Download - Monte-Carlo calculations in reactor design
Monte-Carlo calculations in reactor design
G.B. Bruna
FRAMATOME-ANP
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Monte-Carlo calculations in reactor design
• Samples :– HTR-10 Benchmark analysis,– Rhodium SPND detectors,– Mock-up experiments with void,– Others ....
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• Benchmark problem definition
• Sensitivity studies
• Main Results
HTR-10 Benchmark analysis
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• Benchmark problem definition
• 1) Cold (Temperature 300°K)• 2) U235 enrichment 3.3% à to 9.9%• 3) 31 or 33 element assemblies• 4) Two types of B4C burnable poisons
• 5) 20 different mediums (colors)• 6) He core-cooling channels• 7) 150 fuel elements (30 columns, cylindrical core)• 90 fuel elements (18 columns, annular core)• 8) Four Benchmark configurations :• - 18 columns - 19 columns • - 24columns - 30 columns
HTR-10 Benchmark analysis
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• Heterogeneity levels– Coated micro-balls (first level)
Compact (second level)Fuel assembly : 31 or 33 element compacts (third level)Axial superposition of 5 elements (forth level)
– Radial core loading (fifth level)
HTR-10 Benchmark analysis
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HTR-10 Benchmark analysis
Compact/Element
Burnable Poison
31-Element Assembly
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HTR-10 Benchmark analysis
Hexagonal Compact
HTR-10 Benchmark analysis
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Hexagonal Lattice
HTR-10 Benchmark analysis
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Cubic Lattice
HTR-10 Benchmark analysis
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Radial Heterogeneity inside the Hexagonal Compact
HTR-10 Benchmark analysis
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Unclustered 18-Column Core
HTR-10 Benchmark analysis
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Unclustered 19-Column Core
HTR-10 Benchmark analysis
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Unclustered 24-Column Core
HTR-10 Benchmark analysis
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Unclustered 30-Column Core
HTR-10 Benchmark analysis
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1/4 30-Column Unclustered Core
HTR-10 Benchmark analysis
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Clusters inside 30-Column Core
HTR-10 Benchmark analysis
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Clustered 30-Column Core
HTR-10 Benchmark analysis
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Adjusted Clustered 30-Column Core
HTR-10 Benchmark analysis
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• Sensitivity-studies (1 pcm = 1.E-5)
• Graphite impurities > 5000 pcm (total)• Dummy assemblies ~3000 pcm • Helium channels ~2000 pcm• Bullets lattice arranged vs. random < 200 pcm• Compact heterogeneity < 200 pcm• First-level homogenization < 500 pcm• Second-level homogenization 10000 pcm• Data Libraries JEFF2 vs. ENDF-BVI ~500 pcm
HTR-10 Benchmark analysis
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• Configuration Experiment Calculation
• 18 col. ann. core Sub-critical 0.99700• 19 col. ann. core Over-critical 1.01300
• clustered 24 col. • ann. core 1.0000 1.00110• clustered 30 col.• cylindrical core 1.0000 0.99980
HTR-10 Benchmark analysis
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• Core Average 5 Labs Japan(2), Holland, Russia, USA (ORNL)
• 18 col. ann. core Keff 1.02150
• clustered 24 col. critical rod ins. 82 cm ann. core
• clustered 30 col.• cylindrical core critical rod ins. 123 cm
HTR-10 Benchmark analysis
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• US-3D Device
• Physics of Rhodium SPN Detectors
• Monte-Carlo studies on :– heterogeneity– Rhodium burn-out
Rhodium SPN Detectors
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Rhodium SPN Detectors
CORE
MOVABLEFLUX
MAPPINGSYSTEM
US-3DALARMS
OPERATION AID SYSTEM
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Detectors
n
Generic detector (i, j, k)
Rhodium SPN Detectors
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Real Geometry (Sec. R-R)
Geometry Representation in APOLLO
MCNP APOLLO
Axial heterogeneity
Radial heterogeneity
Rhodium SPN Detectors
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0
0
1
10
100
1000
10000
1112131415161718191
Groupes MAI99
ba
rn
Rh103_DE Rh103_DETGTI
Six Groups Condenseted SectionsGroup E (eV) Without
SelfshieldingWith
SelfshieldingRatio
1 10.E+06 0.0428135 0.0428135 1.0002 9.07E+06 0.460451 0.4583355 0.9953 7.47E+03 3.824724 2.7712796 0.725
4 4.13 117.494919 117.624245 1.0015 0.625 63.2371979 63.316185 1.0016 0.134 82.2589493 82.2589645 1.000
Self-shielding effect
Rhodium SPN Detectors
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Rh10345
0.134 ev 0.625 ev 4.129 ev
5000 b
Gr. 6 Gr. 5 Gr. 4 Gr. 3
7.466 Kev
Gr.2
Gr. 1
0.907 Mev
10 Mev
The Rh microscopic absorption cross-section
Rhodium SPN Detectors
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88%
90%
92%
94%
96%
98%
100%
102%
0 1 2 3 4
GR.1
GR.2
GR.3
GR.4
GR.5
GR.6
Rh reaction rates
Rhodium SPN Detectors
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Rhodium SPN Detectors
Relative contribution of groups to RR.
