ppt

January 25, 2008/ARR 1

Heat and Mass Transfer in Fusion Energy Applications: from the “Very Cold” to the

“Very Hot"

Presented by A. René RaffrayUCSD

SeminarUniversity of California, Los Angeles

Los Angeles, CAJanuary 25, 2008


Unique Set of Conditions Associated with Fusion• Realization of fusion energy imposes considerable challenges in the areas of

engineering, physics and material technology.

• This is typified by the heat and mass transfer aspects, which cover a wide range of conditions, from the very cold to the very hot.

• This seminar highlights this wide range of challenges associated with the heat and mass transfer aspects of fusion technology using examples in both the Inertial Fusion Energy (IFE) and the Magnetic Fusion Energy (MFE) Approaches.

Electricity Generator

Targetfactory

Modular LaserArray

Chamber

Schematic of IFE Power Plant (HAPL) ARIES-CS Power Core


Electricity Generator

Targetfactory

Modular LaserArray

Example of IFE Energy Source Based on Lasers, Direct Drive Targets and Solid Wall Chambers (HAPL)

Target (fabrication at <20K, survival

in chamber during injection)

Chamber conditions(~0.1-1 eV

depending on pre-shot

conditions)

Final optics (+ mirror steering)

Blanket

System (including

power cycle)

Dry wall chamber

(armor must accommodate ion+photon

threat at up to ~2000-3000K)


The Very Cold:

IFE Target Layering


An IFE Target Consists of Multiple Layers with Demanding Fabrication Requirements

Uniformity of DT fuel layer thickness

Inner and outer surface smoothness (order of 1 m)

Example Sector of Spherical Target (HAPL)

• Rep rate of 5-10 Hz leads to ~500,000 targets per day• Mass fabrication production • Need reasonably fast layering technique also to

maintain acceptable tritium inventory

(for target microexplosion physics and thermal radiation shielding)


In Beta Layering, DT-Fuel moves until Inner Surface is Isothermal

• Volumetric heating (tritium decay) causes sublimation until isothermal condition is reached (beta-layering)

3H --> 3He + ß- + anti-neutrino

(max. ß energy = 18.6 keV)

• Inner surface temperature increases with increasing layer thickness

• Thermal gradient causes fuel to redistribute

• Fuel moves from thicker to thinner region

• Uniform temperature field leads to uniform layer thickness

Uniform temperature field on outer target (TP of DT ~19.79K)

A. J. Martin, Beta energy driven uniform deuterium-tritium ice layer in reactor- size cryogenic inertial fusion targets, J. Vac. Sci. Technol. A6 (3) (1988)

T, PMigration

of fuel

1- D simplification

Tem

pera

ture

Radius

Th

icker

layer

(hott

er)

Th

inn

er

layer

(c

old

er)

Unlayered Target

qDT= 0.05 W/cc


• Gas stream heats up as the heat from the beta decay is removed from the particles

• Temperature difference causes a non-uniform layer• Temperature variations of helium gas are only slightly

impressed onto fuel• Successful layering will depend on fluidized bed design

– Minimal temperature gradient– Maximum spin and circulation rate of the pellets to provide a

time-averaged isothermal environment

Helium gas: 0.5 atm, <18K>Fuel

Capsule Fuel

Approximate as semi-infinite slabs

Gas T varies 3 mK across capsule

5 Hz target rotation

5 Hz rotational speed lead to acceptable layer uniformity (~1.2%)

Apply dynamic ∆T to static model of fuel layer movement

3 mK local

∆T

GA Has Proposed a Fluidized Bed for Mass Production of IFE Fuel Pellets

LAYERING

Fluidized Bed

Gas Flow

Frit

SPIN

CIRCULATION

Hotter

Cooler

Temperature at an instant

Fuel outer surface varies only 0.008mK


• STARTING POINT- A fluidized bed has been chosen for mass production

layering of IFE targets (GA)

• Room temperature fluidized bed experiments- For initial observation and characterization of bed

behavior

• Numerical fluidized bed model proposed- Must include particle imbalance

- Validation through theory and experiments

• Experimental water-alcohol layering- Validate layering model - Show proof of principle

