MHD results in a liquid sodium turbulent flow: the VKS experiment F. Daviaud, A.
Kraker, Daniel, News Director has reference to this Academic Journal, PHwiki organized this Journal 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 in addition to numerical simulations of models experiments: essential but difficult sodium MHD equations Dynamo action: instability Rm > Rmc Typical experiments: Rm = 102, Re = 107 , Pm = 10-5
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Role of turbulence on dynamo action Problem of turbulence: v =
Dynamo experiments ~ fusion Constrained dynamos: success in 2000 Riga Karlsruhe Role of turbulence on dynamo action Riga in addition to 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 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 o: bx : by : bz Bourgoin et al. Phys. Fluids 202
Dynamo mechanisms: effect VKS1 : helicity effect (1 propeller) transverse B0 applied transverse J= B0 1) 1st step 2) 2nd step o: bx : by : bz Petrelis et al. PRL 2003 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 in addition to effects o: bx : by : bz transverse B0 applied axial bx + transverse by induced Marié et al., Magnetohydrodynamics 2002 VKS1: fluctuations of B 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 in addition to fluctuations) - basic ingredients as long as dynamo action ( in addition to 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 as long as TM 60 propellers: fc = 44 Hz (Pc =750 kW / 150 kW available) 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 – fluctuations of Bdynamo: intermittency VKS2 experiment: optimisation von Karman flow inside a cylindrical copper container copper shell with sodium at rest (cf. Riga)
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 in addition to changes the neutral mode structure VKS2 experiment: optimisation 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 uni as long as m conductivity surrounded by infinite insulator layer of stationary conductor of same conductivity arround flow finite differences Kinematic dynamo code (J. Léorat)
w=0.4, threshold divided by 4 (power divided by 64!) 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 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 in addition to azimuthal directions Neutral mode structure magnetic field B current density j w=0 w=0.6 B-lines are smoothed : weaker ohmic dissipation Changes of B/j-lines topology Comparison with MND analytical flow TM73 Exp. flow MND Anal. flow For w=0 in addition to =0.8: optimal experimental flow Rmc=180 – analytical flow Rmc=58 Marié, Norm in addition to in addition to Daviaud, Phys. Fluids 2005
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
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