1 New PARCS Cross Section Model School of Nuclear Engineering Purdue University September 2002.
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Transcript of 1 New PARCS Cross Section Model School of Nuclear Engineering Purdue University September 2002.
1
New PARCSCross Section Model
School of Nuclear Engineering Purdue University
September 2002
2
Original XS Model in PARCS (1997)
At most seven cross section data points can be referenced
1 reference state 2 moderator branches 1 branches for each of other
variables: Cr, Tf,Tm,Sb
r: XS at unroded reference state
cr: Control rod XS; : roded fraction;
Tf: Fuel temperature; Tm: moderator temperature
Sb: Soluble Boron Density; Dm: moderator Density
2
2
2
),,,,( DmDm
SbSb
DmDm
TmTm
TfTf
SbDmTmTf crr
3
Example of Original Model comp_num 3 !corner reflector!------------------------------------------------------------------------------ base_macro 2.956090e-01 1.187820e-03 0.000000e+00 0.000000e+00 2.008080e-02 2.459310e+00 2.526180e-01 0.000000e+00 0.000000e+00 dxs_dppm 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 7.761840e-04 8.446950e-05 0.000000e+00 0.000000e+00
comp_num 4 !fuel 1!------------------------------------------------------------------------------ base_macro 2.221170e-01 8.717740e-03 4.982770e-03 6.111896e-14 1.824980e-02 8.031400e-01 6.525500e-02 8.390260e-02 1.101520e-12 dxs_dppm 3.478090e-08 1.285050e-07 -1.120990e-09 -1.761878e-20 -1.085900e-07 -9.765100e-06 7.088070e-06 -2.430450e-06 -3.190845e-17 dxs_dtm -2.033100e-06 2.121910e-07 1.247090e-07 1.430354e-18 8.096760e-07 -1.086740e-04 -3.155970e-05 -4.164390e-05 -5.467221e-16 dxs_ddm 1.356650e-01 1.551850e-03 9.206940e-04 1.023919e-14 2.931950e-02 9.926280e-01 2.526620e-02 2.477460e-02 3.252554e-13 dxs_dtf -3.091970e-05 3.497090e-05 6.401340e-07 7.154124e-18 -2.755360e-05 -1.372920e-04 -3.718060e-05 -5.630370e-05 -7.391879e-16 cdf 1.0069 0.9307 1.0034 0.9646 1.1040 1.4493 1.0096 1.1580
delcr_comp 1 1 -5 7 -11 !compostions that this set applies!------------------------------------------------------------------------------ delcr_base 3.732200e-03 2.477700e-03 -1.027860e-04 -1.214480e-15 -3.192530e-03 -2.199260e-02 2.558750e-02 -2.823190e-03 -3.702378e-14
4
Applications of Original Model:Static and Spatial Kinetics Problems
Eigenvalue Benchmark ProblemsIAEA3D, L336, …
OECD NEACRP Rod Eject Benchmarks Coupled Code Problems
OECD TMI MSLB OECD Peach Bottom Turbine Trip
Problems with Oconnee Control Rod Drive Cracking
(CASMO Tables format)
5
Depletion Capability Added (2000)
Nuclide depletion equation (Bateman)
)()()()()(
tNtNtNdt
tdNBBcCAA
aA
A
B
C
A
n,γ
β β
Absorb netron
''),',',()',',(
),,(4
1),,,(),(),,,(
1
' '
ddEtErEEr
tErStErErtErtv
E
s
ft
Neutron Transport Equation (Boltzmann)
6
Depletion XS Model
2
2
2
),,,,( DmDm
SbSb
DmDm
TmTm
TfTf
SbDmTmTf crr
Burnup and burnup “history” dependence More than seven data points can be referenced
)2,1,,()2,1,,(
)2,1,,()2,1,,(
)2,1,,()2,1,(
2
2
2
2
HISHISBUDmDmDm
HISHISBUDmDmDm
HISHISBUTmTmTm
HISHISBUTfTfTf
HISHISBUSbSbSb
HISHISBUcrcr
7
U.S. NRC Coupled Code Analysis
Lattice Code
(HELIOS/NEWT)
Cross Section Library
(PMAX)
Neutron Flux Solver
(PARCS)
Depletion Code
(DEPLETOR)
T/H code
(RELAP /TRAC)
ΦΣ
8
Application of Depletion Model
DOE NERI Projects: SBWR design HCBWR Design
Iteration required between PARCS and Depletor … computationally inefficient
Not able to handle generalized cross section tables
9
Standard “Two Step” Procedure for
Generating LWR Cross Sections
Lattice Calculation
s
XS library generator
Output files
Cross section library
XS interpreter
Neutronics Calculation
XS of each
region
10
First Step of in NRC Neutronic Code System
GenpXS
Output files
PMAXS
Lattice Codes:SCALEHELIOS
….
