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FREE SURFACE INSTABILITIES PRODUCED BY HIGH-FREQUENCY MAGNETIC FIELDS

FREE SURFACE INSTABILITIES PRODUCED BY HIGH-FREQUENCY MAGNETIC FIELDS. Christian Karcher Technische Universität Ilmenau. Motivation Model Experiments, Analytical Model Results Conculsions Proposals for Collaboration within Common Project. Motivation: Electromagnetic Shaping.

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FREE SURFACE INSTABILITIES PRODUCED BY HIGH-FREQUENCY MAGNETIC FIELDS

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  1. FREE SURFACE INSTABILITIES PRODUCED BY HIGH-FREQUENCY MAGNETIC FIELDS Christian KarcherTechnische Universität Ilmenau • Motivation • Model Experiments, Analytical Model • Results • Conculsions • Proposals for Collaboration within Common Project 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  2. Motivation: Electromagnetic Shaping Forming of a stable dome during electron beam evaporation Supporting meniscus during spin casting of strips 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  3. Experimental ans Analytical Modelling Electromagnetic Shaping of Drops Experiments: Vaclav Kocourek Theory: Michael Conrath Electromagnetic Sealing of Slits Experiments: Jens-Uwe Mohring Theory: Ch. Karcher, A. Potherat Galinstan 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  4. Model Experiment Drop PARAMETERS • drop Galinstan • current 0 - 320 A • frequency 2- 50 kHz • drop volume 0.2 - 11 ml 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  5. I=100A I=0A I Rmin R0 Static Drop Deformation for I < IC Results of analytical model (Conrath, Karcher: EJM B/Fluids 2004) Sketch of squeezing Experimental results (Kocourek, Karcher, Conrath: Phys. Rev.E 2005) 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  6. Drop Instability for I > IC (m = 3) 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  7. Stability Diagram 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  8. Annulus Control parameters I0, w, L, H, a I0coswt 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  9. Karcher, Mohring in MHD (2003), Mohring, Karcher, Schulze in Phys. Rev. E (2005) 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  10. Small surface waves 1 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  11. Dynamics of the free surface 1 a = 3 mm, H = 24 mm, L = 17 mm, f = 21.9 kHz, I = 120 A • Spectrum of different wavelengths (gravity, capillary) • Amplitudes increase upon increasing I0 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  12. Static surface deformation 1 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  13. Dynamics of the free surface 2 21 1 cm a = 3 mm, H = 24 mm, L = 17 mm, f = 21.9 kHz, I = 127 A • Wavelength corresponding to skin depth: 1 ~ 2p d 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  14. Pinch 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  15. 21 1 cm Pinch development a = 3 mm, H = 24 mm, L = 17 mm, f = 47.2 kHz, I = 123 A 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  16. Theoretical Model Cartesian geometry Hele Shaw approximation I coswt I coswt h(y,t) z,w z pa, pM L p x y,v n Liquid metal r,u,s H g Skin depth approximation 2d magnetic pressure: Lorentz force: j, B from vector potentials Ai, Aa Karcher, Mohring Magnetohydrodynamics 2003 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  17. governing equations boundary conditions 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  18. Linear stabilty analysis for basic state evolution equation Most dangerous mode Neutral instability H Physical interpretation Conclusions 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  19. measured: Icp  -0.218 a = 1 mm, H = 24 mm, L = 22 mm Measurement vs. theory a = 3 mm, H = 30 mm 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  20. Conclusions • Electromagnetic shaping with high-frequency magnetic fields • Squeezing of drops up to 15% possible • Onset of drop instabilities; critical parameters depending on drop volume and inductor current frequeny • 3 Types of surface instabilities: small surface waves, large-amplitude static deformation, electromagnetic pinch • First instability well-predicted by simple model based on Hele Shaw and skin depth approximation • High-frequency fields not suited for sealing purposes Acknoledgements DFG: Research Group Magnetofluiddynamics DAAD: PROCOPE program with EPM Grenoble (Professor Yves Fautrelle) 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  21. 1 3 4 2 Proposal for CollaborationI Lorentz force velocimetry (Thess, Kolesnikov, Karcher: Patent 2005) BMBF project; start 01.07.2006 Measurement of mass flow in liquid aluminum, steel, glass, semiconductor melts 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  22. Proposal for Collaboration II 2nd Sino-German Workshop on Electromagnetic Processing of Materials

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