• Find optimized parameters for D2 Layering prior to experiment

• END POINT- Successful D2 layering in Mass Production Layering

Experiment (MPLX) (GA)

Plan for GA/UCSD Collaboration on Target Layering

(UCSD/GA)K. Boehm

HiP cell

Fluidized bed

Target Vacuum Pickup


Desktop Experiment Set-Up to Help Understand Fluidized Bed Behavior Under RT Conditions

• Use unfilled plastic target shells in a nitrogen flow (N2(RT) ~ He(18K)) • Spin rates of unbalanced spheres• One shell was partially filled with whiteout• An unbalanced target needs 2X bed expansion to spin in example case

Fluidized Bed Performance Regular Frit

0

5

10

15

20

25

1.5 2.5 3.5Bed Expansion

Frequency, Hertz

SpinningOffset BallRegular Frit

SpinningFoam BallRegular Frit

CirculatingOffset BallRegular Frit

CirculatingFoam BallRegular Frit


Surface Degradation is Observed During Fluidization

• A random patch of the target surface is scanned under an SEM for roughening study

• Measurements on (60-40) Au–Pd sputter-coated targets

• Unacceptable Au-Pd layer damage for radiation protection and possibly for target physics requirement

• Need to improve coating process and minimize fluidization time

One patch of the shell analyzed

Au-Pd Surface before Fluidization

Surface after 16 hrs of room temperature fluidization


Several Parameters Define Window of Operation for Fluidized Bed

Gas Flow≠0

h

Gas Flow=0

h’

• 3 main objectives- Minimize T across bed (~3 mK per target)- Optimize spin and circulation rates at operating point- Preserve surface quality

- Bed expansion ratio:E= h/h’

- Representative of gas speed or mass flow

Crush target

=1.2 =1.5 =2.0 =4.0 =8.0

1 QDT

Surface Damage

FLUID BED CHARACTERISTICS FOR 4.6 mm, 8.8mg CAPSULE

0

20

40

60

80

100

120

140

160

180

200

0 0.5 1 1.5 2

BED GAS PRESSURE (atm)

∆T ACROSS BED

(mK)E=1.2E=1.5E=2.0E=4.0E=8.0

Example operating point:0.5 atmh/h’= 2T=70mK


Unknowns in Bed Behavior Call for Numerical Analysis

• The behavior of unlayered shells is unknown (unbalanced spheres)

• Experimental observations are restricted to the particles close to the wall

• Tests on the cryogenic apparatus are expensive, time consuming and complex

• Results might be hard to interpret since shells are not easily accessible

• Optimize operating conditions and define narrow window of operation for successful deuterium layering prior to completion of entire setup- gas pressure, flow speed, bed dimensions, additional heating, frit

