1managed by ut-battelle for the department of energy oregon state seminar multi-physics and...
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1 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Multi-Physics and Numerical Complexities of Nuclear Reactor Simulation
Kevin Clarno
Tom Greifenkamp (U of Cincinnati)Stephanie McKee (MIT)
Reactor Analysis Group
of the
Nuclear Science and Technology Division
Oregon State University Nuclear Engineering Seminar
October 28, 2008
2 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Outline
Background on HOW reactor simulation is done
Discussion of some APPROXIMATIONS used
Examples and their EFFECT on the solutions Discussion of WHY solutions are accurate anyways
Conclusions on the need for IMPROVEMENT
But first a word from our sponsors…
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Nuclear @ ORNL Nuclear Science & Technology Division (NSTD)
All things nuclear
Space Nuclear Power Program Electricity generation, propulsion, shielding, materials
Fusion Engineering Division (FED) Teamed with Princeton as the US lead for ITER
Spallation Neutron Source (SNS) Neutron and atomic physics
Research Reactor Division (RRD) Materials testing, irradiation research, and isotope production HFIR: High-Flux Isotope Reactor - 80 MWt with HEU plate fuel
Radiation biology, medical physics, astrophysics, etc.
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NUCLEAR SECURITYTECHNOLOGIES
• Material protection, control, and accounting
• Safeguards
• Arms control assessments
• Export control
• Nuclear threat reduction
• Radiation detection
• Radiation transport
• Transportation technologies
• Fissile material detection
• Fissile material disposition
• Instrumentation
• Nuclear data and codes
• Criticality safety
• Reactor physics
• Radiation shielding
• Advanced/Space reactors
• Thermal hydraulics
• Material and fuel irradiation
• Information/Systems analysis
• Facility safety
• Risk assessment
• Regulatory support
• System instrumentation and controls
• Enrichment technology
NUCLEAR SYSTEMSANALYSIS, DESIGN,
AND SAFETYFUELS, ISOTOPES, AND NUCLEAR MATERIALS
• Nuclear fuels
• Heavy element production
• Stable/radioactive isotopes
• Medical isotope development
• Separations science and technology
• Nuclear process and equipment design
• Robotics
• Remote handling
• Chemical engineering
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Your opportunities at ORNL NESLS – Internships in Nuclear Engineering
Based in Nuclear Science & Technology Division, but not limited too it Highly competitive practicuum www.ornl.gov/sci/nuclear_science_technology/nstip/internship.htm
SULI – Engineering and Science Internships Less competitive, but only $475/week http://www.scied.science.doe.gov/SciEd/erulf/about.html
Wigner & Weinberg Fellowships (post-doc) Very prestigious; ~2 per year at ORNL 20% over competitive salary, 2 yrs of research freedom http://jobs.ornl.gov/fellowships/Fellowships.html
Full-time Staff and Post-Doc Positions Radiation Transport and Criticality Group: 3083, 3074 Nuclear Data Group: 2691 Nonproliferation: 3068, 3070 Reactor Analysis Post-doc: posted soon http://jobs.ornl.gov/
The SCALE nuclear analysis code package is inexpensive Source code is free to NE students and faculty A week-long, hands-on training course is only $1800
NESLS Weekly Stipend
Fourth Year (Senior) $831
Fifth Year (Graduate) $968
Masters Completed $1040
6 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
If you only remember one slide…
Just because it’s always been done one way, doesn’t mean it’s right.Question everything
Just because it was developed before you were born, doesn’t make it wrong.Understand WHY it (appears) to work
Be passionateExpress your passion so that the whole world sees it
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Reactor simulation requires modeling many coupled physics at many scales
ESBWR
Heat Transport
Thermo-Mechanics
Heat Generation
Irradiation Effects
Neutron Transport
Thermal-Hydraulics
Isotopic Transmutation
Heat Conduction
Thermal-Expansion
Irradiation-Induced Swelling
Material Changes
Fuel-, Clad-, Coolant-Chemistry
Thermal-Expansion
Irradiation-Induced Swelling
Material Changes
