ss Hefei, ChinaJuly 19, 2011

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

Contact: druzic@illinois.edu

Flowing Liquid Lithium Limiterfor HT-7

Utilizing TEMHD to maintain a clean Li surface, keep it below 400C, and prevent ejection

ss Hefei, ChinaJuly 19, 2011

Conceptual Design

To flow against a high field one needs to maintain the temperature gradient even outside of the plasma heat flux zone.

How: utilize TEMHD in the return flow legs too:

In a limiter machine such as HT-7, this is easier since there is some heat flux along the entire plasma-facing surface.

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Hot

Heat flux

Cooling channelsInletOutlet

Lithium reservoir

Li flow

BJ

J J

Hot, passively (not cooled) or heated

ss Hefei, ChinaJuly 19, 2011

Velocity and temperature gradientAverage velocity of liquid lithium in the trench

The power transferred by the trench structure is written as

The temperature gradient can be calculated through

)()21( 11 tL

dydTkwL

dydTkhwuh

dydTCQ wallP

QdydTtLkwkL

dydT

HaHa

LLC

HaHaCHaB

SwhC wallP

)()())tanh(1()1()tanh(1

21

112

1

2

2

))tanh(1()1()tanh(1

1

2 HaHa

LLC

HaHaCHady

dTBSu

ss Hefei, ChinaJuly 19, 2011

Top surface temperature and flow velocity for SLiDE

SLiDE’s geometric parameters are used here. Heat flux is 4MW/m^2 (typical value for our experiment, corresponding to 1500W e-beam power) .

Top surface temperature increases with the magnetic field and flow velocity decreases with the magnetic field after 0.01T (100Gauss). This model fits our experimental results

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ss Hefei, ChinaJuly 19, 2011

Apply to HT-7 to find parameters for the trenchTop surface temperature and flow velocity change

(from previous equations).

heat flux (6MW/m^2), toroidal magnetic field (2T), the length of direct heating area along radius direction (80mm), the length of hot region along a single trench (L1) (110mm) and the length of cool region (L2) (30mm).

F. Gao et al, Fusion Eng. Design 83 (2008) 1–5

Q. Li et al, Fusion Eng. Design 85 (2010) 126–129

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ss Hefei, ChinaJuly 19, 2011

Estimate top surface temperature and flow velocity

Top surface temperature is 396C and flow velocity is 0.36m/s.Bottom of trench is assumed to be kept at 200C.

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ss Hefei, ChinaJuly 19, 2011

Pressure drop in return flowThe pressure drop equation

Here Ha is the Hartmann number.

C is the conduction ratio.

is the electrical conductivity of lithium. is the electrical conductivity of the wall material. t is the thickness of SS wall(1.5mm) and w is the width of the liquid lithium flow (5mm). is the density; is the dynamic viscosity; u is the entering flow velocity (about 0.36m/s) and L is the length of the flow (0.13m).

The pressure drop is about 3.6*10^5 Pa.

However if the wall is insulated C is almost infinity. Since Ha is 837 pressure drop becomes which is 427Pa.

L.Barleon, Fusion Eng. Design 14(1991) 401-412

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𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒𝑑𝑟𝑜𝑝=𝜎 𝐵2𝑢𝐿(1𝐻𝑎+

1𝐶+1 )

𝐻𝑎=𝐵𝑤 √ 𝜎𝜌𝜇𝐶=

𝑤𝜎 𝐿𝑖

𝑡 𝜎𝑤𝑎𝑙𝑙

ss Hefei, ChinaJuly 19, 2011

Ejection problem Critical temperature gradient along the lithium surface is

Here is the standard gravity. P is the thermoelectric power (Seebeck coefficient of Li). is the surface tension (0.32N/m at 250C). R is the radius of the ejected droplet and the largest should be half of the width of the lithium trench (1mm).

Resulting critical temperature gradient is 11039 C/m. If the surface temperature gradient is lower than this value there is no ejection. The temperature gradient along the top surface needs modeling but since this value means 200C difference within 2cm the real temperature gradient may be lower than this.

However the incoming current from the plasma is also important for the ejection problem. (need those values for the calculation.)

M.A. Jaworski, Macroscopic motion of liquid metal plasma facing components in a diverted plasma, Journal of Nuclear Materials, In Press, DOI: 10.1016/j.jnucmat.2010.10.074.

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ss Hefei, ChinaJuly 19, 2011

Possible LiMIT design for HT-7 limiter 9

ss Hefei, ChinaJuly 19, 2011

LiMIT design for HT-7 limiter

3 parts: trench, tray and heat sinkTrench and tray are made of stainless steel (SS316) and the

heat sink is made of copper. This limiter is 134mm*254mm*28mm. The heat sink needs cooling.

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ss Hefei, ChinaJuly 19, 2011

Trench 11

Front

Back

ss Hefei, ChinaJuly 19, 2011

Trench

Trench is 130mm*250mm*6.5mm. Thickness of the SS wall is 0.5mm and width of the lithium trench is 2mm. Height of the trench is 5mm. The thickness between the bottom surface of the trench and the bottom of each channel is 1.5mm (the bottom plate under those fan structure).

Both ends of the bottom plate is cut to let lithium flow into the back flow channel (10mm on each side). Minimize the area of free surface to lower the ejection.

The top surface of the trench is as high as the edge of the tray. The distance between the bottom surface of the trench and the tray is 5mm. (for back flow)

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ss Hefei, ChinaJuly 19, 2011

LiMIT design for HT-7 limiter 13

ss Hefei, ChinaJuly 19, 2011

Tray 14

Wall thickness is 2mm. The edge is round shape because of the parallel heat flux. (I’m not sure if this is enough since the toroidal parallel heat flux is a major component of the total heat flux for limiter structure.)

Height of the tray is 11.5mm. Thickness of the bottom is 1.5mm.

ss Hefei, ChinaJuly 19, 2011

Engineering Details

Will follow based on remainder of visit and detailed consultation with HT-7 staff.

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