September 24-25, 2003HAPL Program Meeting, UW, Madison

1

Target Thermo-Mechanical Modeling and Analysis

Presented by A.R. Raffray

Other Contributors:

B. Christensen, J. Pulsifer, M. S. Tillack, X. Wang

UCSD

D. Goodin, R. Petzoldt

General Atomics

HAPL Program Meeting

University of Wisconsin, Madison

September 24-25, 2003

September 24-25, 2003HAPL Program Meeting, UW, Madison

2

Target Survival During Injection:What is the problem and what are the possible solutions?

• Target heat source: energy exchange from chamber protective gas and radiation from chamber wall - Gas pressure up to ~50 mtorr at 1000-4000 K (qcond’’= 4 -12 W/cm2 for Xe)

- Chamber wall temperature ~ 1000-1250 K (qrad’’~ 0.3 -0.7 W/cm2)

- q’’ to reach DT-TP for current target ~ 0.68 W/cm2

• Need ways to increase thermal robustness of target: 1. Design modification to create more thermally robust

target (e.g. add an outer insulating foam layer)2. Possibility of injecting target at lower base temperature

- Andy Schmitt's target calculations show no degradation in gain with no gas in the target center with target temperature down to 11.9 K ( 1-D runs)

- Jim Hoffer and John Sheliak’s experimental results indicate that decreasing the initial DT temperature could still result in a smooth layer

3. Explore possibility of relaxing phase change constraint- Solution must accommodate target physics requirements

DT Vapor0.3 mg/cc

DT Fuel

CH Foam + DT

1 m CH +500 Å Au

1.95 mm

1.50 mm

1.69 mm

CH foam = 20 mg/cc

September 24-25, 2003HAPL Program Meeting, UW, Madison

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• Phase change analysis with new model- effect of initial vapor gap present at DT/plastic outer coat interface (imperfect bond, He-3

bubbles trapped in foam structure…)- importance of plastic shell deformation

- vapor region behavior as a function of heat flux for cases with and without foam

Target survival workshop presentation

• Foam analysis with new model- temperature-dependent properties over a wide operating temperature range

(previous calculations assumed constant properties at higher T’s > 50-100K) - perform parametric analysis for different values of foam thickness and density, and target

initial temperature- effect of surface temperature dependent heat flux

Focus of this presentation

Progress on Target Survival Analysis and Possible Design Solution• Develop integrated 1-D thermo-mechanical target model -

phase change (solid/liquid/vapor)- effect of solid outer coat deflection on vapor region behavior- capability to include outer insulating foam region- fine spatial and temporal resolution

- model has been tested and validated against analytical and numerical solutions

- model + results to be published in journal paper

• Update property data- polystyrene thermal properties over wide temperature range

(important for cases with outer insulating foam region)

Plastic Shell

Vapor Gap

Rigid DT Solid

Simplified Target Cross Section

DT Vapor Core

September 24-25, 2003HAPL Program Meeting, UW, Madison

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Solid Polystyrene Thermal Properties Vary Markedly with Temperature

Temperature (K) Thermal Conductivity (W/m-K) Temperature (K) Specific Heat (J/kg-K)4.2 0.0286 10 32.1810 0.0541 20 102.1920 0.0744 50 270.7540 0.0947 100 460.5560 0.1066 200 799.6880 0.1150 300 1197.42100 0.1215 370 1842.19200 0.1418300 0.1537370 0.1599

Solid Polystyrene Thermal Properties

• Density = 1100 kg/m3

• Density and thermal conductivity are adjusted according to foam porosity

• Updated property data and references can be found at:

http://aries.ucsd.edu/pulsifer/PROPS/

• Rapid rise of Cp with temperature helps foam insulating layer accommodate higher heat fluxes

September 24-25, 2003HAPL Program Meeting, UW, Madison

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Decreasing the Initial Target Temperature Helps but is Not Sufficient by Itself

• For a 0.015 s time of flight (target injected at 400 m/s in a 6 m chamber), the max. allowable q’’ is increased from 0.68 to ~2 W/cm2 when Tinit is reduced from 18K to

14K- This certainly helps but needs to be supplemented by another measure to reach the ~10 W/cm2

desired objective- Target design modification (e.g. insulating layer)- Allowing some level of phase change

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

1 2 3 4 5 6 7 8 9 10

Heat Flux (W/cm 2)

Time (s)

Tinit = 18 KTinit = 16 K

Tinit = 14 K

Effect of Initial Target Temperature on the Time to Reach the Triple Point (19.79 K) for a Target without Insulation

September 24-25, 2003HAPL Program Meeting, UW, Madison

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Target Configuration with Outer Insulating Foam Layer