0%5%
10%15%20%25%30%35%40%45%
1 2 3 4 5 6
Rh reaction rates
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Rhodium SPN Detectors
50.4%
28.4%
21.3%
RR per annular region
Rh reaction rates
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0,0%
5,0%
10,0%
15,0%
20,0%
25,0%
30,0%
35,0%
40,0%
45,0%
1 2 3
Apollo
MCNP
Rhodium SPN Detectors
Rh reaction rates
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• Physical analysis of heterogeneous void
• Monte-Carlo calculations of mock-up experiments:– EPICURE– ERASME– Others
Mock-up experiments with void
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Homogeneous VoidInfinite Medium
Heterogeneous VoidCluster
Void of mock-up experiments
IAEA Benchmark Sample Geometry
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Homogeneous Void Infinite Medium
Heterogeneous Void Cluster
Mock-up experiments with void
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UO2
MOX
Mock-up experiments with void
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• Cluster of 9 {10*10 pin} assemblies in Inf. Med. (pitch 1.26 cm), with a central MOX assembly with Pu enrichment:– HMOX 14.40– MMOX 9.70– LMOX 5.40– (UO2 3.35)
Mock-up experiments with void
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ii
i
ii
i
i
i
i
ii
i
ii
A
PIkk
A
AI
AP
k
*
,
,
Mock-up experiments with void
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• In the wet MMOX cluster, typical values of Kinf* and Imp* are the following:
• Zone Imp* Kinf*
• UO2 0.88 1.3697• MOX 0.12 1.1447• Whole Cluster 1.3427
– *Rouded off values
Mock-up experiments with void
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• In the MMOX cluster with central void, typical values of Kinf*and Imp* are the following:
• Zone Imp* Kinf*
• UO2 1.3697 0.96• MOX 0.7738 0.04• Whole Cluster 1.3458
– *Rounded off values
Mock-up experiments with void
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Wet MOX
XS
Flux
Dry
Mock-up experiments with void
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Dried zone
3.7% UOX
UOX-UOX EPICURE
Mock-up experiments with void
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MOX
3.7% UOX
Low and High Enrich. UOX-MOX EPICURE
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KEFF SSI INDEX inthe 7*7 pin
sample
MeasuredVoid Effect
Computed void effect(MCNP4/JEF2.2)
UH1.2 1.0016 7.5 _ _
UH1.2 30%void
1.0004 < 20 -543 50 -660 80
UH1.2 50%void
1.0005 < 20 -1111 50 -1220 80
UH1.2 100%void
1.0000 20 -2165 50 -2330 80
AVERAGE 1.0006 -1273 50 -1403 80
(Low Enrich. UOX-UOX EPICURE)
Mock-up experiments with void
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CONFIGURATION KEFF SSI INDEX in theVoided Zone
Measured Effect Computed Effect(MCNP4/JEF2.2)
UM 17x17 MOX 7%Reference
0.9986 30 0 0
UM 17x17 MOX 7%Central Bubble
0.9977 (1) < 80 -103 8 -90 40
