Outline Recent trends of advanced core analysis methods Overview - - PDF document

SLIDE 1

Development of GENESIS, a general three- dimensional transport code based on the Legendre polynomial Expansion of Angular Flux method Akio Yamamoto*), Akinori Giho, Tomohiro Endo*) *) Nagoya University

1

2018 Symposium on Nuclear Data, Nov. 28, 2018 Multi-Purpose Digital Hall & Collaboration Room (Ookayama campus, Tokyo Institute of Technology, Meguro, Tokyo)

Outline

 Recent trends of advanced core analysis

methods

 Overview of GENESIS  LEAF method  Geometry treatments  Verification results  Summary

2

SLIDE 2

Recent trends of advanced core analysis methods

3

Recent trends (US)

 (International) Nuclear Energy Research Initiative (NERI,

I-NERI)

 Consortium for Advanced Simulation of Light Water

Reactors (CASL)

 3D transport calculation in heterogeneous geometry

 DeCART, MPACT

4 https://www.casl.gov/

SLIDE 3

Recent trends (ROK)

 DeCART developed by I-NERI project  nTRACER developed by SNU

5 http://neutron.snu.ac.kr/node/7

Recent trends (China)

 Many activities in Xi’an Jiaotong University and related

reactor physics group

 3D pin-by-pin (cell homogenous) transport code

6

• B. Zhang et al., “Heterogeneous Neutron Leakage Model for PWR Pin-by-pin Calculation,”
• Ann. Nucl. Energy, 110, 443 (2017).

SLIDE 4

Recent trends (EU)



CEA and EdF are developing next generation core analysis code for fast reactors

7

• D. Schneider et al., “APOLLO3: CEA/DEN Deterministic Multi-Purpose Code for Reactor Physics Analysis,”
• Proc. PHYSOR2016

Outline of the GENESIS code

8

SLIDE 5

Outline of GENESIS

 Multigroup neutron and photon

transport calculations

 Major target: reactor cores

 Generalized geometry treatment  Deterministic methods

 3D LEAF、

2D MOC

 Multi-group cross sections are provided

by other codes

 Linkages to SRAC2006, Free-FIDO format

are implemented

9

Legendre polynomial Expansion of Angular Flux (LEAF) method

10

SLIDE 6

LEAF method

11

z x y x y z x y z s

LEAF method

12

SLIDE 7

LEAF method

13

s  s   z  z   s z

𝜔, 𝑨 𝜔, 𝑡 𝜔, 𝑨 𝜔, 𝑡

𝑟 𝑡, 𝑨

Planar MOC vs LEAF

14 http://neutron.snu.ac.kr/node/7

z x y z s

Planar MOC MOC for radial direction (2D) Low order calculation (e.g. diffusion, SPn) for axial direction

LEAF No approximation

SLIDE 8

Geometry treatment by GENESIS

15

Geometry – overview

 3D geometry is expressed as stack of planes  Use combinatorial geometry for radial direction 16

https://phys.org/news/2013-07-casl-milestone-validates-reactor-tva.html http://neutron.snu.ac.kr/node/7

SLIDE 9

BWR – 3x3 fuel assemblies BWR – flux regions

SLIDE 10

BWR – 3x3 fuel assemblies KAIST benchmark problem (Cho et al.)

SLIDE 11

C5G7 hexagonal benchmark (Joo et al.) PWR – 4 loop type, full core with baffle reflector

SLIDE 12

Seed – blanket fuel CANDU

SLIDE 13

25

Large FBR

26

FBR fuel assembly with wrapper tube

SLIDE 14

Verification calculations

27

C5G7 3D benchmark problem

28

Rodded A, Rodded B Rodded B

SLIDE 15

C5G7 3D benchmark problem

29

0.13 0.25 0.64 0.34 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Genesis Chaplet-3D CRX MCCG3D RMS difference (%)

RMS error of pin-by-pin fission rate (Rodded-B)

