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Reactor Core Methods Reactor Core Methods
Kord SmithStudsvik [email protected]
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Presentation OutlinePresentation Outline
1. Background for LWR Core Analysis2. Modern LWR Design Requirements3. Factorization of the Core Analysis Space4. Early Analysis Methods5. Lattice Physics Applications6. Prerequisites For Advanced Nodal Models7. Lattice Physics Models8. Advanced Nodal Methods9. Assembly Homogenization10. Fuel Depletion Modeling11. Pin Power Recovery12. Nodal Method Verification13. Refinements/Applications14. Looking to the 21st Century
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1. Applications of Reactor Physics1. Applications of Reactor Physics
Chicago Pile (CP-1, December 2, 1942)
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1. Computational Requirements1. Computational Requirements
One Portable Super Computer:
Enrico Fermi
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1. Simple Core Models1. Simple Core Models
Four- and Six-Factor Formulas:
Fuel thermal “eta”
Thermal utilization factor
Fast fission factorResonance escape probabilityThermal non-leakage probability (geometry)Fast non-leakage probability (geometry)
mod
( )
,
,
....
eff th th fast
fuelf
th fuela
fuela
fuel clad eratora a a
th
fast
k f p L Lwhere
f
pLL
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1. Early Design of Reactors1. Early Design of Reactors
Built special experiments/fit parameters/use simple modelsMeasure eta, thermal utilization, fast fission, etc. Fit data to assumed functional form (e.g., fuel/coolant ratio, pin diameter, etc.)Geometrical approximations (thermal diffusion lengths, buckling, etc.) “Pencil and paper” designs
Built exact mockup criticals
Deduce few-group cross sections from criticals/integral measurements Simple computational models (i.e., 1-D, 2-D homogeneous diffusion theory)
Extensive use of good “Engineering Judgment”
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1. Focus of the 19501. Focus of the 1950’’ss
Hundred of reactors/criticals built of many designs
Analysis Progression:
Integral experiments/simple analytical methods
Integral experiments to deduce parameters/simple computational models
Differential cross sections measurements/complex computational methods/ criticals for testing/verification
Methods driven by Naval Reactors needs, (STR, Nautilus)
Shippingport Nuclear Power Station, critical in 1959
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1. Analytical Concepts of the 19501. Analytical Concepts of the 1950’’ss
Physical insight leads to simple mathematical models Resonance integralsNR and NRIM Approximations Equivalence theoryDancoff factors Resonance escape Slowing down kernels Flux disadvantage factors Fermi age theoryMigration area Thermal utilization factors Thermal diffusion lengths Critical buckling Reflector savings
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1. Extensive Model Improvements1. Extensive Model Improvements see ANLsee ANL--5800 (1963)5800 (1963)
Section 3: Constants for thermal homogeneous systems Thermal neutron spectrum Effective cross sections Thermal group diffusion parameters Slowing down parametersNon-thermal parameters Infinite multiplication
Section 4: Constants for thermal heterogeneous systems Thermal utilization Resonance escape probability Fast effectNeutron diffusion in lattices Integral data
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2. Cross Section Measurements2. Cross Section Measurements
Full energy range (0-20 MeV) measurements needed
Data is independent of reactor design
Requires reasonably complex computational models
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The Sexy Years of Nuclear The Sexy Years of Nuclear EngineeringEngineering
This slide has been intentionally removed
This presentation originally contained a slide which attempted to break the monotony and add levity to the presentation.
I am guilty of having given insufficient attention to the possible negative implications of this slide, and I would like to apologize to all those who have been injured as a result. Rest assured that I am now much more sensitive to such issues. I hope that you can forgive me for this lapse of judgment.
I would like to thank those who have had the courage to bring this to my attention.
