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
February 5-6, 2004HAPL meeting, G.Tech.
2
Outline
• Survivable Target Strategy
• Accommodation and Sticking Coefficients
• Phase Change
• Summary
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
February 5-6, 2004HAPL meeting, G.Tech.
4
Basic 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:
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:
February 5-6, 2004HAPL meeting, G.Tech.
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Chamber Gas Density and Target Heat Flux
Background Gas Density
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
February 5-6, 2004HAPL meeting, G.Tech.
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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
February 5-6, 2004HAPL meeting, G.Tech.
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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 increasing 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)
February 5-6, 2004HAPL meeting, G.Tech.
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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
February 5-6, 2004HAPL meeting, G.Tech.
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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
February 5-6, 2004HAPL meeting, G.Tech.
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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 Shell Preexisting Vapor Bubble
Rigid DT Solid
Simplified Target Cross Section
DT Vapor Core
tv
ro
February 5-6, 2004HAPL meeting, G.Tech.
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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
February 5-6, 2004HAPL meeting, G.Tech.
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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
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
+
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?