Liquid Metal Walls

Francesco A. Volpe, S.M.H. (Taha) Mirhoseini

Dept. Applied Physics and Applied Mathematics

Columbia University, New York, USA

APAM Research Conference, November 11, 2016

Why study the MHD of liquid metals?

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• Outer core of Earth is liquid Fe

• Geodynamo B protects life from Solar wind and cosmic rays

D.P. Lathrop, UMD

Some of the largest telescopes are made of rotating liquid metals

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UBC/Laval LMT, 2.65 m, 1992

NASA-LMT,3 m, 1995-2002

LZT, 6 m, 2003-ILMT, 4 m, 2011 test

Adaptive optics with liquid mirrors?

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Technological and medical applications of liquid metals

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3D printingReconfigurable antennasTunable metamaterials

Flexible electronics

Nanomedicine

Metallurgical applications

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Cast & flow control Recovery of precious & toxic spill

Refractory walls for furnaces?

Rockets?

Liquid metal walls

1. Reduce impurities and recycling[≪ 1mm thick, 1mm/s to 1cm/s]

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Liquid metal walls

1. Reduce impurities and recycling[≪ 1mm thick, 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 theplasma higher plasma b

[~1cm, >10m/s]

Here: [1-10 mm, 10-60 cm/s]

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Liquid walls will tend to be uneven

• Instabilities

– Rayleigh-Taylor

• 1-100 cm, 13-130 ms

– Kelvin-Helmholtz

• >1 cm, ≫ 3 ms

• Turbulence

[Narula 2006]

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Liquid walls will tend to be uneven

• Instabilities

– Rayleigh-Taylor

• 1-100 cm, 13-130 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]

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

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Click to Play

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…

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Of forces considered, only jxB are rapidly, locally adjustable

To sustain the flow:

• Gravity

• Electromagnetic forces

• Magnetic propulsion (𝛻𝐵𝑇)

• Thermoelectric drive (𝛻𝑇)

For adhesion to substrate:

• Capillary forces

• Electromagnetic forces

• Centrifugal

13[Abdou, 2001]

Outline

• Passive stabilization (B only)

• Active stabilization (jxB)

• Feedback stabilization

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Outline

• Passive stabilization (B only)

• Active stabilization (jxB)

• Feedback stabilization

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• CNC-machined from single block

• Duct of constant area but variable shape

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Permanent magnets

Ferromagnetic core

PLA plastic, 3D printed

S

N

N

N

N

S

S

S

“Frozen-in” field from rotating permanent magnets propels liquid metal

Slots for Fe laminations

Free-surface flow in tiltable “tile” exposed to B

Slot for electrodes

Pivot. Inclination can be varied (floor, wall, ceiling)

B from external coil

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Strong B is stabilizing, even in absence of j

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𝐵 = 0 T 𝐵 = 0.4 T

𝐵

𝑢 ≈ 0.2 [𝑚/𝑠]

Navier-Stokes and generalized Ohm’s law𝜕𝐯

𝜕𝑡+ 𝐯 ∙ 𝛻 𝐯 = −

1

𝜌𝛻𝑝 + 𝜈𝛻2𝐯 + 𝑔 +

1

𝜌(𝐣 × 𝐁)

𝐣 = 𝜎 𝐄 + 𝐯 × 𝐁

Contain a stabilizing term 𝜎

𝜌(𝐯 × 𝐁) × 𝐁 of order 𝜎𝑈𝐵2 𝜌

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Strong B is stabilizing

Navier-Stokes and generalized Ohm’s law𝜕𝐯

𝜕𝑡+ 𝐯 ∙ 𝛻 𝐯 = −

1

𝜌𝛻𝑝 + 𝜈𝛻2𝐯 + 𝑔 +

1

𝜌(𝐣 × 𝐁)

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𝛻2𝐯 (𝐻𝑎 = 𝐵𝐿 𝜎 𝜇 = 7 ∙ 104).