Kord Smith
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2. Inexorable Link Between Digital 2. Inexorable Link Between Digital Computing/Reactor AnalysisComputing/Reactor Analysis
ENIAC
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2. Modern LWR Core Design2. Modern LWR Core Design
Fuel procurement analysis: Enrichment specification Burnable absorber design Economics analysis
Reload Core Design: Selection of “optimum” fuel loading pattern Selection of coolant flow and control rod strategy (BWR) Computations of margins to design safety limits
Static Safety Analysis: Calculations of nominal and off-nominal power shapes (“fly spec” analysis) Calculations of rod worths, shutdown margins, reactivity coefficientsDNBR analysis
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2. Modern Design Requirements2. Modern Design Requirements
Transient Safety Analysis: Reactivity insertion accidents Loss of coolant accidents Loss of off-site power
Operational Support: Pre-calculations of core monitoring data Calculations of startup sequences Computation of parameters needed for setting of operating limits
Core monitoring:On-line 3-D computation of margins (MCPR, MLHGR, etc)
Bottom Line: 10,000’s of core calculations required per cycle of operation
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2. Deterministic Transport2. Deterministic Transport
Scale of problem:Number of fuel Assemblies 200Number of axial planes 100Number of pins per assembly 300Number of depletion regions per pin 10Number of angular directions 100Number of neutron energy groups 100
Total unknowns 600 Billion
At 100 FLOPS/unknown on 1 gigaflop machine = 16 CPU hoursNot yet (or even soon) tractable for routine analysis
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2. Direct Monte Carlo?2. Direct Monte Carlo?
Scale of problem:Number of fuel Assemblies 200Number of axial planes 100Number of pins per assembly 300Number of depletion regions per pin 10Number of isotopes to be tracked 100 Total unknowns 6 billion tallies
Further complicating factors LWRs need ~1% statistics on assembly-wise peak pin power 106 histories yields 1.% statistics for one assembly (dominance ratio ~0.75) 106 x 200 x 100 =20 billion histories (~ 5000 hr on 2.0 GHz PC) Source distribution if far more difficult to converge for a full-core
(dominance ratio > 0.995) (50 times harder to converge than single assembly)
If Moore’s Law holds (factor of 2 every 18 months), LWR Monte Carlo core calculations will be reduced to 1 hr (single CPU) in the year 2030!
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2. Core Analysis Limitations2. Core Analysis Limitations
Cross Section KnowledgeExtremely ------------------------------------- small but asymptotic
Engineering LimitationsNot important -------------------------------- significant and asymptotic
Computer ResourcesNone ---------------------------------------------------- better, not asymptotic
Modeling ApproximationsMany --------------------------------------------------- fewer, not asymptotic
Year 1950 1960 1970 1980 1990 2000 ……….
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3. Factorization in the 19503. Factorization in the 1950--19601960’’s s
1-D pin-cell with great detail: Resonance treatment by “equivalence theory”Multigroup energy treatment with ~100 groups Few region cylindrical transport with collision probability methods
2-D assembly calculation with intermediate detail:Homogenize cross sections over square pin-cell regions Collapse pin-cell cross section to few groups (e.g., 2-4) 2-D finite-difference diffusion calculations
~3-D core calculations:Assembly homogenized cross sections Few groups (e.g., 1-2) Radial (1-D or 2-D) / axial (1-D)
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3. PWR Analysis in the 19603. PWR Analysis in the 1960--19701970’’s s
1-D pin-cell with great detail:
Resonance treatment by “equivalence theory”
Multigroup energy treatment with ~100 groups
Few region cylindrical transport with collision probability methods (i.e., LEOPARD code)
2-D core calculations with intermediate detail:
Homogenize cross sections over square pin-cell regions
Collapse pin-cell cross section to few groups (e.g., 2-4)
2-D finite-difference diffusion calculations (i.e., PDQ/HARMONY)
3-D flux synthesis
fine-mesh radial and 1-D axial (KAPL and BAPL)
3-D homogenized core calculations:
Homogenized cross sections
Few groups (e.g., 1-4)
2-D radial / 1-D axial factorization (“poor man’s” flux synthesis)
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3. BWR Factorizations3. BWR Factorizations
1-D pin-cell with great detail: Resonance treatment by “equivalence theory”Multigroup energy treatment with ~100 groups Few region cylindrical transport with collision probability methods
2-D assembly calculation with intermediate detail:Homogenize cross sections over square pin-cell regions Collapse pin-cell cross section to few groups (e.g., 2-4) 2-D finite-difference diffusion calculations
