Tritium Transport in Multi-Region Lead-Lithium Liquid Metal Blankets

1

Presented by Alice Ying

Materials taken from Dr. Hongjie Zhang’s Ph. D. Thesis

NOV. 14-15TH, 20142nd EU-US DCLL Workshop

University of California, Los AngelesEdward K. Rice Room

Tritium transport modeling development at UCLA is guided by the construction of a virtual integrated simulation

predictive capability

2Data from Multiple-effect testing facility, TBM, FNSF

Validation/Verification Database/Constitutive equations

Neutronics Radiation damage rates

Thermo-fluid

Structure/thermo-mechanics

Species (e.g. T, HT) transport

Electro-magnetics

MHDSpecial module

RadioactivityTransmutation

Safety

FNST Blanket

CAD- Geometry

Mesh services Adaptive mesh/mesh refinement

Visualization Data translators: Interpolation

Time step control & concurrent exe-cution of multiple simulations

Analyzer and Adaptor Synchronizer

Consistency Controller

Wrapper

Topology optimizer

Situation Analysis (Constraints)

Meta-level Models

Base Level Computational Simulators

Spatial, Dynamics

Tritium Transport Modeling and Simulation Approach

Multi-step processes – Compute flow and temperature fields accounting coupled effects such as

buoyancy effect on MHD velocity profile– Solve tritium transport models

Multi-solver/simulation platforms– User functions are written to solve interface mass transfer, source terms,

other effects. Advanced mesh generation scheme with prism layers can be inserted to provide fine grid resolution in the boundary layer.

– Utilized parallel solver and capability of CAD model import.

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There is not yet a “single” code powerful enough to solve all the physics involved.

MHD Solver

Neutronics Code

Experimental Database

Thermofluid Code

Dat

a M

appi

ng

Mass Transfer Solver

Use

r Fun

ction

s

Interface mass transfer

Multi-material and domains

Helium bubblesChemical compositions

MHD velocity

Temperature Velocity

Tritium generation

rate

Transport properties

Mul

ti-m

ater

ial a

nd

dom

ains

General equation for a dissolved species (from TMAP [1])

tcoefficienSoret or transportofheat the= Q

s"" species decay to that atoms m"" species offrequency decay eradioactiv =

atoms s"" species offrequency decay eradioactiv =

)(mol/m trapkth"" in the s"" species of atoms ofion concentrat =

s)(mol/m atoms s"" species offlux =

*

s

3

2s

sm

tskc

J

4

Ignore tritium radioactive decay in PbLi– Half-life of tritium: 12.3y, rate of 5.5% per year– Generated tritium atoms are transferred to the extraction system, they stay in the blanket only

for a short time.

Trap effects from defects/irradiation in the structure are not included. Traps resulting from helium bubbles in PbLi blankets are treated separately (add-on).

1 G. R. Longhurst, “TMAP7 User Manual”, Idaho National Engineering and Environmental Laboratory Bechtel BWXT Idaho, LLC, 2004

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Coupling through Material Interfaces

Boundaries and boundary labels for the modeled system

Coupling at the LM/FS interface

Sievert’s law and impose continuity of partial pressures, leading to the concentration discontinuities at interfaces

LMs

FSs

LMT

FST

K

K

c

c

FSLM

LMFS

_

_

_

_

,

,

Continuity of fluxes

LMFSFSLMFSTFSLMLMTLMTLM cDccD

,,

)()( ___ nnu

Coupling at the LM/FCI interface

LMs

FCIs

LMT

FCIT

K

K

c

c

FCILM

LMFCI

_

_

_

_

,

,

LMFCIFCILMFCITFCILMLMTLMTLM cDccD

,,

)()( ___ nnu

Coupling at the FS/HC interface

FSHC,

2

__2 at 2

FSTRHCTDT cKPKJ

HCFS,at 22

TT JJ

Dissociation and recombination

6

Numerical Codes:

MHD solver– HiMAG -- Finite volume method, Structured grids, UCLA– Stream -- Finite volume method, Structured grids, Cradle Japan

(can also solve temperature in the case of mixed convection) Primary Mass transfer solver, Sc/Tetra -- Finite volume method,

Unstructured grids, Cradle Japan– Build and solve the proper tritium transport equations in Sc/Tetra – Solve non-MHD flow and temperature fields.– Handle the blankets geometry complexity.– Write and build our own user functions (in c++) into the mass

transfer solver considering the factors: (1) multiple domains, (2) coupling through the material interfaces, (3) temperature-dependent transport properties, and (4) space-dependent tritium source terms.