design, layering time…


Proposed Numerical Model Consists of Three Parts

• Granular model

• Fluid-Solid interaction

• Layering Model – Thermal/mass transfer

Fluidized Bed Model


Fluidized Bed ModelPart I: Granular Model

• Discrete Particle Method (DPM)• Motion of individual particles tracked by

computing forces acting on the particles at each time step

• Apply Newton’s second law of motion• Spring – dashpot and/or friction slider

model applied for particle collisions• Limitations: Not developed for

unbalanced spheres

Forces are computed based on relative velocity at contact point

Contact point velocity is

not parallel to wall

Orientation defined by Euler angles

Center of mass Geometrical Center

wall

displacement

wall

Normal Force

Tangential Force

Torque around center of mass

For unbalanced sphere:- Contact forces are a function of relative

velocity at contact point- Depends on the orientation of the particle


i

ji

sj

sis

ics rss

sss

rrr

rrr

⋅−

−=

bji

Tji

sji

s

jicg oAss ,,,,

rrr⋅−=

bji

Tji

sji A ,,, ωω r

⋅=

sji

s

jicgjis

jicp vsv ,,,,

rrrr+×=ω

s

jcps

icps

cp vvvrrr

−=

( )( ) effs

ncpeffjijisn cvkrrssF ⋅−⋅+−−= ,

rrrr

( )( )stcp

stcps

tcpsn

st

v

vvFF

,

,,,min r

rrr

⋅⋅⋅−= γμ

stot

sicg

si Fs ×= ,

rrτ sb A ττ ⋅=

Equations to Compute Contact Forces in Model

amFrr

⋅=

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

−−

−−−−

=

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

bz

by

bx

qqqq

qqqq

qqqq

qqqq

q

q

q

q

ω

ω

ω

0

2

1

0123

1032

2301

3210

3

2

1

0

&

&

&

&

Distance between two sphere centers

Distance between two mass centers

Convert spin into space fixed coordinates

Compute contact point velocity

*Single particle experimental observation to determine parameters such as keff and ceff

Apply Forces to:

amFrr

⋅=

Normal and Tangential Force Component*


Fluidized Bed ModelPart II: Fluid/Drag Model

• Problem with fluid cell sizes for traditional porous flow model:- Minimum of seven pellets per fluid cell for cell average to work in

control volume method- Not useful to solve fluid equation for 3x4 grid- Choosing a grid size smaller than the shells leads to complication

determining the “average void fraction” around a sphere

• DNS model to resolve flow around each sphere complex, computationally VERY expensive and not warranted for

the purpose of this model

• The most important information we are trying to get is the particle spin and circulation rate

• Experimental observations show, that the spin of the particles is dominantly induced by collisions, not by fluid interaction

• 1-D Lagrangian model to determine void fraction

- Compute the void fraction for each slice of the fluidized bed, bounded by one radius in each direction of the center of each sphere.

- This “region of interest” moves with each particle from time step to time step

- Once the void fraction is known, the drag force can be computed


Richardson-Zaki Drag Model is Applied Based on Known Void Fraction of Region

( ) 8.3

8.4

6−

⎟⎟⎠

⎞⎜⎜⎝

⎛−= ερρ

π n

tfp

pd u

Ug

df Void Fraction is known

based on 1-D Lagrangian Model

Richardson-Zaki Drag Force for homogeneous fluidized beds:

( )( )25.05.02 832.1_809.3809.3Re Art +−=

( )2

3

f

fpfpgdAr

μ

ρρρ −=

tf

fpt u

d

=ReTerminal Free Fall Velocity is a constant system parameter:

Dellavalle Drag Model to Compute Terminal Free Fall Velocity:

Archimedes Number:

Drag force is added to the total force on the particle at each time step


Particles need to be spaced apart

Initialize position, velocity and quaternion vectors

Start time stepping

Predictor step

Compute forces based on predicted positions

Compute the resulting pressure drop

Determine bed expansion

Correct positions, velocities and accelerations based on the updated forces

Create time averaged statistics

Write Output every 1000 time steps

Particle – wall collisions

Compute void fraction

Compute drag force

Compute effective weight

Compute force due to particle – particle collisionsLoop over all particles

Proposed Fluidized Bed Model


Preliminary Results from Fluidized Bed Model Show Good Qualitative Reproduction of Experimental Results

Exact system parameters need to be determined


Model Has Been Calibrated through a Series of Runs for Balanced Spheres

6e-05

4e-05

3e-05

2e-05

1e-05

5e-05

0.1 0.2

Time (s)k

mn π2=Θ

Total Kinetic Energy in System during Granular Collapse for decreasing time step size

(J)

Nt n

2

Θ=

200 particlesM = 2E-6 KgDiameter = 4 mmK_eff = 1000 N/mC_eff = 0.004 N s/m = 0.0125 N s/m = 0.4I = 5E-12 Kg s^2

Example: Stability and convergence in modeling granular collapse

Next Step: Validation for cases with unbalanced spheres


Layering Model

• Compute the redistribution of fuel based on the fluidized bed behavior

• Solve 1-D equations simultaneously:

• This leads to a layering time constant of

• Time step: ~10-5 s for fluidized bed v. ~30-60s for layering

• Based on the time averaged motion and preferential position, we can compute the average temperature/ temperature difference between the thick and the thin side of the shell