3-D core calculations:Assembly homogenized cross sectionsOne neutron energy group Full 3-D representation (one node per assembly radial) Thermal-hydraulic feedback required
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4. Early BWR Nodal Models4. Early BWR Nodal Models
Coarse Mesh Finite-Difference (CMFD) very inaccurate on assembly-size mesh
FLARE (1964)
where
6
1
6
1
( ),
1
pp p q
pp qpq
pp pqq
kS w S w S
w w
2 2 2(1 )( / 2 ) ( / )pq p pw g M h g M h
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4. Improved Nodal Models4. Improved Nodal Models
TRILUX
PRESTO
POLCA
SIMULATE
PANACEA
NODE-B
Common Features:
One unknown per assembly
One or one-and-a-half groups (fast/thermal leakage corrections)
Some “tunable” parameters
Albedo reflector models
Shortcomings:
Accuracy, 5-10% on assembly-averaged powers, dependent on core loadings
Memory requirements 20 Kbytes; CPU times ~ minutes per statepoint
Inconsistent (don’t satisfy diffusion equation in fine-mesh limit)
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5. Early Lattice Physics5. Early Lattice Physics
BWR bundle design requires 2-D lattice analysis: Large water gaps require enrichment distributions to control
local peaking Internal water rods used to enhance moderation at high voidGadolinium used as a burnable absorber Control blades are very localized absorbers
Early lattice codes simply used 2-D diffusion computations to capture spatial effects. Corrections used to treat finite-mesh (e.g., g-factors) Corrections used to treat transport effects (e.g., blackness theory)Depletion is performed for each pin
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5. WIMS: first 5. WIMS: first ““truetrue”” lattice codelattice code
WIMS pioneered the concept of modularity 69 group UKNDL libraryNumerous resonance models Pin-cell modelNumerous 2-D models:
Diffusion theory
Collision probability
Discrete ordinates
Method of Characteristics (much later) Depletion capabilities Parameter edits for many types of downstream tools:
Fine-mesh diffusion theory
Fine-mesh transport theory
Assembly-homogenized data for nodal codes
Applications in gas reactors, fast reactors, HWRs, and LWRs
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5. LWR lattice codes5. LWR lattice codes
WIMS (UKAEA) PHEONIX (ASEA ABB Westinghouse BNFL) CPM (Studsvik/EPRI) CASMO (Studsvik Scandpower)HELIOS (Studsvik Scandpower)DIT (C-E ABB Westinghouse BNFL)APOLLO-2 (CEA/Framatome/EDF)MULTI-MEDIUM (KWU Siemens Siemens/Framatome) TGBLA (Toshiba/G-E)DRAGON (Ecole Polytechnique Montreal)
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5. Data For 25. Data For 2--D Cartesian ModelD Cartesian Model
Physical Geometry 1-D Cylindrical 2-D Homogenized(white b.c.) Geometry
Problems:
1-D approximate b.c.
Preserving reaction rates in x-y geometry
x-y mesh effects
Transport-to-diffusion effects
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5. Fine5. Fine--mesh Diffusion Modelsmesh Diffusion Models
Use Lattice calculation directly to produce x-y data Select characteristic pin-types:
Edge pins
Water holes
Pins next to water holes
Burnable absorbers Compute SPH homogenization to approximately preserve reaction rates Iteratively compute “g-factors” to preserve average reaction rates
Extend lattice calculations to four ¼ bundles (colorset) Better estimates of edge pin reaction rates, flux gradients
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6. Advanced Nodal Models6. Advanced Nodal Models
Propositions: If one could solve accurately assembly-homogenized nodal diffusion problems,
one might be able to produce 3-D reactor solutions 100 times faster than using 2-D pin-by-pin methods.
By using lattice data directly, many of the difficulties of making pin-cell homogenized diffusion models match lattice results could be avoided.
Fast accurate nodal methods could permit transient analysis to be performed with much higher accuracy than obtained with existing methods
Accurate nodal methods can be used for both PWRs and BWRs
Required steps: Efficient assembly lattice physics toolsAccurately solve 3-D diffusion equations Define assembly-homogenized parameters directly from lattice calculations Reconstruct pin-wise powers and reaction rates Treat depletion effects
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M&C Solution to Methods M&C Solution to Methods DisagreementDisagreement
This slide has been intentionally removed
This presentation originally contained a slide which attempted to break the monotony and add levity to the presentation.
I am guilty of having given insufficient attention to the possible negative implications of this slide, and I would like to apologize to all those who have been injured as a result. Rest assured that I am now much more sensitive to such issues. I hope that you can forgive me for this lapse of judgment.
I would like to thank those who have had the courage to bring this to my attention.
