ARIES: Fusion Power Core and Power Cycle Engineering

1
Thermal Behavior and Operating Requirements of
IFE Direct-Drive Targets

• A.R. Raffray1, R. Petzoldt2, J. Pulsifer3,
• M. S. Tillack1, and X. Wang3
• 1Mechanical and Aerospace Engineering Department
  and Center for Energy Research, University of
  California, San Diego, EBU-II, Room 460, La
  Jolla, CA 92093-0417
• 2Inertial Fusion Technology Division, MS 13-501,
  General Atomics, La Jolla, CA 92186-5608
• 3Center for Energy Research, University of
  California, San Diego, EBU-II, Room 460, La
  Jolla, CA 92093-0417
• Presented at the 15th Topical Meeting on the
  Technology of Fusion Energy
• Washington, D.C.
• November 2002

2
Abstract

• During injection, inertial fusion energy (IFE)
  direct drive targets are subject to heating from
  energy exchange with the background gas and
  radiation from the wall. This heat deposition
  could lead to deuterium-tritium (DT) phase change
  and target deformation violating the target
  physics symmetry requirements.
• This paper assesses the thermal behavior of the
  target under such conditions and explores
  possible ways of extending the target lifetime
  through design modification(s) and/or through a
  better understanding of the effect of energy
  deposition and phase change on the target density
  symmetry.

3
Typical Direct Drive Target Configuration
Spherical shell 4 mm in diameter Composed
mainly of solid DT at 18K Injected in IFE
chamber at velocities up to about 400 m/s
For maximum energy yield from the fusion
micro-explosion - Temperature of DT layer must
be held at 18.5 K - High degree of spherical
symmetry and surface smoothness must be
maintained
4
Injected Target Heating through Energy Exchange
from Background Gas

• Background gas (e.g. xenon or helium) might be
  needed for chamber wall protection
• Energy transfer from impinging atoms of
  background gas on target
• - Enthalpy transfer
• - Condensation (latent heat transfer) in the
  case of gas with boiling point and melting point
  above target temperature (18K) (e.g. for Xe)
• - Possible recombination of ions at the surface
  if plasma conditions remain in the chamber
• - Much uncertainty remains regarding plasma
  conditions during injection
• - For simplicity, plasma effects are not
  included in the calculations presented here
• - Results will be revisited as new information
  on plasma remnants in the chamber becomes
  available.

5
Condensation from Xe as Background Gas
No data found for condensation
coefficient, ?c, for Xe at 1,000's K
condensing on an 18 K surface. ?c
0.99-0.6 for 2,500K Ar beam condensing on a
15 K Cu/Ar with incident angle of 0o-60o.
It seems prudent to assume ?c values of 1
to estimate Xe condensation heat fluxes.
6
Condensation from He as Background Gas
Heat flux on the target from He are comparable
to those from Xe case even in the absence of
condensation. - Latent heats have only a
small effect on the overall energy transfer
which is governed by change in gas
enthalpy - Molecular flux of He target is
higher than that of Xe for same P and T Use
of He has the advantage that the He atoms after
transferring their energy to the 18 K target
will likely be reflected back thereby
shielding the target from subsequent He atom
collisions.
7
Radiation Heat Transfer from Chamber Wall
Simple estimate given by

• Where Tw is the wall temperature (assumed as a
  black body)
• ?S-B is Stefan-Bolzmann constant, and ?? the
  target surface reflectivity.

Highly reflective target surface is required
to minimize total absorbed heat flux. For
very thin (275375 Å) gold coating, a
reflectivity of about 96 is
anticipated. Effort underway to estimate more
accurately the radiated energy absorption
and reflection based on a multi-layer wave
model. As an illustration, qrad ranges
from 2300 W/m2 for Tw1000K to 11,000 W/m2 for
Tw1500 K.
8
Initial Target Thermal Analysis
Transient thermal analysis using
ANSYS - Target is not tumbling - 2-D heat
flux distribution from DSMC
results - Temperature dependent DT
properties including latent heat of fusion
at triple point to model phase change
Max. temp. limit to prevent unacceptable target
deformation not well known - Previous
assumption was to maintain DT below its triple
point (19.79 K) Heat flux to reach triple
point only 6000 W/m2 for a 6-m radius chamber
qcond from 1000K/7.6 mtorr or 4000 K/2.5 Xe
or qrad from Tw1275K Major constraint on
background gas density that might be required for
wall protection.
9
Add Outer Insulating Foam Layer to Enhance Target
Thermal Robustness

