survivable target strategy and analysis

15
February 5-6, 2004 HAPL meeting, G.Tech. 1 Survivable Target Strategy and Analysis Presented by A.R. Raffray Other Contributors: B. Christensen, M. S. Tillack UCSD D. Goodin, R. Petzoldt General Atomics HAPL Meeting Georgia Institute of Technology Atlanta, GA February 5-6, 2004

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Survivable Target Strategy and Analysis. Presented by A.R. Raffray Other Contributors: B. Christensen, M. S. Tillack UCSD D. Goodin, R. Petzoldt General Atomics HAPL Meeting Georgia Institute of Technology Atlanta, GA February 5-6, 2004. Outline. Survivable Target Strategy - PowerPoint PPT Presentation

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Page 1: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

1

Survivable Target Strategy and Analysis

Presented by A.R. Raffray

Other Contributors: B. Christensen, M. S. Tillack

UCSD

D. Goodin, R. PetzoldtGeneral Atomics

HAPL MeetingGeorgia Institute of Technology

Atlanta, GAFebruary 5-6, 2004

Page 2: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

2

Outline

• Survivable Target Strategy

• Accommodation and Sticking Coefficients

• Phase Change

• Summary

Page 3: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

3

Overall Strategy to Develop a Survivable Target

• Uncertainty in chamber gas requirements and resulting heat flux on target

- Min. gas density set by chamber wall protection

- Max. gas density set by target placement and tracking accuracy

- Uncertainty in accommodation and sticking coefficients for high temp. chamber gas on cryogenic target

• Prudent to consider dual target approach and address key issues- Basic target

- Thermally robust target with insulated foam coating

- Increase target heat flux accommodation through low temp. target and possible allowance of phase change

• Once sufficient information available down-select “best”target design

• Integrated “team” approach

Page 4: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

4

Base Target Strategy

Basic TargetInitial Temp. = 18 K

Allowable q’’ = 0.7 W/cm2

Xe Temp. ~4000 K Xe Pres. ~ 0 (@300K)

Low Temp. TargetInitial Temp. = 16 K

Allowable q’’ = 1.5 W/cm2

Xe Pres. ~ 2 mtorr

Basic Target with Phase Change

Initial Temp. = 18 KAllowable q’’ = 6.5 W/cm2

Melt Depth = 34 mXe Pres. ~ 20 mtorr

Low Temp. Target with Phase Change

Initial Temp. = 16 KAllowable q’’ = 6.5 W/cm2

Melt Depth = 30 mXe Pres. ~ 23 mtorr

NumericalModel

Outer Coat/DT Phase Change/DT Solid Interaction, Vapor Growth, Impact on Target Symmetry

Is Low Temperature Acceptable for DT

Layering?

Experiment

PhysicsSimulation

Will Liquid Layer/Vapor Bubbles Meet Physics

Requirements?

DT/foamMechanicalProperties

Exper.

Vapor Bubble/Phase

Change Exper.?

Which target design(s) fit

within background gas requirements?

Timeline(?) Downselect in mid-Phase II

LANL NRL UCSD, GA

LLE(UR)

Chamber Effort

Schafer,GA

Legend:

Page 5: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

5

Insulated Target Strategy

Insulated Target Standard Design

150 m of Insulation10 % Dense InsulationInitial Temp. = 18 K

Allow. q’’ = 12 W/cm2

Xe Temp. ~4000 K Xe Pres.~50mtorr (@300 K)

Low Temp. Insulated Target

Initial Temp. = 16 KAllowable q’’ > 18 W/cm2

Xe Pres. ~ 70 mtorr

Insulated Target with Phase Change

Initial Temp. = 18 KAllowable q’’ = 20 W/cm2

Melt Depth = 2.5 mXe Pres. ~80 mtorr

Low Temp. Insulated Target with Phase Change

Initial Temp. = 16 KAllowable q’’ = 20 W/cm2

Melt Depth = 0 mXe Pres. ~80 mtorr

Is Low Temperature Acceptable for Layering?