⎥⎦

⎤⎢⎣

⎡−=

1

1

2

2

T

P

T

P

lR

C

ICE

diff

ρδ&

Mass Transfer Equation

[ ]fICEICE

ICE hqk

t

hTT ρδδ &&+⎥

⎦

⎤⎢⎣

⎡+⋅=−

1221

Heat Transfer Equation

q

ht fe ′′=

&

Latent heat

Volumetic heating


Experimental Demonstration of Layering Proposed Using H2O – IPA Mixture

• Water-alcohol filled shells (freezing point ~240K)

• Fluidized be with cooling stream of N2 or He

• Vol. heat source (IR with bandpass filter or microwave)

• Objectives- Analyze fluidizing behavior for unbalanced shells- Demonstrate target layering process- Investigate the effects of volumetric heating and other bed

parameters on the layering process- Validate layering model

Fluidized Bed

IR- Halogen LightAbsorption Coefficient of Ice

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.00E+01

1.00E+02

1.00E+03

0.00E+00 5.00E+02 1.00E+03 1.50E+03 2.00E+03 2.50E+03 3.00E+03

wavelength (nm)

absorption (cm-1)

Absorption of Ice

TOO MUCH HEAT GETS ABSORBED IN FIRST LAYER

TOO TRANSPARENT

Small margin

Room temperatureand pressure

T~240 K in vacuum

Honed copper tubes as waveguides

Bandpass filter

IR halogen lamp

Glass window

Vacuum vessel

Fluidized Bed

Reflective coating to trap radiation


From the Very Cold to the Very Hot:

IFE Target Injection


The Cryogenic Direct-Drive Target will be Subjected to Challenging Conditions when

Injected into an IFE Chamber

IFE Chamber (R~6-10 m)

Chamber Gas: protective gas (Xe) and/or burn products (D, He)

Chamber wall ~ 1000–1500 K, q’’ rad = 0.2 – 1.2 W/cm2

Target Injection (~100 m/s)

Target Implosion Point


Modeling Target Injection Using DS2V

Example Temperature Field Around a Direct Drive Target

- Xe flowing at 400 m/s in the positive x-dir.

- 4000 K stream temperature.

- 3.22x1021 m-3 stream density.

- Sticking coefficient = 0

- Target surface temperature = 18 K

Assumptions• Axially symmetric flow.

• Target is stationary; gas stream velocity to simulate injection.

• Target surface temperature is constant (~18K).

• Sticking coefficient = 0 or 1,

•Accommodation coefficient = 1

• Target doesn’t rotate.


Thermal Modeling Indicates Limited Gas Density in Chamber to Prevent Target DT Reaching its Triple Point

• For a 16 K target injected at 100 m/s in a 10.5 m chamber, q’’ to reach the TP ~0.5 W/cm2

• Radiation q’’ ~ 0.2 W/cm2 for a 1000K wall and target =0.96

• From DS2V, for a target injected at 100 m/s in 1000 K D2, q’’ = 0.3 W/cm2 for D2 density of ~4 mTorr

• Not much margin left for increases in radiation due to reflectivity change

0.01

0.1

1

10

0.1 1 10Pressure (mTorr)

Heat Flux (W/ sq cm)

T=1000K V=100mpsT=1000K V=400mpsT=4000K V=100mpsT=4000K V=400mps

1-10 m Polymer Shell with Au or Pd Reflective Coating

290 m Solid DT/Foam

190 m Solid DT

DT Vapor Core

~ 4 mm


What About the Effect of 3He Nucleation Sites?

electronHeH +→ 23

13

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-5

0

1

2

3

4

5

6

x 10-6

Tim

e

(delta time =

5 min)

Mole fraction of 3He diffused into the Trap

Radial distance from the center of the trap (m)

Mol

ar f

ract

ion

of

3H

e

• 3He generated into the DT by tritium decay (half life = 12.3 years) could accumulate in clusters and provide nucleation sites

