Passive, Active and Feedback Stabilization of Thick, Flowing Liquid Metal Walls

Transcription

1 21 st MHD Control Workshop, San Diego, CA, November 7-9, 2016 Passive, Active and Feedback Stabilization of Thick, Flowing Liquid Metal Walls Francesco A. Volpe, S.M.H. (Taha) Mirhoseini Dept. Applied Physics and Applied Mathematics Columbia University, New York, USA

2 Liquid metal walls 1. Reduce impurities and recycling [ 1mm thickness, 1mm/s to 1cm/s] Thick walls 2. Remove heat [~1m, 1mm/s (turbulent) to 1m/s (laminar)] 3. Attenuate neutrons [~1m, 1mm/s (turbulent) to 1m/s (laminar)] 4. Increase survivability to disruption 5. If rotating, they stabilize the plasma higher plasma b [~1cm, >10m/s] Here: [1-10 mm, cm/s] 3

3 Liquid walls will tend to be uneven Instabilities Rayleigh-Taylor cm, ms Kelvin-Helmholtz >1 cm, 3 ms Turbulence Non-uniform forces Non-axisymmetric error fields Inhomogeneous temperature inhomogeneous resistance current TEMHD viscosity shear-flow, convection density convection Modes in plasma [Narula 2006] 5

4 LM flows and becomes uneven under effect of time-varying non-uniform field, fast flow and solid wall roughness Click to Play 13

5 Liquid walls will need to be stabilized Otherwise, they could 1. bulge and interact with plasma Contaminate it Cool it Act as limiter Disrupt it 2. deplete and expose substrate to heat and neutrons, and plasma to less benign plasma-facing material Increased sputtering, erosion, recycling, Tritium retention 7

6 Of forces considered, only jxb are rapidly, locally adjustable To sustain the flow: Gravity Electromagnetic forces Magnetic propulsion ( B T ) Thermoelectric drive ( T) For adhesion to substrate: Capillary forces Electromagnetic forces Centrifugal [Abdou, 2001] 8

7 Outline Passive stabilization (B only) Active stabilization (jxb) Feedback stabilization 9

8 Outline Passive stabilization (B only) Active stabilization (jxb) Feedback stabilization 10

9 Frozen-in field from rotating permanent magnets propels liquid metal CNC-machined from single block Duct of constant area but variable shape N S Permanent magnets N S S N Ferromagnetic core PLA plastic, 3D printed S N Slots for Fe laminations 11

10 Free-surface flow in tiltable tile exposed to B B from external coil Slot for electrodes Pivot. Inclination can be varied (floor, wall, ceiling) 12

11 Strong B is stabilizing, even in absence of j u 0.2 [m/s] B B = 0 T B = 0.4 T 13

12 Strong B is stabilizing Navier-Stokes and generalized Ohm s law v t + v v = 1 ρ p + ν 2 v + g + 1 (j B) ρ j = σ E + v B Contain a stabilizing term σ ρ (v B) B of order σub2 ρ that dominates over convective term v v (ratio=44 in our exp) and over viscous term ν 2 v (Ha = BL σ μ = ). 15

13 Velocity fluctuations are damped by effective viscous drag B 2 Simplified Navier-Stokes v t = 1 ρ p pump, thermoel. drive, magn. propulsion + g gravity + σ ρ (v B) B effective viscous drag δv Ohm δj = σbδv Lorentz δf = σb 2 δv /n Incompressibility v = 0 δv also small 16

14 Outline Passive stabilization (B only) Active stabilization (jxb) Feedback stabilization 17

15 jxb acts as effective gravity, stabilizing I=60 A B=0 T I=60 A B 0.2 T I=60 A B 0.4 T 18

16 jxb acts as effective gravity, stabilizing I=120 A B=0 T I=120 A B 0.2 T I=120 A B 0.4 T Broader coverage of substrate? 19

17 Outline Passive stabilization (B only) Active stabilization (jxb) Feedback stabilization For Lithium and B = 5 T, j = 0.1 A/cm 2 suffices to defy gravity Could be induced by modes in plasma applied currents might need to be adjusted in f/back with thickness 20

18 Feedback control by array of electrodes will enforce uniform thickness under more challenging circumstances δ δ Similar to feedback control of plasma instabilities by coil arrays + V 22

19 jxb actuator pushes LM Electrode - Ruler Electrode + I = 0 A I = 100 A ON OFF DC Current Generator Original LM surface Shunt Resistor I = 200 A B V + Liquid Metal 23

20 Surface Level Decrease (cm) Local deformation is linear with applied current Applied DC Current (A) Offset due to surface tension 24

21 Same plate electrodes used for actuators succeeded as resistive sensors of LM thickness Same electrodes as sensors and actuators: Imposing uniform resistance = imposing uniform thickness! 25

22 Measurements of LM thickness were extended to a matrix of pin-electrodes Current Terminals Electrodes Current Terminals Plastic Pot Voltage Terminals 26

23 Measurements of LM thickness were extended to a matrix of pin-electrodes 27

24 Kirchhoff + generalized Ohm mxn equations to extract height in each electrode Where Can be rearranged as I = Ah and inverted: h = A 1 I 28

25 Finite poloidal or toroidal vxb introduce need for coupling with v and B diagnostics But in our case v B E Also, if v R = B R = 0, then v B φ = v B θ = 0 no perturbation to E φ and E θ 29

26 Measurements of LM thickness were extended to a matrix of pin-electrodes, simultaneously 30

27 ~10 ms time-resolution and ±0.5 mm precision were achieved Shaker & Fast camera images Waves are non-linear, due to shallow liquid and large lat. oscillation ±0.5 mm noise 31

28 Videos & papers Videos: Go to and search for Volpe Group Papers: Sensors and actuators: PPCF 58, (2016) Latest on sensors: RSI 87, 11D427 (2016) Passive and active stabilization: Magnetohydr., submitted (2016) 32

29 Summary & Conclusions Liquid metal walls need to be stabilized Was stabilized Passively, by strong B Effective viscosity Actively, by applied jxb Effective gravity Will be stabilized By jxb optimized in real-time, in feedback with measurements of LM thickness Sensors and actuators 33

30 Ongoing and future work: put it all together! (sensors, actuators, flow, floor, wall, ceiling) Flow adhering to ceiling (q =145 o ) Cylindrical wall, 90 cm long 34