April 4-5, 2002 A. R. Raffray, et al., Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

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Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

A. R. Raffray, J. Pulsifer, M. S. Tillack, X. Wang

University of California, San Diego

With input from T. Knowles (ESLI) and T. Renk (SNL)

HAPL Review

GA, San Diego

April 4-5, 2002

April 4-5, 2002 A. R. Raffray, et al., Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

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Energy Deposition as a Function of Penetration Depth in Carbon Flat Wall Under RHEPP Ion Spectra

• Ion Beam data obtained from T. Renk in terms of time, voltage and current density for each ion

- 5.11x104 J/m2

- Energy Split:

- 16% H+

- 26% C++

- 57% C+

• Energy deposition computed as a function of penetration depth for given ion spectra

based on SRIM stopping power data

0.0x100

1.0x1010

2.0x1010

3.0x1010

4.0x1010

5.0x1010

6.0x1010

7.0x1010

0.0x100 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6 2.5x10-6 3.0x10-6

Penetration Depth (m)

Total (H++C++C++)

H++C++

H+

RHEPP Case

Carbon density = 2000 kg/m3

Energy density = 5.11x104 J/m2

April 4-5, 2002 A. R. Raffray, et al., Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

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How Does the RHEPP Energy Deposition Compares with the 154 MJ DD Target Spectra Case for R=6.5 m?

• Energy Deposition fromRHEPP dominated by C ions

• Energy deposition from DD target spectra dominated by deuterium and tritium ions

• C and H ions have different penetration depths and energy deposition profiles

• RHEPP reproduces the debris ion energy deposition level and penetration depth within a factor of 2

0.0x100

1.0x1010

2.0x1010

3.0x1010

4.0x1010

5.0x1010

6.0x1010

7.0x1010

0.0x100 1.0x10-6 2.0x10-6 3.0x10-6 4.0x10-6 5.0x10-6 6.0x10-6

Penetration Depth (m)

Total

(H++C++C++)

Assuming all

energy as H+

RHEPP Case

Carbon density = 2000 kg/m3

Energy density = 5.11x104 J/m2

Fast ions, 154MJDD Spectra

Debris Ions,154MJDD Spectra

April 4-5, 2002 A. R. Raffray, et al., Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

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Volumetric Heat Generation as a Function of Space and Time in Carbon Flat Wall Under RHEPP Ion Spectra

0.0x1002.0x10174.0x10176.0x10178.0x10171.0x10181.2x1018

Carbon density = 2000 kg/m3

April 4-5, 2002 A. R. Raffray, et al., Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

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Temperature History for Carbon Flat Wall Under RHEPP Ion Spectra

• Updated sublimation model for C from Philipps’ recommendation

• IFE reactor-like CFC thermal conductivity as a f(T) (~235 W/m-K for T >1800 °C)- Max. Temp. 4370°C

- Corresponding sublimated thickness calculated as ~ 0.032 m per shot

for 5.1x104 J/m2)

• Measurement from T. Renk on POCO Graphite ~20 m after 75 shots, ~0.27 m per shot for 5.5x104 J/m2

• Not clear what grade of POCO graphite was used but k would be much lower

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0.0x100 5.0x10-7 1.0x10-6 1.5x10-6 2.0x10-6 2.5x10-6 3.0x10-6 3.5x10-6

Surface

0.33 micron

1.7 microns

6 microns

96 microns

Time (s)

2.5 mm Carbon Slab

C density=2000 kg/m3

Under RHEPP Ion SpectraInitial Temperature = 35°CSublimation Loss = 0.032 m

April 4-5, 2002 A. R. Raffray, et al., Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

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Maximum C Temperature and Sublimation Loss per Shot as a Function of Energy Density and kcarbon for Same RHEPP Ion

Energy Level

• Sublimation model from Philipps’ data derived for T<4000K

• As expected, thermal conductivity plays a key role and it is possible to sublimate ~1 m per shot at energy density of 4 x104 J/m2 if k < 100 W/m-K

• POCO graphite seems to have low k and would be a poor material to validate CFC grade armor