• Time between layering and injection = 4-10 hrs

•• Estimated nucleus radiusEstimated nucleus radius-- 0.4 microns after 4 hrs0.4 microns after 4 hrs-- 1.6 microns after 18 hrs1.6 microns after 18 hrs

• 2-D model to more accurately simulated bubble nucleation and growth


2-D Thermal Diffusion Model with Stretched Grid and Bubble Growth

• Bubble grows as fast as heat for the phase change can be delivered to the interface

• As the bubble starts growing, the pressure in the bubble drops even further

• Bubble grows step wise depending on the Bubble grows step wise depending on the gridgrid

• Conservation of energy requires variable Conservation of energy requires variable time stepstime steps

• In order to determine the length of the time In order to determine the length of the time step, the heat flux to the bubble needs to be step, the heat flux to the bubble needs to be computedcomputed

• As the bubble grows from one grid to another, the temperature field is adjusted

Bubble grows radially outward starting somewhere in the domain

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+⋅=′′

θδδ

δδ T

rr

Tkq

1&


Temperature Field Around the Bubble

• Small thermal boundary layer

Time: 4.86 E-6sRadius: 2.94 E-6m

Time: 3.52 E-5sRadius:8.66-6m

Time: 8.53 E-5sRadius:1.09E-5m

Time: 1.47E-4sRadius:1.34E-5m




Comparison with LANL DT Bubble Growth Experimental Observation

•• Two stages of bubble growthTwo stages of bubble growth-- Could be explained by the temperature fieldsCould be explained by the temperature fields

•• Bubble grows into the solid layerBubble grows into the solid layer-- Low strength of DT around triple pointLow strength of DT around triple point

•• Small bubbles nucleate later but grow fast for a Small bubbles nucleate later but grow fast for a longer longer period of timeperiod of time

-- Higher superheat requiredHigher superheat required

-- Higher surrounding temperature results in a faster Higher surrounding temperature results in a faster growthgrowth

Comparing Bubble Growth (LANL experiments and numerical simulation)

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

1.4E-04

0 0.02 0.04 0.06 0.08 0.1 0.12

time (seconds)

bubble diameter (meters)

bubble T=18K, p=22 000Pa, R_min=1.6E-6m

meltlayer heat flux =1W/cm 2̂

LANL BUBBLE UPPER

LANL BUBBLE LOWER

bubble T= 18K, p =22 000Pa, R_min = 4E-7m


• Melt layer around the target does not violate symmetry requirements• Bubbles do violate symmetry• Nucleus of a certain size present in the DT• Temporal separation of melt layer occurrence and bubble nucleation• If melt layer acceptable for target physics requirement and limiting criterion based

on bubble growth, possibility of significant impact on target and chamber design- Increase heat flux by a factor of 3-10

Applying Model to Characterize Target Design Limitations


High Temperature Operation in IFE

IFE Chamber


What are the Threats on the Chamber Wall?

• X-ray, ion and neutron fluxes to the chamber wall several times per second.

• Neutron flux penetrates deeper and not an issue for armor.

• Need to develop armor that can accommodate X-ray and (more importantly) ion threats.

Target micro-explosion

Chamber wall

X-rays Fast & debris ions Neutrons

Direct Drive

Target (MJ) X-rays

4.94 (1.3%)

Neutrons

274.3 (74.7%)

Gammas

0.017 (0.005%)

Burn Product Fast Ions

47.14 (12%)

Debris Ions Kinetic Energy

40.71 (16%)

Total

367.1

Example energy partitioning for 350 MJ-class direct drive target

(HAPL reference from J. Perkins, Oct. 2005)


Ion and Photon Threat Spectra Cover Appreciable Energy Ranges

• Example spectra for 350 MJ-class direct drive target (HAPL reference, J. Perkins, Oct. 2005).


Ion Power Deposition Occurs in a Very Thin Armor Region (~m’s) over a Few s

• Example case for 10.75 m chamber without protective gas to avoid target survival and placement issues.• Only thin armor region sees large energy deposition and temperature transients (next slide).• This led to the configuration choice of a

thin armor layer (~ 1 mm) on a FS substrate.• Blanket at the back sees quasi steady state (similar to MFE).• W chosen as preferred armor material (high-temperature capability, no tritium concern).• Armor lifetime is a key issue and is the focus of the R&D in this area.