Fuel-, Clad-, Coolant-Chemistry
8 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Nuclear reactors are complex systems with a hierarchical structure
15 m
eter
s
Reactor Vessel Radial Slice
8 metersReactorCore
ESBWR
Single Lattice
20 c
m
5 m
m
Single Pincell
9 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Neutron transport: discretizing all space + energy/direction Cross section data:
Defined with 106 data-points to describe resonances
We cannot solve a problem with:5 orders of magnitude in space106 degrees of freedom per spatial elementPlus discretizing the direction of travel
If you don’t know about this, ask Palmer
10 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Neutron transport for reactors is modeled with a multi-level approach Level 1: Single Pincell
High-fidelity 1-D space on a small domain High-fidelity in energy Approximate BCs and state
Up-scale data to a coarser scale Provide “homogenized” or “effective” data
11 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
“Effective” multi-group cross section (g)
A weighted average of the continuous cross section ()
With an approximation to the neutron flux (W)
-100 -50 0 50 1001e+00
1e+01
1e+02
1e+03
1e+04
1e+05
Relative Neutron Energy
Flux
Group Cross-section
Cross-section
(b
arn
s)
( )( ) ( )
( )r,E r,E
r,Eg
g
g
Wr
W
σσ =
12 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
“Effective” multi-group cross section (g)
A weighted average of the continuous cross section ()
With an approximation to the neutron flux (W)
-100 -50 0 50 1001e+00
1e+01
1e+02
1e+03
1e+04
1e+05Flux
Group Cross-section
(b
arn
s)
Relative Neutron Energy
Cross-section
( )( ) ( )
( )r,E r,E
r,Eg
g
g
Wr
W
σσ =
13 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
1.E-06
1.E-03
1.E+00
1.E+03
1.E-04 1.E+00 1.E+04 1.E+08
Energy (eV)
Various Cross Sections
0.0E+00
2.0E-07
4.0E-07
Neutron Flux
1.E-06
1.E-03
1.E+00
1.E+03
1.E-04 1.E+00 1.E+04 1.E+08
Energy (eV)
Various Cross Sections
0.0E+00
2.0E-07
4.0E-07
6.0E-07
Neutron Flux
Neutron transport for reactors is modeled with a multi-level approach Level 1: Single Pincell
High-fidelity 1-D space on a small domain High-fidelity in energy Approximate BCs and state
Up-scale data to a coarser scale Provide “homogenized” or “effective” data
Level 2: Single Lattice Moderate-fidelity 2-D space on a larger domain Moderate-fidelity in energy Approximate BCs and state
Level 3: Full Reactor Core Low-fidelity for the full 3-D spatial domain Very low-fidelity in energy True BCs Coupled with other physics for true state
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Coupled physics?
1.E-06
1.E-03
1.E+00
1.E+03
1.E-04 1.E+00 1.E+04 1.E+08
Energy (eV)
Various Cross Sections
0.0E+00
2.0E-07
4.0E-07
Neutron Flux
1.E-06
1.E-03
1.E+00
1.E+03
1.E-04 1.E+00 1.E+04 1.E+08
Energy (eV)
Various Cross Sections
0.0E+00
2.0E-07
4.0E-07
6.0E-07
Neutron Flux
Level 1 & 2: Lattice Physics Pick a geometry Pick a thermal-fluid “base state” Solve all Level 1’s for each Level 2 Solve Level 2 transport problems
At a given time (burnup) for the base-state Solve depletion equations for a time-step
Quasi-static time-integration (burnup) Upscale data at the base-state for every time-step
At each time-step, “branch” to a new state Upscale data at each branch-point Include all branches to cover operational range
Level 3: Core Physics Solve coupled T-H/neutronics equations
T-H is as coarse-grained as neutronics Interpolate on “lattice physics” data
Solve depletion/kinetics equations for a time-step Quasi-static time-integration
15 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Thermal-hydraulics is more empirical (an outsiders view) Level 1: Microscopic level
Boiling water correlationsComputational Fluid Dynamics (in the future?)
Level 2: Bundle-levelSub-channel simulations (COBRA) Non-nuclear experimentsPower-flow, etc. correlations
Level 3: Full Reactor Core“Effective” 1-D T-H with cross-flow simulations
Embedded with assembly-specific proprietary data
RELAP, TRAC(E), etc.
16 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Where are the APPROXIMATIONS? Physics-Based Approximations
Are we accounting for all of the physics? Do we fully account for the fine-to-coarse scale complexity?
