april 6-7, 2002 a. r. raffray, et al., modeling of inertial fusion chamber 1 modeling of inertial...
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April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
1
Modeling of Inertial Fusion Chamber
A. R. Raffray, F. Najmabadi, Z. Dragojlovic, J. Pulsifer
University of California, San Diego
US/Japan Workshop on Power Plant Studies and related Advanced Technologies
San DiegoApril 6-7, 2002
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
2
Why We Need Chamber Modeling
• Key IFE chamber uncertainty is whether or not the chamber environment will return to a sufficiently quiescent and clean low-pressure state following a target explosion to allow a second shot to be initiated within 100–200 ms- Target and driver requirement on chamber conditions prior to each shot
• Chamber condition following a shot in an actual chamber geometry is not well understood
- Dependent on multiple processes and variables
- A predictive capability in this area requires a combination of computer simulation of increasing sophistication together with simulation
experiments to ensure that all relevant phenomena are taken into account and to benchmark the calculations
• The proposed modeling effort includes:- Scoping calculations to determine key processes to be included in the code- Development of main hydrodynamic code- Development of wall interaction module
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
3
Cavity Gas, Target, and Wall Species
Chamber Dynamics Chamber Wall Interaction
Time of flight to wall:
X-rays ~20 ns
Neutrons ~100 nsAlphas ~400 nsFast Ions ~1 sSlow Ions ~1-10 s
• Photon transport & energy deposition
• Ion transport & energy deposition• Heating & ionization• Radiation• Gas dynamics (shock, convective
flow, large gradients, viscous dissipation)
• Condensation• Conduction• Cavity clearing Timescale: ns to 100 ms
• Convection & cooling
Timescale: ms
• Photon energy deposition• Ion energy deposition• Neutron & energy deposition• Conduction • Melting• Vaporization• Sputtering• Thermo-mechanics/
macroscopic erosion• Radiation damage• Blistering (from bubbles of
implanted gas)• Desorption or other degassing
process Timescale: ns to 100 ms
Coolant
Chamber Physics Modeling
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
4
Scoping Calculations Were First Performed to Assess Importance of Different Effects and Conditions
• Chamber Gas– At high temperature (> ~ 1 ev), radiation from ionized gas can be
effective
– In the lower temperature range (~ 5000K back to preshot conditions)• Conduction (neutrals and some electrons)
• Convection
• Radiation from neutrals
• Other processes?
– The temperature of the gas might not equilibrate with the wall temperature• May have implications for target injection
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
5
Effectiveness of Conduction Heat Transfer to Cool Chamber Gas to Preshot Conditions
• Simple transient conduction equation for a sphere containing gas with an isothermal boundary condition(Tw)
- kXe is poor (~0.015 W/m-K at 1000K, and ~0.043 W/m-K at 5000 K)
- At higher temperature electron conductivity of ionized gas in
chamber will help
(assumed ~ 0.1 W/m-K for ne = no and 10, 000 K)
- Argon better conducting gas
• T decreases from 5000K to 2000K in ~2 s for kg = 0.03 W/m-K
• Even if kg is increased to 0.1 W/m-K, it does not help much (~ 0.6 s)
Cooling of chamber via conduction at 50 mTorr
0
2000
4000
6000
8000
10000
12000
0.0 1.0 2.0 3.0 4.0 5.0
Time (s)
Tem
pera
ture
(K
)
Xe (k = 0.03) Xenon (k = 0.1) Argon (k = 0.1)
Temperature History Based on Conduction from 50 mTorr Gas in a 5 m Chamber to a
1000K Wall
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
6
Effectiveness of Convection Heat Transfer to Cool Chamber Gas to Preshot Conditions
• Simple convection estimate based on flow on a flat surface with the fluid at uniform temperature
• Use Xe fluid properties
• Assume sonic velocity - c ~ 500 m/s
- Re ~ 700 for L = 1 m
- Nu ~ 13
- h ~ 0.4 W/m2-K
• Lower velocity would result in lower h but local eddies would help