Coolant

FSW

q


Temperature History and Gradient for W Armor in a 10.75 m Chamber Subject to the 350 MJ-Class Baseline Target Threat

Spectra (from HAPL)• 1-mm W on 3.5 mm FS at 580 °C.• No chamber gas.• Time-of-flight spreading of ion energy deposition results in much lower temperature

rise than assumption of instantaneous energy deposition.• Peak temperature ~2400°C.


Impact of Threat Spectra on W Armor Lifetime • Several possible mechanisms could lead to

premature armor failure:- Ablation.- Melting (is it allowable?).- Surface roughening & fatigue (due to cyclic thermal

stresses).- Accumulation of implanted helium.- Fatigue failure of the armor/substrate bond.

• Because the exact IFE ion and X-ray threat spectra on the armor cannot be duplicated at present, experiments are performed in simulation facilities as part of the HAPL program:- Ions (RHEPP@SNL).

- Laser (Dragonfire@UCSD).- Fatigue testing of the W/FS bond in ORNL infrared facility.- He management is addressed by conducting implantation experiments (UNC, UW)

along with modeling of He behavior in tungsten (UCLA).

AblationDepth

T or T

No net ablation, but surface roughening

Threshold for ablation

Threshold for roughening

Net Ablation


Long Term Exposure Experiments Suggest Roughening Threshold and Temperature Dependence for W, for example:

• Results from the RHEPP ion beam facility at SNL (0.8-1.6 MeV) indicates roughening threshold for powder metallurgy W (PM W) at ~ 1 J/cm2 at RT. - some improvement with heated W samples.- single crystal W better.- rhenium (Re) and Re/W alloy much better.

• Does roughening matter if it does saturate and does not lead to armor failure? Probably not.• Additional testing and diagnostics needed for confirmation of initial experimental indications on

saturation and threshold for W armor. • For HAPL, as an initial armor survival constraint from these early results, a temperature limit of

2400°C was assumed for the W armor (e.g. corresponding to a RHEPP fluence of ~1.2 J/cm2).

• Results from Dragonfire laser testing facility at UCSD (YAG laser, 10 Hz) with W (~3000°C) indicate possible roughening saturation after ~105 shots.

• Also, PM W behavior seems to depend more on T than T.11A, 200mJ, 773K, Max: 3,000K (~2,200K T)

103 shots 105 shots104 shots


Another Major Issue is Ion Implantation Effect on W

• He retention and surface blistering characteristics of W

• Carbide formation and change of thermophysical properties of surface

• R&D activities as part of HAPL program include:

• He implantation/anneal cycle experiment(UNC/ORNL)

- ~850°C base T, ~1.3 MeV He, pulsed implantation and anneals at 2000°C

over ~1000 cycles to fluences of ~1020 He/m2

• He + D implantation in IEC facility (UW)

- ~800°C base T, ~10-100 keV ion, pulsed implantation to fluences of ~1022 He/m2

• Modeling of implanted ion behavior including bubble formation and

behavior (HEROS code at UCLA)

• He ion irradiation of W at 800 °C shows significant surface damage at modest exposure

• Need better understanding (including pulse effect and net mass loss)

• Possibility of porous material to enhance release and relieve thermal stress


0

1

2

3

4

5

6

1.0E+15 1.0E+16 1.0E+17 1.0E+18 1.0E+19 1.0E+20

Dose per He implantation (ions/m2)

Effective Diffusion Activation Energy ( eV)

Single crystalPolycrystalline

IFE Case ~5 x 1016 atoms/m2

1 MeV He Implantation and Release in W (UNC)

• He retention in W decreases drastically when a given He dose is spread over an increasing number of pulses, each one followed by W annealing to 2000°C • Simple diffusion model suggests values of

effective activation energy as a function of dose• Results suggest porous material with 50-100 nm microstructure would keep at% of retained He in W to a few %

- Vacuum plasma spray porous W with ~10-100 nm microstructure (PPI/UCSD).


