mhd results in a liquid sodium turbulent flow: the vks experiment

26th June - 1st July, 2006 Warwick, UK

VKS collaboration: CEA - CNRS - ENS Lyon - ENS Paris

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



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



0)( , )(

0)( ,)()(

vdivvPpgradRvgradvRt

v

BdivBvgradBRBgradvRt

B

mmm

mm

3 control parameters: ,LVRm ,mPV

LBN

2

BBrotRm

)(

MHD equations

Dynamo action: instability Rm > Rmc

Typical experiments: Rm = 102, Re = 107 , Pm = 10-5



Role of turbulence on dynamo action

Rmc

Noise intensity

Rmc <v>

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• Ponty et al, PRL 2006• Laval, Blaineau, Leprovost, Dubrulle, FD: PRL 2006

1

10

100

1 10 100 1000

Rm

Re

Taylor-Green flow:

Vx=sinx cosy cosz

Vy=-cosx siny cosz

Vz=0



Turbulent dynamo projects : competition*Karlsruhe

VKS

Dynamo experiments



Dynamo experiments ~ fusion?

VKS2 ٱ



Constrained dynamos: success in 2000

Riga

Karlsruhe



Role of turbulence on dynamo action

• 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



VKS1 : experimental conditions

B

PH

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 = 6.106)• Hall probe B• pressure probe P

Maximal magnetic Reynolds number: Rm=0 R2 2 40



VKS1 experiment in CEA/Cadarache



VKS1 : effect (differential rotation)

axial B0 applied transverse by induced

B0

Btt Bi

Bx

By

Bz

o: bx : by : bz

Bourgoin et al. Phys. Fluids 202



V B0 Bf B0= Bi++

Dynamo mechanisms: effect



VKS1 : helicity effect (1 propeller)

transverse B0 applied transverse J= B0

1) 1st step

B0

Vtor

J1

B1

By

Bz

Bx

2) 2nd step

Vpol

B1

J

B

B

Bx

Bz

By

o: bx : by : bz

Petrelis et al. PRL 2003



V1

B0

V2

B1

Bf

j ~ B

Dynamo mechanisms: effect



VKS1 : comparison with code (1 propeller)

Experiment:

: bx : by : bz

Numerics:

: bx : by : bz

transverse B0

difference: boundary conditions, turbulence ?Marié et al., EPJB 2003



VKS1 : helicity and effects

o: bx : by : bz

transverse B0 applied axial bx + transverse by inducedMarié et al., Magnetohydrodynamics 2002



VKS1: fluctuations of B

0 2 4 6 8 10 12 14 16-6

-4

-2

0

2

4

6

8

10

12

14

t [s]

B [

G]

BxByBz

-0.5 0 0.5 1 1.5 2 2.5-3

-2

-1

0

1

2

3

4

log10(F [Hz])

log10(s

pect

rum

)

24 Hz-1

-11/3

BxByBz

Evolution of B in presence of transverse B0=3G ( = 24 Hz)

• > 24 Hz : spectrum of Kolmogorov type

• < 24 Hz : spectrum f-1 ~ Karlsruhe exp.



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

- Rmc = 60 based on mean flow for TM 60 propellers:

fc = 44 Hz (Pc =750 kW / 150 kW available)



VKS2 experiment (since 2005)

• VKS2: a dynamo / mean flow

- max Rm = 55 > Rm

c = 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?



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



+

R

w

rdrdzV

rdrdzVV

T

P zr

22

• 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



-0.9 0 0.91

0

1

z/R

r/R

Experimental mean flow (LDV or PIV)

poloidal

toroidal



- 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

r0

w

FF T

FFT

Kinematic dynamo code (J. Léorat)



0 0.2 0.4 0.6 0.8 10

60

120

180

w

Rm

cw=0.4, threshold divided by 4

(power divided by 64!)

180

40

Influence of conducting shell on Rmc

Ravelet et al.,Phys. Fluids 2005



Comparison between codes

• Stefani et al.

EJM/B 2006• Nore et al. 2006

max



max



Stationary in timeAzimuthal 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

1800 cRmw396,0 cRmw

Neutral mode structure



0 0.9 1.8-1

-0.5

0

0.5

1

z

r

0 0.9 1.8

-1

-0.5

0

0.5

1

z

r

0 0.9 1.8-1

-0.5

0

0.5

1

z

r

0 0.9 1.8

-1

-0.5

0

0.5

1

z

r

magnetic field B

current density j

w=0 w=0.6

B-lines are smoothed : weaker ohmic dissipation

Current loops can now close outside the flow

Changes of B/j-lines topology



-0.9 0 0.91

0

1

z/R

r/R

Comparison with MND analytical flow

-1 0 1-1

0

1

z/R

r/R

)sin()51)(1(

)2

sin()1(4

)cos()21()1(2

2

2

zrrrv

zrrv

zrrrv

z

r

TM73 Exp.flow

MNDAnal.flow

For w=0 and Γ=0.8:- optimal experimental flow Rm

c=180

- analytical flow Rmc=58

Marié, Normand and Daviaud, Phys. Fluids 2005



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%

0 0.2 0.4 0.6 0.8 10

50

100

Rm

c

w

42.95+14.83*exp(-w / 0.20)

580 cRmw431 cRmw



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



Experimental plateform



container



Inside of container



Response to a transverse applied B0



Transverse applied B0 : time series of Binduced

Rm=15 Rm=47



Transverse applied B0 : PDF of Binduced

Bx: bimodal, By: exponential tails

Rm = 40



PDF of Bx

PDF of By

high B-state

low B-state



Transverse applied B0 : spectra of Binduced

Slopes ≠ VKS1



Mean Binduced=f(Rm) rms Binduced=f(Rm)

Transverse B0 : evolution of Binduced with Rm

No saturation: ≠ VKS1

Bx

By

Bz



Transverse B0 : comparison exp. / simulation

<Bx>

<By>

<Bz>



Response to a localized B0

M: magnet

(1000 -10 G)

P: Hall probe



Localized B0 : time series of Binduced at Rm = 25

Intermittency, no coherence between components



Localized B0: evolution with Ω of mean and rms Binduced

Bxrms

Byrms

Bzrms

<Bx>

<By>

<Bz>



Localized B0: spatial decay of rms Binduced

Bxrms

Byrms

Bzrms

Decay length: 100 mm ~ integral scale



Localized B0 : PDF of fluctuations of Binduced

Rm = 25

Bxrms

Byrms

Bzrms

Exponential tails ~ random advection of scalar field



Localized B0 : spectra of Binduced



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



Comparison mean / instantaneous flow (PIV)

Mean: 5000 fields sampled at 5 Hz



Shear layer: vortices

mhd results in a liquid sodium turbulent flow: the vks experiment

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