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Simulations on Stirring with Rotating and Traveling Magnetic Fields

Simulations on Stirring with Rotating and Traveling Magnetic Fields K. Frana, J. Stiller ILR, TU Dresden, Germany & A. Cramer FZ Rossendorf, Germany. SFB 609. Supported by DFG. Motivation and Objectives. Central topic: Stirring with alternating magnetic fields. Rotating (RMF)

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Simulations on Stirring with Rotating and Traveling Magnetic Fields

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  1. Simulations on Stirring with Rotating and Traveling Magnetic Fields K. Frana, J. StillerILR, TU Dresden, Germany & A. CramerFZ Rossendorf, Germany SFB 609 Supported by DFG 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  2. Motivation and Objectives Central topic: Stirring with alternating magnetic fields • Rotating (RMF) • Traveling (TMF) • Pulsating (PMF) • Design of tailored superposition fields rotating traveling 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  3. Numerical Methods Direct Numerical Simulation Mathematical Model • Field frequency: ω<1/μσR2 • Flow velocity: u<ωR • Resolve all scales • No turbulence model < Maxwell equationsdecouple Methods and Codes • Low-induction / low frequency • approximation: • Navier-Stokes problem foru • Lorentz force: fj×B0 • Current density: jσ(t A0) • Electrical potential: 20 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  4. Computational Ressources • 2004 • 2 SGI O3800 approx. 200 CPUs, Central computing facility (URZ) • Heavily overcrowded • A few up-to-date PCs • 2005 (since October) • SGI Prism, 6 Itanium, 2 GPUs, 30 GB RAM (ILR) • 128 CPU Opteron Cluster (64 CPUs dedicated to ILR) • 25 Athlon64 PCs + Server + 6 TB RAID (ILR) • SGI Altix, 200 Itanium (URZ) 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  5. MULTIMAG Facility at FZR Example: measured Br distribution in TMF Iron-free coil system • Superposition of rotating, traveling, pulsating and DC fields • Electric power supply: 500kW • Measuring volume: D = 365mm, H = 400mm 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  6. Results: Traveling Magnetic Field Code validation: Scaling … • Lorentz force: fzFr2/2 • Forcing parameter:FσωB2kR5 / (4ρν2) • Reference data: Linear stability analysis (Grants & Gerbeth 2004) 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  7. Results: Traveling Magnetic Field Code validation: … and linear instability • Theory (GG2004) • Critical forcing Fc = 120400 • Mode: k = 3 • Frequency: λi,c = 219.0 • Simulation • Linear FEM • Tetrahedral grid, Δx ≈ R/30 • Most unstable mode: k = 3 • Frequency: λi,c = 218.1 • Similar/better results using • SEM/SM code semtex: • On the way 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  8. Results: Rotating magnetic field Near critical flow, H/D= 1 Ta = 1.1·105 ≈ 0.89Tac Ta = 1.3·105 ≈ 1.06Tac • Linear stability analysis, experimental studyby Grans & Gerbeth (2001 – 2004) • Undisturbed flow practically stable forTa/ Tac = 0.89, 0.98 • But susceptible to finite perturbations(1%, random) • Precursor of linear instabiliy shows up,but nonlinear effects prevail Ta = 1.2·105 ≈ 0.98Tac 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  9. Results: Rotating magnetic field H/D= 1, Ta= 1.3·105 ≈ 1.06Tac Contours of azimuthal velocity Vortex (Q) contours Is this flow axisymmetric? 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  10. Results: Rotating magnetic field DNS: Ta= 3·105 ≈ 7.5Tac Snapshot of instantaneous velocity • Key features • Large-scale azimuthal fluctuations • Taylor-Görtler vortices Q contours of fluctuation velocity 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  11. Results: Rotating magnetic field DNS: Ta= 3·105 ≈ 7.5Tac • Wave and frequency spectra • Locally 2D: higher fluctuaction energy in r,z-components – effect of TG „rolls“ • Globally 3D, 66% of energy in modes 1-3, scaling indicates non-equilibrium • Taylor hypothesis applies, good agreement with experiment 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  12. Results: Rotating magnetic field DNS + Experiment, H/D = 1.5, scaling of mean velocity Profiles of azimuthal mean velocity Scaling of some mean-flow parameters 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

  13. Further Research • Spin-up in rotating and traveling Fields (video) • LES for higher (more realistic) forcing • Integration of thermal transport Cooperation – possible in either of these fields 2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields

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