Required PXe as a Function of Yield to Maintain TW,max<2400°C for 1800 MW Fusion Power and Different Rchamber

0

10

20

30

40

50

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400 450

Xe

Pre

ssu

re (

@S

T)

(mto

rr)

Rep

etit

ion

Rat

e

Yield (MJ)

3.5 mm FSTcoolant=572°C

h=67 kW/m2-K

chamber60 40

1 mm WR (m)5.7

6.5

7

8

10

Armor Survival Constraints Impact the Overall IFE Chamber Design and Operation

• W temperature limit of 2400°C assumed for illustration purposes (~1.2 J/cm2 roughening threshold from RHEPP results)

• Limit to be revisited as R&D data become available

• Example chamber parameters for 0 gas pressure:- Yield = 350 MJ; R=10.5 m; Rep. rate ~ 5 for 1750 MW fusion

• Desirable to avoid protective chamber gas based on target survival and injection considerations

• Large chamber maintained as baseline for HAPL

• Possibility of advanced chambers explored, in particular use of magnetic intervention to stir away the ions and help achieve a more compact chamber


High Temperature Operation in MFE

MFE Divertor


The Divertor Challenge in MFE: How to Accommodate the Heat and Particle Fluxes

ARIES-CS Compact Stellarator Concept as example of MFE Device

• Provide region for ion neutralization and fusion ash pumping

• W armor considered for power plant application

- high temperature capability - relatively high sputtering threshold

• Provide region for ion neutralization and fusion ash pumping

• W armor considered for power plant application

- high temperature capability - relatively high sputtering threshold

Field line tracing model to estimate

divertor heat flux for ARIES-CS


ARIES-CS Divertor Design

• UCSD/FZK collaboration• Design for a max. q’’ of at least 10 MW/m2 • He coolant and tungsten-alloys as structural material and for armor• Previous concepts include:

• UCSD/FZK collaboration• Design for a max. q’’ of at least 10 MW/m2 • He coolant and tungsten-alloys as structural material and for armor• Previous concepts include:

• Build on the W cap design and explore possibility of a new mid-size configuration with good q’’ accommodation potential, reasonably simple (and credible) manufacturing

Cooling finger with W caps (~1-2 cm) (FZK):- minimize use of W as structural material - accommodate higher q’’- many small units (~105-106)required, raising

reliability and maintenance concerns

Plate configuration (~ 1m) (FZK):-fewer units ~100-1000-not well suited for thermal gradient accommodation


T-Tube Divertor Concept (also applicable to Tokamaks)

• W allow cartridge inside outer tube• Cooling with discrete or continuous jets• W armor layer• Graded transition connection from W alloy to FS

manifold to reduce differential thermal expansion and stress

• W allow cartridge inside outer tube• Cooling with discrete or continuous jets• W armor layer• Graded transition connection from W alloy to FS

manifold to reduce differential thermal expansion and stress W alloy

outer tube

W alloy inner cartridge

W armor


Set Tube Length for Acceptable Deflection

• Deflection <0.2 mm for L=10 cm and D = 1.5 cm• Deflection <0.2 mm for L=10 cm and D = 1.5 cm


Excellent Thermal-Hydraulic Performance• Results from and FLUENT (CFD) and CFX indicates that for q’’ = 10 MW/m2:

- High jet heat transfer coefficient- W alloy temperature within ~600-1300°C (assumed ductility andrecrystallization limits, but

requires further material development)

• Results confirmed through dedicatedexperiments at Georgia Tech.

• Results from and FLUENT (CFD) and CFX indicates that for q’’ = 10 MW/m2:- High jet heat transfer coefficient- W alloy temperature within ~600-1300°C (assumed ductility andrecrystallization limits, but

requires further material development)

• Results confirmed through dedicatedexperiments at Georgia Tech.