UM 17x17 MOX 7%Bubble at +30 cm
0.9986 (1) < 80 -40 8 0 40
UM 17x17 MOX 7% 3Piled-up Bubbles
0.9961 (1) < 80 -230 8 -250 40
UM 17x17 MOX 17x17 5Piled-up Bubbles
0.9957 (1) < 80 -282 8 -290 40
UM 17x17 MOX 11%Reference
1.0007 40 0 0
UM 17x17 MOX 11%Central Bubble
0.9991 (1) < 150 -130 16 -160 40
AVERAGE VOIDEFFECT
_ -157 10 -158 40
(UOX-MOX EPICURE)
Mock-up experiments with void
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1) CONFIGURATION MODERATIONRATIO
SSI INDEX(Fuel)
MCNP4JEF2.2
MCNP4BVI
PU 11% ERASME SHexagonal
0.5 235 1.0042 1.0123
PU 11% ERASME R Hex. 0.9 100 1.0032 1.0065
PU 11% ERASME R Hex.SBC = 1150 ppm
0.9 106 1.0060 _
PU 11% ERASME RHex. SBC = 2490 ppm
0.9 110 1.0030 1.0077
AVERAGE _ _ 1.0041 1.0088
2) CONFIGURATION
PU 11% ERASME LPSqrd
2.1 30 1.0020 0.9994
PU 11% ERASME LGSqrd
2.1 < 40 1.0032 1.0032
PU 11% ERASME LGSqrd Control Rods
2.1 < 40 1.0039 1.0026
AVERAGE _ _ 1.0030 1.0017
(ERASME Series Experiments)
Mock-up experiments with void
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CONFIGURATION MODERATION
RATIO
SSI INDEX MCNP4JEF2.2
MCNP4BVI
GODIVA (5) 0 > 200 1.0003 0.9993
JEZEBEL (4) 0 > 360 0.9955 0.9968
ERASME (7) 0.5 à 2.1 >30<235
1.0036 1.0053
URANIUM LowCoolant/Fuel Ratio (4)
0.27 à 0.78 >10<80
1.0036 _
EPICURE (15) 1.2 >7<150
0.9993 _
AVERAGE (35) 1.0004
(Synopsis of All Experiments)
Mock-up experiments with void
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20 21 22 23 24 25 26 27 28
28 -0.2
27 2.9 -0.2
26 -0.6 1.7 2.3
25 -2.9 -0.7 -1.4 -1.6
24 -2.7 -1.7 -2.6 -5.0 -3.1
23 -1.3 -3.1
22 0.0 -3.7
21 -2.5
20 1.4 1.3
20 21 22 23 24 25 26 27 28
28 -3.3
27 --3.0 -5.0
26 -2.5 -1.6 -4.6
25 0.2 -1.6 -0.3 -1.8
24 2.8 -0.7 -1.9 -3.9 -1.9
23 2.1 1.2 2.6 0.1 -1.5 -0.5
22 2.0 5.2 4.2 1.1 1.2 3.1 -1.6
21
20
(Low Enrich. EPICURE with bubble)
Mock-up experiments with void
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20 21 22 23 24 25 26 27 28
28 2.0
27 -1.0 2.2
26 2.7 0.3 2.3
25 3.2 -1.0 -1.4 1.3
24 4.7 0.7 -2.9 1.7 0.0
23 -1.5 1.6
22 0.7 2.9
21 2.7 -3.7
20 0.0 0.9
20 21 22 23 24 25 26 27 28
28 -7.0
27 --6.0 -6.2
26 -4.8 -6.0 -5.5
25 -2.7 -4.0 -7.0 -4.0
24 -0.8 -0.7 -1.8 -0.3 -1.6
23 -3.0 -2.1 -2.2 -0.7 0.0 -2.0
22 -2.8 -1.4 -2.3 -1.1 0.7 -1.5 -2.3
21 -0.4 -1.4 -4.3
20 0.0 -1.4
(High Enrich. EPICURE with bubble)
Mock-up experiments with void
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• Discrepancies on reactivity are lower than 100 pcm on the average of 35 experiments, without any significant trend;
• No biases have been observed between JEF-2.2 and ENDFB-VI libraries, except for very hard spectra where ENDFB-VI overestimates reactivity up to 1000 pcm.
Mock-up experiments with void
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Others ...
• Other Monte-Carlo studies :– Criticality,– Sub-critical approach to divergence, – Fluence and vessel life-time.