Input files
for depletion at various base states
and branches at some burnup points
11
Base State and Branches Performed with Lattice Physics
Code
Base state Branches
0GWD/T Fuel temp.
Tf1, Tf2…
mod temp.
Tm1, Tm2…
Mod. den.
Dm1, Dm2…
Soluble B.
ppm1, …
Control
rod …
5GWD/T
4GWD/T
3GWD/T
1GWD/T
2GWD/T
Fuel temp.
Tf1, Tf2…
mod temp.
Tm1, Tm2…
Mod. den.
Dm1, Dm2…
Soluble B.
ppm1, …
Control
rod …
12
Cross Section Library in NRC Neutronic Code System
PMAXS
Dependent Variables:
.......
,:2
,:
)(,:
,,,,,,,,:&
,:,:
...,,,,,,:
1
'
powerfluxFunctionsFormD
smultiplierfunctionsformninformatioDetector
ncalculatioMCPRforJfFactorsPeakingLocal
YYYYSectionsCrossSamariumXenon
parametersHeatDecayparametersNeutonDelay
CDFADFSectionsCrossPrinciple
Power
PmIXeISmPmXeISma
Xea
HH
ggtrffa
Independent Variables:
etcfunctionFormfactorLocalforLocation
GroupHeatDecayGroupNeutronDelay
groupenegyNeutronIDLatticevariablesOther
HTmHTfHSbHMdHCrvariablesHistory
TmTfSbMdCrvariablesousInstantane
,,
,,
,,:
,,,,:
,,,,:
13
PMAXS Depletor
Neutronic Calculation
XS of each region at given history
value
XS Model: Interpret XS base on
instantaneous variables
Power distributio
n
PARCS T/H Code:
RELAP
TRAC ….
Second Step of in NRC Neutronic Code
System
14
Format of PMAXS in Depletion
Cross Section ModelAppendix B. PMAXS format
----------------------------------------------------------------------
PMAXS (version 1.0, revision-01) ----------------------------------------------------------------------
Last revised 4/2/01 The Format of Purdue Macroscopic Cross Section (XS) Set ----------------------------------------------------------------------
Existence
File Data always
File identification
Fuel Assembly wise data (repeat for all kinds of assemblies) always
Assembly identification Assembly control data Assembly Group independent data Assembly Energy bound information data Reference state data always
Identification of the base state Control data of the base state State data of the base state Principal cross sections of the base state Scattering cross sections of the base state LORD > 0 Xe/Sm cross sections of the base state ISXE=1 Soluble boron cross section of the base state ISSB = 1 Delayed neutron data of the base state NDFAM > 0 Decay heat data of the base state NDCAY > 0 Power form function of the base state IPFF = 1 Group-wise form function of the base state IGFF=1 Detector information of the base state ISDE=1 Soluble Boron branch case IBSB > 0 Identification Control data State data (repeat for all soluble boron branch case) Derivation of the principal cross sections
15
Motivation for New PARCSCross Section Model
Old Model has limited accuracy and applicability for practical cross section data sets which are multi-dimensional tables (e.g. Ringhalls)
New Model performs multi-dimensional interpolation to construct partial derivates
This increases the range of applicability and yet preserves applicability of old PARCS XSEC files
16
Advantages of New Model
If there are more than 2 points in a line, then New Model is actually quadratic interpolation.