COMSOL is used for cross checking and methodology evaluation Data Mapping

– Mapping the MHD data into the Sc/Tetra solver using the user-defined function.

User defined function to apply tritium transfer boundary conditions at LM/FS or FCI structure interface has been built into Sc/Tetra thermo-fluid code

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LMs

FSs

LMT

FST

K

K

c

c

FSLM

LMFS

_

_

_

_

,

,

LMFSFSLMFSTFSLMLMTLMTLM cDccD

,,

)()( ___ nnu

)(

)(

_/_

___

LMTLMFSFST

LMLMTLMTLMFSLMT

CKCM

ccDJ

nu

)(

)(

__/

__

FSTLMTLMFS

FSTFSLMFST

CCKM

cDJ

n

FSLM ,

LMFS ,

Stiff-spring method

Ensured flux continuity while obeying Sieviet law at the PbLi/Solid interface

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Code validation

Cases

Validated with co-permeation of Deuterium and Hydrogen through Pd from experiments by K. Kizu, A. Pisarev, T. Tanabe, J. of Nuclear Materials, 289 (2001) 291-302

Validated with US-JA TITAN experiment of tritium/hydrogen permeation through α-Fe/PbLi sample, collaborated between INL and the University of Tokyo.

Validated with in-reactor tritium release experiment from lithium-lead with tritium generation source term, conducted in the fast neutron reactor “YAYOI” of the University of Tokyo

Validated with analytical solution of mass transfer in a absorption-convection-permeation problem

Validation of UCLA Code: Transient H transport modeling through a-Fe/PbLi system

downHc ,2

PbLiHc ,

FeHc ,

upHp ,2

PbLiHFeH Kcc __

PbLiSFeS KKK __

2/1,__ 2 upHFeSFeH PKc

Recombination

Local chemical equilibrium

Sieverts’ law

Convective flux

2_, PbLiHrrH cKJ

Downstream-side Ar

Upstream-side H2

Modeling Methodology• 3D Mass transfer equations are solved using both

COMSOL and SC/Tetra.

• Species equilibrium, recombination flux and Sieverts’ Law at interfaces are computed using C++ user function

Experimental Set-up

Experimental data generated through US-JA TITAN collaborations

Kr= recombination coefficient Ks= solubilityK= equilibrium partition coefficient

0 2 4 6 8 100

50

100

150

200

250

300P

H2 = 105Pa

Ar Flow rate = 5ccm

Pe

rme

ate

d H

2 C

on

cen

tra

tion

in A

r p

urg

e g

as(

pp

m)

Time (hr)

Cal. Exp. 673K 773K 873K 973K

H2 concentration CH2,down in Ar purge gas

References:• Data provided by Satoshi Fukada• P. FAUVET and J. SANNIER, “HYDROGEN BEHAVIOUR IN

LIQUID 17Li83Pb ALLOY”, Journal of Nuclear Materials 155-157 (1988) 516 5l9

• F. Reiter, “Solubility and diffusivity of hydrogen isotopes in liquid Pb-17Li”, Fusion Engineering and Design 14 (1991) 207-211

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Cases studied and results

Buoyancy effect on tritium transport in PbLi MHD flows with permeable wall

Tritium transport in a DCLL-type poloidal duct with FCI and PES

Tritium transport in a DCLL U-shaped flow

Tritium transport in HCLL configuration and comparison with DCLL case

Helium bubble effects

Critical yet interesting tritium transport features can only be revealed/seen through sophisticated, multi-physics simulations

gXB

Downward flow

x

y

Re=1E4 Gr=1E8Ha=400

Buoyancy induced reversed flowVelocity Profile (m/s)

