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2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer
Simulations on Stirring with Magnetic Fields1
Simulations on Stirring with Rotating and Traveling Magnetic Fields
K. Frana, J. Stiller ILR, 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 Fields2
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 Fields3
Numerical Methods
Mathematical Model
• Field frequency: ω < 1/μσR2
• Flow velocity: u < ωR<
Maxwell equationsdecouple
Low-induction / low frequencyapproximation:
• Navier-Stokes problem for u
• Lorentz force: f j ×B0
• Current density: j σ(t A0 )
• Electrical potential: 2 0
Direct Numerical Simulation
• Resolve all scales
• No turbulence model
Methods and Codes
MG-FEMFrana, Stiller
2001
• Linear FEM, 2nd order• Parallel, universal• Used in production runs
MG-SEMFladrich, Stiller
2004
• Spectral elements• Parallel, universal• h-adaptive, in validation
SEMTEXBlackburn, Sherwin
2004
• 2d-SEM + Fourier SM• Axisymmetric geometry• Goes for production
2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer
Simulations on Stirring with Magnetic Fields4
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 Fields5
MULTIMAG Facility at FZR
Iron-free coil system Example: measured Br distribution in TMF
• Superposition of rotating, traveling, pulsating and DC fields
• Electric power supply: 500 kW
• Measuring volume: D = 365 mm, H = 400 mm
2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer
Simulations on Stirring with Magnetic Fields6
Results: Traveling Magnetic Field
Code validation: Scaling …
• Lorentz force:
fz F r2 / 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 Fields7
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 Fields8
Results: Rotating magnetic field
Near critical flow, H/D = 1
Ta = 1.2·105 ≈ 0.98 Tac
Ta = 1.3·105 ≈ 1.06 TacTa = 1.1·105 ≈ 0.89 Tac
• 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
2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer
Simulations on Stirring with Magnetic Fields9
Results: Rotating magnetic field
H/D = 1, Ta = 1.3·105 ≈ 1.06 Tac
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 Fields10
Results: Rotating magnetic field
DNS: Ta = 3·105 ≈ 7.5 Tac
Snapshot of instantaneous velocity
Q contours of fluctuation velocity
Key features
• Large-scale azimuthal fluctuations
• Taylor-Görtler vortices
2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer
Simulations on Stirring with Magnetic Fields11
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 = 3·105 ≈ 7.5 Tac
2nd Sino-German Workshop on EPM, Dresden, Oct. 17-18, 2005 Frana, Stiller, Cramer
Simulations on Stirring with Magnetic Fields12
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 Fields13
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
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