- Set h between 0.1 and 1 W/m2-K representing an example range
• T decreases from 5000K to 2000K, in
~0.1 s for h = 0.4 W/m2-K
• Increasing h to 1 W/m2-K helps but any reduction in h rapidly worsens the situation (e.g. ~0.4 s for 0.1 W/m2-K)
Convection at 50 mTorr
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Time (s)
Tem
pera
ture
(K
)
h=0.1 h = 0.4 h=1
Temperature History Based on Convection from 50 mTorr Gas in a 5 m
Chamber to a 1000K Wall
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
7
Effectiveness of Radiation Heat Transfer to Cool Chamber Gas from Mid-level Temperature (~5000K) to Preshot Conditions
• Xe is monoatomic and has poor radiation properties - Complete radiation model quite
complex
- Simple engineering estimate for scoping calculations
- No emissivity data found for Xe
- Simple conservative estimate for Xe using CO2 radiation data
- T decreases from 5000K to 2000K, in ~1 s
(would be worse for actual Xe radiation properties)
Temperature History Based on Radiation from 50 mTorr Gas in a 5 m
Chamber to a 1000K Wall
For CO2 at 2000 K, g ~ 10-5
g ~ g at Tw (1000 K); g ~ 10-4
qr’’= w (gTg4 – gTw
4)
CO2
Xe
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
8
Effectiveness of Heat Transfer Processes to Cool Chamber Gas (Xe) to Preshot Conditions is Poor
Conservative estimate of Xe temperature (K) following heat transfer from 5000K
Time: 0.1 s 0.2 s 0.5s ~1 s
Conduction:
k=0.03 W/m-K 4700 4500 3600 2700
k=0.1 W/m-K 3900 3200 2200 1500
Convection:
h=0.1 W/m2-K 3800 3000 1650 1200 h=0.4 W/m2-K 1950 1220 ~1000 h=1 W/m2-K 1250
Xe Radiation:
(assum. CO2 and ) 3500 2850 2300 2200
• It seems that only possibility is convection with high velocity and small length scales (optimistic requiring enhancement mechanisms) and/or appreciable gas inventory change per shot (by pumping)
• Background plasma in the chamber might help in enhancing heat transfer (e.g. electron heat conduction, recombination)
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
9
Chamber Physics Modeling
Chamber RegionSource Wall Region
Driver beams
Momentum input
Momentum Conservation Equations
Wall momentum transfer(impulse)
Fluid wall momentum
equations
Energy Equations Phase change
Condensation
Conduction
Energy input
Thermal capacity
Radiation transport
Transport + deposition
Condensation
Pressure (T)
Impulse
Pressure (T)
Pressure (density)
Viscous dissipation
Mass input
Mass Conservation Equations (multi-phase, multi-species)
Evaporation,Sputtering,Other mass transfer
Condensation
Evacuation
Energy deposition
Convection
Thermal stress
Stress/strain analysis
Condensation Aerosol formation
Thermal shock
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
10
Numerical Modeling of IFE Chamber Gas Dynamics
• Build Navier-Stokes solver for compressible viscous flow
- Second order Godunov algorithm.
- Riemann solver used as a form of upwinding.
- Progressive approach
- 1-D --> 2-D
- inviscid --> viscous flow
- rectangular geometry --> 2-D and 3-D arbitrary geometry (to be done)
- grid splitting into sub-domains for multi-geometry modeling
• Perform code verification
- 1-D and 2-D acoustic wave propagation
- Conservation laws
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
11
Example Case to Illustrate Code Capability: Square Chamber Cavity With a Rectangular Beam Channel – Centered Initial Disturbance
• Inviscid flow
• Initial pressure and density disturbance centered, zero velocity field
• Reflective wall boundary conditions
• Ambient Xe (T = 800K, = 1.3028 10-4 kg/m3, p = 7.857 Pa)
0
2
4
6
8
10
12
14
16
18
0 0.05 0.1 0.15 0.2 0.25
time [s]
pm
ax [
Pa]
0
2
4
6
8
10
12
14
16
18
0 0.05 0.1 0.15 0.2 0.25
time [s]p
ma
x [
Pa]
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
12
Comparison Between Viscous and Inviscid Flow for Example Xe Case
7.85
7.86
7.87
7.88
7.89
7.9
7.91
7.92
7.93
7.94
0 0.01 0.02 0.03 0.04
time [s]
pm
ax [
Pa
]
7.85
7.86
7.87
7.88
7.89
7.9
7.91
7.92
7.93
7.94
0 0.01 0.02 0.03 0.04
time [s]
pm
ax [P
a]
Inviscid
Viscous
The effect of viscosity is significant.