• Simple assumption adjust thickness of
  DTfoam layer accordingly to maintain same
  overall dimension

• Properties of cryogenic foam based on
  those of polystyrene
• - Density and thermal conductivity
  adjusted according to foam region
  porosity
• - Thermal conductivity further scaled by 2/3
  to account for possible optimization of
  porous micro-structure to minimize the
  conductivity.
• - As conservative measure, higher thermal
  conductivity values found in the literature
  used, ranging from 0.088 W/m-K at 19 K to
  0.13 W/m-K at 40 K
• - Heat capacity values used range from 100
  J/kg-K at 20 K to 225 J/kg-K at 40 K

10
DT Interface Temperature History for q2.2
W/cm2 and for Different Thicknesses(mm)of 25
Dense Outer Foam Region

• Transient analyses performed using ANSYS
• - q 2.2 W/cm2
• - e.g. corresponding to condensation from
  10 mTorr/4000 K Xe
• - Outer foam region density 25
• 130 mm (32 mm of equivalent solid
  polystyrene) would be sufficient to
  prevent DT from reaching the triple
  point after 0.015 s (corresponding to a
  target velocity of 400 m/s in a chamber of
  radius 5 m).
• As comparison, DT would reach the triple
  point after about 0.0022 s in the absence of
  the outer foam layer.

11
Summary of Thermal Analysis Results on
Effectiveness of Insulating Outer Foam Layer

• To increase target thermal robustness
• - maximize both thickness and porosity of
  outer foam layer while
• - accommodating target physics and structural
  integrity requirements.
• Increasing plastic coating thickness
  from 1 ?m to 10 ?m provides only
  marginal improvement.

12
Another Means to Extend Target Lifetime is by
Relaxing DT Thermal Limit and Allow Some Phase
Change

• What is the effect on target density symmetry
  relative to target physics requirements?
• The target is covered by a 1 mm solid plastic
  coating
• - Vapor might form at DT-foam/plastic coating
  interface resulting in density variation
• - Nature of bond between DT-foam and plastic
  coating key factor Perfect bond---gt vapor
  formation through homogeneous nucleation.
• - However, under target conditions,
  homogeneous nucleation is virtually zero at
  Tlt 26 K and dramatically increases as T--gt 34 K.
• Imperfect bond
• - Heterogeneous nucleation could be a problem
  for nucleation sites of the order of 1 mm.
• Finite gap
• - Surface evaporation
• - This worse-case scenario was further
  assessed.

13
Thermo-mechanical Model for Rigid DT
Both liquid and vapor densities of DT are lower
than the DT solid density
DVtotal volumetric change of target VsEquivalent
solid volume of phase change region Vl and
Vvliquid and vapor volumes of phase change
region DVthvolumetric thermal expansion of
plastic coating
14
Simple Model Development

• The initial solid volume, Vs, that has undergone
  phase change is given by

• Assume that a mass fraction xl of the phase
  change region, dp-c, is liquid and (1-xl) is
  vapor

• The volumetric expansion of the plastic coating
  is given by

• Substitution in DV/V eqn. leads to a quadratic
  equation for P

15
Thermo-Mechanical Analysis Procedure

• The phase change thickness and DT interface
  temperature were first estimated as a function of
  incident heat flux from a series of 2-D ANSYS
  runs and used as input for the thermo-mechanical
  model.

• The model solves for the pressure of the DT
  liquid and vapor for a given vapor region
  thickness.
• Iterate to obtain vapor/liquid interface
  temperature and pressure consistent with
  saturation conditions from the phase diagram.