Numerical-Based Approximations Do the equations model the physics correctly? Do we “upscale” from fine-to-coarse consistently? Do we couple the physics correctly?
Even in transients?
Verification-Based Uncertainty Are there bugs in the codes? In the input decks? Do the codes work together consistently?
Sensitivity/Uncertainty Questions Uncertainty in data, numerical convergence Is error introduced going between solvers? What is the effect on the solution from each error? Are the uncertainties coupled?
17 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Several quick examples
Examples:Radial depletion and temperature-gradient in fuel
Do we couple the physics correctly?
Double-heterogeneity in a burnable absorber Are we accounting for the fine-to-coarse complexity?
Geometric and material changes during burnup Are we accounting for all of the physics?
Work in progress:Integration of TRITON and NESTLE
Do we “upscale” from fine-to-coarse consistently
Sensitivity/uncertainty tools within SCALE TSUNAMI and generalized perturbation theory in TRITON
18 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Approximation: “Fuel” is a single composition at a single temperature
Reality: Temperature varies radially
Conductivity in an oxide is small Isotopic concentrations varies radially
Due to resonance absorption
Effect: On End-of-Life isotopic concentrations
But your predecessors developed a fix: Use a single “effective” temperature
Engineering “fixes” can account for poorly-modeled coupled-physics
0
5 0 0
1 0 0 0
1 5 0 0
2 0 0 0
2 5 0 0
3 0 0 0
0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 4 . 5 5 . 0
R a d i a l D i s t a n c e f r o m C e n t e r ( m m )
Temperature (K)
H i g h P o w e r T e m p e r a t u r e P r o f i l e
H i g h P o w e r A v e r a g e T e m p e r a t u r e
N o m i n a l P o w e r T e m p e r a t u r e P r o f i l e
N o m i n a l P o w e r A v e r a g e T e m p e r a t u r e
F u e l C l a d d in gG a p
1 0 6 6 K
2 0 5 8 K
Radial temperature and depletion profile
Correct Standard Depletion OnlyValue % Error % Error
U238 2.1E-02 -0.1% -0.1%U235 1.8E-04 3.1% 3.5%Pu239 1.4E-04 5.2% 4.4%Pu241 4.3E-05 3.8% 3.7%
( )SCseffF TTTT −+=9
4,
Correct Standard Depletion Only Effective TValue % Error % Error % Error
U238 2.1E-02 -0.1% -0.1% 0.0%U235 1.8E-04 3.1% 3.5% 0.1%Pu239 1.4E-04 5.2% 4.4% 1.2%Pu241 4.3E-05 3.8% 3.7% 0.5%
0 . 0 E + 0 0
5 . 0 E - 0 5
1 . 0 E - 0 4
1 . 5 E - 0 4
2 . 0 E - 0 4
2 . 5 E - 0 4
3 . 0 E - 0 4
3 . 5 E - 0 4
1 2 3 4 5 6 7 8 9 1 0
R a d i a l R i n g N u m b e r ( 1 i s t h e i n n e r m o s t r i n g )
Atom Density (a/b-cm)
U - 2 3 5
P u - 2 3 9
P u - 2 4 1
19 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Several quick examples
Examples:Radial depletion and temperature-gradient in fuel
Do we couple the physics correctly?
Double-heterogeneity in a burnable absorber Are we accounting for the fine-to-coarse complexity?
Geometric and material changes during burnup Are we accounting for all of the physics?
Work in progress:Integration of TRITON and NESTLE
Do we “upscale” from fine-to-coarse consistently
Sensitivity/uncertainty tools within SCALE TSUNAMI and generalized perturbation theory in TRITON
20 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Heterogeneity of a burnable absorber
Single-heterogeneity 238U within a pin has a radial variation of “effective” cross sections This effect is reduced because the pin is in a lattice of other pins with 238U 1-D calculation accounts for this “single-heterogeneity”
Double-heterogeneity in particle fuel 238U within a fuel particle has a radial variation of “effective” cross section This effect is reduced because particle in a cluster of other particles within
a pebble It’s further reduced because the pebble is surrounded by other pebbles
Double-heterogeneity in a burnable absorber A BA is composed of pressed grains of Gd2O3 and UO2
Gd within a grain has a radial variation of “effective” cross section
The Gd2O3 grain is in a mixture of other grains within the BA
The BA is in a lattice of other pins, some of which have more Gd
21 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Model: Single BA in a mini-assembly
Vary grain-size to determine the double-het effect0 is a ‘standard’ single-het approach
Grains are generally 10-30 microns in diameterMicrostructure of fuel can effect macro-scale reactor performance,
but is small here.