vmax = 0.0975 m/s
pmax = 7.86 Pa
max = 1.3032 10-4 kg/m3
vmax = 0.0078 m/s
pmax = 7.8573 Pa
max = 1.3035 10-4 kg/m3
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
13
• Ion and photon energy deposition calculations based on spectra
- Photon attenuation based on total photon attenuation coefficient in material
- Use of SRIM tabulated data for ion stopping power as a function of energy
• Transient Thermal Model
- 1-D geometry with temperature-dependent properties
- Melting included by step increase in enthalpy at MP
- Evaporation included based on equilibrium data as a function of surface temperature and corresponding
vapor pressure- For C, sublimation based on latest recommendation from
Philipps
• Model calibrated and example cases run
• To be linked to gas dynamic code
Wall Interaction Module Development
Example IFE Chamber Wall Configuration UnderEnergy Deposition
Photons
Melt Layer
Re- radiation
q'''(from photons and ions)
q''(subl./evap.)
q''(cond.)
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
14
• Scoping analysis performed - Vaporization, physical sputtering, chemical sputtering, radiation enhanced sublimation
Other Erosion Processes to be Added (ANL)
• These results indicate need to include RES and chemical sputtering for C (both increase with
temperature)
• Physical sputtering relatively less important for both C and W for minimally attenuated ions
(does not vary with temperature and peaks at ion energies of ~ 1keV)
Plots illustrating relative importance of erosion mechanisms for C and W for 154 MJ NRL DD target spectra
Chamber radius = 6.5 m.
CFC-2002U
Tungsten
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
15
Example Cases Run for 154 MJ NRL Direct Drive Target Spectra
10.0E+8
1.0E+10
1.0E+11
1.0E+12
1.0E+13
1.0E+14
1.0E+15
1.0E+16
1.0E+17
1.0E+18
1.0E+19
1.0E-1 1.0E+0 1.0E+1 1.0E+2 1.0E+3 1.0E+4 1.0E+5
4HeD
TH
Au
Ion Kinetic Energy (keV)N
o. of
Ion
s p
er
Un
it E
nerg
y (#
/keV
)
3He
12C
10.0E+8
1.0E+10
1.0E+11
1.0E+12
1.0E+13
1.0E+14
1.0E+15
1.0E+16
1.0E+17
1.0E+1 1.0E+2 1.0E+3 1.0E+4 1.0E+5
4He
D
T
H
N
Ion Kinetic Energy (keV)
No. of
Ion
s p
er
Un
it E
nerg
y (#
/keV
)
3He
Photons
Debris Ions
Fast Ions
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
16
Spatial Profile of Volumetric Energy Deposition in C and W for Direct Drive Target Spectra
• Tabulated data from SRIM for ion stopping power used as input
1x107
1x108
1x109
1x1010
1x1011
1x1012
1x10-8 1x10-7 1x10-6 1x10-5 1x10-4 1x10-3 1x10-2
Debris ions,W
Fast ions, C
Photons, W
Photons, C
Fast ions, W
En
ergy
dep
osit
ion
(J/
m3 )
Penetration depth (m)
Energy Deposition as a Function of PenetrationDepth for 401 MJ NRL DD Target
Debris ions, C
C density = 2000 kg/m3
W density = 19,350 kg/m3
1x106
1x107
1x108
1x109
1x1010
1x1011
1x10-8 1x10-7 1x10-6 1x10-5 1x10-4 1x10-3 1x10-2
Debris ions,W
Fast ions, C
Photons, W
Photons, C
Fast ions, W
Ene
rgy
dep
osit
ion
(J/m
3 )
Penetration depth (m)
Energy Deposition as a Function of PenetrationDepth for 154 MJ NRL DD Target
Debris ions, CC density = 2000 kg/m3