16
DT Evaporated Region Thickness as a Function of
Maximum Heat Flux for Different Plastic Coating
Thicknesses
Is 1 density variation acceptable based on
target physics requirements? - For the 289 mm
foamDT region--gt 3 mm vapor region - e.g. for
8 mm plastic coating maximum allowable q4.2
W/cm2 A thicker plastic coating is preferred
to minimize vapor region thickness
17
Hoop Stress as a Function of Maximum Heat Flux
for Different Plastic Coating Thicknesses
A maximum q of 5-5.5 W/cm2 for a plastic
region thickness of 8 mm is allowable based on
the ultimate tensile strength of polystyrene
18
DT Vapor and Maximum Interface Temperatures as a
Function of Maximum Heat Flux
Homogeneous nucleation increases dramatically
as T--gt 34 K, corresponding to q gt 6 W/cm2
19
Equivalent Heat Flux as a Function of DT
Evaporated Thickness
Equivalent q required to evaporate vapor
region is small for vapor region thicknesses
1-10 mm (ltlt heat flux on target)
20
DT Evaporated Thickness as a Function of Maximum
Heat Flux for Different Plastic Coating
Thicknesses for a Case with a 72-mm 25 Dense
Insulating Outer Foam Layer
Based on the 1 density variation (3 mm vapor
region ), the maximum allowable q is now
8.6 W/cm2 for a 8 mm plastic coating (compared
to 4.2 W/cm2 for case without insulating foam
layer)
21
Hoop Stress as a Function of Maximum Heat Flux
for Different Plastic Coating Thicknesses with a
72-mm 25 Dense Insulating Outer Foam Layer
A maximum q of 9.5 W/cm2 for a plastic
region thickness of 8 mm is allowable based on
the ultimate tensile strength of polystyrene
22
DT Vapor and Maximum Interface Temperatures as a
Function of Maximum Heat Flux for a Case with a
72-mm 25 Dense Insulating Outer Foam Layer
23
Conclusions (I)

• The potential benefit on target lifetime of
  adding an insulating foam layer and/or of better
  understanding vapor formation processes have been
  examined.
• For a typical target configuration the maximum
  q for DT to reach its triple point is only
  about 0.6 W/cm2 for a 6-m radius chamber.
• This would place an important constraint on
  background gas density that might be required for
  wall protection.
• Adding a 130-mm 25 dense outer foam layer would
  increase the allowable qfor DT to reach its
  triple point to 2.2 W/cm2 and a 152mm 10 dense
  insulating foam layer would increse q up to 7.5
  W/cm2.
• For increased target thermal robustness, it is
  preferable to have the maximum thickness and
  porosity outer foam layer which can still
  accommodate the target physics and structural
  integrity requirements.

24
Conclusions (II)

• Allowing for vapor formation would relax the
  target thermal constraint
• A simple thermo-mechanical model was developed to
  help in better understanding the DT phase change
  process.
• - A thicker plastic coating was found
  preferable to reduce the vapor region
  thickness.
• - A 1 change in region density corresponds to
  3mm of vapor region at the DT-foam/plastic
  coating interface.
• - If this were acceptable, the maximum
  allowable q is 4 W/cm2 for the original
  target design and 9 W/cm2 for a target design
  with 72-mm thick, 25-dense outer insulating
  foam layer and an 8-mm thick plastic coating.
• - In both cases, the corresponding hoop
  stresses in the plastic coating are less than
  the anticipated ultimate tensile strength.

25
Conclusions (III)

• The results from the simple thermo-mechanical
  model have helped to highlight the benefits of
  relaxing the DT vapor formation constraint and of
  including design modifications such as an
  insulating outer layer.
• - However, this model has limitations and a
  better understanding of the phase change
  processes would be obtained from a fully
  integrated model including the interactions of
  all key processes.
• - For example, the assumption of surface
  evaporation is conservative and infers the
  presence of a minute gap at the DT-foam and
  plastic coating interface
• - For a good-quality interface bond, DT boiling
  is more likely to occur through nucleation which
  should be included in the model.
• This also indicates the need for an experimental
  effort to better characterize the quality and
  behavior of this bond ideally by using or
  possibly by simulating the actual materials.
• In addition, guidance is needed from the target
  physics perspective to understand better the
  constraints and limitations imposed on such
  actions.