october 27-28, 2004 hapl meeting, pppl 1 target survival during injection presented by a.r. raffray...

October 27-28, 2004HAPL meeting, PPPL

1

Target Survival During Injection

Presented by A.R. Raffray

Other Contributors: K. Boehm, B. Christensen, M. S. Tillack

UCSD

D. GoodinGeneral Atomics

HAPL MeetingPPPL

Princeton, NJOctober 27-28, 2004


2

Outline• Reminder: Why is target survival important?

• Our modeling activities:- Detailed characterization of heat flux on target- Modeling of target thermo-mechanical behavior

• What we have learned from recent studies:- Characterization of limiting heat flux based on TP- Effect on target survival of:

- Lower initial temperature- Thermally robust design (insulating layer)- Injection velocity- Allowing for phase change

• Simplifying assumption in model:- Continuous vapor region instead of individual bubble formation

• Scoping study of 3He effect on bubble formation

• Future effort


3

Why Is Target Survival Important?

• Spherical symmetry

• Surface smoothness

• Density uniformity

• TDT (<19.79 K?)

• Better definition is needed

Physics requirements:

IFE Chamber (R~6 m)

Protective gas (Xe, He) at ~4000 K heating up target

Chamber wall ~ 1000–1500 K, causing q’’rad on target

Target Injection (~400 m/s)

Target Implosion Point

• Degradation of Targets in the Chamber Must Not Exceed Requirements for Successful Implosion


4

We Have Characterized Target Heat Loads for Thermo-Mechanical Analysis of the Target

Heat loads:

• Energy transfer from impinging atoms of background gas

- Enthalpy transfer (including condensation) or convective loading

- Recombination of ions (much uncertainty remains regarding plasma

conditions during injection)

• Radiation from chamber wall

- Dependent on reflectivity of target surface and wall temperature

- Estimated as 0.2 – 1.2 W/cm2 for = 0.96 and Twall = 1000 – 1500 K

• Convective loading analysis using DSMC Temperature field around a direct

drive target (from DS2V)

Flow= 0= 0

Example Results*:

• The heat flux decreases when sticking coefficient, = 0 due to the shielding influence of low temperature reflected particles interacting with the incoming stream.

*More details in: B. Christensen, R. Raffray, M. Tillack, “Thermal Loading of a Direct Drive Target in rarefied Gas,” presented at the 16th ANS TOFE, Sept. 2004, to appear in Fusion Science & Technology.

1.E+03

1.E+04

1.E+05

1.E+06

0 1 2 3Position on Surface (m)

Heat Flux (W/m

2)

T = 4000 K, sigma = 1

T = 4000 K, sigma = 0

T = 1300 K, sigma = 1

T = 1300 K, sigma = 0

n = 3.22x1021 m-

3

decreasing

(rad)


5

We Have Developed a 1-D Thermo-Mechanical Model of the Target, Including Phase Change, to Help Understand and Assess

Target Behavior During Injection*

*More details in: B. Christensen, R. Raffray, M. Tillack, “Modeling DT Vaporization and Melting in a Direct Drive Target,” presented at the 16th ANS TOFE, Sept. 2004, to appear in Fusion Science & Technology.

• The model solves the coupled thermal (heat conduction, phase change) and mechanical (thermal expansion,

deflection of shell and solid DT) response of a direct drive target during injection.

- 1D transient energy equation in spherical coordinates discretized and solved using forward

time central space (FTCS) finite difference method

- Temperature-dependent material properties

- Apparent cp model to account for latent heat

of fusion (at melting point)

- Interface boundary conditions:€

∂T∂t

=1

ρc p (T)

∂T

∂r

2k

r+∂k

∂r

⎛

⎝ ⎜

⎞

⎠ ⎟+ k∂ 2T

∂r2

⎡

⎣ ⎢

⎤

⎦ ⎥

€

j =M

2πR

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2psatTs

1/ 2−pvapTvap

1/ 2

⎡

⎣ ⎢

⎤

⎦ ⎥

Outer polymer shell deflection based on membrane theory for shell of radius rpol and thickness tpol:

Inner solid DT deflection based on thick spherical shell with outer and inner radii, ra and rb :

€

δpolymer =prpol

2 (1− υ pol )

2Epol tpol

€

Δra =− praEDT

(1− υDT )(rb3 + 2ra

3 )

2(r 3 − rb3 )

− υ DT ⎡

⎣ ⎢

⎤

⎦ ⎥


6

DT gas

1.5 mm

DT solid0.19 mm

DT + foam

x

Dense plastic overcoats (not to scale)

0.289 mm

Insulating foam

High-Z coat

We Have Determined the Heat Load Limits for the Base Target and Looked at Ways to Accommodate Higher Loads*

• Target with Insulating Layer as Back-Up Option- Impact on physics and fabrication being assessed

*More details in: B. Christensen, R. Raffray, M. Tillack, “Modeling DT Vaporization and Melting in a Direct Drive Target,” presented at the 16th ANS TOFE, Sept. 2004, to appear in Fusion Science & Technology.

