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THERMAL LOADING OF A DIRECT DRIVE TARGET IN

RAREFIED GAS

B. R. Christensen, A. R. Raffray, and M. S. Tillack

Mechanical and Aerospace Engineering Department and Center for Energy Research, University of California,

San Diego, La Jolla, CA 92093-0438, christensen@fusion.ucsd.edu

Presented at the 16th ANS TOFE

Madison, WI

September 14-16, 2004

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The Cryogenic Direct-Drive Target will be Subjected to Challenging Conditions when

Injected into an IFE Chamber

IFE Chamber (R~6 m)

Example Protective Gas: ~1021 m-3 Xe at 1000 – 4000K, q’’condensation ~ 1-10 W/cm2

Chamber wall ~ 1000–1500 K, q’’ rad = 0.2 – 1.2 W/cm2

Target Injection (~400 m/s)

Target Implosion Point

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Introduction• For each fusion micro explosion (~ 10 Hz), ions and

heat loads threaten to damage the reactor wall and driver optics. A background gas, such as Xe, could reduce the damage on the wall from ion and heat loading.

• The thermal loading of a target (radiation from the chamber wall and convection from the protective gas) may threaten the symmetry, smoothness, or uniformity requirements placed on a target.

• The radiation loading is simply calculated using the Stefan-Boltzman law (0.2 – 1.2 W/cm2).

• The convective loading is computed using DS2V, a commercial DSMC program. - The DSMC method is used due to the high Knudsen number (Kn = 0.4 – 40) for a target in a low density (n= 3x1019 – 3x1021 m-3) protective gas.

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Modeling Target Injection Using DS2V

Temperature Field Around a Direct Drive Target

- Xe flowing at 400 m/s in the positive x-dir. - 4000 K stream temperature.

- 3.22x1021 m-3 stream density.

- Sticking coefficient = 0.

- Target surface temperature = 18 K.

Assumptions• Axially symmetric flow.

• Target is stationary, Xe stream velocity = 400 m/s.

• Target surface temp. = 18 K = constant.

• Sticking coefficient = 0 or 1,

•Accommodation coefficient = 1

• Target doesn’t rotate.

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The Number Flux at the Target Surface Decreases with Increasing Sticking Coefficient

(sigma) when the Stream Density is High

• The number flux is a strong function of stream temperature and position on the target surface.

• Kinetic theory and DS2V show good agreement.

1.E+22

1.E+23

1.E+24

1.E+25

0.0 1.0 2.0 3.0Angle from Trailing Edge (rad)

Number Flux (atoms/m

2s)

T = 4000 K, sigma = 0T = 1300 K, sigma = 0T = 4000 K, sigma = 1T = 1300 K, sigma = 1Kinetic Theory, T = 4000 KKinetic Theory, T = 1300 K

High Density Stream, n = 3.22x1021 m-3

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For a High Density Stream the Heat Flux Decreases with a Decreasing in Sticking Coefficient

• The heat flux is decreased when sigma = 0 due to the influence of low temperature reflected particles interacting with the incoming stream (see the first viewgraph).

• For the low density cases there is less interaction between reflected and incoming particles.

• The rapid change in heat flux with position suggests that the average maximum heat flux could be reduced by rotating the target.

1.E+03

1.E+04

1.E+05

1.E+06

0.E+00 5.E-01 1.E+00 2.E+00 2.E+00 3.E+00 3.E+00Position on Surface (m)

Heat Flux (W/m

2)

T = 4000 K,sigma = 1T = 4000 K,sigma = 0T = 1300 K,sigma = 1T = 1300 K,sigma = 0

High Density Stream, n = 3.22x1021 m-3

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The Influence of the Sticking Coefficient () and the Accommodation Coefficient () on the Maximum Heat Flux (@

Leading Edge).

• Parameters: 400 m/s injection into Xe @ 3.22x1021 m-3 and 4000 K. (Max. heat flux (with = 1 and =1) = 27 W/cm2.

• In general, reducing a causes the heat flux to reduce more rapidly with .

• Note that the heat flux decreases when =1 for < 0.8. If there were no interactions between reflected and incoming particles the normalized heat flux would be unity for all .

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Normalized Heat Flux

α = 0

α = 0.5

α = 1

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A Summary of the Expected Heat Flux (@ the Leading Edge) as a Function of Chamber

Conditions

All heat flux values are reported in W/cm2.

n = 3.22x1019 m-3 n = 3.22x1020 m-3 n = 3.22x1021 m-3

c Tgas=1300K Tgas=4000K Tgas=1300K Tgas=4000K Tgas=1300K Tgas=4000K

0 0.3 - 1.3 0.4 - 1.4 0.9-1.9 2.3-3.3 4.4 - 5.6 14.1 - 15.1

1 0.32 -1.32 0.47 - 1.47 1.3 - 2.3 2.7-3.7 11.5 - 15.5 27.3 - 28.3

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The Effect of the Injection Velocity, Xe Density, and on the Maximum Incident Heat Flux (@

the leading edge)

• When = 1 the relationship between the heat flux and the Xe density is linear for each injection velocity.

• It is apparent that the shielding effect occurs over the density and velocity range studied, and is a stronger effect as the density is increased.

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+19 1.E+20 1.E+21 1.E+22

Density (m -3)

Heat Flux (W/m

2)

sigma = 1, V = 400 m/ssigma = 0, V = 400 m/ssigma = 1, V = 100 m/ssigma = 0, V = 100 m/s

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Maximizing the Protective Gas Density

• DS2V is used to predict heat flux as a function of protective gas density and injection velocity.

• An integrated thermomechanical model is used to predict the response of a target to an imposed heat flux. The maximum allowable heat flux for a given time of flight is obtained.

• Coupling the data from DS2V and the integrated thermomechanical model, the maximum protective gas density for a given injection velocity is obtained.

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For a Basic Target, There is an Optimum Injection Velocity when = 1.

0.0E+00

5.0E+19

1.0E+20

1.5E+20

2.0E+20

2.5E+20

3.0E+20

3.5E+20

100 150 200 250 300 350 400

Injection Velocity (m/s)

Maximum Density (m

-3) Tinit = 18 K

Tinit = 16 K

Tinit = 14 K

0.0E+00

5.0E+19

1.0E+20

1.5E+20

2.0E+20

2.5E+20

100 200 300 400 500 600Injection Velocity (m/s)

Maximum Density (m

-3) Tinit = 18 K

Tinit = 16 K

Tinit = 14 K

(sticking coefficient) = 1 (sticking coefficient) = 0

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For an Insulated Target, a High Injection Velocity Significantly Increases the Maximum Allowable

Gas Density100 mm, 10% dense insulator, (sticking coefficient) = 1

0.00E+00

5.00E+20

1.00E+21

1.50E+21

2.00E+21

2.50E+21

100 200 300 400 500 600Injection Velocity (m/s)

Maximum Density (m

-3)

Tinit = 18 KTinit = 16 KTinit = 14 K

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Summary

• The heat flux caused by the interaction of the target with the protective chamber gas can be modeled using DS2V (a commercial DSMC program).

• The sticking (condensation) coefficient and the accommodation coefficient affect the heat flux at the target surface.

• Experimental determination of the sticking (condensation) coefficient and accommodation coefficient are needed.

• There may be an optimum injection velocity that allows for the maximum amount of protective gas.