MHD results in a liquid sodium turbulent flow: the VKS experiment

1. MHD results in a liquid sodium turbulent flow: the VKS experiment F. Daviaud, A. Chiffaudel, B. Dubrulle, C. Gasquet, J. Burguete, L. Marié, F. Ravelet, R. Monchaux, V. Padilla CEA/Saclay S. Fauve, F. Pétrélis, N. Mordant, M.Berhanu ENS-Paris J.-F. Pinton, P. Odier, M. Bourgoin, R. Volk, M. Moulin ENS-Lyon Warwick, UK

2. spontaneous growth of a magnetic field in a moving conducting fluid • instability in the presence of noise because ofturbulence • at the origin of the fields observed : • Earth Sun • theories and numerical simulations of models • experiments: essential but difficult sodium The dynamo problem Warwick, UK

3. 3 control parameters: MHD equations Typical experiments: Rm = 102, Re = 107 , Pm = 10-5 Dynamo action: instability Rm > Rmc Warwick, UK

4. Rmc Rmc <v> Noise intensity • Problem of turbulence: v = <v> + v’ • kinematic dynamo: <v> gives Rmc <v> (induction eq.) • Leprovost-Dubrulle (EPJB 2005): Rmc= f(noise) Role of turbulence on dynamo action Warwick, UK

5. Ponty et al, PRL 2006 • Laval, Blaineau, Leprovost, Dubrulle, FD: PRL 2006 Role of turbulence on dynamo action Taylor-Green flow: Vx=sinx cosy cosz Vy=-cosx siny cosz Vz=0 Warwick, UK

6. Dynamo experiments Turbulent dynamo projects : competition *Karlsruhe VKS Warwick, UK

7. ٱVKS2 Dynamo experiments ~ fusion? Warwick, UK

8. Constrained dynamos: success in 2000 Riga Karlsruhe Warwick, UK

9. Riga and Karlsruhe: «small» noise • Rmc experiment = Rmc mean flow • but exp. saturation Energy ≠ laminar • Madison: « large» noise; 2006: no dynamo action? • → VKS project since 1998: « large » noise • VKS1 experiment (2000-2003): no dynamo action • VKS2 experiment (2005) : Rm max > Rmc mean flow Role of turbulence on dynamo action Warwick, UK

10. B  R  P H Von Karman flow in a cylindrical container (70 l) sodium loop (250 l) VKS1 : experimental conditions • H=2 x R = 0,4 m • 2 motors 75 kW • 2 propellers • frequency : 0 à 25 Hz • (Reynolds number Re = 6.106) • Hall probe  B • pressure probe  P Maximal magnetic Reynolds number: Rm=0 R2 2  40 Warwick, UK

11. VKS1 experiment in CEA/Cadarache Warwick, UK

12. Btt Bi B0 By Bz Bx VKS1 :  effect (differential rotation) o: bx: by: bz axial B0applied  transverseby induced Bourgoin et al. Phys. Fluids 202 Warwick, UK

13. V B0 Bf = + Bi B0 +  Dynamo mechanisms:  effect Warwick, UK

14. Vtor B0 B1 J1 BH JH Vpol B1 Bz BH Bz By Bx By Bx 1) 1st step VKS1 : helicity  effect (1 propeller) o: bx: by: bz 2) 2nd step transverse B0 applied transverse J=  B0 Petrelis et al. PRL 2003 Warwick, UK

15. j ~  B B0 B1 Bf V1 V2 Dynamo mechanisms: effect Warwick, UK

16. VKS1 : comparison with code (1 propeller) transverse B0 Experiment: : bx: by: bz Numerics: : bx: by: bz difference: boundary conditions, turbulence ? Marié et al., EPJB 2003 Warwick, UK

17. o: bx: by: bz VKS1 : helicity  and  effects transverse B0applied  axial bx + transverseby induced Marié et al., Magnetohydrodynamics 2002 Warwick, UK

18. VKS1: fluctuations of B • Evolution of B in presence of transverseB0=3G ( = 24 Hz) •  > 24 Hz : spectrum of Kolmogorov type •  < 24 Hz : spectrum f-1~ Karlsruhe exp. Warwick, UK

19. VKS 1 : • - new results on magnetic induction (mean and fluctuations) • - basic ingredients for dynamo action ( and  effects) but • no dynamo • Limitations: • - absence of cooling system 40 secs runs at full power • - problems with seals  argon bubbles inside, reliability • - Rmc = 60based on mean flow for TM 60 propellers: •  fc = 44 Hz (Pc =750 kW / 150 kW available) VKS1 experiment: conclusion Warwick, UK

