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**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

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**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

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**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

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**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

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**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

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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.

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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

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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, (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

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**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)

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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

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**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

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**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

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

Tritium concentration profile

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**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

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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

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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

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**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%

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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.

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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

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**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.

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**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.

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