Tritium Transport in the Buoyancy Affected PbLi MHD flows

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High tritium

concentration

Tritium concentration (mol/m3)

High tritium

concentrationDownward Upward

Using analyzed parameters

Coupled MHD flow and heat transfer analysis

1.8 T used in the analysis

DCLL duct with PES

PbLi flow

Color scheme: tritium concentration

PES at back wall

Behind FW

Color scheme: Purple: T diffusive flux, Black: velocity, Rainbow: T concentration

Tritium transport in a DCLL duct with PES slot

PES- pressure equalization slot Fr

ont w

all

2a=0.06m, 2b=0.06m, RAFS wall 0.002m, FCI 0.002m, PES 0.003m, Gap 0.002m

FCI and PES affect tritium transfer behavior and permeation rate through-

– changing the local MHD velocity distribution, which in turn affects tritium diffusion and convection.

– providing a path for tritium to migrate though PES and interact between the core and the gap. Rich phenomena !

PES locations affect tritium transport in a DCLL-type poloidal duct

Tritium concentration profile

Ha, FCI conductivity effects on Tritium transport in a DCLL-type poloidal duct

If a PES is on the wall parallel to the magnetic field, tritium loss rate increases by 15% because the velocity is reduced near the front wall.

No PES PES in the wall // B

PES in the wall B⊥

generation (mol/s) 1.406e-8 1.410e-8 1.412e-8permeation (mol/s) 1.76e-10 1.99e-10 1.87e-10Losses 1.25% 1.42% 1.32%

Tritium permeation rate vs. FCI electric conductivity

Tritium Losses for Three PES Configurations

Tritium losses for three PES configurations as Ha changes

• As the FCI electric conductivity decreases, the effect of electromagnetic coupling between the flow in the gap and the bulk flow reduces;

• Thus the velocity in the gap drops and tritium permeation rate increases;

• Over the range of reference electric conductivity of the FCI from 5 to 500 Ω-1m-1, tritium permeation rate decreased by about 46%.

Case Average PbLi velocity in channel

Total tritium generation indomain

Tritium exit from outlet

Integrated permeation to coolant

% loss due to permeation

DCLL duct 7 cm/s 1.409e-8 mol/s 1.387e-8 mol/s 2e-10 mol/s 1.8 HCLL BU (2) 0.8 mm/s 2.494e-8 mol/s 2.063e-8 mol/s 4.308e-9 mol/s 17

By flowing PbLi in DCLL for heat removal results in a lower tritium partial pressure and permeation compared with HCLL

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1.8 T used in the analysis

Mass flow rate: 0.33 kg/s

Flow and tritium near the turn-around region next to FW

HCLL BU Analyzed

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Tritium transport in a DCLL U-shaped flow

The reference DCLL design: Three U-shaped duct flow with FCI and FS walls connected through inlet/outlet with manifolds

The analyzed DCLL central U-shape channel as representative of the three channels

The inlet manifold design will determine the fraction of PbLi liquid flow in the gap. (There was no communication between the core and the gap in this U-shaped duct.)

The resulting effect on the tritium permeation may be important.

Two cases analysis was carried out:– The gap inlet velocity = the core inlet velocity

– The gap inlet velocity = 10% of the core inlet velocity

Velocity in the Gap between FCI and the Structural Wall Affects Tritium Transport in

DCLL

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DCLL U-shaped Channel The gap inlet velocity = the core inlet velocity

The gap inlet velocity= 10% of the core inlet velocity

Tritium generation rate (mol/s) 9.72e-8 9.72e-8Tritium inventory (mol) 2.64e-6 3.57e-6T exit rate from outlet (mol/s) 9.60e-8 9.44e-8T permeation rate (mol/s) 1.16e-9 2.81e-9Losses percentage (%) 1.2% 2.9%

