1. Chamber Dynamic Response Modeling
Zoran Dragojlovic

2. Accomplishments IFE Chamber dynamics code SPARTAN is developed:
Simulation of Physics by Algorithms based on Robust Turbulent Approximation of Navier-Stokes Equations.
SPARTAN current features:
2-D Navier Stokes equations, viscosity and thermal conductivity included
arbitrary geometry
Adaptive Mesh Refinement
SPARTAN tests:
Acoustic wave propagation.
Viscous channel flow.
Mach reflection.
Analysis of discretization errors to find code accuracy.
Initial conditions from BUCKY code are used for simulations.
Two Journal articles on SPARTAN are in preparation.

3. Adaptive Mesh Refinement
Motivation: efficient grid distribution results in reasonable CPU time.
Grid organized into levels from coarse to fine.
Solution tagging based on density and energy gradients.
Grid is refined at every time step.
Solution interpolated in space and time between the grid levels.
Referenced in: Almgren et al., 1993.
chamber
beam channel
wall

4. Example of Adaptive Mesh Refinement
geometry
max
min
density contour plot

5. IFE Chamber Dynamics Simulations
Objectives
Determine the influence of the following factors on the chamber state at 100 ms:
viscosity
blast position in the chamber
heat conduction from gas to the wall.
Chamber density, pressure, temperature, and velocity distribution prior to insertion of next target are calculated.

6. Numerical Simulations
IFE Chamber Simulation
2-D cylindrical chamber with a laser beam channel on the side.
160 MJ NRL target
Boundary conditions:
Zero particle flux, Reflective velocity
Zero energy flux or determined by heat conduction.
Physical time: 500 ms (BUCKY initial conditions) to 100 ms.

7. Numerical Simulations
Initial Conditions
1-D BUCKY solution for density, velocity and temperature at 500 ms imposed by rotation and interpolation.
Target blast has arbitrary location near the center of the chamber.
Solution was advanced by SPARTAN code until 100 ms were reached.

8. Effect of Viscosity on Chamber State at 100 ms
Estimating Viscosity:
Neutral Xe gas at 800K: m = 5.4 x 10-5 Pas (data is not available for higher temperatures).
Ionized Xe at (10,000 – 60,000)K: m = (4.9 x – 4.4 x 10-9) Pas
Simulations are done with ionized gas values (to be conservative).
Simulations indicate viscosity is important even at such small values.
Analysis should include a combination of neutral and ionized gas.

9. Effect of Viscosity on Chamber State at 100 ms
max
min
inviscid flow at 100 ms
viscous flow at 100 ms
pressure, pmean = Pa
pressure, pmean = Pa
temperature, Tmean = K
(rCvT)mean = J/m3
temperature, Tmean = K
(rCvT)mean = J/m3
Temperature is more evenly distributed with viscous flow.

10. Effect of Viscosity on Chamber State at 100 ms
Pressure across the chamber at 0.1s.
Pressure at the chamber wall versus time.
- viscous
- inviscid
pressure [Pa]
6.5
0.0
13.0
distance [m]

11. Effect of Blast Position on Chamber State at 100ms
max
min
centered blast at 100 ms
eccentric blast at 100 ms
pressure, pmean = Pa
pressure, pmean = Pa
temperature, Tmean = K
temperature, Tmean = K
Both cases feature random fluctuations, little difference in the flow field.

12. Effect of Blast Position on Chamber State at 100 ms
pressure at the wall
pressure at the mirror
Mirror is normal to the beam tube.
Pressure is conservative by an order of magnitude.
Pressure on the mirror is so small that the mechanical response is negligible.

13. Effect of Wall Heat Conduction on Chamber State at 100 ms
Estimated Thermal Conductivity:
Neutral Xe gas at 800K: k = W/m-K (data is not available for higher temperatures).
Ionized Xe at (10,000 – 60,000)K: k = (0.022 – 1.94) W/m-K
Initial simulations are done with ionized gas values (to assess impact of ionized gas conduction).
Simulations indicate substantial impact on gas temperature with higher conductivity value.
Analysis should include a combination of neutral and ionized gas.

14. Effect of Wall Heat Conduction on Chamber State at 100 ms
max
min
insulated wall
wall conduction
pressure, pmean = Pa
pressure, pmean = Pa
temperature, tmean = K
temperature, tmean = K
Wall heat conduction helps to achieve a more quiescent state of the chamber gas.

15. Chamber Gas Dynamics
max
min
pressure
temperature
density

16. Future Work Transport of various species in the chamber.
Objective: find patterns of material deposition on wall, mirrors and beam channels.
Multi-species (ions, electrons, gases, particulates)
Temperature evolution in the chamber:
Turbulence models.
Radiation heat transport
Equation of State

17. Supporting Slides

18. Numerics Governing Equations Arbitrary Geometry
Adaptive Mesh Refinement
Error Analysis

19. Governing Equations
Navier-Stokes in conservative form:

20. Solution Algorithm Second order Godunov algorithm. References:
Colella (1985)
Colella &Glaz (1985)
Colella & Woodward (1984).
Riemann solver used as a form of upwinding.

21. Adaptive Mesh Refinement
Describe adaptive mesh refinement.

22. Arbitrary Geometry 6.5 1 20 D. Modiano, P. Colella, March 2, 2000
A High-Order Embedded Boundary Method FB
Fx(i,j)
Fx(i+1,j)
Fy(i,j)
Fy(i+1,j)
U(i,j)
inside fluid domain
outside of fluid domain
6.5 1 20
carrier gas
embedded boundary

23. Error Analysis
Describe error analysis.

24. Science Factors which affect the chamber state after 100 ms:
convection at the wall
viscosity
target blast position
geometry

25. Conclusions Numerical engine is ready for adding physics.
Effects on the chamber clearing are singled out and studied. The findings are …

26. Future Work Addition of gravity with cylindrical geometry.
Addition of species transport equations and real gas state equation.
Addition of low eddy simulation algorithms for sub-grid sized eddies.

27. Effect of Wall Heat Conduction on Chamber Clearing
Temperature prediction assuming pure conduction:
Average temperature in the chamber after s:
Assuming conduction only: K
Conduction + convective mixing: K
Convective mixing only: K.

28. Effect of Wall Heat Conduction on Chamber Clearing
t=0.444s
blue: reflective wall
red: wall conduction
T [K]
r[m]

29. Summary
Chamber dynamic response was analyzed by using the CFD code SPARTAN.
Effects of viscosity, blast position and gas to wall conduction were addressed.
Significance of the effects considered.
Need to implement more physics.

30. Supplement Slide To Effect of Viscosity on Chamber State After 100 ms
inviscid flow at 100 ms
viscous flow at 100 ms
pressure, max = Pa
pressure, max = Pa
velocity, max = m/s
velocity, max = m/s
Fluctuations are more intensive with viscous flow.