the development of the 3d fuel behavior code offbeat...the development of the 3d fuel behavior code...
TRANSCRIPT
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The development of the 3D fuel behavior code OFFBEAT
A. Scolaro, EPFL
I. Clifford, PSI
C. Fiorina, EPFL
A. Pautz, EPFL - PSI PSI 07/11/2019
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Motivations for a novel fuel performance code
OpenFOAM Fuel BEhavior Analysis Tool (OFFBEAT):
- developed since 2 years at the LRS-EPFL and at the PSI.
- main focus are local multi-physics and multi-dimensional aspects of fuel behavior.
Recent fuel failure (Swiss NPP) and followup analysis at PSI.
- need for higher-fidelity tools.
Existing 2D/3D codes (BISON, ALCYONE, DIONISIO etc.) not easily accessible.
Lab expertise with OpenFOAM® C++ library
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C. Fiorina et al. “GeN-Foam: a novel OpenFOAM® based multi-physics solver for 2D/3D transient analysis of nuclear reactors”, 2015
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Not “just" CFD! OpenFOAM is a toolbox for PDEs solution and multi-physics problems.
Many applications outside of CFD, e.g.:
• Chemistry and combustion or fluid-structure Interaction.
• Nuclear Reactor Analysis (GeN-Foam at EPFL-PSI).
OpenFOAM as a toolbox for engineering applications3
Z. Tukovic et al. “OpenFOAM Finite Volume Solver for Fluid-Structure Interaction”, 2018
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OpenFOAM comes with useful features:• inherently 3D library, but 2D and 1D is
also possible;
• unstructured meshes and arbitrary geometry;
• data pre- and post-processing;
• equation discretization, meshing and parallel solution.
No need to modify underlying numerics!
Open-source code• EPFL now collaborating center on a new
IAEA project.
OpenFOAM as a toolbox for engineering applications4
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Finite Volume Method and segregated approach
OpenFOAM based on the FVM:
• simple problem definition and implementation.
• strongly conservative.
FVM and FEM share a number of features1.
FVM is gaining momentum for solid mechanics applications 2.
Segregated approach: each physics or component solved separately.
Iterations take care of explicit terms: solution is still implicit!
P. Cardif et al. “A Lagrangian cell-centred finite volume method for metal forming simulation”, 2016
1 Idelsohn, Onate, Finite volumes and finite elements: Two ‘good friends’, 19942 P. Cardif, Thirty years of the finite volume method for solid mechanics, 2018
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Outline
Motivations and main features
OFFBEAT structure
OFFBEAT development summary
Coupling and interaction possibilities
Conclusions
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OFFBEAT – StructureMaterial properties
• Densification
• Swelling
• Growth
• Relocation
• FRAPCON 1.5D
Behavioral models
• Density
• Conductivity
• Heat capacity
• Emissivity
• Poisson’s ratio
• Young’s modulus
• Heat conduction • Small strain
• Forsberg-Massih • Fixed source
• TUBRNP• Elasticity
• Zr pastic creep
Thermal sub-solver Mechanics sub-solverGap/Plena gas model
FGR models Heat Source Mechanical laws
• Gap conductance
• Frictionless contact
• Frictional Contact
Boundary conditions
For UO2 and
Zr.
Modular approach: independent C++ classes.
Classes exchange fields and communicate via functions.
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OFFBEAT – StructureMaterial properties
• Densification
• Swelling
• Growth
• Relocation
• Isotropic Cracking
• FRAPCON 1.5D
Behavioral models
• Density
• Conductivity
• Heat capacity
• Emissivity
• Poisson’s ratio
• Young’s modulus
• MOX properties
• Heat conduction • Small strain
• Large strain
• Forsberg-Massih
• Mechanistic
FGR
• Fixed source
• TUBRNP• Elasticity
• Zr pastic creep
• UO2 Creep
Thermal sub-solver Mechanics sub-solverGap/Plena gas model
FGR models Heat Source Mechanical laws
• Gap conductance
• Frictionless contact
• Frictional Contact
Boundary conditions
• TH model
Clad. outer T
For UO2 and
Zr.
Straightforward extension:
• Swapping existing with similar classes.
• Reusing open-source codes.
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Outline
Motivations and main features
OFFBEAT structure
OFFBEAT development summary
Coupling and interaction possibilities
Conclusions
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Previous works under linear-elastic framework
Asymmetric heat exchange under dryout conditions 1.
Preliminary validation of fuel centerline for 8 rods low burnup rods of the IFPE database2.
