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
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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