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