Lithium/Molybdenum Infused Trenches ( LiMIT )

PFC/FNST UCLAAugust 3-6, 2010

Nuclear, Plasma, and Radiological EngineeringCenter for Plasma-Material Interactions

Contact: [email protected]

Lithium/Molybdenum Infused Trenches (LiMIT)

David Ruzic, Wenyu Xu, Vijay SurlaPFC meeting UCLA, August 2010


Outline

Thermoelectric MHD theoryInfused trenches divertor plate design Calculations

Flow needed to remove heat Flow predicted from TEMHD 3-D computer simulation

Ejection issue and force balance Future work at IllinoisConclusion

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Thermoelectric effect

Like a thermocouple, a voltage is created at a junction of two metals dependent on the temperature.[1]

A current will flow based on that voltage difference:

where σ is the conductivity, and ΔS is the difference in Seebeck coefficients.[2]

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Lithium

Molybdenum

TSj

j

j

There is a large difference in S between Li and most other metals and it increases with T.[3]

0 20 40 60 80 100 120 140 160 180 200 2200

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20

30

40

Experimental Data Bidwell (1924)

See

beck

Coe

ffici

ent (

V

/K)

Temperature ( oC)

Seebeck Coefficient of LiBlack: our measurements Lithium


Does it work? Yes! SLiDE ResultsSheet electron beam (like a divertor heat

flux stripe) hits a well diagnosed tray of molten Li in the presence of a magnetic field

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Theoretical vs experimental velocities :

[4] M.A. Jaworski, et al. Phys. Rev. Lett. 104, 094503 (2010)

Movie is of a case where the “Jaworski” number is near 1 and TEMHD and TCMHD (Marangoni effect) are balanced, so flow osscilates between swirling and splitting.


LiMIT Design

Left is a cross-section of NSTX showing the “shelf-like” inner divertor plates.

Right is the LiMIT concept: molybdenum tiles with radial trenches containing lithium. The trenches run in the radial (polodial) direction such that they lie primarily perpendicular to the torroidal magnetic field.

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Inner divertor shelf

Divertor Strikepoint Stripe


Lithium Flow in the Trenches is Self-Pumping

Concept for heat removal using TEMHD. The Li flows in the slots of the Mo plate powered by the vertical temperature gradient. This vertical temperature gradient generates vertical current, which when “crossed” by the torroidal magnetic field, will create a radial force on the Li driving it along the slot. This flow will transfer the heat from the strike point to other portions of the divertor plate. The bulk of the Mo plate could be actively cooled for a long-pulsed device or passively cooled for something like NSTX. Under the plate the Li flows back naturally.

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The top surface of the Li is hotter than the surface that is deeper. Therefore there is a VERTICAL temperature gradient Hot

Heat flux

Cooling channelsInlet

Outlet

Passive Li replenishment

Li flow BJF


Thermoelectric Driven Flow Calculation

Look just at one channel. All channels are equivalent

The width of Li (w) is 1mm and the width of the Mo (t) trench is 1mm. The depth of Li (h) is 5mm. The length of the Li (L) is 100mm. The magnetic field is 1T. The heat flux on top surface is 20MW/m2 and the footprint of the heat flux is 2mm*10mm.

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Heat flux: divertor strike point width, 1cmt

w

h Grad T TE current Flow

L

B

Z direction

This represents the divertor heat flux maximum value for the calculations here, but the concept should work for even higher values..


Heat load on LiMIT: What Velocity is Needed? 8

To see if a flowing surface can remove that much power with a lower temperature rise, we can use the following equation [5] :

Here the first term is the heat conduction term and the second is the heat convection which transfers the heat along the trench. ΔT+ is the temperature difference across the depth of Li and ΔTll is the temperature difference between the inlet and outlet of the Li trench. When the heat flux is assumed to be 20MW/m2 on 1 cm, and both temperature differences are assumed to be 200K, the velocity needed is only u=9.9cm/s. With this flow the temperature rise would only be 200K.

The assumed heat flux means the 1mm Li slot needs to handle 400W heat load. (400W = 20MW/m2 X 2mm X10mm)

To put this in the proper perspective, the temperature rise over the 5 second shot of an uncooled one-half inch thick (1.2cm) Mo plate the same size as our imagined Li/Mo trench/finger can be calculated using as follows: E = 400W*5s = 20,000 J. V = (0.2cm)(1.2cm)(10cm) = 2.4 cm3 Cv=2.57 J cm-3 K-1 for Mo. Therefore the temperature rise for a passive plate is 324K.

TVcE v


What Velocity is Generated by TEMHD ? 9

The Seebeck coefficient for Mo is about 13μV/K (at 400C). The value for Li reported in the literature [3] is 23μV/K (at 400C). However, we have measured this number ourselves and obtained much higher values closer in line with those of Bidwell. This higher number 43μV/K (at 400C) will be used first, for a difference of 30μV/K, but then results with one-third of that value will also be included.

The current and velocity can be calculated with these two equations

[1]

[1]

Here P is the difference of Seebeck coefficient (thermoelectric power) between two material. Ha is the Hartmann number . C is a parameter coming from the conservation of current.