0
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
0 . 1 1 1 0 1 0 0
G r a i n D i a m e t e r ( m i c r o n s )
Relative Difference in Eigenvalue (pcm)
a
0 %
1 %
2 %
3 %
4 %
5 %
6 %
7 %
8 %
9 %
1 0 %
Relative Difference in BP Rod Relative Power
aE i g e n v a l u e ( l e f t a x i s )
B P R o d P o w e r ( r i g h t a x i s )
0 . 9 7 1
0 . 9 7 2
0 . 9 7 3
0 . 9 7 4
0 . 9 7 5
0 . 9 7 6
0 . 9 7 7
0 . 0 1 0 . 1 1 1 0 1 0 0
G r a i n D i a m e t e r ( m i c r o n s )
Eigenvalue (Kinf)
3 6 . 5 %
3 7 . 0 %
3 7 . 5 %
3 8 . 0 %
3 8 . 5 %
3 9 . 0 %
3 9 . 5 %
4 0 . 0 %
Relative Power in BP Rod
E i g e n v a l u e ( l e f t a x i s )
B P R o d P o w e r ( r i g h t a x i s )
22 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Several quick examples
Examples:Radial depletion and temperature-gradient in fuel
Do we couple the physics correctly?
Double-heterogeneity in a burnable absorber Are we accounting for the fine-to-coarse complexity?
Geometric and material changes during burnup Are we accounting for all of the physics?
Work in progress:Integration of TRITON and NESTLE
Do we “upscale” from fine-to-coarse consistently
Sensitivity/uncertainty tools within SCALE TSUNAMI and generalized perturbation theory in TRITON
23 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Geometric changes during irradiation
- 1 0 0
0
1 0 0
2 0 0
3 0 0
4 0 0
H o t D e n s i f i e d C o l l a p s e d S w e l l e d
B o u n d i n g G e o m e t r i c S t a t e
Relative Difference of k
inf
(pcm)
W i t h o u t A x i a l
E x p a n s i o n
W i t h A x i a l
E x p a n s i o n
Cold: As-built geometry of fuel, gap, and cladding
Hot: Thermal-expansion (+1%) of clading and fuel (minutes) Relative reduction in volume-fraction of moderator Axial increase of the active core
Densified: Voids in oxide migrate to surface and fuel contracts (-2%) (days to weeks) Fuel radius and core height are reduced
Collapsed: Pressure from coolant compresses
cladding upon fuel (after cycle 1) Gap is eliminated, temperature drops Relative increase in moderator
Swelled: Irradiation-induced swelling leads to
fuel expansion (+3.5%) (EOL) Relative decrease in moderator
Geometric changes in fuel have a measurable, but small, effect on macro-scale reactor performance
24 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Fuel and Cladding Chemistry Effects Xenon and krypton:
Are produced in fuel, migrate to gap and the upper plenumAre strong neutron absorbers
-36 pcm per % of fission gas release (up to 10%)Lower the thermal-conductivity of the gap
Fuel temperature depends on gap-conductance
Corrosion and Crud on outer surface of cladding Increases the effective clad diameter, reducing moderatorContains absorbing materials
In BWRs, it has lead to very large axial offsets 8-12 pcm per micron (up to 100 microns)
In PWRs, it can contain boron from water
Hydriding in cladding Increases moderation due to additional H
0.4 pcm per ppm of H (up to 1000 ppm)
These are mostly localized errors that are small in a global sense
25 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Several quick examples
Examples:Radial depletion and temperature-gradient in fuel
Do we couple the physics correctly?
Double-heterogeneity in a burnable absorber Are we accounting for the fine-to-coarse complexity?
Geometric and material changes during burnup Are we accounting for all of the physics?
