Progress Report on SPARTAN Chamber Dynamics Simulation Code

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Progress Report on SPARTANChamber Dynamics
Simulation Code

• Farrokh Najmabadi, Zoran Dragojlovic
• HAPL Meeting
• September 24-25, 2003
• University of Wisconsin, Madison
• Electronic copy http//aries.ucsd.edu/najmabadi
  /TALKS
• UCSD IFE Web Site http//aries.ucsd.edu/IFE

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Improvements in Numerical Algorithms Has Led to 5
Times Reduction in Simulation Time

• We have implemented a new embedded boundary
  algorithm which has a more robust convergence
  properties
• This has allowed changes in computational order
  and timing.
• We have achieved a factor of 5 speed-up of the
  code for uniform cell dimensions. This is the
  same as what was achieved with AMR before.
• Automatic Mesh Refinement (AMR) algorithm has to
  be modified for this new embedded boundary
  algorithm (to be completed in October).
• It appears that our previous error estimates for
  SPARTAN was too conservative. Results here are
  for 4-cm cells (as opposed to 1-cm cells before).
  This has also speeded up SPARTAN simulations.
• A paper titled, An Embedded Boundary Method for
  Viscous, Conducting Compressible Flow, will be
  shortly submitted to J. of Computational Physics.

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Progress in Refining Physics Has Continued

• We implemented Sutherland law for estimation of
  viscosity and thermal conductivity of gases as a
  function of temperature.
• It was recommended in the SPARTAN E-meeting to
  account for background plasma by
• Using coronal equilibrium data for gas (Xe)
  ionization levels and radiation
• Using law of mixtures to include background gas
  and plasma thermal conductivities and
  viscosities
• We have completed coding of SPARTAN to account
  for background plasma. We are awaiting data to
  perform simulations.
• A paper titled, Simulation of IFE Chamber
  Dynamic Response by a Second Order Godunov Method
  with Arbitrary Geometry, was submitted to IFSA
  2003.

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Simulation Results
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Impact of Viscosity and Conductivity on Chamber
Conditions Were Studied

• 6.5-m radius chamber with one laser channel (wall
  at 700oC)
• 160 MJ NRL target in a chamber filled with Xe (50
  mTorr)
• Hand-over from Bucky is at 500 ms after
  explosion
• Initial shock wave has not hit the wall

• Simulation Cases
• No Viscosity, No Conductivity
• No Viscosity, With Conductivity
• With Viscosity, No Conductivity
• With Viscosity, With Conductivity

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Reference Case No Viscosity, No Conductivity

• Convergence of shock waves sets up hot spots in
  the chamber.
• Flow mixing is too slow to equalize the
  temperature.

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Case 2 No Viscosity, With Conductivity

• Gas conductivity distributes the gas temperature
  (hot regions vs hot spots).
• Peak, average, minimum gas temperatures are
  reduced.
• About 25 of gas thermal energy is conducted away
  to the wall.

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Case 3 With Viscosity, No Conductivity

• Gas viscosity enhances flow mixing, peak
  temperatures are reduced.
• Average gas velocity is decreased, average gas
  temperature is increased. Larger eddies are
  formed.

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Chamber Conditions at 100 ms
Reference Case Viscosity No Conductivity No Case II Viscosity No Conductivity Yes Case III Viscosity Yes Conductivity No Case IV Viscosity Yes Conductivity Yes
Pmax (Pa) 710 720 836 730
pmin (Pa) 326 249 326 289
pave (Pa) 571 387 572 391
Tmax (K) 1.87 X 105 7.92 X 104 1.88 X 105 8.57 X 104
Tmin (K) 1.94 X 104 5.77 X 103 1.85 X 104 5.01 X 103
Tave (K) 5.14 X 104 3.79 X 104 6.36 X 104 3.88 X 104
Vmax (m/s) 1,220 806 610 521
rmax (kg/m3) 6.87 X 10-4 25 X 10-4 7.99 X 10-4 27 X 10-4
rmin (kg/m3) 7.59 X 10-5 1.27 X 10-4 7.78 X 10-5 1.22 X 10-4
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Chamber Conditions at 100 ms
Ref. Case
Case 3
Case 4 (Full Navier Stocks)
Case 2
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Impact of Laser Beam Channels

