electromagnetic levitation: global instabilities and the flow inside a molten sample
DESCRIPTION
J. Priede 1,2 , G. Gerbeth 2 , V. Shatrov 2 , Yu. Gelfgat 1 1 Institute of Physics, University of Latvia (IPUL) LV-2169 Salaspils, Latvia 2 Forschungszentrum Rossendorf (FZR), D-01314 Dresden, Germany. Electromagnetic levitation: global instabilities and the flow inside a molten sample. - PowerPoint PPT PresentationTRANSCRIPT
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
Rossendorf
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
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
Rossendorf
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.
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
Rossendorf
Electromagnetic levitation- principleElectromagnetic levitation- principle
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
Rossendorf
Spontaneous oscillations and rotationSpontaneous oscillations and rotation
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
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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
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
Rossendorf
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
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
Rossendorf
Spin-up rate versus AC frequencySpin-up rate versus AC frequency
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
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Rotation rate of sphere versus frequencyRotation rate of sphere versus frequencyof uniform alternating magnetic fieldof uniform alternating magnetic field
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
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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) !
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
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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 !
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
Rossendorf
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
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
Rossendorf
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
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
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Electromagnetic solutionElectromagnetic solution
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
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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
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
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Stabilization with a permanent Stabilization with a permanent magnet systemmagnet system
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
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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
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
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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
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
Rossendorf
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
Sino-German Workshop on Electromagnetic Processing of Materials, Shanghai, Oct. 11-13, 2004 Forschungszentrum
Rossendorf
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