The velocity with a higher thermoelectric power is 118 cm/s and the velocity is 39cm/s with the smaller thermoelectric power, still enough to remove the heat. Both of these numbers are much greater than the 9.9 cm/s on the last slide.

dzdTP

CuB

CCjs

11*

1

)tanh()tanh(**

HaCHaHaHa

dzdT

BPu

wBHa

Mo

Li

tw

C


Further Analysis: 3D – FLUENT Calculation

What will really happen to the temperature of the Li when the strike point heat flux hits LiMIT? Is the 200K gradient assumption reasonable? A simple 3D heat transfer model is run with FLUENT.

FLUENT has convection flow and 3D heat transfer included.

Boundary Conditions: The Li flows through the slot between two Mo plate and flow back below the Li slot. The inlet velocity is set to be 100 cm/s. The initial temperature is 500K. The top heat flux is 20MW/m2 with a 2mm*10mm rectangle shape. The bottom temperature is set to be 500K as a constant. Will we remain under 700K as the one-D calculation indicated?

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Mo plate20MW/m2 heat flux

Li channel

Back flow of Li


Answer: Almost, but that is OK

Left figure is the temperature distribution of the top surface of Li slot and right figure is the temperature change along the center line of the top surface.

The temperature difference between the inlet and the outlet is less than 100K – great! However the temperature immediately at the strike point reaches a maximum of 750K (480C) over 1 mm. There will be evaporation there – which gives additional cooling not included in the model. Some evaporation (radiative cooling) is acceptable and even desired. Also, a higher gradient in T gives a larger thermoelectric current.

The temperature of most of the Li surface is under 650K (380C) which proves the ability of the LiMIT concept to handle a high heat flux through TEMHD.

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0.00 0.02 0.04 0.06 0.08 0.10

500

550

600

650

700

750

800

Tem

pera

ture

(K)

Distance to the inlet (m)

Temperature along the center line of the top surface


Does the Radial Temp. Gradient Cause Ejection?

One concern about using free surface Li is the ejection problem. The temperature gradient along the Li flowing direction will generate a thermoelectric current along the same direction and the Lorentz force may could eject the Li into the plasma.

Similar to the capillary porous system (CPS) [6] which effectively has very narrow channels, LiMIT’s trench design has very narrow slots (1 mm) to utilize the capillary force to hold the Li in place.

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Li

Mo

Heat flux

Grad T TE current

Lorentz ForceB


Does it Work? Capillary Force Balance 13

The thermoelectric current parallel to the Li flowing direction is [1]. Here the temperature difference is also assumed to be 200K and the temperature gradient dT/dy=2000K/m. Under these conditions jTEMHD=1.78*105A/m2. So total current along the Li trench is 0.89A and the force from the TEMHD is 0.089N. Here P is chosen to be 30μV/K (the high value)

The capillary force is 2ΣL and Σ=0.3N/m [7] at 600K. So the capillary force is about 0.06N. Close, but slightly less than the ejection force.

However this is the worse case. Mitigating factors: The capillary force is not effected by the thermoelectic power, P. It P is actually smaller,

the forces will balance. Also, if the trenches were 0.66 mm wide instead of 1mm wide, then the two forces would balance.

The temperature difference in the radial direction could be less than 200K. The leading edges of the Mo fingers could be Mo-sprayed, greatly increasing the

surface area and therefore the capillary force. This would easily hold the Li in. The part of the Li with the highest ejection force is also the hottest Li and has likely

already evaporated anyway!

dydTP

CjTEMHD

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Future Work at Illinois on SLiDE 14

The SLiDE experiment at Illinois is being reconfigured to test this concept. We expect to be able to show radial flows of Li along radial trenches in a Mo plate and measure the flow velocity compared to calculations. An electron beam is used to provide the heat flux while the magnet can generate about 800 Gauss magnetic field parallel to the tray surface. The temperature rise of the Li will also be monitored and compared to theory.

Return channels (lithium hydraulic engineering) will also be tested to find a design compatible with tokamak operation.

E-beam line source

Li TrayMagnet coil

Heat Stripe for SLiDE’s Electron Beam

B


ConclusionA Mo trench structure with flowing Li is proposed as a

potential method to absorb the high heat flux at the divertor region. Thermoelectric effect is utilized to drive the Li flowing along the radius trench direction.

The heat transfer ability is estimated based on the 1-D heat transfer model and simulated in the 3-D domain. Both give positive results showing the ability of flowing Li to mitigate the peak heat flux and to transfer the heat without an unacceptable temperature increase.

The ejection problem is analyzed and should be able to be suppressed by the capillary force.

A simple trench structure system is under construction at UIUC to validate this design. This type of divertor structure should “stay on the radar” for future fusion devices. There is significant interest for using it on HT-7 in China.

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Reference

[1] M.A. Jaworski, Ph. D. thesis, University of Illinois, Urbana, IL (2009)

[2] J.A. Shercliff, Thermoelectric magnetohydrodynamics, J. Fluid Mech. 91, 231 (1979)

[3] P. Ioannides, et al. Journal of Physics E 8, 315 (1975)

[4] M.A. Jaworski, et al. Phys. Rev. Lett. 104, 094503 (2010)

[5] M.A. Jaworski, et al. Journal of Nuclear Materials 390–391, 1055–1058(2009)

[6] V. A. Evtikhin, et al., Fusion Engineering and Design 49–50 (2000) 195–199.

[7] M. A. Abdou,et al. On the exploration of innovative concepts for fusion chamber technology: APEX interim report.282 Technical Report UCLA-ENG-99-206, University of California, Los Angeles, November 1999.

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Lithium/Molybdenum Infused Trenches ( LiMIT )

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