Tritium generation, inventory and permeation with a change of the gap inlet velocity

Tritium concentrations (mol/m3) at mid-planes of a U-shaped DCLL channel for different gap inlet velocity

Back

Back

velocity (m/s)

U-shaped duct

Regarding He bubble: Initial Progress of the Effect of Helium Bubble on Tritium Transport in PbLi Mix-Convection MHD Flow

CT_LM CT2_bubbleCbubbles

Example Case • Re=1E5 Gr=1E8 Ha=400• Downward flow• Uniform He-nano-

bubbles generate rate at 1e11(1/m3s)

• Bubble size r = 20nm • No bubble

agglomeration• Results show that the

amount of absorbed T in He-bubbles is low and it may have no significant effect on atomic T concentration.

Coupled PbLi Mix-Convection MHD Flow with Multi-Species

He nano-bubbles represented as a passive scalar carried by PbLi flow

Tritium absorption within bubbles is captured using the species equilibrium model.

bubbleLMTbubbleTLMbubbleT Jct

c

__2

_2

2

1u

)( __2__ LMTbubbleTLMSbubbleLMT CPKaMJ

gXB

Downward flow

x

y

bubbleLMTTLMTLMLMTLMLMT JScTDct

c

____ ))((u

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Scenario

Average permeation flux (mol/m2/s)

Ratio between the tritium permeation rate across the bubble and the total (%)

Tritium partial pressure in bubble (Pa)

1 5.3e-11 1.9e-1 1.37e-52 5.7e-11 2.5e-2 1.00e-53 5.54e-11 6.3e-2 1.04e-5

• A higher velocity provides a lower bubble concentration and a lower amount of tritium trapped inside the bubbles.

• Over the range of mean velocity from 0.7 mm/s to 0.07 m/s, the He bubble concentrations dropped by two orders of magnitude from 1.4e6 to 1.4e4, and the amount of tritium trapped in the bubbles decreased by about 6 orders of magnitude from 9.0e17 to 9.6e11.

Tritium concentration maps for three different scenarios of size and number

of bubbles attached to the wall

M-shaped velocity profile and the concentration of tritium trapped inside bubbles

U0= 0.07 m/s DCLL like velocity

More on He-bubbles

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Summary We now have a 3D computational predictive capability for analyzing tritium

transport phenomena affected by multi-physics and geometric features Through this capability,

– Identified the effect of the design features and material uncertainties on tritium transport and permeation

– Quantified the difference of tritium inventory and permeation rate between DCLL and HCLL blanket concepts

– To provide guidance on the PbLi blanket designs to comply with tritium control requirements with regard to the reduction in tritium permeation

Recommendations Surface effect: Oxidized and clean wall surfaces have different surface

properties (e.g., adsorption, desorption, and recombination constants). Thus tritium permeation could be affected by the surface conditions. The proposed model is capable of accounting for such phenomena through the use of sticking coefficients. However, data is needed.

He bubble effects- The amount of tritium trapped into helium bubbles is insignificant at low tritium partial pressure regime such as in DCLL concepts. However, at high tritium partial pressure, which occurs in a HCLL concept, the amount of tritium trapped into helium bubbles is markedly high. Further modeling and analyses are necessary to evaluate the impact of helium bubbles especially for the low PbLi velocity blankets. (can be a problem for tritium removal if not removed.)

The current solubility data results in a ~ 80% difference in permeation rate. Dedicated experimental campaigns aimed at obtaining more reliable material properties are needed.

Backup -- MHD velocity profile

-1.0 -0.5 0.0 0.5 1.00

1

2

3

4

5

U

z

Calculated solution Hunt's (1965) exact solution

Comparison between analytical and numerical solutions. The agreement is quite good in the core, while in the side layer the computed velocity is slight lower than Hunt’s solution.

MHD velocity profile obtained by using Stream code for a duct flow

FCI with PES flow field comparisons between Stream and Ming-Jiu Ni’s solution