mass transfers  Many defects occurs during solidification due to fluid flows, both in the liquid and mushy zone : segregations, structures Both topics are strongly influenced by AC magnetic fields

1 : Action on free surfaces : static deformations

The electromagnetic forces are responsible for two kinds of effects : static free surface deformation : dome effect, levitation free surface agitation : surface stirring, emulsion …

Example of non-symmetric static free surface coil liquid metal drop  60 mm substrate Scheme of the apparatus

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

Example of static deformations (AC HF ) Axisymmetric shaping may not be always possible!

1 : Action on free surfaces : agitation

Free surface motions (AC LF ) Low frequency magnetic fields generate various types of surface waves Forced (symmetric) waves Unstable (non-symmetric) waves symmetry breaking digitation emulsion

gallium circular drop (AC LF=1.5 Hz ) simple transition axisymmetric forced waves  azimuthal unstable waves

gallium elongated drop ( AC LF ) simple transition snake-type

gallium elongated drop (AC LF + DC) the symmetry breaking is suppressed B AC = % B DC B DC = 2.2 T B AC = 0.3 T

Emulsion of a gallium drop ( AC LF = 6 Hz ) droplet formation

Increase of the area / 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 A

Evolution of the non-dimensional perimeter versus the coil current coil current log (I) drop perimeter log ( p + ) 2/3 emulsion threshold theoretical minimum

two-frequency system : bulk + surface stirring main frequency f 1 = 14 kHz modulation frequency f 2 = Hz Enhancement of mass transfer through liquid-liquid interfaces molten salt +Zr liquid Al-Cu

The surface stirring promotes the transfer of Zirconium from the salt to the liquid metal Sans modulationAvec modulation Without surface agitation with surface agitation after 40 mn after 10 mn Al-Cu Fluoride salt Al-Cu dark layer containing Zirconium

2 : Action on solidification : segregation control by moderate AC fields

Modèle FHP Stirring in the mushy zone Laminar flow regime Darcy approximation in the mushy zone Hypotheses : Columnar solidification Two-phase statistical model + envelope model Some effects of AC fields on solidification can be understood by numerical modelling

Case of rotating magnetic fields 2 cm 1 cm Alloy : Pb-Sn10%wt Cooling rate : 1K/min rotary stirrer mushy zone liquid zone  10 mm heat extraction z gravity

Résultats Cm Results in the pure-natural convection mixing concentration maps [ Cm min = 4,7 % ; Cm max = 19,3 %] Time : 1350 seconds horizontal cross-section at h = 5 mm. channels

Contexte Sarrazin – Hellawell experiment 88 (Pb-Sn) Freckles Dark channels

Cartes Cm h = 0 mm. h = 5 mm. h = 15 mm. h = 10 mm. h = 20 mm. Cm min = 5,13% ; Cm max = 25% Central channel Effect of a moderate rotating e.m.s. Appearance of a central segregation

Pompage d’Eckman Interpretation : stirring in the mushy zone The solute is drained from the wall toward the centre The mushy zone is « washed » by the fluid flow High pressure Low pressure Rotation of the liquid Flow in the mushy zone + 

Effect of moderate travelling fields on the segregations during solidification Two kinds of electromagnetic forces : force of constant amplitude F 0 force with a sinusoidal amplitude F 0 sin(2  t/p) F0F0 10  5 mm 2D-ingot e.m. stirrers Extracted heat flux

Brassage Effect of steady electromagnetic forces Pb-10wt%Sn,F 0 = 1000 N.m -3 Evolution of the averaged solute concentration (Medina et al. 2004) Natural convection electromagnetic stirring (b) Mushy zone Liquid zone Segregated channels Heat flux

TMF effect B = 0 B = 0,35 T B = 0,07 T Experimental evidence : Zaidat et al. (2004) Al-Ni3.5wt.% Travelling magnetic field Cylindrical rod R =5mm B = 30 mT 1mm Central channel segregate

Al-7wt%Si, 10  5 mm 2D-ingot, G T = 1000 K/m, Cooling rate = 24 K/min constant e.m. force modulated force (period = 10 s) averaged solute concentration Freckle suppression by modulated electromagnetic forces

Time evolution of the solidification of a Al- Si 7%wt ingot under modulated e.m. stirring Initial fluid motion liquid fraction

Conclusions 1.Free surfaces AC magnetic fields may be destabilizing even at high frequencies It is possible to create various functions : stirring, emulsion 2.Segregations during solidification The liquid pattern has a significant influence on the segregation stirring in the mushy zone is able to control (partly) the segregations

interpretation by energy balance Magnetic energy : with vol = h a 2, A  p l Surface energy : thus : Emulsion occurs when : l < l c l A

Stability diagram of a mercury drop Inductor current (A) Frequency (Hz) f5f5 f6f6 f4f4 f7f7 unstable region stable region

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