• It is very important to conduct experiments on well characterized material and with good diagnostics (surface T and mass loss)

l

l

l

l

l

t

t

t

n

n

1000

1500

2000

2500

3000

3500

4000

4500

5000

1.5E+4 2.5E+4 3.5E+4 4.5E+4 5.5E+4 6.5E+4

l k(CFC)

t k =100 W/m-K

n k =50 W/m-K

Energy Density (J/m2)

Energy Density Varied forSame Ion Energy Levelfrom RHEPPC density = 2000kg/m3

l

l

l

l

l

t

t

t

n

n

1.00E-18

1.00E-17

1.00E-16

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-9

1.00E-8

1.00E-7

1.00E-6

1.0E+4 2.0E+4 3.0E+4 4.0E+4 5.0E+4 6.0E+4 7.0E+4

l k(CFC)

t k =100 W/m-K

n k =50 W/m-K

Energy Density Varied forSame Ion Energy Levelfrom RHEPP

C density = 2000kg/m3

Energy Density (J/m2)

April 4-5, 2002 A. R. Raffray, et al., Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

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Carbon Fiber: Geometry Model

yy

Energy Deposition

Distance from tip of fiber

Probability for energy front to contact fiber:

over second unit cell, P2 = (1-P1 ) d/(y-d)over third unit cell, P3 = (1-P1-P2 ) d/(y-2d), etc...

yeff =yP1+2yP2+3yP3...+nyPn

over first unit cell, P1 = d/y

up to Pn=(1-P1-P2-...Pn-1) d/(y-(n-1)d)where n=y/d

ESLI fiber characteristics Fiber length 2500m

Fiber diameter 6.5m

Fiber k ~100-200 W/m-K

1.5% fiber volume fraction

98.5% void fraction

Fiber separation, y 47m

yeff 215m

EnergyFront

High PorosityCarbonFiber Surface

θ

=L 2.5mm

d

yeff

April 4-5, 2002 A. R. Raffray, et al., Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

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Carbon Fiber: Energy Deposition Model

EnergyFront

High PorosityCarbonFiber Surface

θ

Lfiber

:For point A qa=qslab(a1)cosθ

yeff

a1

b1

c1

d1

A

B

C

D

d2

c2

:For point B qa=qslab(b1)sinθ

:For point C qa=qslab(c1+c2)sinθ

:For point D qa=qslab(d1+d2)sinθ

dfiber

• Penetration depth set as a function of location in fiber based on angle of incidence and including shadowing effect from upstream fibers

• Energy deposition calculated as a function of penetration depth and including angle effect which effectively increase the area seeing the ion flux

April 4-5, 2002 A. R. Raffray, et al., Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

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ANSYS 5.7 MAR 26 200211:50:39 PLOT NO. 1NODAL SOLUTIONTIME=.169E-06 TEMP (AVG) RSYS=0PowerGraphicsEFACET=1AVRES=MatSMN =17.567 SMX =4292

1

MX

17.567 492.528 967.489 1442 1917 2392 2867 3342 3817 4292

2.5mm-FLAT-CWALL:Tini=30C,K=f(T),Cp=f(T)

Results for Carbon Fiber Under RHEPP Ion Spectrum

Angle Max. Temp.(°C) Avg. Fract. Subl. LossLeft Right Fiber Tip Overall.

0° 4390 4390 1* 0.0155.2° 4092 4352 0.43 0.006510° 4170 4292 0.31 0.004620° 4213 4041 0.15 0.0023

* Fractional sublimation loss of 1 is equivalent to ~0.032m per shot

• Sublimation loss for fiber based on temperature distribution at tip

• Major difference with flat plate is very low density of fiber (0.015)

• In agreement with post-experimental examination of fiber showing no visible ablation or loss of

material

Temperature Contour at Time Corresponding

to Tmax for 10° Case

April 4-5, 2002 A. R. Raffray, et al., Modeling Analysis of Carbon Fiber Velvet Tested in RHEPP Ion Beam Facility

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Concluding Remarks from Fiber Analysis

• Difficult to model flat POCO graphite case in the absence of fully characterized property data and temperature surface temperature measurement

- Need to use actual material or material closely-ressembling (in properties) reactor grade armor

- Need to fully characterized material properties

- Need to conduct experiments with adequate diagnostics

• Based on the fiber model (and consistent with experimental observation), much less material is ablated from the fiber- Incidence angle effect on local sublimation

- More importantly, fiber density effect on total sublimation