April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber 1 Modeling of Inertial...

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


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


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


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


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


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


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


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)


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


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


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]


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


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.)


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


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


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


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


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


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)

April 6-7, 2002 A. R. Raffray, et al., Modeling of Inertial Fusion Chamber 1 Modeling of Inertial...

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