• The maximum allowable heat flux was analyzed for several target configurations where failure is based on the triple point limit to ascertain the effect of:- Initial target temperature

- Thermal insulation (e.g with 10% dense foam)

- Injection velocity

- Allowing for phase change

(ms)


7

Is There an Optimum Injection Velocity Based on Target Survival?

• Two competing factors:

- Higher velocity results in a higher atomic number flux on target, and thus, a higher heat flux on the target but over a shorter time (shorter flight time).

0.0E+00

5.0E+19

1.0E+20

1.5E+20

2.0E+20

2.5E+20

3.0E+20

3.5E+20

100 200 300 400

Injection Velocity (m/s)

Maximum Density (m

-3) Tinit = 18 K

Tinit = 16 K

Tinit = 14 K

0.0E+00

5.0E+19

1.0E+20

1.5E+20

2.0E+20

2.5E+20

100 200 300 400 500 600


Maximum Density (m

-3) Tinit = 18 K

Tinit = 16 K

Tinit = 14 K

= 1 = 0

0.0E+00

5.0E+20

1.0E+21

1.5E+21

2.0E+21

2.5E+21

100 200 300 400 500 600


Maximum Density (m

-3)

Tinit = 18 K

Tinit = 16 K

Tinit = 14 K

100 m, 10% dense

insulator, = 1

- The max. allow. Xe gas density (4000 K) to reach the TP increases with injection velocity for a sticking coefficient,

=0 and shows a peak for =1

- It increases significantly with injection velocity for insulated target even for =1 as the effect of the shorter time for

thermal diffusion across the insulation outweighs the corresponding higher heat flux


8

The Potential of Exceeding the Triple point (Allowing Phase Change) Was Explored

• If only melting is assumed (no vapor gap), 3 possible failure criteria are identified:

- Assumed threshold of spontaneous homogeneous nucleation of vapor bubbles in the DT liquid

(~0.8Tc).

- Ultimate strength of thick inner DT solid (~0.3 MPa) or of thin outer polymer shell (~30 MPa) is exceeded.

- Melt layer thickness exceeds a critical value (unknown, based on physics requirements).

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

4 5 6 7 8 9 10Heat Flux (W/cm2)

Survival Time (s)

Time to 0.8Tc

Time to Tc

Time to PolymerUltimate Stress

Tinit = 16 K

• 0.8 Tc is limiting criterion in this case

- Allowable heat flux is increased by ~ 3–8 times over the cases where the DT triple point temperature is used as the failure criterion.

- But is this criterion acceptable?

DT liquid

CH

DT solid

DT vapor

qo’’


9

The Presence of a Vapor Layer Generally Results in Higher Pressure on the Outer Shell

• Possible failure criteria:- Ultimate strength of the DT solid or polymer shell is exceeded.

• For cases considered, the polymer ultimate strength was reached before the DT ultimate strength

- Vapor layer thickness exceeds a critical value (unknown, based on physics requirements).

0

0.005

0.01

0.015

0.02

0.025

0.03

1 2 3 4 5 6

Heat Flux (W/cm2)

Time to Polymer Ultimate Strength (s)

Tinit = 14 K

Tinit = 16 K

Tinit = 18 K

DT liquid

CH

DT solid

DT vapor

qo’’DT vapor

• If a vapor layer is present, the allowable heat flux is increased by ~ 1.5–3 times over the cases where the DT triple point temperature is used as the failure criterion

For some combinations of Tinit and qo’’, the vapor layer closes, suggesting that bubbles

can be minimized or eliminated in some circumstances• This is due to DT expanding faster than the

polymer shell

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 0.004 0.008 0.012 0.016Time (s)

Vapor Layer Thickness (

m)

q'' = 4.0 W/cm2

q'' = 2.5 W/cm2

q'' = 1.0 W/cm2

Tinit = 14 K


10

The Integrated Thermo-Mechanical Model Has Helped Us Understand the Target Behavior and the Factors Affecting Its Survival During Injection.

However, There is a Major Simplification in the Model So Far: 1-D Vapor Region

Instead of Bubble Formation • Unlikely to have continuous vapor region at DT/shell interface

• Conditions (superheat, critical radius) might not induce spontaneous homogeneous nucleation. However:- Even a limited number of bubble formation might be unacceptable.