Does Foam Insulator MeetManufacturing and Physics

Requirements?

Manufacturing Process and Cost Study?

PhysicsSimulation

Does Liquid Layer/Vapor Bubbles Meet Physics

Requirements?

Experiment

DT/foamMechanicalProperties

Exper.

NumericalModel

Outer Coat/DT Phase Change/DT Solid Interaction, Vapor Growth, Impact on Target Symmetry

Vapor Bubble/Phase

Change Exper.?

Which target design(s) fit

within background gas requirements?

Timeline(?) Downselect in mid-Phase II

LANL NRL UCSD, GA

LLE(UR)

Chamber Effort

Schafer,GA

Legend:

Page 6: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

6

Chamber Gas Density and Target Heat Flux

Background GasDensity

Target Placement &Tracking, and Repeatability

Armor+System Analysis

Resulting heat flux on target based on gas &

target surface conditions

SPARTAN/ DSMC

Model & expt.for sticking &

accomm. coeff.

Minimum Gas Density

Maximum Gas Density

Which target design(s) fit within

background gas requirements?

Sufficient Chamber Wall Protection?

LANL NRL UCSD, GA

LLE(UR)

Chamber Effort

Schafer,GA

Legend:

Downselect in mid-Phase II

Page 7: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

7

Several Factors Influence the Heat Flux on the Target from the Chamber Gas

• The condensation or ‘sticking’ coefficient

• The accommodation coefficient (≈ “fraction of energy transfer”)

• Target shielding by cryogenic particles leaving the surface of the target

• Evaporation/sublimation of condensed background gas due to radiation heat transfer

Incoming High Temperature Background Gas (T ~ 4000 K)

Condensed Material

Outgoing Cryogenic Gas

Radiation From Chamber Walls

IFE

TARGET

Page 8: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

8

Condensation (Sticking) Coefficient of High Temperature Gas on Cryogenic Target(Very Little Data Found, Applicable to our Prototypical Conditions)

2 x 1014 s-1cm-2

4 x 1015 s-1cm-2

4 x 1016 s-1cm-2

CO2 Beam on Cu Target

Ar Beam on Cu Target

1400 K

300 K

• Condensation coefficient is a function of several parameters, including:- Ttarget, Tgas, flux, angle of incidence...

• Condensation coefficient decreases rapidly with Ttarget past a certain point (Brown, et al., 1969) - No obvious mechanisms causing

the threshold (i.e melting or boiling point of gas species)

- MP (Ar) = 83.8 K- BP (Ar) = 87.3- MP (CO2) = 194.6 K

- BP (CO2) = 217.5 K

• For an insulated target the surface temperature will increase rapidly; thus the condensation coefficient will decrease rapidly

Con

den

sati

on C

oeff

icie

nt

Con

den

sati

on C

oeff

icie

nt

Target Temperature (K)

Target Temperature (K)

Page 9: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

9

DSMC Results of Heat Flux for No Sticking and Complete Accommodation

• Results shown in Frost (1975) indicates accommodation close to unity for 1400K Ar over a wide range of Cu target temperature and surface conditions (77-280 K)

• Effect of shielding from no sticking for accommodation of unity show a slight reduction in heat flux due to shielding effect

0.0E+00

5.0E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03 5.0E-03 6.0E-03 7.0E-03

Distance Around Target (m)

Heat Flux (W/m

2)

100 mtorr, Complete Condensation

100 mtorr, Complete Reflection

Xenon Gas @ 4000 K, vT = 400 m/s Surface Temperature = 18 K (Constant)

Complete Accommodation

0.0E+00

5.0E+02

1.0E+03

1.5E+03

2.0E+03

2.5E+03

0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03 5.0E-03 6.0E-03 7.0E-03

Distance Around Target (m)

Heat Flux (W/m

2)

1 mtorr, Complete Condensation

1 mtorr, Complete Reflection

~ 15-20 % Maximum Reduction for High Density Case, 100 mTorr Xe

Minor Effect for Low Density Case, 1 mTorr Xe

Page 10: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

10

A Significant Reduction in Accommodation Coefficient Would be Very Beneficial as the Heat Flux on the Target

Would Vary Accordingly

• Recent results from CERN indicate a possibility of much lower sticking coefficients for various gases (H2, CH4, CO, CO2) on

cryogenic (5-300K) targets (and perhaps accommodation coefficient?)

