2 nd Sino-German Workshop on EPM, Dresden, Oct , 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields 1 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

2 nd Sino-German Workshop on EPM, Dresden, Oct , 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 rotatingtraveling

2 nd Sino-German Workshop on EPM, Dresden, Oct , 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields 3 Numerical Methods Mathematical Model Field frequency: ω < 1/μσR 2 Flow velocity: u < ωR < Maxwell equations decouple Low-induction / low frequency approximation: Navier-Stokes problem for u Lorentz force: f  j ×B 0 Current density: j  σ(  t A 0  ) Electrical potential:  2   0 Direct Numerical Simulation Resolve all scales No turbulence model Methods and Codes MG-FEM Frana, Stiller 2001 Linear FEM, 2 nd order Parallel, universal Used in production runs MG-SEM Fladrich, Stiller 2004 Spectral elements Parallel, universal h -adaptive, in validation SEMTEX Blackburn, Sherwin d-SEM + Fourier SM Axisymmetric geometry Goes for production

2 nd Sino-German Workshop on EPM, Dresden, Oct , 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields 4 Computational Ressources 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)

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

2 nd Sino-German Workshop on EPM, Dresden, Oct , 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields 6 Results: Traveling Magnetic Field Code validation: Scaling … Lorentz force: f z  F r 2 / 2 Forcing parameter: F  σωB 2 kR 5 / (4ρν 2 ) Reference data: Linear stability analysis (Grants & Gerbeth 2004)

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

2 nd Sino-German Workshop on EPM, Dresden, Oct , 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields 8 Results: Rotating magnetic field Near critical flow, H/D = 1 Ta = 1.2·10 5 ≈ 0.98 Ta c Ta = 1.3·10 5 ≈ 1.06 Ta c Ta = 1.1·10 5 ≈ 0.89 Ta c Linear stability analysis, experimental study by Grans & Gerbeth (2001 – 2004) Undisturbed flow practically stable for Ta/ Ta c = 0.89, 0.98 But susceptible to finite perturbations (1%, random) Precursor of linear instabiliy shows up, but nonlinear effects prevail

2 nd Sino-German Workshop on EPM, Dresden, Oct , 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields 9 Results: Rotating magnetic field H/D = 1, Ta = 1.3·10 5 ≈ 1.06 Ta c Contours of azimuthal velocityVortex (Q) contours Is this flow axisymmetric?

2 nd Sino-German Workshop on EPM, Dresden, Oct , 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields 10 Results: Rotating magnetic field DNS: Ta = 3·10 5 ≈ 7.5 Ta c Snapshot of instantaneous velocity Q contours of fluctuation velocity Key features Large-scale azimuthal fluctuations Taylor-Görtler vortices

2 nd Sino-German Workshop on EPM, Dresden, Oct , 2005 Frana, Stiller, Cramer Simulations on Stirring with Magnetic Fields 11 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 Results: Rotating magnetic field DNS: Ta = 3·10 5 ≈ 7.5 Ta c

2 nd Sino-German Workshop on EPM, Dresden, Oct , 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 velocityScaling of some mean-flow parameters

2 nd Sino-German Workshop on EPM, Dresden, Oct , 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