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

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

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Electromagnetic levitation: Electromagnetic levitation: global instabilities and the flow global instabilities and the flow

inside a molten sampleinside a molten sample

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


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OutlineOutline1.1. Introduction and basic principles.Introduction and basic principles.2.2. Physical spin-up mechanism of spherical samples.Physical spin-up mechanism of spherical samples.3.3. Stabilization by means of DC magnetic fields.Stabilization by means of DC magnetic fields.4.4. Various technical solutions and their experimental Various technical solutions and their experimental

verifications.verifications.5.5. Instabilities of the melt flow in the levitated droplet;Instabilities of the melt flow in the levitated droplet;6.6. Stabilzing effect of external DC magnetic fields and Stabilzing effect of external DC magnetic fields and

global droplet rotation.global droplet rotation.7.7. Conclusions.Conclusions.


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Electromagnetic levitation- principleElectromagnetic levitation- principle


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Spontaneous oscillations and rotationSpontaneous oscillations and rotation


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Problem definitionProblem 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


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Example: spin-up in uniform fieldExample: spin-up in uniform fieldUniform 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


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Spin-up rate versus AC frequencySpin-up rate versus AC frequency


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Rotation rate of sphere versus frequencyRotation rate of sphere versus frequencyof uniform alternating magnetic fieldof uniform alternating magnetic field


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Oscillatory instabilitiesOscillatory instabilities

Basic idea: nonuniform AC magnetic field similarly to standing wave can be represented as two oppositely travelling fields (waves) !


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Summary of spontaneous rotationSummary of spontaneous rotationand oscillationand oscillation

> c : Bifurcation from the rest state to spontaneous rotationor oscillation

m > c : maximum growth rate of instability

Rotation Oscillation

uniform field linear field linear field

c 11.6 27.7 11.6

m 18.8 47.2 18.8

There is no oscillatory instability for the uniform field !


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Effects of damping d.c. magnetic fieldsEffects of damping d.c. magnetic fields

in general : damps all rotations, except around its axisvertical field : rotation damped, oscillations nothorizontal field : oscillations damped, rotations notstrength : BDC ~ BAC (~5mT) sufficient

to prevent any instabilities• no strong d.c. fields are necessary,• but the field geometry has to be

carefully selected


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Implementation of d.c. fieldsImplementation 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


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Electromagnetic solutionElectromagnetic solution


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Permanent magnet system to Permanent magnet system to suppress oscillating and rotary suppress oscillating and rotary

disturbances of a levitated spheredisturbances of a levitated sphere


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Stabilization with a permanent Stabilization with a permanent magnet systemmagnet system


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Flow in a levitated dropFlow in a levitated drop2 control parameter: frequency and strength B

Non-dimensional: skin-depth interaction parameter

Reynolds number

20

2R

2

24

BRN

maxRe Rv

Axisymmetric basic flow, 3-D instabilities at Re ~ 100 (m = 2,3,4)

(Phys. Fluids, Vol. 15, No. 3, 668-678, 2003)

Uniform field linear field uniform field + DC-field


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Flow in a levitated rotating Flow in a levitated rotating dropdrop

Additional control parameter: Ekman number 2RE

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


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Stability of axisymmetric Stability of axisymmetric base flow (base flow ( = 0.1) = 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


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ConclusionsConclusions•There are several purely electromagnetic instability There are several purely electromagnetic instability mechanisms which may be responsible for spontanous mechanisms which may be responsible for spontanous sample rotations and oscillations; sample rotations and oscillations;

•Sample stabilization against rotations and oscillations Sample stabilization against rotations and oscillations by means of DC fields have been experimentally verified;by means of DC fields have been experimentally verified;

•Stability of melt flow against 3D small-amplitude Stability of melt flow against 3D small-amplitude perturbations have been numerically investigated;perturbations have been numerically investigated;

•Stabilization of the melt flow by means of external DC Stabilization of the melt flow by means of external DC fields and global sample rotation have been numerically fields and global sample rotation have been numerically analyzedanalyzed

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

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