Fuel modeled as linear-elastic axisymmetric fuel rods
1 I.Clifford et al.,Studies on the effects of local power peaking on heat transfer under dryout conditions in BWRs, 20192 A.Scolaro et al., The OFFBEAT multi-dimensional fuel behavior solver, (soon available on NED)
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Preliminary FCT Validation –Results (1)
0-2 MWd/kg 2-15 MWd/kg
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25-40 MWd/kg15-25 MWd/kg
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Preliminary FCT Validation –Results (2)
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Renovated industrial and research interest.
Optimal testing ground for many important features.
Necessary ingredients for PCMI scenario analysis:
• Pellet-Cladding contact model
• Zircaloy rate-independent plasticity model;
• Zircaloy thermal and irradiation creep;
• Fuel isotropic cracking and creep.
• Frictional contact forceStarting Nov 2019
Current Main Focus –Analysis of PCMI/PCI Scenarios07/1
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Contact Model
Penalty method contact model with conservative surface mapping (AMI):
p = α*g*E
α = penalty factor, g = penetration, E = stiffness
Low penalty factor: helps convergence but might change the physics.
High penalty factor: more accurate but needs stronger under-relaxation.
Alternative approaches?
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Punch test from the NAFEMS. Hard problem (almost point contact)!
Contact Model Benchmark
Interfacial pressure on the cylinder outer surface
Level 1 Level 2
Level 3 Level 4
Normal Stress
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Zircaloy Plasticity and Creep Models
Rate independent von Mises plasticity model with linear strain hardening1.
Limbäck-Anderson creep model based on implementation in Peregrine 2.
Prandtl-Reuss flow-rule for multi-axial stress states Δ𝛆c,i =3𝛔dev
2σeffΔεc,eff
𝚫εc = f(σ) … but σ= 2𝛍ε+ 𝛌tr(ε) - 2𝛍εtc - 2𝛍𝚫εc
1 Simo, J.C. and Hughes, T.J.R., Computational Inelasticity, 19982 W. Liu et al. Numerical method of modeling creep of zirconium-alloy cladding in a multi-physics fuel performance code, 2013
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Plasticity Model Implementation
Residuals
Converged?
Assume elastic increment:
∆εn = ∆εel,n +∆εp,n-1
Calculate trial stress:
σtr,n(∆εel,n )
Start
t +𝜟t
Mechanics
Subsolver:
𝝏𝟐(𝛒𝑫)
𝝏𝒕𝟐= 𝜵 ⋅ 𝝈
End
t +𝜟t
Yes No
Iteration
n = n+ 1
Calculate plastic strain increment:
𝚫εp,n = 𝚫𝛌𝐧𝐧𝐧
Update stress tensor:
σn = 2𝝁εn+ 𝝀tr(εn) - 2𝝁εtp - 2𝝁𝜟εp,n
Yield criterion:
f(σtr,n, εp) >= 0 ?Yes
No
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Creep Model Implementation
Residuals
Converged?
Assume elastic increment:
∆εn = ∆εel,n
Calculate trial stress:
σtreff,n (∆εel,n )
Calculate effective stress:
σeff,n = σtreff,n - 3 𝝁𝜟εc,n−1
Calculate creep strain increment:
𝚫εc,n = f(σeff,n)𝜟t
Update stress tensor:
σn = 2𝝁εn+ 𝝀tr(εn) - 2𝝁εtc - 2𝝁𝜟εc,n
Start
t +𝜟t
Mechanics
Subsolver:
𝝏𝟐(𝛒𝑫)
𝝏𝒕𝟐= 𝜵 ⋅ 𝝈
End
t +𝜟t
Yes No
Iteration
n = n+ 1
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Plasticity and Creep Models Benchmarks
Plasticity 3D NAFEMS benchmark
Creep benchmark from Liu et al.
Code predictions match analytical results.
ParameterAnalytical
SolutionOFFBEAT
ሶεi [s-1] 3.08 E-10 3.08 E-10
ሶεth [s-1] 77.82 E-10 77.86 E-10
εp 3.527 E-3 3.529 E-3
εc,eff 4.336 E-3 4.339 E-3
εc,radial 1.987 E-3 1.990 E-3
εc,azimuth 4.331 E-3 4.334 E-3
εc,axial 2.344 E-3 2.344 E-3
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Plasticity benchmark Creep benchmark
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Plasticity Model – Test Case
6 pellets, MPS in the middle.
