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: stiller@tfd.mw.tu-dresden.de

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)