Survey of experimental results

Transcription

1 Survey of experimental results Philippe CARDIN, Observatoire de Grenoble, France Caramulo, September 5, 2003

2 Do we need experiments? Proofs of theory Checks of numerical simulations. Studies in different regimes Real models of natural objects Inputs for theories or simulations Improvement in technology Discoveries September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 2

3 Outline 1. Introduction : some physical properties 2. Historical approach to experimental dynamos : Two successful experiments 4. A new generation of experimental dynamos... September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 3

4 Outline 1. Introduction : some physical properties 2. Historical approach to experimental dynamos : Two successful experiments 4. A new generation of experimental dynamos... September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 4

5 The magnetic Reynolds number UL Re m = = η µσul Necessary condition for dynamo action : Re m >~50 µ is difficult to change (Martin et al, 2000; Frick et al, 2002) σ Na = 3 σ Ga = 10 σ Hg σ Na decreases with T At T 100 C, µσ Na 10 For L = 1m, τ diff 0.1 s Size L and velocity U should be as large as possible September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 5

6 The magnetic Reynolds number UL UL ν Re = = = η ν η Re m P m For liquid metals, P m 10-6 Liquid metal dynamo occurs for large Re (>10 6 ) Turbulent dynamos β effect (effective η increases with turbulence). (Reighart and Brown, 2001) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 6

7 Velocity / Size Velocity is limited by the available power. Po 3 ρη R L 3 m For liquid sodium: ρη 3 = 1 Pour Rm = 50, L = 1 m, Po 100 kw (Nataf, 2003) The problem is to cool down the experiment (O.1K/s) Large L is necessary. Sodium is cheap (< 10 /l) and light (r < 1000). Sodium is dangerous (reductor, water => explosion H2). Large experiments are expansive. September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 7

8 Experiments ; necessary conditions Rm> 50 imposes the use of sodium U > 5m/s, which means a power of a few hundreds KW (cooling unit too) L > 1m, which means a few tons of liquid sodium An adequate velocity field (in space and time) to start and maintain a dynamo September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 8

9 Outline 1. Introduction : some physical properties 2. Historical approach to experimental dynamos : Two successful experiments 4. A new generation of experimental dynamos... September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 9

10 (Lehnert,1958) Na b t /B <0.25 b pr /B < cm 58 litres of sodium. Ω< 500 rpm Rm < 5 «ω effect» September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 10

11 (Lowes and Wilkinson,1963; 1968) (Herzenberg, 1958) 2 * 100 W 7 cm Ferromagnetic materials (µ > µ 0 ) + Mercury September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 11

12 (Lowes and Wilkinson,1963; 1968) µ r ~ 200 Re m ~ 200 September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 12

13 (Steenbeck et al.,1967) 15 cm 51 cm U = 0-11 m/s «α effect» September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 13

14 U (mv) (Steenbeck et al.,1967) 40 - U (mv) 40 - U α v 2 B v 2 B (T) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 14

15 (Steenbeck et al.,1967) U/U theo U theo α µ 0 σv 2 Bl 2 N = σlb 2 /ρv September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 15

16 50 rpm (Gans,1970) Rem 20 Na 25 cm 3600 rpm Megater, Léorat September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 16

17 Outline 1. Introduction : some physical properties 2. Historical approach to experimental dynamos : Two successful experiments 4. A new generation of experimental dynamos... September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 17

18 The Riga dynamo (Ponomarenko,1973) dynamo z translation helicoidal flow At rest Kinematic approach, With infinite geometry. B exp(ikz) exp(iωt) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 18

19 First attempt Imposed magnetic field Induced magnetic field Leningrad, 1987 (Gailitis et al., 1987, 1989); (Gailitis 1992). September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 19

20 First attempt; results. (Gailitis et al., 1987, 1989); (Gailitis 1992). Improvements: (Gailitis, 1996); (Christen et al., 1998) (Stefani et al.,1999) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 20

21 Riga Dynamo (120 kw, 1500 litres Na, 2200 rpm) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 21

22 Riga; growth of the magnetic field (Gailitis et al., 2001) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 22

23 Riga; comparison Num./Exp. (Gailitis et al., 2002) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 23

24 Riga: Motor power measurements 10 KW (Gailitis et al., 2001) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 24

25 Riga: Saturation (Gailitis et al., 2001) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 25

26 The Karlsruhe dynamo (G.O.Roberts,1972) dynamo (Busse,1992): r 0,d,a/r 0 <<1 Re m, H Rem, C > 8 π 2 Re m, H Re m, C > 16a πr d 1 + πr0 2 September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 26

27 Karlsruhe: the set up (1600 litres Na, 630 kw) m 52 cylindres 0.21 m 1.7 m 0.19 m V C or V H up to 120 m 3 /h September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 27

28 Dynamo modulus in Karlruhe September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 28

29 Pr Müller and the dynamo modulus September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 29

30 View of the building in Karlsruhe September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 30

31 Dynamo effect in Karlsruhe experiment (Müller and Stieglitz, 2000) (Stieglitz and Müller, 2001) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 31

32 Stability diagram in Karlsruhe dynamo (Stieglitz and Müller, 2001) (Rädler et al, 1998) (Tilgner, 1997) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 32