20. VKS2 experiment (since 2005) • VKS2: a dynamo / mean flow • - max Rm= 55 > Rmc = 43optimisation • - max P = 300 kW > Pc = 150 kW • - cylindrical shell of sodium at rest (of thickness 0.4 R) • Study of: • - effect of turbulence on a dynamo mean flow : dynamo? • - non linear saturation regimes; scaling of <B> • - fluctuations of Bdynamo: intermittency? Warwick, UK

21. von Karman flow inside a cylindrical copper container • copper shell with sodium at rest (cf. Riga) VKS2 experiment: optimisation Warwick, UK

22. VKS2 experiment: optimisation • Topology of the mean flow (geometry of the impellers) : optimal impellers of radius 0.75 with curved blades • Numerical variation of the ratio of the mean poloïdal flow to the mean toroïdal flow: an optimal value close to 0.7-0.8 • Conducting shell thickness : strongly reduces the threshold and changes the neutral mode structure Warwick, UK

23. Experimental mean flow (LDV or PIV) poloidal toroidal Warwick, UK

24.  FFT z FFT 0 w r Kinematic dynamo code (J. Léorat) - mean velocity field - temporal integration of induction equation • axially periodic flow • cylinder of uniform conductivity • surrounded by infinite insulator layer of stationary conductor of same conductivity arround flow finite differences Marié et al., EPJB 33, 469, 2003 Warwick, UK

25. 180 40 Influence of conducting shell on Rmc w=0.4, threshold divided by 4 (power divided by 64!) Ravelet et al.,Phys. Fluids 2005 Warwick, UK

26. Comparison between codes • Stefani et al. • EJM/B 2006 • Nore et al. 2006 max Warwick, UK

27. max Warwick, UK

28. Neutral mode structure Stationary in time Azimuthal dependance m=1 • concentrated near axis in 2 twisted banana-shaped regions • 2 folded sheets of transverse field near the boundary : external dipole • bananas are still here • Sheets have grown in axial and azimuthal directions Warwick, UK

29. Current loops can now close outside the flow Changes of B/j-lines topology B-lines are smoothed : weaker ohmic dissipation magnetic field B w=0 w=0.6 current density j Warwick, UK

30. Comparison with MND analytical flow MND Anal. flow For w=0 and Γ=0.8: • optimal experimental flow Rmc=180 - analytical flow Rmc=58 TM73 Exp. flow Marié, Normand and Daviaud, Phys. Fluids 2005 Warwick, UK

31. Neutral mode structure of « MND » analytical flow • eigenmode already have developped sheets of transverse dipolar field • layer of stationary conductor: threshold reduction of only 26% Warwick, UK

32. H=2 x R = 0,6 m  170 l sodium • 4 motors 75 kW  P =300 kW; T = 1000 Nm • 2 propellers :0 à 35 Hz VKS2 experiment • cooler • new mechanical seals Warwick, UK

33. Experimental plateform Warwick, UK

34. container Warwick, UK

35. Inside of container Warwick, UK

36. Response to a transverse applied B0 Warwick, UK

37. Transverse applied B0 :time series of Binduced Rm=15 Rm=47 Warwick, UK

38. Transverse applied B0 : PDF of Binduced Rm = 40 Bx: bimodal, By: exponential tails Warwick, UK

39. high B-state PDF of Bx low B-state PDF of By Warwick, UK

40. Transverse applied B0 :spectra of Binduced Slopes ≠ VKS1 Warwick, UK

41. Transverse B0 :evolution of Binduced with Rm Bx By Bz Mean Binduced=f(Rm) rms Binduced=f(Rm) No saturation: ≠ VKS1 Warwick, UK

42. Transverse B0 : comparison exp. / simulation <Bx> <By> <Bz> Warwick, UK

43. Response to a localized B0 M: magnet (1000 -10 G) P: Hall probe Warwick, UK

44. Localized B0 : time series of Binduced at Rm = 25 Intermittency, no coherence between components Warwick, UK

45. Localized B0: evolution with Ω of mean and rms Binduced Bxrms Byrms Bzrms <Bx> <By> <Bz> Warwick, UK

46. Localized B0: spatial decay ofrms Binduced Bxrms Byrms Bzrms Decay length: 100 mm ~ integral scale Warwick, UK

47. Localized B0 : PDF of fluctuations of Binduced Bxrms Byrms Bzrms Rm = 25 Exponential tails ~ random advection of scalar field Warwick, UK

48. Localized B0 : spectra of Binduced Warwick, UK

49. Response of the von karman turbulent flow to: • - transverse field : fluctuations; amplification >1; no saturation • localized field : influence of fluctuations, intermittency • VKS2: dynamo /mean field simulations •  influence of turbulence on threshold, dynamics, saturation? • next run in July 2006 Conclusion Warwick, UK

50. Comparison mean / instantaneous flow (PIV) Mean: 5000 fields sampled at 5 Hz Warwick, UK