- Presence of 3He would promote nucleation.

- Presence of defects at interface or within site might also promote nucleation (heterogeneous nucleation).

• 3He would be formed prior to injection and might be in such quantity that 3He bubble formation might not only occur in the liquid during injection but also in the solid prior to injection.

• Recent results from LANL DT heating experiments show the huge potential for bubble formation.

• This is the one area where we really need better understanding and which will be the focus of our near-term effort to help analyze the LANL experimental results as well as to apply them to the target situation.


11

Critical Radius Vs. Molar Fraction/Max.Solubilityof He-3 in DT

1.0E-07

1.0E-06

1.0E-05

0 10/100 20/100 30/100 40/100 50/100

molar fraction, x/xs

critical radius (m)

Critical Radius 19.79K 1kPa Critical Radius 19.79K 10kPa Critical Radius 19.79K 20kPa fraction after 24 hours fraction after 8 hoursfraction after 2 hours

Scoping Study of Potential Impact of 3He on Bubble Formation

• The presence of 3He decreases the critical radius, rcrit, for bubble formation in liquid DT (and, thus, enhances nucleation).

• rcrit is plotted as a function of the molar fraction of 3He normalized to the

maximum solubility limit.

• Based on available solubility data (data for low P not found), x/xs is shown for

concentrations of 3He corresponding to 2 hrs, 8 hrs and 24 hrs after layering,

respectively.

• rcrit decreases with increasing 3He concentration, the effect being more marked for higher pressures.

Density of He-3 Atoms as a function of time after layering

01E+242E+243E+244E+245E+246E+247E+248E+249E+241E+25

0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05Time (s)

# of He-3 per m^31 hr 1 day

• 3He formation due to radioactive decay of T as a function of time.

• ~4.8x1024 atoms of 3He/m3 after a day.


12

Can 3He Bubble Formation Occur in Solid DT?Number of He-3 in a bubble as a function of

bubble radius and pressure

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

0.0E+00 1.0E-06 2.0E-06 3.0E-06

Radius of Bubble (m)

No. of He-3 Atoms

Pressure = 22kPa

Pressure = 10 kPa

• It depends on the existence of defect at interface or in the foam and on the bubble surface energy requirements

• However, 3He atoms need time to diffuse and coalesce to form bubble

• Let us assume a critical radius of 0.5 m. The corresponding number of 3He is ~ 4x107 atoms.

Radius of the assmed DT spherical volume containing sufficient He-3 atoms to form one bubble

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-06

1.0E-05

1.2E-05

1.4E-05

1.6E-05

1 10 100 1000 10000 100000 1000000

Time following layering (s)

Radius of DT volume (m)

• The volume (and characteristic dimension) of DT containing this number of 3He atoms is shown as a

function of time following layering.

1E-17

1E-16

1E-15

1E-14

1E-13

1E-12

1E-11

1E-10

1.0E+02 1.0E+03 1.0E+04 1.0E+05

Time after layering (s) (~1minute to ~1day)

Necessary diffusion (m^2/s)

Necessary Diffusion coefficientself diffusion of H 14Kself diffusion 16Kself diffusion 18K

• The corresponding diffusion coefficient required for the 3He atoms to diffuse and coalesce is shown below.

• We have not found data for diffusivity of 3He in DT, but based on H self-diffusion, 3He could start coalescing very soon after layering (<1 hour).


13

Summary• Our 1-D integrated thermo-mechanical model has helped us understand the

target behavior and the factors affecting its survival during injection.

• However, a major simplification in the phase-change model is the assumption of a continuous vapor region instead of individual bubble formation.

• Scoping studies show that 3He formation between layering and injection could substantially lower the critical radius for nucleation in the DT liquid and even provide the possibility of bubble formation in the solid if small defects are

present (to be further studied).

• The implosion physics requirements on density non-uniformity seem quite demanding but have not yet been clearly defined. It is not clear what size

and number density (if any) of bubbles would be acceptable.

• DT heating experiments at LANL have also shown formation of bubbles.

• Our next-step effort is to develop a bubble formation and behavior model (homogeneous + heterogeneous nucleation) which can then be coupled to

the 1-D thermo-mechanical model to help in better understanding this important issue and to help in analyzing & guiding the experimental work incoordination with our LANL colleagues.

october 27-28, 2004 hapl meeting, pppl 1 target survival during injection presented by a.r. raffray...

Documents

target modeling

target survival important

modeling activities

tp effect

continuous vapor region

lower initial temperature

tillack ucsd

outline reminder