DT gas

1.5 mm

DT solid0.19 mm

DT + foam

x

Dense plastic overcoats (not to scale)

0.289 mm

Insulating foam

High-Z coat

10m Foam Linearly Decreasing Density

Fully Dense Polystyrene

80-130m Constant Foam Density

5m Outer Plastic Shell

2m Inner Plastic Shell

5%, 10%, or 25% Dense Polystyrene

10m Foam Linearly Increasing Density

Inner Surface of Shell Outer Surface

Outer Plastic Shell

Foam Insulator

Inner Plastic Shell DT

Graded change in foam density assumed in the

analysis

September 24-25, 2003HAPL Program Meeting, UW, Madison

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0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 2 4 6 8 10 12 14 16 18 20

Input Heat Flux (W/cm 2)

Time (s)

Tinit = 18 KTinit = 16 K

Tinit = 14 K

Combined Effect of Insulating Foam and Lower Initial Target Temperature on the Time to Reach the DT Triple Point

70

120

170

220

270

320

0 2 4 6 8 10 12 14 16 18 20

Heat Flux (W/cm 2)

Temperature (K) Tinit = 18 K

Tinit = 16 K

Tinit = 14 K

• Example case: 100m, 10% dense foam layer

- Major improvement: Allow. q’’ up to ~ 18 W/cm2 for Tinit=14 K

(corresponding to Xe at ~75 mtorr/4000K)

• Maximum foam temperature can be quite high but below polystyrene glass transition temperature of 370 K (and of melting point)

September 24-25, 2003HAPL Program Meeting, UW, Madison

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Example Results of Effect of Foam Insulator Density and Thickness on the Time to Reach the DT Triple Point

00.005

0.01

0.015

0.020.025

0.03

0.0350.04

0.045

0.05

0.0550.06

0 2 4 6 8 10 12 14 16 18 20

Input Heat Flux (W/cm 2)

Time to Reach T.P. (s)

100 Microns, 10%

150 Microns, 10% 100 Microns, 25%

150 Microns, 25%

Tinit = 16 K

• From previous ANSYS estimates based on constant properties at high T’s and coarser mesh, q’’ to reach T.P. = 15.5 W/cm2 for a 152m, 10% dense foam layer and ~15.5 K initial target temp.

• New results show even higher heat flux accommodation for similar case (150m, 10% dense, 16 K initial temp.) : max. q’’>>20 W/cm2

• Max. foam temp. < 370°C

• Very encouraging results; would open up the chamber gas density window substantially(~100mtorr Xe) and/or even allow to some degree for accommodation of energy transfer from residual plasma- Can it be done?- Fabrication, integrity and physics

considerations- To be discussed during target survival

workshop70

120

170

220

270

320

370

0 2 4 6 8 10 12 14 16 18 20

Heat Flux (W/cm 2)

Temperature (K)

100 Microns, 10% Dense

150 Microns, 10% Dense

100 Microns, 25% Dense

150 Microns, 25% Dense

Tinit = 16 K

September 24-25, 2003HAPL Program Meeting, UW, Madison

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Heat Flux Into the Target as a Function of Time for Several Xe Gas Temperatures and for Target Surface Temperature History for a

Case with 100 microns, 10% Dense Insulating Foam Region

0.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

1.00E+05

1.20E+05

1.40E+05

0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02 2.50E-02 3.00E-02

Time (s)

Heat Flux (W/m

2)

Temp_Xe = 1000 K

Temp_Xe = 2000 K

Temp_Xe = 4000 K

• As the target temperature surface increases, the energy transfer from the chamber gas decreases

• This helps somewhat but the effect is relatively small as illustrated above for 100m, 10% dense foam layer configuration

September 24-25, 2003HAPL Program Meeting, UW, Madison

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Conclusions

• Insulating foam enhances tremendously target thermal robustness- 100 m, 10% dense foam, Tinit=16 K --->q’’=18W/cm2

- 150 m, 10% dense foam, Tinit=16 K --->q’’>>20W/cm2 - allows for protective gas density 50-100 mtorr, which substantially open the armor

survival window- could even accommodate some residual plasma - performance can be demonstrated and is predictable- fabrication and integrity of foam must be confirmed- are effects on target physics acceptable?

• Phase change allowance can help accommodate additional heat fluxes

- pre-existing vapor bubbles could close if bubble size is below a critical value and heat flux above a

critical value- limit on q’’ is then homogeneous nucleation - ~5 W/cm2 for previous target configuration- Possibility of going to even high heat fluxes with insulating foam layer

Plastic Shell

Local Vapor Region

Rigid DT Solid

tv,o

ro

DT Vapor Core

Simplified Target Cross Section

More details presented at Target Survival Workshop