Simulation of Gas Dynamics in The IFE Chamber by SPARTAN

CodeZoran Dragojlovic, Farrokh Najmabadi (UCSD)

Marcus Day (LBNL)

Objectives of Chamber Physics Modeling

(project sponsored by HAPL program)• Understand the response of IFE Chamber to high

energy targets.• Understand the most critical issues for selected

IFE chambers.• Develop state of art computational model, make it

available to the community.• Develop benchmark physics models for integrated

modeling.• Use the code to plan experiments.

Current Features of SPARTAN Code

– 2-D Navier Stokes equations – viscosity and thermal conductivity are based on

empirical laws– arbitrary geometry– adaptive mesh refinement– globally 2nd order accurate– between 1st and 1.5th order accurate boundary

conditions

Validation Problems

• Objectives:– verify shock propagation– verify diffusive terms in Navier-Stokes equations– verify arbitrary geometry– verify the order of convergence

• Cases:– acoustic wave propagation– mach reflection– viscous flow in a straight channel– reflection of wave against arbitrary straight and cyllindrical walls– propagation of a weak planar wave down an arbitrary channel

Validation Problems

acoustic wave propagation in domain with rectangular geometry

10.1 11.2 12.1 12.9 r[m]

initial disturbance

Mach reflection

Validation Problems

Validation Problemsviscous flow in a straight channel

reflection against slanted wallSPARTAN Code

Pember et al. (LBNL)

traveling wave in a slanted chanel

initial density final density

x-momentum y-momentum density*energy

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

Example of Adaptive Mesh Refinement

maxmin

geometry

density contour plot

IFE Chamber Dynamics SimulationsObjectives• 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.

Numerical Simulations• 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.

pressure

temperature

density

Chamber Gas Dynamicsmaxmin

Effects of Viscosity, Blast Position and Wall Heat Conduction onChamber State at 100 ms, Summarized

Viscosity:

Blast Position:

inviscid flow at 100 ms

pressure, pmean = 569.69 Pa

temperature, Tmean = 5.08 104 K

(ρCvT)mean = 1.412 103 J/m3

pressure, pmean = 564.87 Pa

temperature, Tmean = 4.7 104 K

(ρCvT)mean = 1.424 103 J/m3

viscous flow at 100 ms

Viscosity makes a difference due to its strong dependence on temperature. Kinematic viscosity law assumes a fully ionized gas.

pressure, pmean = 564.87 Pa

temperature, Tmean = 4.7 104 K

centered blast at 100 ms

pressure, pmean = 564.43 Pa

temperature, Tmean = 4.74 104 K

eccentric blast at 100 ms

No significant effect. Large disturbance due to eccentricity of blast cancels out with small disturbances due to grid scale turbulence.

Effects of Viscosity, Blast Position and Wall Heat Conduction onChamber State at 100 ms, Summarized

Wall Heat Conduction:

pressure, pmean = 564.431 Pa

temperature, Tmean = 4.736 104 K

insulated wall

pressure, pmean = 402.073 Pa

temperature, Tmean = 2.537 104 K

wall conduction

Wall heat conduction makes a difference. Conductivity law assumes a fully ionized gas, so the effect might be exaggerated.

Future Work• Geometrical capability: implement cylindrical coordinate system.

• Improve modeling of temperature/pressure evolution in the chamber:• Equation of state;• Radiation heat transport;• Turbulence models.

• Implement multi-species capability:• Neutral gases, ions, and electrons to account for different thermal

conductivity, viscosity, and radiative losses.

• Evaluation of long-term transport of various species in the chamber (e.g., material deposition on the wall, beam tubes, mirrors)• Atomics and particulate release from the wall;• Particulates and aerosol formation and transport in the chamber.