Kord Smith
Reactor Core MethodsSmith - April 8, 2003
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7. Lattice Calculations7. Lattice Calculations
Complete set of lattice calculations for a BWR includes:
Depletion calculations:
Each depletion has about 50 burnup points
Depletions for 3 different voids (0, 40, 80%) both with/without control rods
Branches from each depletion, for all independent variable, at 20 points:
Void (3 points)
Fuel temperature (3 points)
Control rod (each type)
Bypass void (3 points)
Spacer type, detector type
Complete (HFP at least) set of calculations includes:
[50 x 3 x 2] + [20 x 3 x 2 x (3 + 3 + 1 + 3 + 2)] = 1740 total state points
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7. Lattice Physics Models 7. Lattice Physics Models
Discrete ordinates in homogenized Cartesian geometry
Collision Probability Methods (CP)
Current Coupling Collision Probability Methods (CCCP)
Method of Characteristics (MOC)
Monte Carlo Methods
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7. CCCP Spatial/Angular Coupling7. CCCP Spatial/Angular Coupling
MOX Pincell k-eff vs. angular representation
1.255
1.26
1.265
1.27
1.275
1.28
0 10 20 30 40
2 surfacesegments4 surfacesegments8 surfacesegments
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7. Long Characteristics (MOC)7. Long Characteristics (MOC)
Modeling Approximations:
Cyclic azimuthal tracking
Exact boundary conditions
Product quadrature (azimuthal x polar)
Flat Source (Step Characteristics)
Programming Considerations:
Efficient ray tracing
Minimize operations
Minimize storage
Minimize stride
1700 Statepoints requires about 1 CPU hr on 2.0 GHz PC
/ cos / cos, , , , , , (1 )
4m mg k j g k j
mgm m
g i j k g i j k mg
Qe e
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8. Advanced Nodal Methods8. Advanced Nodal Methods
Higher-order difference equations
QUABOX/CUBBOX
Classical finite-element methods
Many unknowns with 4-th or 5-th order expansions
Iterative solutions are costly because of tight coupling
Response matrix methods
High-order surface spatial representations needed
Intra-assembly heterogeneity and depletion difficult to model
Transverse integrated nodal methods
Most successful advanced nodal methods (as of 1980)
Most widely used for production analysis today
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8. Transverse Integration8. Transverse Integration
Transverse LeakageFit to Quadratic Polynomial
( , , ) ( , , ) ( , , ) ( , , ) ( , , )g g g g g g ag g gD x y z D x y z D x y z x y z Q x y zx x y y z z
' ' ' '' 1 ' 1
1( , , ) ( , , ) ( , , )G G
g g fg g gg gg geff
Q x y z x y z x y zk
1 1( ) ( ) ( ) ( ) ( )g gx ag gx gx gy gzD x x Q x L x L xx x y z
1 1( ) ( , , )
1( ) ( , , )
1( ) ( , , )
gx g
y
gy g gy
z
gz g gz
x dy dz x y zy z
and
L x dz D x y zz dy
L x dy D x y zy dz
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8. Polynomial Approximations8. Polynomial Approximations
4
0
0
1
22
3
24
( ) ( )
,( ) 1
( )
1( ) 321 1( ) ( )( )2 21 1 1( ) ( )( )( )20 2 2
gx gxn nx a f x
wheref x
xf xx
f x
f x
f x
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8. Popular Nodal Methods8. Popular Nodal Methods
Nodal Expansion Method (NEM, 1975-77)
Polynomial 1-D flux expansions
Quadratic transverse leakage fit
Partial current inner iterations
Analytic Nodal Method (ANM, 1972-1979)
Analytic solution to 1-D coupling equations
Buckling, flat, and quadratic polynomial transverse leakages
Node-averaged fluxes iteration
NGFM, DIF3-D Nodal, ILLICO, NESTLE, …..
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8. Non8. Non--linear acceleration methodslinear acceleration methods
Non-linear Iterative Acceleration (1983)
Applicable to most nodal kernels (NEM, ANM, etc.)
