numerical and experimental studies on electromagnetic stirring
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Numerical and Experimental Studies on Electromagnetic Stirring J. Stiller , K. Frana, R. Grundmann TU Dresden, Germany & A. Cramer, K. Varshney, G. Gerbeth FZ Rossendorf, Germany email: [email protected]. SFB 609. Supported by DFG. Motivation and Objectives. - PowerPoint PPT PresentationTRANSCRIPT
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring1
Numerical and Experimental Studies on Electromagnetic Stirring
J. Stiller, K. Frana, R. Grundmann TU Dresden, Germany
&
A. Cramer, K. Varshney, G. GerbethFZ Rossendorf, Germany
email: [email protected]
SFB 609
Supported by DFG
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring2
Motivation and Objectives
Central topic: Stirring with alternating magnetic fields
• Rotating (RMF)• Traveling (TMF)• Pulsating (PMF)
• Design of tailored superposition fields
Rotating Field
• Aspect ratio H/D
• Taylor number
2
42
2 RB
Ta
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring3
Previous work …
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring4
Previous work …
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring5
Previous work …
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring6
… Achievements
Ru
max,u
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring7
… Achievements
Ru
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring8
Numerics I
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• Under consideration
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring9
Numerics II
• PSPG, linear shape functions
• AB2 time integration
• 2nd order in space and time
• 8 … 12 million elements
• local grid refinement to resolve Bödewadt layers
• linear stability threshold[Grants & Gerbeth 2002] reproduced within 0.2%
Initial grid ~ 105 tets,32 partitions
Finite Element Solver
Convergence study: RMF driven flowin infinite cylinder
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring10
MULTIMAG Facility at FZR
Iron-free coil system Example: measured Br distribution in TMF
• Superposition of rotating, traveling, pulsating and DC fields
• Electrical power supply: 500 kW
• Measurement volume: D = 365 mm, H = 400 mm
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring11
Measurement Techniques
„Standard“ vs. miniaturized PD sensors Calibration curves of the PD sensors
Potential difference Sensors• Mini-sensor is only weakly invasive
• Turbulence measurements possible
• Expensive electronics required
Ultrasonic Doppler Velocimetry• Non-invasive
• Measurement of velocity profiles
• Less sensitive than PD
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring12
Results: RMF I
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
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring13
Results: RMF II
TG vortices at various Taylor numbers
1.125 Tac 7.5 Tac2.5 Tac
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring14
Results: RMF III
Turbulence spectra at 7.5 Tac
Comparison of frequency and wave spectra at r/R = ¾, assuming validity ofTaylor’s hypothesis
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring15
Results: RMF III
Comparison of frequency and wave spectra at r/R = ¾, assuming validity ofTaylor’s hypothesis
Turbulence spectra at 7.5 Tac
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring16
Results: RMF III
• DNS resolved
Comparison of frequency and wave spectra at r/R = ¾, assuming validity ofTaylor’s hypothesis
Turbulence spectra at 7.5 Tac
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring17
Results: RMF III
• DNS resolved
• Slope k4 or steeper inshort-wave part of inertial subrange
• No harmonics
• Significantcontribution of frequencies1/2 …1/10 ωF
Comparison of frequency and wave spectra at r/R = ¾, assuming validity ofTaylor’s hypothesis
Turbulence spectra at 7.5 Tac
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring18
Results: PMF
Pulsating magnetic field: Experiment
Vertical profile of axial velocity near rim (UDV, bottom left)
Observations• 90% of kinetic energy
is „turbulent“
• Low-frequencyoscillations are dominant
f
Setup and expected flow
Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth
Numerical and Experimental Studies on Electromagnetic Stirring19
Summary
Conclusions• Excellent agreement between DNS and experimental results for RMF driven flow up
to ~ 10 Tac
• Taylor-Görtler vortices and associated large-scale fluctuations provide an efficient mixing mechanism which is complemented by the mean secondary flow
• Both, RMF and PMF driven flows, are dominated by long-lived structures which give rise to low-frequency oscillations and thus render RANS methods useless
Perspectives• Continued investigation of magnetically driven flows based on DNS and
experiments: TMF, PMF, combined fields, spin-up
• Large-Eddy-Simulations at higher Reynolds numbers
• Tailored fields for more efficient stirring and mixing
• Non-isothermal flows
• Electromagnetic flow control for CG model configuration (joint effort in SFB 609)