THE NONSTATIONARY DYNAMO PROJECT(water – Ga – Na experiments)

Peter FrickSergey DenisovStanislav KhripchenkoVitaliy NoskovDmitriy SokoloffRodion StepanovIgor ShardakovAndrey Sukhanovskiy

Laboratory of Hydrodynamics,Institute of Continuous Media Mechanics,Perm, RUSSIA

DYNAMO IN LABORATORY

number Prandtl magneticP

number Reynolds magneticRm

number Reynolds Re

mm

m

UL

UL

10030Rm*

)(10P 5 Nam

STATIONARY DYNAMO EXPERIMENTS

Riga - cylindrical crew dynamo (2000) Karlsruhe – two-scale dynamo (2000) Cadaraches – VKS2 (Von Karman flow in a

cylinder) Grenoble – spherical Couette-Taylor Madison – S2T2 flow in a sphere Mariland – Couette-Taylor flow in a 3m

sphere

SCREW DYNAMO IN A BRAKED TORUS

Energy accumulation Pulse screw flow Toroidal geometry

Water A Water B Ga Na Radius of the torus, (m ) 0.103 0.154 0.088 0.4 Radius of the cross-section, )(m 0.027 0.04 0.023 0.12

Mass of the channel, )(kg 5.6 24.5 15.3 300

Moment of inertia, )( 2mkg 0.072 0.58 0.132 50

Mass of fluid, )(kg 1.25 4.86 5.58 115

Moment of inertia, )( 2mkg 0.018 0.15 0.045 20

Frequency of rotation, .)..( SPR 50 30 50 50

Maximal velocity, )/( sm 32 29 27 140

Effective Re 510 5105 5105 6104 Effective Rm - - 1.5 40 Minimal braking time, )(s 0.1 0.18 0.05 0.1

Energy of rotation, )(J 3104.4 3103.17 3106.6 610 Dissipation power, )(Wt 4104.4 4107.8 5103.1 710

Temperature, )( Co 20 20 20 120

EXPERIMENTAL SET-UPS

WATER EXPERIMENT

MHD channel: thickness of the wall

)0cosh()cosh(

)cosh()cosh()(

rrv

0 5 10 15 20 25 30x

30405060708090

100

mR

*

d=1

d=0.3

d=0.1

d=0

d - thickness of shell

- parameter of velocity profiles

MHD channel: conductivity

0

10

20

30

40

50

60

70

0 2 4 6 8 10

d=0.05rd=0.15rd=0.30r

crRm

fluidwall

18

NONSTATIONARY SCREW DYNAMOnumerical simulation

1.

1.5

2.

t

h

t

h

downstream

upstream t

v

rd

fluidshell

15.0

5/

NONSTATIONARY SCREW DYNAMO2D-numerical simulation

)( 22yx hh

Channel cross-section downstream the diverter

t=0.05s t=0.1s t=0.145s t=0.385s

NONSTATIONARY SCREW DYNAMO3D-numerical simulation

Cylinder under periodicalboundary conditions:- diverter at the top,- (red),- (blue),- magnetic field lines (green)

sTb 1.0

0zh0zh

together with W.Dobler

NONSTATIONARY SCREW DYNAMO3D-numerical simulation

Wolfgang Dobler and Rodion Stepanov

Rm = 40

)(

2

58.5

0225.0

0875.0

max

0

0

ACandDC

kAI

kgM

mr

mR

Ga

GALLIUM EXPERIMENT

Local transverse field in Ga flow

1 – channel 5 - box2 – diverter 6 – motor

3 – magnet 7 - brake 4 – 3D probe

Solid rotation

G

Bz

By

Bx

G

Bz

By

Bx

Imposed field

Induced field

Induction mechanism

Solid-like rotation

Local rotation

Time evolution

t

G

Bz

By

Bx

t

G

Bz

By

Bx

no diverters right diverters

\phi=90 degr.

empty channel Ga without diverters

Right diverters Left diverters

no diverters right diverters left diverters

t=0.08s

t=0.15s

t=0.3s

Symmetries

Decay

t

E B

Kinetic energy(water experiment)

Magnetic energy(gallium experiment)

Magnetic Field Pulsations

0 0.5 1 1.5 21.

5.9

10.8

15.7

20.625.530.435.340.245.150.

1 5 10 50 100 500Hz

0.00001

0.0001

0.001

0.01

0.1

1

F

2.

Wavelet plan

Pulsations energy in the band 10<f<40 Hz

0J

ALPHA-EFFECT (Ga-experiment)

f

0~ BJ

40 10/ BB

0J

0B

WELCOME !Contact persons:

Peter Frick frick@icmm.ruRodion Stepanov rodion@icmm.ru

Workshop website: http://pdd2005.icmm.ru