Can obtain good accuracy even with smaller number of branches
17
Ringhalls Stability Benchmark
Ringhals XS in TABLES format
Multiple 3-Dimensional tables Multiple Control rod compositions
),,(),,(
),,(),,(
),(),,,,,(
HCRCRDEXPCRDVOIEXP
TFUVOIEXPVOIHVOEXP
HVOEXPCRDTFUVOIHCRHVOEXP
HCRCRD
TFUVOI
base
18
Application of New Model to Ringhalls
),,,,(),,,,(
),,,,(),,,,(
),,,(),,,(),,,,(
mrm
rrmrrrm
i
rrrrii
rrrrr
TmTfSbDmTmTm
TmTfSbDmTfTf
TmTfSbDmSbSb
TmTfSbDmDmDm
TmTfSbDmTmTfSbDmTmTfSbDm
rTfTfTf 2/)( rm TfTfTf
If the XS at blue point are also available, New Model gives same XS as Model 2 better than Model 1Other wise New Model gives same XS as Model 1 better than Model 2
The partials will be obtained by piece wise linear interpolation
19
Important to Choose Best Sequence to Evaluate
Variables
mD
K
BD
K
fT
K
mT
K
mD Very Strong Strong Strong Very Strong
BD Strong Normal Normal Very Strong
fT Weak Weak Weak Normal
mT Almost no Almost no Almost no Strong
Suggested sequence: Dm DB Tf Tm
20
Example: Moderator temperature and density
450
500
550
600
0.30.4
0.50.6
0.70.8
0.9
0.86
0.88
0.9
0.92
0.94
0.96
Temperature
Original
DensityTm
Dm
415 515 615
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Selected point
Original Data point
),(),(),(),( mrmrr
DmTmDmDm
DmTmTmTmDmTmDmTm
21
Effect of Different Sequence: Using Temperature then Density
450500
550600
0.4
0.6
0.8
10.86
0.88
0.9
0.92
0.94
0.96
Temperature
linear interpolation
Density
450500
550600
0.4
0.6
0.8
1-0.04
-0.02
0
0.02
0.04
Temperature
error of linear interpolation, rms=0.01202
Density
),(),(),(),( mrmrr
DmTmDmDm
DmTmTmTmDmTmDmTm
22
Effect of Different Sequence: Using Density then Temperature
0.30.4
0.50.6
0.70.8
0.91
450
500
550
600
0.86
0.88
0.9
0.92
0.94
0.96
Density
linear interpolation
Temperature
),(),(),(),( mrmrr
TmDmTmTm
TmDmDmDmTmDmTmDm
0.30.4
0.50.6
0.70.8
0.91
450
500
550
600
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
x 10-3
Density
error of linear interpolation, rms=0.00098
Temperature
90% error reduced
23
Tree structure of states at which XS/partials are calculated or stored Ref. CR
calcul
XS Dm
partials calcul
XS SB
partials calcul
XS Tf
partials calcul
XS Tm
partials
Dm1 Dm1m Tf1 Tf1m
Tmr Tfr Tm1 Tm1m
Sbr
Tf2 Tf2m
Dmr
Sb1 Sb1m Dm2 Dm2m
Sb2 Sb2m
1: no
Dm3 Dm3m
Sbr
Tm2 Tm2m Tmr
2:SS
Tm3 Tm3m
Sbr
Tfr
Dmr Sbr Tfr Tmr
3:B4C
Sb3 Sb3m
Tf3 Tf3m
XS at reference states Calculate & Store
XS calculate
XS already calculated
Partials store
24
New PMAXS/XSEC Format Existence
1 Branches information NBRA>1 XS Set wise data Always
2 XS Set identification Always 3 Dimension data Always 4 Burnup and Restart information NEXP>1 History case wise data (repeat for each history case) Always 5 History case identification Always Reference state data Always 6 State identification Always XS Data Block (repeat for each burnup point) Always 7 Burnup point identification NBURN>1 8 Principal cross sections Always 9 Scattering cross sections Always 10 ADF Optional 11 CDF Optional 12 Local Power Peaking Factors Optional 13 Power form function Optional 14 Group-wise form function Optional 15 Detector information Optional 16 Xe/Sm cross sections Optional 17 Delayed neutron data Optional 18 Decay heat data Optional 19 End Label of XS Block Always Control rod branch cases (same structure with Ref. state case) IBCR>0 Moderator density branch cases (same structure) IBMD>0 Soluble Boron branch cases (same structure) IBSB > 0 Fuel temperature branch cases (same structure) IBTF>0
Moderator temperature branch cases (same structure) IBTM >0
*The data in XS Block are original data for reference state, data difference for CR branch case, and partials
for other branches
Existence 1 Branches information (repeat for all type of branches structures) NBRA>1 XS Set wise data Always
