Tuxedo

1
Can a Direct-Drive Target Survive Injection into
an IFE Chamber?
A. R. Raffray, B. R. Christensen and M. S. Tillack
Mechanical and Aerospace Engineering Department
and the Center for Energy Research
18-19 October 2004
Japan-US Workshop on IFE Target Fabrication,
Injection and Tracking Osaka, Japan
2
Degradation of targets in the chamber must not
exceed requirements for successful implosion
Physics requirements

• Spherical symmetry
• Surface smoothness
• Density uniformity
• TDT (
• Better definition is needed

3
We have characterized target heat loads and the
resulting thermomechanical behavior in order to
help define the operating parameter windows
Heat loads

• Energy transfer from impinging atoms of
  background gas
• Enthalpy transfer (including condensation) or
  convective loading
• Recombination of ions (much uncertainty remains
  regarding plasma conditions during injection)
• Radiation from chamber wall
• Dependent on reflectivity of target surface and
  wall temperature
• Estimated as 0.2 1.2 W/cm2 for e 0.96 and
  Twall 1000 1500 K

Analyses performed

• Convective loading using DSMC
• Integrated thermomechanical model developed at
  UCSD, including phase change behavior of DT

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1. Computation of energy transfer from background
gas using DS2V
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The DSMC method has been used to study targets in
a low density (3x1019 3x1021 m3) protective
gas where Kn is moderately high (0.440)
Temperature field around a direct drive target

• Assumptions
• Axially symmetric flow
• Stationary target
• Xe stream
• velocity 400 m/s
• T 4000 K
• density3.22x1021 m-3
• Target surface fixed at T 18 K
• Sticking coefficient 0
• Accommodation coefficient 0
• No target rotation

Flow
s 0
a 0
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If the stream density is high, the number flux
at the target surface increases when the sticking
coefficient (s) decreases
n 3.22x1021 m-3
decreasing s

• Instead of screening incoming particles,
  stagnated particles add to the net particle flux
• Kinetic theory and DS2V show good agreement

7
Conversely, if the stream density is high, the
heat flux at the target surface decreases when
the sticking coefficient decreases
n 3.22x1021 m-3

• The heat flux decreases when s 0 due to the
  shielding influence of low temperature reflected
  particles interacting with the incoming stream
• For the low density cases there is less
  interaction between reflected and incoming
  particles.

decreasing s

• The strong dependence of heat flux on position
  suggests that the time-averaged peak heat flux
  could be reduced significantly by rotating the
  target.

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The sticking coefficient (s) and accommodation
coefficient (a) both have a large impact on the
maximum heat flux at the leading edge

• Region of no screening

• Parameters
• 400 m/s injection into
• Xe _at_ 3.22x1021 m-3
• 4000 K
• max. heat flux 27 W/cm2 (with a 1 and s 1)

Experimental determination of the sticking
coefficient and accommodation coefficient is
needed
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2. Integrated thermomechanical modeling of
targets during injection
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Background

• A 1-D integrated thermomechanical model was
  created to compute the coupled thermal (heat
  conduction, phase change) and mechanical (thermal
  expansion, deflection) response of a direct drive
  target
• The maximum allowable heat flux was analyzed for
  several target configurations where failure is
  based on the triple point limit
• The potential of exceeding the triple point
  (allowing phase change) was explored
• In the following, we discuss
• a description of the model
• validation of the model
• the effect of initial target temperature
• the effect of thermal insulation
• the effect of injection velocity
• the effect of allowing a melt layer to form
• the effect of allowing a vapor layer to form

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The 1D transient energy equation is solved in
spherical coordinates

• Discretized and solved using forward time central
  space (FTCS) finite difference method
• Temperature-dependent material properties
• Apparent cp model to account for latent heat of
  fusion (at melting point)

Interface Boundary Condition
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Deflection of polymer shell and DT nonlinearly
affects the pressure and vapor layer thickness

• Outer polymer shell deflection
• Membrane theory for shell of radius rpol and
  thickness tpol

• Inner solid DT deflection
• Thick spherical shell with outer and inner radii,
  ra and rb

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The model was validated using an exact solution
for a solid sphere

• Initial temperature TTm (the melting point)
• Surface suddenly raised to Ts25 K at t0
• The solution converged to the exact solution as
  the mesh size was decreased.
• The melt layer thickness is correctly modeled.
• Slight error exists in the temperature profile.