• Experiments with prototypical materials and conditions would help better understand and estimate the actual accommodation and sticking coefficients

• In the mean time, for current analysis it seems prudent to assume unity for both coefficients until data become available

Page 11: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

11

Modeling the Behavior of a Vapor Bubble

Assumptions• 1-D heat transfer

• DT liquid remains static

• The cryogenic polymer shell behaves according to the theory of elasticity

• Solid portion of DT is rigid

• Pre-existing bubble due to defect at plastic/DT interface or presence of 3He

Plastic ShellPreexisting Vapor Bubble

Rigid DT Solid

Simplified Target Cross Section

DT Vapor Core

tv

ro

Page 12: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

12

Deflection of the Plastic Shell due to DT Vapor Pressure Two Possible Cases:

• Membrane theory (valid for r/t > 10) for a sphere with a uniform internal pressure

• From bending theory, max. deflection under the center of the load*

Uniform Internal Pressure, P

r

t

- Where A is a numerical coefficient =f (ro , R, t, )

- This equation is valid for any edge support positioned 3 degrees or more from the center of the load

δ =Pr2(1− μ )

2Et

δ =APR (1− μ 2 )

Et2

*Roark’s Formulas for Stress & Strain, 6th Edition, p. 546

t

ro

RP

Page 13: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

13

Comparison of the Calculated Deflection of the Plastic Shell by Membrane and Bending Theory for a Pressure of 104 Pa for Several

Vapor Bubble Sizes , ro

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 3.0E-05 3.5E-05 4.0E-05

Vapor Bubble Size, r o (m)

Deflection (m)

Membrane Theory

Bending Theory (Roark)

ro

R

• Bubble size for which bending theory approaches membrane theory is independent of pressure, ~ 37 m in this case

• Would need much smaller bubble size in target to avoid large “membrane-like” deflections

Page 14: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

14

Pre-existing Vapor Bubbles Could Close if Initial Bubble is Below a Critical Size and

the Heat Flux Above a Critical ValuePlastic Shell

Local Vapor Bubble

Rigid DT Solid

tv,o

ro

• Encouraging results for self-healing• Need verification with 2-D model + experimental data• Physics requirements (bubble has close but are solid+liquid layers ok?)

0.00E+00

1.00E-06

2.00E-06

3.00E-06

4.00E-06

5.00E-06

6.00E-06

7.00E-06

8.00E-06

0 1 2 3 4 5 6 7 8 9 10

Heat Flux (W/cm2)

Vapor Thickness (m)

Rigid, tv_o = 1e-6 m

Rigid, tv_o = 3e-6 m

Bending, tv_o = 1e-6 m, ro = 5e-6 m

Bending, tv_o = 3e-6 m, ro= 5e-6m

Bending, tv_o = 1e-6 m, ro = 7e-6 m

t = 0.015 s

Tinit = 18 K

+

Page 15: Survivable Target Strategy and Analysis

February 5-6, 2004HAPL meeting, G.Tech.

15

Summary• A dual-target strategy is proposed: basic target + thermally

robust target

• Converge on final target design once sufficient information is obtained on:- Target fabrication and behavior- Heat loads on target (chamber gas density, sticking + accommodation coefficients)- Physics requirements

• Small pre-existing vapor bubbles (defects) could be eliminated by solid to liquid phase change (self-healing)- Depends on heat flux and size of bubble- Based on 1-D model and assumptions such as rigid solid DT- Need experimental data and 2-D model to better understand- Is this acceptable based on target physics requirements?