Electromagnetic levitation: global instabilities and the flow inside a molten sample

1. J. Priede1,2, G. Gerbeth2, V. Shatrov2, Yu. Gelfgat1 1Institute of Physics, University of Latvia (IPUL) LV-2169 Salaspils, Latvia 2Forschungszentrum Rossendorf (FZR), D-01314 Dresden, Germany Electromagnetic levitation: global instabilities and the flow inside a molten sample Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

2. Outline • Introduction and basic principles. • Physical spin-up mechanism of spherical samples. • Stabilization by means of DC magnetic fields. • Various technical solutions and their experimental verifications. • Instabilities of the melt flow in the levitated droplet; • Stabilzing effect of external DC magnetic fields and global droplet rotation. • Conclusions. Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

3. Electromagnetic levitation- principle Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

4. Spontaneous oscillations and rotation Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

5. Problem definition uniform field (heating): B = Bocos(t)ez linear field (positioning): B = Bocos(t)(r-3zez) skin depth:  = 1/()1/2 non-dimensional frequency:  = R2 = (R/)2 Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

6. Example: spin-up in uniform field Uniform AC field = two counter-rotating fields: Bo = Bocos(t)ez = Bo(cos(t)ez ±½sin(t)ex)=B++B-, where B± =½Bo(cos(t)ez ±½sin(t)ex) • Torque in AC field for slow sample rotations (<<): • 1/2[M(-)-M(+)]  -dM/d  =  , • where = -dM/d is spin-up rate • < 0   = 0 STABLE • > 0    0 UNSTABLE Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

7. Spin-up rate versus AC frequency Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

8. Rotation rate of sphere versus frequencyof uniform alternating magnetic field Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

9. Oscillatory instabilities Basic idea: nonuniform AC magnetic field similarly to standing wave can be represented as two oppositely travelling fields (waves) ! Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

10. Summary of spontaneous rotationand oscillation  > c : Bifurcation from the rest state to spontaneous rotation or oscillation m > c : maximum growth rate of instability There is no oscillatory instability for the uniform field ! Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

11. Effects of damping d.c. magnetic fields in general: damps all rotations, except around its axis vertical field : rotation damped, oscillations not horizontal field : oscillations damped, rotations not strength : BDC ~ BAC (~5mT) sufficient • to prevent any instabilities • no strong d.c. fields are necessary, • but the field geometry has to be carefully selected Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

12. Implementation of d.c. fields 2 alternatives: • electromagnetic - vertical, damps rotation, via d.c. offset to the a.c. current - an additional horizontal field damps oscillations • permanent magnets - appropriate arrangement of magnetic poles provides a cusp-field which is 3-dimensional Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

13. Electromagnetic solution Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

14. Permanent magnet system to suppress oscillating and rotary disturbances of a levitated sphere Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

15. Stabilization with a permanent magnet system Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

16. Flow in a levitated drop 2 control parameter: frequency  and strength B Non-dimensional: skin-depthinteraction parameter Reynolds number Uniform field linear field uniform field + DC-field Axisymmetric basic flow, 3-D instabilities at Re ~ 100 (m = 2,3,4) (Phys. Fluids, Vol. 15, No. 3, 668-678, 2003) Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

17. Flow in a levitated rotating drop Additional control parameter: Ekman number Experiments at IFW with Nd-Fe-B: R ~ 3.5 mm, F = 6...8 Hz,  = 7.8 g/cm3,  = 0.8x10-6 m2/s  ~ 0.25, N ~ 3x106, E ~ 2x10-3 Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

18. Stability of axisymmetric base flow ( = 0.1) Global rotation of relevance for E < 2x10-2 Global rotation destabilizes the flow only within 7x10-3 < E < 2x10-2 (Rec ~ 20, m = 2) For E < 7x10-3 the flow is stabilized for decreasing E Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004

19. Conclusions • There are several purely electromagnetic instability mechanisms which may be responsible for spontanous sample rotations and oscillations; • Sample stabilization against rotations and oscillations by means of DC fields have been experimentally verified; • Stability of melt flow against 3D small-amplitude perturbations have been numerically investigated; • Stabilization of the melt flow by means of external DC fields and global sample rotation have been numerically analyzed Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004