Reactor Core Methods - Nuclear Energy Agency · Data is independent of reactor design ... 2-D assembly calculation with intermediate detail: ... Reactor Core Methods.

Reactor Core Methods Reactor Core Methods

Kord SmithStudsvik [email protected]

Reactor Core MethodsSmith - April 8, 2003

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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


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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?

Reactor Core Methods - Nuclear Energy Agency · Data is independent of reactor design ... 2-D assembly calculation with intermediate detail: ... Reactor Core Methods.

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