W density = 19,350 kg/m3
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
17
Spatial and Temporal Heat Generation Profiles in C and W for 154MJ Direct Drive Target Spectra
0.0x100
1.0x1016
2.0x1016
3.0x1016
4.0x1016
5.0x1016
Temporal and Spatial Profile of Ion Power Deposition inC Armor from 154 MJ DD Target Spectrum
0.0x100
1.0x1016
2.0x1016
3.0x1016
4.0x1016
5.0x1016
Temporal and Spatial Profile of Ion Power Deposition inW Armor from 154 MJ DD Target Spectrum
• Assumption of estimating time from center of chamber at t = 0 is reasonable based on discussion with J. Perkins and J. Latkowski
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
18
Temperature History of C and W Armor Subject to 154MJ Direct Drive Target Spectra with No Protective Gas
• Initial photon temperature peak is dependent on photon spread time (sub-ns)
• For a case without protective gas and with a 500°C wall temperature: - C Tmax < 2000°C- W Tmax < 3000°C- Some margin for adjustment of parameters
such as target yield, chamber size, coolant temperature and gas pressure
400
600
800
1000
1200
1400
1600
1800
1.0x10-12 1.0x10-11 1.0x10-10 1.0x10-9 1.0x10-8 1.0x10-7 1.0x10-6
Surface
1 micron
5 microns
10 microns
100 microns3-mm Tungsten slab
Density = 19350 kg/m3
Coolant Temp. = 500°C
h =10 kW/m2-K154 MJ DD Target SpectraPhoton energy dep. only
Time (s)
Tem
per
atu
re (
¡C)
200
600
1000
1400
1800
2200
2600
3000
0.0x
100
1.0x
10-6
2.0x
10-6
3.0x
10-6
4.0x
10-6
5.0x
10-6
6.0x
10-6
7.0x
10-6
8.0x
10-6
9.0x
10-6
1.0x
10-5
Surface
1 micron
5 microns
10 microns
100 microns
Time (s)
Tem
pera
ture
(¡C
)
3-mm Tungsten slab
Density = 19350 kg/m3
Coolant Temp. = 500°C
h =10 kW/m2-K154 MJ DD Target Spectra
400
600
800
1000
1200
1400
1600
1800
2000
0.0x
100
1.0x
10-6
2.0x
10-6
3.0x
10-6
4.0x
10-6
5.0x
10-6
6.0x
10-6
7.0x
10-6
8.0x
10-6
9.0x
10-6
1.0x
10-5
Surface
1 micron
5 microns
10 microns
100 microns
Time (s)
Tem
per
atu
re (
¡C)
3-mm Carbon Slab
Density= 2000 kg/m3
Coolant Temperature = 500°C
h =10 kW/m2-K154 MJ DD Target Spectra
Sublimation Loss = 9x10-18 m
April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber
19
Future Effort Will Focus on Model Improvement and on Exercising the Code (1)
• Exercise code: - Investigate effectiveness of convection for cooling the chamber gas- Assess effect of penetrations on the chamber gas behavior including interaction
with mirrors- Investigate armor mass transfer from one part of the chamber to another
including to mirror - Assess different buffer gas instead of Xe- Assess chamber clearing (exhaust) to identify range of desirable base pressures
- Assess experimental tests that can be performed in simulation experiments
• Improve Code - Extend the capability of the code (full inclusion of multi-species capability)
- Implement adaptive mesh routines for cases with high transient gradients and start implementation if necessary
- Implement aerosol formation and transport models (INEEL)- Implement more sophisticated mass transport models in wall interaction
module (ANL)