RIA-like scenario: 500 kJ/kg pulse of 40ms, total
transient time of 50s.
Perfectly plastic cladding.
Stress concentration in front of defect.
Geometry warped 50x
t = 36 ms t = 50 s
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Creep Model – Test Case
Axi-symmetric model with 10 pellets.
Dish and chamfers included.
Pellets attached through land.
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Two simulations: elastic and creep/plastic cladding.
Penalty factor = 1
Mesh: 26000 cells.
5 hours on one core (Intel® Xeon® CPU E5-1660 v4 with 8 3.2 GHz cores)
Creep Model – Test Case07/1
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Creep Model –Results07/1
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Creep Model – Test Case
End of phase at constant power,
t = 5000 hrs
End of simulation,
t = 5000 hrs + 160 s
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Development of OFFBEAT –Near future plans
Test-cases show feasibility for PCMI scenarios. Need for mechanical behavior validation:
• elongation and cladding deformation.
• PCMI benchmark from NEA.
• 3D validation?
Near future development efforts related to PCMI:• Fuel isotropic cracking and creep model.
• Frictional contact force.
PCI scenarios:• Coupling with thermochemistry (and CFD?)
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Outline
Motivations and main features
OFFBEAT structure
OFFBEAT development summary
Coupling and interaction possibilities
Conclusions
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Tc,o
OFFBEAT –Multi-physics and Coupling Possibilities
TRANSURANUS
Serpent
OpenFOAM CFD solvers
or GeN-FOAM
2D/3D
information
Initial
conditions
T Q(r)
q’’
T = temperature
Q(r) = power distribution
q’’ = heat flux
Tc,o = clad outer temperature
OFFBEAT
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SCIANTIX
Gap-gas conditions,
gaseous swelling
Farther down the road (?)
Fission rate
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Tc,o
OFFBEAT –Serpent Coupling
TRANSURANUS
Serpent
OpenFOAM CFD solvers
or GeN-FOAM
2D/3D
information
Initial
conditions
T Q(r)
q’’
T = temperature
Q(r) = power distribution
q’’ = heat flux
Tc,o = clad outer temperature
OFFBEAT
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SCIANTIX
Gap-gas conditions,
gaseous swelling
Fission rate
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Fuel power profile evolves with burnup!
• Complicated function of rod (and assembly) design parameters and enrichment.
Main effect: lower centerline temperature.
Traditionally in fuel performance codes either:
• impose radial profile or
• use simplified neutronics model e.g. TUBRNP module in TRANSURANUS
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Traditional approach:
+ computational cost.
+ well validated with traditional UO2 fuel in PWRs.
- fitting parameters for new fuel.
- one-group diffusion with strong absorbers.
- asymmetric cases?
Coupling fuel performance and neutron transport codes:
+ no need for fitting parameters.
+ could be used with strong absorbers or in non convential configurations.
+ could handle asymmetric cases.
- computational cost.
Motivations for OFFBEAT/Serpent Coupling07/1
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OFFBEAT/Serpent Coupling Scheme
Using the Serpent Multi-Physics
Interface.
A Python wrapper code coordinates the
two codes
Temperatures from OpenFOAM to
calculate cross sections.
Power profile from transport calculation.
Burnup simulation: compositions
handled within Serpent.
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PYTHON WRAPPER CODE, step (n)
SERPENT
Execute OFFBEAT
Update interface
Relax and write power
Run Serpent, Predictor
Wait for Serpent
BOS flux, cross sections, depleted material
Wait for OFFBEAT
Run Serpent,Corrector m
Q(n)
EOS flux, cross sections, depleted material
T(n)
m > mmaxNo
Yes
T(n-1)
BOS compositions
Next step
Beginning of step
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Fuel
Cladding
Water
Gas
Fuel Radius
Material
Linear power
Radial mesh
4.65 mm
UO2 (3.5 wt-% enriched)
20 W/mm
20 burnup zones
Gap width 190 µm
Cladding thickness
Material
0.535 mm
Zircaloy-4
Temperature
Boron concentration
Pitch
600 K
420 ppm
1.496 mm
Neutrons per cycle
Inactive cycles
Active cycles
Burnup scheme
Burnup step
Maximum burnup
Substeps
50,000
50
300
CE/LI
2 MWd/kg
102 MWd/kg
10
Serpent Parameters
Model DetailsPWR UO2 Rod
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Fuel
Cladding
Water
Gas
PWR UO2 Rod –Adaptive Search Mesh
Adaptive search mesh algorithm: Check only limited number of OFFBEAT
cells for each interaction point. Adaptive algorithm saves memory gradually refining mesh
Attention must be paid to statistics of each cells.