2 XS Set identification Always 3 Dimension data Always Reference state data Always 6 State identification Always XS Block Always 8 Principal cross sections Always 9 Scattering cross sections Always 10 ADF Optional 11 CDF Optional 12 Local Power Peaking Factors Optional 13 Power form function Optional 14 Group-wise form function Optional 15 Detector information Optional 16 Xe/Sm cross sections Optional 17 Delayed neutron data Optional 18 Decay heat data Optional 19 End Label of XS Block Always Control rod branch cases (same structure with Ref. state case) IBCR>0 Moderator density branch cases (same structure) IBMD>0 Soluble Boron branch cases (same structure) IBSB > 0 Fuel temperature branch cases (same structure) IBTF>0
Moderator temperature branch cases (same structure) IBTM >0 *The data in XS Block are original data for reference state, data difference for CR branch case, and partials for other branches
25
New Model Successfully Applied to Previous TRACM/PARCS Benchmarks
OECD MSLB & PBTT Benchmarks: NEMTAB format
* NEM-Cross Section Table Input ** T Fuel Rho Mod. Boron ppm. T Mod. 5 6 0 0******** X-Section set # 1 1** Group No. 1**************** Diffusion Coefficient Table * .5000000E+03 .7602200E+03 .8672700E+03 .9218800E+03 .1500000E+04 .6413994E+03 .7114275E+03 .7694675E+03 .7724436E+03 .7813064E+03 .8100986E+03 .1467049E+01 .1469641E+01 .1470751E+01 .1471347E+01 .1477128E+01 .1401975E+01 .1404351E+01 .1405441E+01 .1405939E+01 .1411216E+01 .1353822E+01 .1356107E+01 .1357086E+01 .1357581E+01 .1362596E+01 .1352366E+01 .1354638E+01 .1355630E+01 .1356125E+01 .1361236E+01 .1345620E+01 .1347891E+01 .1348843E+01 .1349338E+01 .1354390E+01 .1322122E+01 .1324319E+01 .1325308E+01 .1325803E+01 .1330615E+01**************** Total Absorption X-Section Table
26
Application of New XSEC Model to OECD Ringhalls Instability
Benchmark
Axial Power Distribution (HZP)
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30
Axial level
Re
lati
ve
Po
we
r
Entree No ADF Entree ADF PARCS-PMAXS-No ADF PARCS-PMAXS-ADF PARCS-ENTREE XS-No ADF
PARCS-ENTRÉE XS-NoADFKeff = 1.11430
ENTRÉE-ADFkeff=1.11508
ENTRÉE -No ADFkeff=1.11473
PARCS-PMAXS-ADFKeff = 1.11400
PARCS-PMAXS-No ADFKeff = 1.11465
27
Continuing Cross Section Work
Future work New interface between PARCS and Depletor
(12/31/02) GENPXS to convert other lattice code cross
sections to PMAXS (e.g. CASMO, ORNL SCALE/NEWT) (FY03)
28
Modifications of Cross Section Model for ESBWR
Task 3: Modifications in Spatial Kinetics FeedbackTask 3.1: Lattice Physics (Purdue) Improve cross section model in PARCS for ATRIUM-10 and GE-
12/14 The cross section model in PARCS will be improved to
provide feedback based on both bypass liquid temperature and channel internal fluid field.
Concerning fuel temperature feedback, the cross section model will be updated to handle both full length and part length fuel rods.
Perform lattice physics calculations The work on this subtask will be completed by November 30,
2002.
29
Advanced BWR Fuel Design Advanced BWR Fuel Design
GE-12 Fuel ConfigurationGE-12 Fuel Configuration
30
ATRIUM-10ATRIUM-10FramatomeFramatome
SVEA-96 (ABB)SVEA-96 (ABB)WestinghouseWestinghouse
1/3 part length1/3 part length
full lengthfull length
2/3 part length2/3 part length
Advanced BWR Fuel Design
31
Modifications for ESBWR (cont.)
Task 3.2: Monte Carlo Studies (Purdue) A new energy partitioning algorithm will be
developed for PARCS taking into account bypass water regions, water rod regions, intra-channel fluid regions, and fuel rods.
A Monte Carlo calculation will be performed to validate this new algorithm. All results will be documented.
The Monte Carlo study will be completed by December 31, 2002.
32
Modifications for ESBWR (cont.)
Task 3.3/3.4: Modify Mapping / Test Spatial Kinetics Feedback (ISL)
Modify Mapping to Accommodate new assembly cross section model
To test the spatial kinetics feedback with a Browns Ferry full core model will be built and a sample steady-state and control rod move transient calculation will be performed.
The spatial kinetics model feedback testing will be completed by February 28, 2003.
33
ESBWR Core Configuration ESBWR Core Configuration