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Strong B is stabilizing

Simplified Navier-Stokes𝜕𝐯

𝜕𝑡= −

1

𝜌𝛻𝑝

pump,thermoel. drive,

magn. propulsion…

+ 𝑔gravity

+𝜎

𝜌(𝐯 × 𝐁) × 𝐁

effectiveviscous drag

𝛿𝑣⊥Ohm

𝛿𝑗⊥ = 𝜎𝐵𝛿𝑣⊥Lorentz

𝛿𝐹⊥ = −𝜎𝐵2𝛿𝑣⊥/𝑛

Incompressibility 𝛻 ∙ 𝐯 = 0 → 𝛿𝑣∥ also small

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Velocity fluctuations are damped by effective viscous drag ∝ 𝐵2

Outline

• Passive stabilization (B only)

• Active stabilization (jxB)

• Feedback stabilization

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jxB acts as effective gravity, stabilizing

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I=60 AB=0 T

I=60 AB≈0.2 T

I=60 AB≈0.4 T

jxB acts as effective gravity, stabilizing

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I=120 AB=0 T

I=120 AB≈0.2 T

I=120 AB≈0.4 T

Broader coverage of substrate?

Outline

• Passive stabilization (B only)

• Active stabilization (jxB)

• Feedback stabilization

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For Lithium and 𝐵 = 5 T,𝑗 = 0.1 A/cm2 suffices to defy gravity

Could be induced by modes in plasma applied currents might need to be adjusted in f/back with thickness

Feedback control by array of electrodes will enforce uniform thickness under more challenging circumstances

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+ −𝑉

𝛿𝛿

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+ −𝑉

𝛿𝛿

Similar to feedback control of plasma instabilities by coil arrays

Feedback control by array of electrodes will enforce uniform thickness under more challenging circumstances

jxB actuator pushes LM

I = 0 A I = 100 A

I = 200 A

0 100

ON

OFF

DC Current Generator

Liquid Metal

Elec

tro

de

-

B

Shunt Resistor

V+−

Ru

ler

Elec

tro

de

+

Original LM surface

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Local deformation is linear with applied current

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-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200

Surf

ace

Leve

l Dec

reas

e (

cm)

Applied DC Current (A)

Offset due to surface tension

Same plate electrodes used for actuatorssucceeded as resistive sensors of LM thickness

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Same electrodes as sensors and actuators:Imposing uniform resistance = imposing uniform thickness!

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

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Current Terminals

Current Terminals

PlasticPot

Electrodes

VoltageTerminals

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3

45

6

7

89

10

1112

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

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Kirchhoff + generalized Ohm mxn equations to extract height in each electrode

• Where

• Can be rearranged as 𝐈 = 𝐀𝐡 and inverted: 𝐡 = 𝐀−1𝐈

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Finite poloidal or toroidal vxB introduce need for coupling with v and B diagnostics

• But in our case 𝐯 × 𝐁 ≪ 𝐸

• Also, if 𝑣𝑅 = 𝐵𝑅 = 0, then 𝐯 × 𝐁 𝜙 = 𝐯 × 𝐁 𝜃 = 0 no

perturbation to 𝐸𝜙 and 𝐸𝜃

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

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~10 ms time-resolution and ±0.5 mm precision were achieved

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“Shaker” &

Fast camera images

Waves are non-linear, due to shallow liquid and large lat. oscillation

±0.5 mm noise

Videos & papers

• http://pl.apam.columbia.edu

• Videos:– Go to and search for ‘Volpe Group’

• Papers:– Sensors and actuators: PPCF 58, 124005 (2016)

– Latest on sensors: RSI 87, 11D427 (2016)

– Passive and active stabilization: Magnetohydr., submitted (2016)

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Summary & Conclusions

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• 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

Ongoing and future work: put it all together! (sensors, actuators, flow, floor, wall, ceiling)

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Flow adhering to “ceiling” (q =145o)

Cylindrical wall, 90 cm long

Galinstan

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Melting elements by a resistive furnace in lab to produce Galinstan; a) Tin, b) Indium, c) Gallium and d) Galinstan

(b)(a) (c) (d)

Alloy Galinstan (Ga, In, Sn) Lithium Tin

Density 6400 [kg/cm3] 5300 [kg/cm3] 7000[kg/cm3]

Melting Point -19oC 181oC 232oC

Electrical Conductivity 17% of Copper’s 16% of Copper’s 14% of Copper’s

Toxicity Low Low Low

Corrosivity Very high (corrodes all the metals) Very high Low

New stainless steel pump with Fe laminations expected to yield faster flows, for centrifugal exp.

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AC Motor Drive

AC Motor

Electromagnetic Pump

EPDM Pipes

Initial test at low speed

Other sensors: LIDAR, Ultrasound and Infra-red

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LIDAR

Might not work on shiny surface

Expensive

[Photo: Keyence]

Ultrasound

Liquid metal

1D measurement

4D ultrasound medical imaging?

Stereo 3D IR-camera

• Resolution: 1200 x 1000 pixels• Frames: 30 fps