Higher number of cells more neutrons needed for smooth results.
Possible problem for asymmetric cases.
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Fuel
Cladding
Water
Gas
PWR UO2 Rod –Adaptive Search Mesh
Adaptive search mesh algorithm: Check only limited number of OFFBEAT
cells for each interaction point. Adaptive algorithm saves memory gradually refining mesh
Attention must be paid to statistics of each cells.
Higher number of cells more neutrons needed for smooth results.
Possible problem for asymmetric cases.
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PWR UO2 Rod - Results
Total Plutonium concentration evolution
Similar predictions at
low/medium burnup.
Different results at high
burnup.- Saturation for TUBRNP
- Buildup for coupling
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PWR UO2 Rod –Radial Profile
Power profiles comparison
239Pu radial profiles
No significant difference
for the radial profiles
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BWR UO2 Gd Rod
Serpent Parameters
Model Details
BWR Serpent model
Gad OFFBEAT
No gad 4
No gad 3
No gad 2
No gad 1
No gad 5
Gad
Cladding
Water
Radius
Material
Power density
Gd-pins content
Temperature
Radial mesh
(coupled)
5 mm
UO2 (3 wt-% enriched)
20 W/g
3 wt-%
873.15 K
10 burnup zones
Cladding thickness
Material
Temperature
0.5 mm
Zircaloy-2
573.15 K
Neutrons per cycle
Inactive cycles
Active cycles
Burnup scheme
Burnup step (<10 MWd/kg)
Burnup step (>10 MWd/kg)
Maximum burnup
Substeps
50,000
50
300
CE/LI
0.25 MWd/kg
5 MWd/kg
100 MWd/kg
10
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Total Plutonium concentration evolution
• More pronounced
differences.
• Differences start at the
beginning of the irradiation.
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BWR UO2 Gd Rod –Radial Profile
239Pu radial profiles
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BWR UO2 Gd Rod –Radial Profile
Gd evolution with burnupPower profiles comparison
High burnup
Power profiles comparison
Low burnup
Power profile
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Gd evolution
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OFFBEAT/Serpent Coupling – Follow up
Preliminary tests provide promising (and expected) results.
Computational cost is high no relevant gain for traditional fuel.
Interesting solution for: • new fuel types obtaining fitting parameters?• experiments with non-traditional features.• asymmetric scenarios.
Y. Robert (now PhD student at Berkley) will continue to work on the project.
Aim is to prove feasibility of OFFBEAT/Serpent coupling for more realistic scenarios.
Examples:• 2D assembly with Gd-rods or void channel with angular binning of neutron flux.• 3D partial insertion of control rods in PWR.
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Tc,o
OFFBEAT –SCIANTIX Coupling
TRANSURANUS
Serpent
OpenFOAM CFD solvers
or GeN-FOAM
2D/3D
information
Initial
conditions
T Q(r)
q’’
T = temperature
Q(r) = power distribution
q’’ = heat flux
Tc,o = clad outer temperature
OFFBEAT
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SCIANTIX
Gap-gas conditions,
gaseous swelling
Fission rate
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Tc,o
Collaboration with the JRC Karlsruhe
TRANSURANUS
Serpent
OpenFOAM CFD solvers
or GeN-FOAM
2D/3D
information
Initial
conditions
T Q(r)
q’’
T = temperature
Q(r) = power distribution
q’’ = heat flux
Tc,o = clad outer temperature
OFFBEAT
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SCIANTIX
Gap-gas conditions,
gaseous swelling
Fission rate
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Collaboration with the JRC Karlsruhe
Visiting stay starting soon (thanks to ENEN+).
Primary objective: analysis of fuel creep experimental results. use advanced tools for designing and interpreting non-traditional experiments?
Secondary objective: first strategy for OFFBEAT-TRANSURANUS coupling.
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TRANSURANUS
2D/3D
information
Initial
conditions
OFFBEAT
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Conclusions
OFFBEAT, a new open-source fuel behavior solver with focus on multi-
dimensional and multi-physics aspects of fuel behavior.
Efforts have focused on implementation, mainly for PCMI/PCI
capabilities.
Need for more validation and applications!
OFFBEAT is open to various coupling possibilities:
- OpenFOAM CFD (or GeN-Foam)
- SCIANTIX
- Serpent
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Merci