All iterations performed with 7-point (3-D) stencil
Minimized computer storage and CPU requirements
Accuracy in solving 3-D homogenized diffusion equation
~1.0% on nodal powers
3-D PWR/BWR statepoints about 5 CPU seconds on 2.GHz PC
T-H, cross section evaluation, boron searches, Xe search
1 1i i i i
g g g ggg gJ D D
x x
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9. Homogenization Equations9. Homogenization Equations
Known Reference Heterogeneous Solution:
Homogenized Equations:
Homogenized Constraints:
' ' ' '' 1 ' 1
1( ) ( ) ( ) ( ) ( ) ( ) ( )G G
g ag g g fg g gg gg geff
J r r r r r r rk
ˆˆ ( ) ( ) ( )
ˆ ( ) ( )
ii
i i
g g g gVV
g gS S
r r dr r dr
and
J r dS J r dS
' ' ' '' 1 ' 1
1ˆ ˆ ˆˆ ˆ ˆ ˆˆ( ) ( ) ( ) ( ) ( ) ( ) ( )G G
g ag g g fg g gg gg geff
J r r r r r r rk
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9. Homogenization Paradox9. Homogenization Paradox
Homogenized Parameters:
Which Surface?
ˆˆ ( ) ( )
( )
ˆ ( )
( )
i
i
i
i
g gVig
gV
gSi
gg
S
r r dr
r dr
and
J r dSD
r dS
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9. Koebke9. Koebke’’s Heterogeneity Factorss Heterogeneity Factors
Iterate on diffusion coefficients until HF+ and HF- are the same
Continuity (discontinuity) condition:
HF+
HF+
HF-
HF-
1 1i i i iHF HF
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9. Discontinuity Factors9. Discontinuity Factors
Let + - heterogeneity factors be different (Discontinuity Factors)
Approximate DF’s from single-assembly lattice calculation (ADFs)
HetHom
HetHom
ADF+ I
ADF- I+1
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9. Applications of ADFs9. Applications of ADFs
Use of ADFs reduces typical homogenization errors by about a factor of three:
PWRs 3-5% errors reduced to ~ 1.0%
BWRs 10% errors reduced to ~ 2.0-3.0%
Little computational burden:
Available as edits from lattice calculation
Treat as additional homogenization parameters
DFs very useful in treating PWR baffle/reflector as explicit nodes
1-D fuel/baffle/reflector problem used to generate DFs
Accounts for transport/diffusion effects
Accounts for inherent spatial/spectral approximations in nodal model.
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10. Intra10. Intra--assembly Depletion Effectsassembly Depletion Effects
First developed by Wagner and Koebke at KWU
Intra-assembly depletion (spatial) effects treated with space dependent cross sections (homogenized)
Track assembly-surface exposures and assume quadratic profiles of exposure
Treat spatially varying cross section contributions as addition non-linear sources – like transverse leakages.
1 1( ) ( ) ( ) ( ) ( ) ( ) ( )g gx ag gx gx gy gzD r x r x Q x L x L xx x y z
' ' ' '' 1 ' 1
1( , , ) ( ) ( , , ) ( ) ( , , )G G
g g fg g gg gg geff
Q x y z r x y z r x y zk
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10. Assembly Spectral Interactions10. Assembly Spectral Interactions
Interface instantaneous (spectral) effects
Interface depletion (spectral) effects
Important in 2 groups, reduced in importance as more groups are used
2 21
1 2
21
2
( )io a
o
a
a
2 21
1 20 0
21
20
( ) ( )1 1( )( ) ( )
( )1( )
E E
hao
Eo
a
e ede deE e E e
be de
E e
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11. Pin Power Recovery11. Pin Power Recovery
After nodal solution, pin powers must be recovered, as pin-wise limits are used in safety/licensing
Response matrix methods (Henry, MIT) indirectly yield pin powers
Large amount of data required
Accuracy limited by surface spatial expansions
Imbedded local calculations:
ROCS/MC
Perform assembly 2-D pin-by-pin diffusion with b.c. from 3-D nodal
Use axial shapes from 3-D nodal
Reasonably computationally intensive
SIMULA/SIMTRAN (Aragones and Ahnert)
Non-linear iteration methods used with coarse mesh 3-D LD F-D
Multiple planes of 2-D pin-by-pin diffusion
Direct pin power reconstruction by superposition of nodal and lattice powers
Pioneered by Wagner and Koebke at KWU
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11. Pin Power Reconstruction11. Pin Power Reconstruction
Assume separability of pin-wise powers from lattice code and the homogenized power shape from nodal code.
