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VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK MHD results in a liquid sodium turbulent flow: the VKS experiment.

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Presentation on theme: "VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK MHD results in a liquid sodium turbulent flow: the VKS experiment."— Presentation transcript:

1 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK 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

2 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK The dynamo problem spontaneous growth of a magnetic field in a moving conducting fluid instability in the presence of noise because of turbulence at the origin of the fields observed : Earth Sun theories and numerical simulations of models experiments: essential but difficult  sodium

3 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK  3 control parameters: MHD equations Dynamo action: instability Rm > Rm c Typical experiments: Rm = 10 2, Re = 10 7, Pm = 10 -5

4 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Role of turbulence on dynamo action Rm c Noise intensity Rm c Problem of turbulence: v = + v’ kinematic dynamo: gives Rm c (induction eq.) Leprovost-Dubrulle (EPJB 2005): Rm c = f(noise)

5 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Role of turbulence on dynamo action Ponty et al, PRL 2006 Laval, Blaineau, Leprovost, Dubrulle, FD: PRL 2006 Taylor-Green flow: Vx=sinx cosy cosz Vy=-cosx siny cosz Vz=0

6 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Turbulent dynamo projects : competition *Karlsruhe VKS Dynamo experiments

7 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Dynamo experiments ~ fusion? ٱ VKS2

8 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Constrained dynamos: success in 2000 Riga Karlsruhe

9 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Role of turbulence on dynamo action Riga and Karlsruhe: «small» noise - Rm c experiment = Rm c 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 > Rm c mean flow

10 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS1 : experimental conditions B P H   R Von Karman flow in a cylindrical container (70 l) sodium loop (250 l) H=2 x R = 0,4 m 2 motors 75 kW 2 propellers frequency  0 à 25 Hz (Reynolds number Re = 6.10 6 ) Hall probe  B pressure probe  P Maximal magnetic Reynolds number: R m =  0  R 2 2   40

11 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS1 experiment in CEA/Cadarache

12 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS1 :  effect (differential rotation) axial B 0 applied  transverse b y induced B0B0 B tt BiBi Bx By Bz o: b x  : b y  : b z Bourgoin et al. Phys. Fluids 202

13 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK V B0B0 BfBf B0B0 =BiBi +  + Dynamo mechanisms:  effect

14 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS1 : helicity  effect (1 propeller) transverse B 0 applied  transverse J=  B 0 1) 1 st step B0B0 V tor J1J1 B1B1 By Bz Bx 2) 2 nd step V pol B1B1 JJ BB BB Bx Bz By o: b x  : b y  : b z Petrelis et al. PRL 2003

15 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK V1V1 B0B0 V2V2 B1B1 BfBf j  ~  B Dynamo mechanisms:  effect

16 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS1 : comparison with code (1 propeller) Experiment: : b x : b y : b z Numerics: : b x : b y : b z transverse B 0 difference: boundary conditions, turbulence ? Marié et al., EPJB 2003

17 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS1 : helicity  and  effects o: b x  : b y  : b z transverse B 0 applied  axial b x + transverse b y induced Marié et al., Magnetohydrodynamics 2002

18 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS1: fluctuations of B Evolution of B in presence of transverse B 0 =3G (  = 24 Hz)  > 24 Hz : spectrum of Kolmogorov type  < 24 Hz : spectrum f -1 ~ Karlsruhe exp.

19 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS1 experiment: conclusion 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 - R m c = 60 based on mean flow for TM 60 propellers:  f c = 44 Hz (P c =750 kW / 150 kW available)

20 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS2 experiment (since 2005) VKS2: a dynamo / mean flow - max R m = 55 > R m c = 43  optimisation - max P = 300 kW > P c = 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 - fluctuations of B dynamo : intermittency?

21 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS2 experiment: optimisation von Karman flow inside a cylindrical copper container copper shell with sodium at rest (cf. Riga)

22 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK 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 VKS2 experiment: optimisation

23 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Experimental mean flow (LDV or PIV) poloidal toroidal

24 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK - mean velocity field - temporal integration of induction equation Marié et al., EPJB 33, 469, 2003 axially periodic flow cylinder of uniform conductivity surrounded by infinite insulator layer of stationary conductor of same conductivity arround flow finite differences z r 0 w FFT  Kinematic dynamo code (J. Léorat)

25 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK w=0.4, threshold divided by 4 (power divided by 64!) 180 40 Influence of conducting shell on Rmc Ravelet et al.,Phys. Fluids 2005

26 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Comparison between codes Stefani et al. EJM/B 2006 Nore et al. 2006 max

27 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK max

28 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK 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 Neutral mode structure

29 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK magnetic field B current density j w=0w=0.6 B-lines are smoothed : weaker ohmic dissipation Current loops can now close outside the flow Changes of B/j-lines topology

30 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Comparison with MND analytical flow TM73 Exp. flow MND Anal. flow For w=0 and Γ=0.8: - optimal experimental flow Rm c =180 - analytical flow Rm c =58 Marié, Normand and Daviaud, Phys. Fluids 2005

31 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK 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%

32 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK VKS2 experiment 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 cooler new mechanical seals

33 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Experimental plateform

34 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK container

35 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Inside of container

36 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Response to a transverse applied B 0

37 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Transverse applied B 0 : time series of B induced Rm=15Rm=47

38 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Transverse applied B 0 : PDF of Binduced Bx: bimodal, By: exponential tails Rm = 40

39 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK PDF of Bx PDF of By high B-state low B-state

40 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Transverse applied B 0 : spectra of Binduced Slopes ≠ VKS1

41 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Mean B induced =f(Rm)rms B induced =f(Rm) Transverse B 0 : evolution of Binduced with Rm No saturation: ≠ VKS1 Bx By Bz

42 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Transverse B 0 : comparison exp. / simulation

43 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Response to a localized B 0 M: magnet (1000 -10 G) P: Hall probe

44 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Localized B 0 : time series of B induced at Rm = 25 Intermittency, no coherence between components

45 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Localized B 0 : evolution with Ω of mean and rms Binduced B xrms B yrms B zrms

46 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Localized B 0 : spatial decay of rms Binduced B xrms B yrms B zrms Decay length: 100 mm ~ integral scale

47 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Localized B 0 : PDF of fluctuations of Binduced Rm = 25 B xrms B yrms B zrms Exponential tails ~ random advection of scalar field

48 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Localized B 0 : spectra of Binduced

49 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Conclusion 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

50 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Comparison mean / instantaneous flow (PIV) Mean: 5000 fields sampled at 5 Hz

51 VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris 26th June - 1st July, 2006Warwick, UK Shear layer: vortices

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