1. Tritium Transport in Multi-Region Lead-Lithium Liquid Metal Blankets
Presented by
Alice Ying
Materials taken from
Dr. Hongjie Zhang’s Ph. D. Thesis
Nov th, 2014
2nd EU-US DCLL Workshop
University of California, Los Angeles
Edward K. Rice Room

2. FNST Blanket CAD- Geometry
Tritium transport modeling development at UCLA is guided by the construction of a virtual integrated simulation predictive capability
Neutronics Radiation damage rates
Thermo-fluid
Structure/
thermo-mechanics
Species (e.g. T, HT) transport
Electro-magnetics
MHD
Special module
Radioactivity
Transmutation
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
Data from Multiple-effect testing facility, TBM, FNSF
Validation/Verification
Database/Constitutive equations

3. Tritium Transport Modeling and Simulation Approach
There is not yet a “single” code powerful enough to solve all the physics involved.
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.
MHD Solver
Neutronics
Code
Experimental Database
Thermofluid Code
Data Mapping
Mass Transfer Solver
User Functions
Interface mass transfer
Multi-material and domains
Helium bubbles
Chemical compositions
MHD velocity
Temperature
Velocity
Tritium generation rate
Transport properties

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

5. Coupling through Material Interfaces
Coupling at the LM/FS interface
Sievert’s law and impose continuity of partial pressures, leading to the concentration discontinuities at interfaces
Continuity of fluxes
Boundaries and boundary labels for the modeled system
Coupling at the LM/FCI interface
Coupling at the FS/HC interface
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.

7. 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
Stiff-spring method
Ensured flux continuity while obeying Sieviet law at the PbLi/Solid interface

8. 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, (2001)
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

9. Validation of UCLA Code: Transient H transport modeling through a-Fe/PbLi system
Experimental data generated through US-JA TITAN collaborations
Recombination
Local chemical equilibrium
Sieverts’ law
Convective flux
Downstream-side Ar
Upstream-side H2
Experimental Set-up
Kr= recombination coefficient
Ks= solubility
K= equilibrium partition coefficient
H2 concentration CH2,down in Ar purge gas
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
References:
Data provided by Satoshi Fukada
P. FAUVET and J. SANNIER, “HYDROGEN BEHAVIOUR IN LIQUID 17Li83Pb ALLOY”, Journal of Nuclear Materials (1988) 516 5l9
F. Reiter, “Solubility and diffusivity of hydrogen isotopes in liquid Pb-17Li”, Fusion Engineering and Design 14 (1991)

10. 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

11. Tritium Transport in the Buoyancy Affected PbLi MHD flows
Coupled MHD flow and heat transfer analysis g X B
Downward flow x y
Re=1E4
Gr=1E8
Ha=400
Buoyancy induced reversed flow
Velocity Profile (m/s)
High tritium concentration
Tritium concentration (mol/m3)
Downward
Upward
Using analyzed parameters

12. Tritium transport in a DCLL duct with PES slot
Behind FW
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.
PES at back wall
2a=0.06m, 2b=0.06m, RAFS wall 0.002m, FCI 0.002m, PES 0.003m, Gap 0.002m
Front wall
Rich phenomena !
Color scheme:
Purple: T diffusive flux,
Black: velocity,
Rainbow: T concentration
DCLL duct with PES
1.8 T used in the analysis
Color scheme: tritium concentration
PbLi flow
PES- pressure equalization slot

13. PES locations affect tritium transport in a DCLL-type poloidal duct
Tritium concentration profile

14. Tritium permeation rate vs. FCI electric conductivity
Ha, FCI conductivity effects on Tritium transport in a DCLL-type poloidal duct
Tritium Losses for Three PES Configurations
No PES
PES in the wall // B
PES in the wall ⊥ B
generation (mol/s)
1.406e-8
1.410e-8
1.412e-8
permeation (mol/s)
1.76e-10
1.99e-10
1.87e-10
Losses
1.25%
1.42%
1.32%
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.
Tritium permeation rate vs. FCI electric conductivity
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%.
Tritium losses for three PES configurations as Ha changes

15. By flowing PbLi in DCLL for heat removal results in a lower tritium partial pressure and permeation compared with HCLL
HCLL BU Analyzed
Flow and tritium near the turn-around region next to FW
1.8 T used in the analysis
Mass flow rate: 0.33 kg/s
Case
Average PbLi velocity in channel
Total tritium generation in
domain
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

16. 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

17. Velocity in the Gap between FCI and the Structural Wall Affects Tritium Transport in DCLL
Tritium concentrations (mol/m3) at mid-planes of a U-shaped DCLL channel for different gap inlet velocity
Back
velocity (m/s)
U-shaped duct
Tritium generation, inventory and permeation with a change of the gap inlet velocity
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
Tritium inventory (mol)
2.64e-6
3.57e-6
T exit rate from outlet (mol/s)
9.60e-8
9.44e-8
T permeation rate (mol/s)
1.16e-9
2.81e-9
Losses percentage (%)
1.2%
2.9%

18. Regarding He bubble: Initial Progress of the Effect of Helium Bubble on Tritium Transport in PbLi Mix-Convection MHD Flow
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.
CT_LM
CT2_bubble
Cbubbles g X B
Downward flow x y
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.

19. 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
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.
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-5 2
5.7e-11
2.5e-2
1.00e-5 3
5.54e-11
6.3e-2
1.04e-5

20. Summary Recommendations
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.

21. Backup -- MHD velocity profile
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
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.