Example Case:• Jet slot width = 0.4 mm• Jet-wall-spacing = 1.2-1.6 mm• Specific mass flow = 2.12 g/cm2 • Mass flow per tube = 48 g• P = 10 MPa, P ~ 0.1 MPa•T ~ 90 K for q’’ = 10 MW/m2

• THe ~ 605 - 695°C


Design Optimized for Reasonable Stresses

• Results from ANSYS for q’’ = 10 MW/m2:- Maximum thermal stress ~ 370 MPa

• Graded transition connection from W alloy to FS manifold results in acceptable stresses

• Results from ANSYS for q’’ = 10 MW/m2:- Maximum thermal stress ~ 370 MPa

• Graded transition connection from W alloy to FS manifold results in acceptable stresses

th,max ~ 370 MPa


Divertor Unit Cell Design Allows for Assembly in Manifolding Units and Integration in Plates of

Required Sizes• T-tubes assembled in a manifold unit.• Typical divertor target plate (~1m x ~1 m) consists of a number of manifold

units.

Details of T-tube manifolding to keep FS manifold structure within its temperature limit


Fabrication Method Being Investigated at Plasma Processes Inc. (PPI, Huntsville, AL)

• Vacuum Plasma Spray (VPS) posible• New EL-Form process method preferred

- High temperature electroforming based on electrodeposition of compact layers of metals onto a mandrel of the desired shape. - Deposits >99% of theoretical density as deposited- Avoid possible shrinkage linked with long term post-processing sintering or HIPing

• Vacuum Plasma Spray (VPS) posible• New EL-Form process method preferred

- High temperature electroforming based on electrodeposition of compact layers of metals onto a mandrel of the desired shape. - Deposits >99% of theoretical density as deposited- Avoid possible shrinkage linked with long term post-processing sintering or HIPing

• Co-axial tube successfully manufactured as part of SBIR I effort

• Prototypical geometry + heat flux testing as part of Phase II


Only Very Few Off-Normal Events Could be Allowed in a Fusion Power Plant

• Disruptions can result in heat loads on the divertor (ITER, 6-25 MJ/m2 over ~1.5-3 ms)• Melting and evaporation would occur• Very few such events allowed (cannot shut down the power plant + armor lifetime)

• Disruptions can result in heat loads on the divertor (ITER, 6-25 MJ/m2 over ~1.5-3 ms)• Melting and evaporation would occur• Very few such events allowed (cannot shut down the power plant + armor lifetime)

Temperature History of W Divertor Armor Under 3 MJ/m2 over 3 ms Disruption Heat Load

(3 mm W armor, 2 mm W tube thickness; q''=10MW/m2; h =20 kW/m2-K)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03 5.0E-03 6.0E-03

Time (s)

Temperature (°C)

Tmax,WTcool

Divertor W Phase Change Thickness Following 3 MJ/m2 over 3 ms

Disruption Heat Load (3 mm W armor, 2 mm W tube thickness

q''=10MW/m2; h =20 kW/m2-K)

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03 5.0E-03 6.0E-03 7.0E-03 8.0E-03 9.0E-03 1.0E-02

Time (s)

W Phase Change Thickness (m)

W Evaporated LayerW Melt Layer

Maximum W Armor Phase Change Thickness as a Function of Energy Density for Example Disruption Case over Deposition Times of 1 and 3 ms

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

0 1 2 3 4 5 6

Energy Density (MJ/m2)

Maximum Phase Change

Thickness (m)

Evap. for 1 ms

Evap. for 3ms

Melt for 1 ms

Melt for 3 ms

Poly. (Evap. for 1 ms)

Poly. (Evap. for 3ms)

2-mm W alloy3-mm W armor

Heh = 20 kW/m2-KT = 700°C

Energy Deposition


Summary

• Realization of fusion energy imposes considerable demands in the areas of engineering, physics and material technology, as typified by the heat and mass transfer aspects, which cover a wide range of conditions, from the very cold to the very hot, e.g.:

- IFE target: < 20K

- IFE pre-shot chamber environment: ~1000-10000 K

- IFE chamber wall: ~1500-3000 K

- MFE divertor normal/off-normal conditions: ~1500/4000 K

• Exciting challenges

• Much progress toward credible solutions but more work needs to be done.

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