Work in progress:Integration of TRITON and NESTLE
Do we “upscale” from fine-to-coarse consistently
Sensitivity/uncertainty tools within SCALE TSUNAMI and generalized perturbation theory in TRITON
26 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Processed Nuclear
Data
End-to-End reactor analysis with open-source codes is difficult
Cross Section Library
3-D Neutron Transport,
Transmutation, Expansion NESTLE, NESTLE,
PARCS, etc. PARCS, etc.
T/H code
RELAP, RELAP, TRACE, etcTRACE, etc
T2N, T2N, PXS, PXS, etc.etc.
2-D Neutron Transport
NEWTNEWT
1-D Neutron Transport
CENTRMCENTRM
SCALESCALE
System Response
Data
Geometry Data
Heat Transfer
Data
TRITON Input
Isotopic Transmutation
ORIGENORIGEN
Advanced Reactor Analysis
SCALE Output
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Processed Nuclear
Data
NESTLE is being integrated with SCALE to make the whole process easier
SCALESCALE
All In-Core Physics
NESTLENESTLE
2-D Neutron Transport
NEWTNEWT
1-D Neutron Transport
CENTRMCENTRM
Isotopic Transmutation
ORIGENORIGEN
SCALESCALE
TRITON-NESTLE
Input
To “upscale” consistently
To ensure the consistency is maintained
To enable S/U analysis
For steady-state analyses
28 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Processed Nuclear
Data
Perhaps in the future it could be extended to transients?
SCALESCALE
Heat Transfer
Data
All In-Core Physics
NESTLENESTLE
Advanced Reactor Analysis
2-D Neutron Transport
NEWTNEWT
1-D Neutron Transport
CENTRMCENTRM
Isotopic Transmutation
ORIGENORIGEN
Out-of-Core T/H
RELAP, RELAP, TRACE, etcTRACE, etc
SCALESCALE
TRITON-NESTLE
Input
29 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Several quick examples
Examples:Radial depletion and temperature-gradient in fuel
Do we couple the physics correctly?
Double-heterogeneity in a burnable absorber Are we accounting for the fine-to-coarse complexity?
Geometric and material changes during burnup Are we accounting for all of the physics?
Work in progress:Integration of TRITON and NESTLE
Do we “upscale” from fine-to-coarse consistently
Sensitivity/uncertainty tools within SCALE TSUNAMI and generalized perturbation theory in TRITON
30 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
239Pu Fission Sensitivity Profiles:Sensitivity of keff to cross-sectiondata on an energy-dependent basis
ck=0.90
ck=0.65
TSUNAMI: Tool for S/U Analysis with XSDRN (1-D) and KENO-VI (3-D)
Determination of critical experiment benchmark applicability to nuclear criticality safety analyses
The design of critical general physics experiments (GPE)
The estimation of computational biases and uncertainties for the determination of safety subcritical margins
31 Managed by UT-Battellefor the Department of Energy Oregon State Seminar
Conclusions
Just because it’s always been done one way, doesn’t mean it’s right.Do we couple the physics correctly?Are we accounting for the fine-to-coarse complexity?Are we accounting for all of the physics?Do we “upscale” from fine-to-coarse consistently?
Just because it was developed before you were born, doesn’t make it wrong. Engineering “fixes” can account for poorly coupled physics Effects of fuel microstructure and geometric/material changes are small
Disclaimer: For existing LWRs with less than 5% enriched UO2 fuel, etc… These ASSUMPTIONS should not extend beyond this limited knowledge basis
Be passionateNuclear energy should be the primary solution for US energy needsBut we are restrained by a limited knowledge basisThere is much to be learned and new resources available
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What resources?
Interdisciplinary ResearchWe need to move away from “transport people” and “T-H experts” to
work and learn together Our physics aren’t separable, and we shouldn’t be either
MathematiciansGreat progress has been made with Krylov solvers, finite-element
methods, wavelet-basis functions, multi-grid acceleration, etc. Transfer the technology they developed to nuclear engineering
Open-source Software and ToolsUse them:
LAPACK, VisIt, MPI, HDF5, OpenMP, DOXYGEN, ZOLTAN, CUBIT, Metis, PETSc, Python, or their equivalent
If you’re writing code and don’t know what these are, find out
Big ComputersThe age of faster processors is gone - accept it - 3 GHz is it.
Learn how to write code for parallel chips and clusters