1. Iteratively determine flux shapes along the edges of the nodes:
Assume quadratic flux variation along an edge
Used edge-averaged fluxes, and continuity of flux and derivatives at corner points as constraints
2. Assume a non-separable form for the radial flux expansion within a node3. Use node-average fluxes, surface-averaged fluxes, and surface-averaged
fluxes, and corner point fluxes/derivatives as expansion constraints4. Use surface-integrated and node-average exposures to approximate the
intra-nodal shape of fission cross sections5. Integrate over “pin-cell” regions to get homogenized “pin” powers6. Multiply homogenized powers by lattice pin powers (peaking factors)
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12. Direct Nodal Method Verification12. Direct Nodal Method Verification
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12. Nodal Method Accuracy12. Nodal Method Accuracy
Operating Reactors
PWRs
Axially-integrated reaction rates ~ 1.0% rms
3-D reaction rates ~ 3.0% rms
BWRs
Axially-integrated reaction rates ~ 1.5% rms
3-D reaction rates ~ 3.0-6.0% rms
Pin powers vs. BOL criticals
Axially-integrated pin powers ~1.0% rms
Numerical tests vs. 2-D full core lattice depletion calculations
PWRs
Assembly powers ~1.0% rms
Pin powers ~1.5% max
MOX pin powers ~2.5% max
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13. Nodal Refinements13. Nodal Refinements
Hexagonal Geometry
KWU, ANL
Conformal Mapping (Chou)
MOX applications:
Analytic expansion functions
Form function refinements
Transport effects
More energy groups
Microscopic isotropic tracking
Elimination of nodal/reconstruction inconsistencies:
Finite-element like non-separable flux expansions (AFEN)
Iterative solution improvements
“re-homogenization” enhancements
Nodal methods (VARIANT code at ANL)
Direct treatment of cross sections heterogeneity
High-order heterogeneous flux expansions
Direct treatment of transport effects
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13. Extended Applications13. Extended Applications
Formal Core Loading Optimization:
Stochastic optimization
Simulated annealing (FORMOSA, SIMAN)
Genetic Algorithms
Direct Searches
10,000 to 100,000 of patterns are depleted to determine a core design
2-D initially and 3-D is presently feasible
On-line Core monitoring
Direct 3-D core calculations on-line
Automatic predictions of future reactor state
On-line computation of refueling shutdown margins
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13. Expanding Transient Applications13. Expanding Transient Applications
Growing application of 3-D transient methods
New physics testing procedures
Dynamic rod worth measurements
Eliminate traditional licensing approximations
Limits for PWR peak enthalpies for ejected rod accidents
Linking to systems thermal-hydraulic codes
Elimination of point and 1-D approximations
Virtually unlimited applications for systems analysis
Full scope training simulator core models
4-10 Hz executions with core design nodalization
Realistic cycle-specific core models (INPO 96-02)
Just-in-time training
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13. BWR transient applications13. BWR transient applications
Direct 3-D evaluations of decay ratios
On-line BWR stability analysis
On-line BWR stability predictions for proposed maneuvers
Out of Phase
In Phase
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14. New Factorization Boundaries14. New Factorization Boundaries
Direct 3-D pin-by-pin models (see PHYSOR 2002, Seoul, Korea)
Diffusion and transport
Pin-cell homogenization approximations?
Data explosion with detailed isotopics?
New “Synthesis” methods (see PHYSOR 2002, Seoul, Korea)
Direct use of full-core 2-D lattice calculations
Simplified axial transport coupling (very fine radial mesh)
Expanded Monte Carlo Applications
Lattice physics applications?
Steady-state core depletions?
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14. Accuracy Limitations14. Accuracy Limitations
Limits to accuracy improvements
Mechanical knowledge
Assembly mechanics (e.g., BWR channel bowing)
Crud buildup (e.g., axial offset anomaly)
Manufacturing uncertainties (e.g., IFBA coatings)
Fuel cycling history (e.g., fission gas migration)
Feedback modeling
Where is the water?
Local hydraulic information
Pin-wise fuel temperatures
Cross section uncertainties
Availability of refined ENDF sets
Unresolved resonance models
Thermal scattering models
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14. Concerns for the Future14. Concerns for the Future
Knowledge retention:
Who under the age of 40 understands resonance theory?
What is crystalline binding?
What is reactivity?
Too much reliance on the “black boxes” ?
When have we exceeded the applicability of the methods?
How do we establish analysis uncertainties?
Are we capable of building new reactor types?
How many people understand existing safety/licensing?
Is DOE capable of building a new generation reactor?
When will utilities be ready to invest in the next generation?