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Reducing the initial temperature of a basic
target increases the maximum allowable heat flux

• DT triple point temperature is assumed as limit.
• Take the required target survival time to be
  16.3 ms.
• Decreasing the initial temperature from 16 K to
  14 K does not have as large of an effect as a
  decrease from 18 K to 16 K.

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An insulating foam on the target could allow very
high heat fluxes

• Failure is assumed at the DT triple point
  temperature
• Required target survival time assumed 16.3
  ms.
• Initial target temperature 16 K.
• A 150 mm, 25 dense insulator would increase the
  allowable heat flux above 12 W/cm2, nearly an
  order of magnitude increase over the basic target.

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For a basic target, using the TP limit, there is
an optimum injection velocity when s 1
s 1
s 0

• DS2V is used to predict heat flux, and the
  integrated thermomechanical model is used to
  predict the response
• This optimum occurs due to a competition between
  increasing heat flux vs. lower thermal penetration

17
For an insulated target, higher injection
velocity significantly increases the maximum
allowable gas density
100 mm, 10 dense insulator, s (sticking
coefficient) 1
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If only melting occurs, the allowable heat flux
is increased by 38 times over the cases where
the DT triple point temperature is used as the
failure criterion

• Possible failure criteria
• Homogeneous nucleation of vapor bubbles in the DT
  liquid (0.8Tc).
• Ultimate strength of the DT solid or polymer
  shell is exceeded.
• Melt layer thickness exceeds a critical value
  (unknown).

Tinit 16 K

• For targets with initial temperatures of 14 K,
  16 K, and 18 K, 0.8Tc was reached before the
  ultimate strength of the polymer was exceeded.
• The maximum allowable heat fluxes were found to
  be (_at_ 16.3 ms)
• 5.0 W/cm2 (Tinit 18 K)
• 5.5 W/cm2 (Tinit 16 K)
• 5.7 W/cm2 (Tinit 14 K)

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However, the amount of superheat (with melting
only) indicates a potential for nucleating
growing bubbles

• Due to the presence of dissolved He-3 gas, and
  small surface defects (nucleation sites), vapor
  formation is expected to occur before 0.8Tc.
• For bubble nucleation and growth to occur (at
  nucleation sites), the liquid must be superheated
  by 2-3 K, where the superheat is defined as

Tinit 14 K
5.5 W/cm2
2.5 W/cm2
1.0 W/cm2

• For a basic target with initial temperatures of
  16 K, the super heat is 2-3 K for input heat
  fluxes 2.5 W/cm2.
• For a initial temperature of 14 K, the superheat
  is negative when the heat flux is 1.0 W/cm2 (see
  figure to the right).

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If a vapor layer is present, the allowable heat
flux is increased by 1.53 times over the cases
where the DT triple point temperature is used as
the failure criterion

• Possible failure criteria
• Ultimate strength of the DT solid or polymer
  shell is exceeded.
• Vapor layer thickness exceeds a critical value
  (unknown).
• For targets with initial temperatures of 14 K,
  16 K, and 18 K, The polymer ultimate strength was
  reached before the DT ultimate strength.

• The maximum allowable heat fluxes were found to
  be (_at_ 16.3 ms)
• 2.2 W/cm2 (Tinit 18 K)
• 2.5 W/cm2 (Tinit 16 K)
• 2.9 W/cm2 (Tinit 14 K)

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For some initial temperatures and heat fluxes,
the vapor layer closes, suggesting that bubbles
can be minimized or eliminated in some
circumstances
Tinit 18 K

• For a target with an initial temperature of 18 K
  the vapor layer thickness increases rapidly for
  heat fluxes 2.5 W/cm2.
• For a target with an initial temperature of 14 K
  the vapor layer thickness goes to zero when the
  heat flux ? 1.0 W/cm2.
• This vapor layer closure occurs because the DT
  expands (due to thermal expansion and melting)
  faster that the polymer shell expands (due to
  thermal expansion and the vapor pressure load).

Tinit 14 K
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Future model development activities are guided by
the desire to plan and analyze experiments

• The coupled thermal and mechanical response of a
  direct drive target has helped us understand the
  behavior of the target and limiting factors on
  target survival
• However, the simple 1D vapor model does not
  account for real-world heterogeneities

• Future numerical model improvements will include
  a prediction of the nucleation and growth
  (homogeneous or heterogeneous from He3) of
  individual vapor bubbles in the DT liquid
• We are evaluating the feasibility of a 2D model
  of the energy equation