• 6.5-m radius chamber with one laser channel (wall
  at 700oC)
• 160 MJ NRL target in a chamber filled with Xe (50
  mTorr)
• Hand-over from Bucky is at 500 ms after
  explosion
• Initial shock wave has not hit the wall

• Simulation Cases (Full Navier Stocks)
• One Beam Channel (Reference Case)
• Two Beam Channels (90o apart)
• Two Beam Channels (180o apart)
• Four Beam Channels

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Case 2 Two Beam Channels, 90o

• Turbulence seeded by beam channels lead to a
  more uniform chamber condition.

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Case 3 Two Beam Channels, 180o

• Both beam lines are 20 m long (similar to Ref.
  Case), only a portion is shown.
• Even in symmetric two-beam case, the peak
  temperature is reduced and chamber environment is
  more uniform,

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Case 4 Four Beam Channels

• All beam lines are 20 m long (similar to Ref.
  Case), only a portion is shown.
• 4-beam channel case was terminated at 72 ms due
  to computer failure.
• Peak temperature at 100 ms is estimated at 4 X
  104 K

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Chamber Conditions at 100 ms(All Navier Stokes
Cases)
Reference Case One Beam Channel Case II Two Beam Channels (90o) Case III Two Beam Channels (180o) Case IV Four Beam Channels
Pmax (Pa) 730 560 682 487
pmin (Pa) 289 222 267 184
Tmax (K) 8.57 X 104 6.28 X 104 8.2 X 105 6.48 X 104
Tmin (K) 5.01 X 103 4.4 X 103 4.9 X 104 3.15 X 103
Vmax (m/s) 521 381 327 563
rmax (kg/m3) 27 X 10-4 29 X 10-4 25 X 10-4 22 X 10-4
rmin (kg/m3) 1.22 X 10-4 1.3 X 10-4 1.1 X 10-5 1.2 X 10-4
Values at 72 ms. Peak temperature at 100 ms is
estimated 4 X 104 K
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Observation from Recent SPARTAN Simulations

• Chamber evolution occurs in two phases
• Flow is dominated by shock bouncing (first 30-50
  ms)
• Large scale eddies is setup and gas parameters
  evolve smoothly.
• Diffusive processes lead to a more uniform
  chamber environment. Peak temperatures, pressure,
  and velocity are reduced by a factor of two or
  more compared to the case with no
  conductivity/viscosity.
• Laser beam channels seed large scale eddies in
  the chamber. The resulting flow mixing leads to
  further reduction of peak temperatures, pressure,
  and velocity. It also enhances heat transfer to
  the wall.
• Peak temperature in the chamber is still too
  high. But
• Geometrical effects will further reduce the peak
  temperatures more beam channel, a cylindrical
  chamber to shorten chock bouncing period.
• Effects of background plasma (conductivity,
  viscosity, and radiation)

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SPARTAN Research Plan for 2003-2004(from April
Meeting)

• Incorporate cylindrical symmetry.
• Completed. We are performing convergence studies
  at present.
• Implement and test contributions of viscosity,
  thermal conductivity, and radiation from
  background plasma.
• Models are incorporated and tested in SPARTAN.
  Need the coronal equilibrium data.
• Implement multi-species capability. (after Jan.
  2004)
• Implement of Equation of State. (To be
  implemented before Jan. 2004)
• Parametric investigation of chamber dynamics with
  different gas, gas pressure, target yield,
  chamber size, beam ports, etc.
• Investigated impact of no. of beam channels.
• Need a series of Bucky runs (Xe, He, and D
  background) with different pressures.

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Needed Data and Bucky Runs

• Coronal equilibrium data ne/nn, ni/nn, Prad/ne
  as a function of temperature (0.5-100 eV) for Xe,
  He, D, and T.
• Bucky Runs with Xe, He, and D gas in the chamber
  at 10 and 50 mTorr.
• Chamber conditions in different times to find out
  the optimum hand-over time from Bucky to SPARTAN