1. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 1 J. Stiller, K. Frana, R. Grundmann TU Dresden, Germany & A. Cramer, K. Varshney, G. Gerbeth FZ Rossendorf, Germany email: stiller@tfd.mw.tu-dresden.de SFB 609 Supported by DFG

2. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 2 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

3. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 3 Previous work …

4. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 4 Previous work …

5. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 5 Previous work …

6. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 6 … Achievements

7. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 7 … Achievements

8. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 8 Numerics I 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 2004 2d-SEM + Fourier SM Axisymmetric geometry Under consideration

9. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 9 Numerics II PSPG, linear shape functions AB2 time integration 2 nd 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 ~ 10 5 tets, 32 partitions Finite Element Solver Convergence study: RMF driven flow in infinite cylinder

10. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 10 MULTIMAG Facility at FZR Iron-free coil system Example: measured B r distribution in TMF Superposition of rotating, traveling, pulsating and DC fields Electrical power supply: 500 kW Measurement volume: D = 365 mm, H = 400 mm

11. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 11 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

12. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 12 Results: RMF I 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

13. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 13 Results: RMF II TG vortices at various Taylor numbers 1.125 Ta c 7.5 Ta c 2.5 Ta c

14. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 14 Results: RMF III Turbulence spectra at 7.5 Ta c Comparison of frequency and wave spectra at r/R = ¾, assuming validity of Taylor’s hypothesis

15. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 15 Results: RMF III Comparison of frequency and wave spectra at r/R = ¾, assuming validity of Taylor’s hypothesis Turbulence spectra at 7.5 Ta c

16. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 16 Results: RMF III DNS resolved Comparison of frequency and wave spectra at r/R = ¾, assuming validity of Taylor’s hypothesis Turbulence spectra at 7.5 Ta c

17. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 17 Results: RMF III DNS resolved Slope k  4 or steeper in short-wave part of inertial subrange No harmonics Significant contribution of frequencies 1/2 … 1/10 ω F Comparison of frequency and wave spectra at r/R = ¾, assuming validity of Taylor’s hypothesis Turbulence spectra at 7.5 Ta c

18. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 18 Results: PMF Pulsating magnetic field: Experiment Vertical profile of axial velocity near rim (UDV, bottom left) Observations 90% of kinetic energy is „turbulent“ Low-frequency oscillations are dominant f Setup and expected flow

19. Sino-German Workshop on EPM, Shanghai, Oct. 11-12, 2004 Stiller, Frana, Grundmann, Cramer, Varshney, Gerbeth Numerical and Experimental Studies on Electromagnetic Stirring 19 Summary Conclusions Excellent agreement between DNS and experimental results for RMF driven flow up to ~ 10 Ta c 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)