33 B-spectra in Karlsruhe f -1 spectra f -3 f F (Hz) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 33

34 Two succesful experimental dynamos Good prediction of the onset with laminar (average) flow and ideal boundary conditions. Kinematic and mean field approaches. Saturation mechanism? (Tilgner et Busse, 2002) Motions of the liquid sodium initially at rest. (Pétrélis et Fauve, 2001) claim that a turbulent scaling is in agreement with the experiment whereas a laminar scaling predict a field orders of magnitude too small. September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 34

35 Outline 1. Introduction : some physical properties 2. Historical approach to experimental dynamos : Two successful experiments 4. A new generation of experimental dynamos... September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 35

36 The Maryland group A convective dynamo? 20.3 cm (Shew et al.,2002) 6000 rpm, E ~ 10-8, Λ ~ 1, Rm < cm 1.5 litres 6000 rpm Rm<8 (Lathrop et al., 2001) 90 litres 61 cm (Aubert el al.,2001) predict if R=1 m and 100kW of heat, Re m = 1 September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 36

37 Mechanically forced motions S2T2 kinematic model (Dudley and James, 1989) R mc = 55 2 * 7.4 kw 15 litres D = 31.2 cm (Lathrop et al., 2001) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 37

38 Decay rates m=0 m=1 (Peffley et al., 2001) R mc ~ 200? September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 38

39 Hunting for dynamos 1 Cu plate 3 Cu rings 5 Cu plates + baffles Different propellers BEST Herzenberg type (Shew et al., 2002) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 39

40 MHD Turbulence 15 litres 31.2 cm N = σlb 2 /ρv Re m = rpm var B (Sisan et al., 2003) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 40

41 The maryland project Ω 2 Ω 1 D=3m, 15 tonnes Sodium. 260 kw * 3= 780 kw. Rem < 400. Ω sphère (Lathrop, 2003) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 41

42 Van Karman experiments : VKG 5 litres gallium R = 10cm 2*11 kw Rm<16 Magnetic expulsion (Odier et al., 1998;2000) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 42

43 Van Karman Sodoium 70 litres sodium, 2*75 kw, 1500 rpm, Rm<50 R=20 cm, H=2R September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 43

44 View of the Cadarache experiment September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 44

45 VKS: optimisation of the flow Poloidal / Toroïdal cm of cupper R mc ~ 70 or R mmax ~ 55 (Marié et al., 2001) (Bourgoin et al., 2002) LDV et UDV September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 45

46 VKS: MHD effects ω effect α effect N << 1 B o passive Expulsion (Bourgoin et al., 2002) (Marié et al, 2002) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 46

47 VKS : spectra (Bourgoin et al., 2002) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 47

48 Madison Experiment Optimisation of S2T2 kinematic model (Dudley and James, 1989) R mc = 47 2* 50 kw 1750 rpm 1 m (Forest et al., 2002) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 48

49 Madison: Onset of the average flow (Forest et al., 2002) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 49

50 Diameter=1m 150 kw V~20m/s C 35 kw cooling 120G axial R m ~250 > 100 View of the Madison experiment September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 50

51 Ponomarenko type The Perm project Water: 2 kw, 3000 rpm 0.2 à 0.5 s breaking τ=1-2 s. (Frick et al, 2002) Sodium experiment: R=0.4 m, r=0.12 m 115 litres Na 3000 rpm Vmax=140 m/s Rm=40 Breaking 0.1 s September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 51

52 Perm: Optimisation of the flow Amplification factor of 3 0.1s Increase of µ 0.2 s. Dependent of the initial magnetic field (Dobler et al., 2003) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 52

53 Socorro group: α ω type dynamo (Colgate et al., 2002) Taylor-Couette flow (ω effect ) + Sodium plumes (α effect ) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 53

54 Socorro: design of the experiment 30.5cm Na 30.5cm <8000 tpm <2000 tpm 61cm 100 kw Rem~120 Water experiment Sodium tank (Colgate et al., 2002) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 54

55 The Grenoble project. 1 litre de gallium, 3000 rpm. (Brito et al., 1995; 1996) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 55

56 An Ω quenching effect? (Brito et al., 1995) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 56

57 Convective study Temperature T2 Temperature T1 September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 57

58 Thermal convection in rapidly rotating shell (Aubert et al., 2001) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 58 5 litres of gallium, up to 1000 tpm. With toroidal magnetic field Without magnetic field Nicolas. Gillet

59 Ultrasonic velocity measurements (Aubert et al, 2001; Aubert et al., 2003) U ΩD conv = αgf ρc Ω D p September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 59

60 Viscosity measurement Spin-up experiment At t=0, Ω =300 rpm --> Ω=340 tpm Brito et al, 2003 September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 60

61 (Greenspan, 1968) theory u φ ( s, t) = s Ω exp 1/ 2 E Ω t (1 s R / 4 ) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 61

62 Turbulent viscosity measurement September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 62

63 The DTS experiment 45 litres of Na, 2*10 kw Rm < 30 Spherical Couette experiment (Cardin et al., 2002) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 63

64 A magnetostrophic experimental dynamo: A planetary dynamo model R m = 100 a = 1 m Power = 600 kw Ω = 450 rpm Ω = 150 rpm B = 0.3 T (Cardin et al., 2002) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 64

65 Conclusion? (Nataf,2003) September 5, 2003 Caramulo, Survey of experimental results - P. Cardin 65