C5G7 3D void benchmark problem

30

Void-A Void-B

SLIDE 16

C5G7 3D void benchmark problem

31

Pin-by-pin fission rate in Void-A condition (axially integrated)

C5G7 3D void benchmark problem

32

• 0.29% -0.14% -0.12%

0.02% 0.01% 0.17% 0.03% 0.05% 0.20% 0.06% 0.04% 0.18% 0.06% 0.08%

• 0.01% -0.04% -0.07% -0.09% -0.12%

0.02% 0.02% 0.04% 0.05%

• 0.02% -0.02% -0.03% -0.02% -0.04%

0.02% 0.03%

• 0.03% -0.05% -0.20% -0.30%

1.00%

• 0.15%

0.06%

• 0.13% -0.06%

0.13%

• 0.04%

0.14%

• 0.03%

0.28%

• 0.04%

0.13% 0.03% 0.16% 0.01%

• 0.05%

0.07%

• 0.05% -0.04%

0.08%

• 0.17%

0.02% 0.10% 0.04%

• 0.03%

0.01% 0.00%

• 0.03% -0.01%

0.01% 0.01% 0.00%

• 0.20% -0.13% -0.24%

0.80%

• 0.10% -0.15%

0.04% 0.06% 0.10%

• 0.02%

0.18% 0.18% 0.00% 0.11% 0.10% 0.05%

• 0.08% -0.04% -0.04% -0.22% -0.01%

0.04% 0.02%

• 0.02% -0.03%
• 0.02% -0.02%
• 0.01% -0.03% -0.10% -0.32% -0.23%

0.60% 0.02%

• 0.05%

0.06%

• 0.02% -0.03%

0.09% 0.18% 0.09% 0.20% 0.12% 0.04% 0.03% 0.08% 0.02% 0.05%

• 0.02% -0.01% -0.06%

0.04% 0.06%

• 0.02% -0.03% -0.03% -0.02% -0.03%

0.02% 0.02%

• 0.12% -0.13% -0.21%

0.40% 0.00% 0.13% 0.09%

• 0.02%

0.12% 0.05% 0.04%

• 0.05%

0.01%

• 0.04%

0.08% 0.09% 0.12% 0.01% 0.10% 0.12%

• 0.09% -0.11% -0.06% -0.16%

0.02% 0.06% 0.01%

• 0.06%

0.01%

• 0.03% -0.03% -0.04%

0.00%

• 0.01% -0.01% -0.18% -0.20% -0.28%

0.20% 0.16%

• 0.04%

0.00% 0.08%

• 0.17%

0.13% 0.12%

• 0.12%

0.11% 0.05%

• 0.02%

0.05% 0.02%

• 0.22%

0.01% 0.04%

• 0.05% -0.03%
• 0.04% -0.04%

0.01%

• 0.05%
• 0.33% -0.16%

0.00% 0.05% 0.15%

• 0.04%

0.09% 0.05%

• 0.17%

0.04% 0.08% 0.11% 0.08% 0.05%

• 0.12%

0.06% 0.10% 0.05% 0.11%

• 0.07% -0.09% -0.05% -0.11% -0.03%

0.08%

• 0.04% -0.04%

0.00%

• 0.03% -0.01% -0.05% -0.03%

0.04%

• 0.06% -0.15% -0.17% -0.26%
• 0.20%

0.08%

• 0.05%

0.18% 0.19%

• 0.04%

0.12% 0.07%

• 0.10% -0.13% -0.06%

0.10% 0.13%

• 0.01%

0.17% 0.13%

• 0.01% -0.03% -0.06% -0.13% -0.04%

0.08% 0.08% 0.01%

• 0.03% -0.02% -0.04% -0.05% -0.02%

0.02% 0.04% 0.02%

• 0.09% -0.23% -0.20%
• 0.40%

0.18% 0.29% 0.12%

• 0.01%

0.11%

• 0.12%
• 0.13%

0.14% 0.05% 0.12% 0.16% 0.00%

• 0.07% -0.09%
• 0.20%

0.12% 0.04%

• 0.01%

0.00% 0.05% 0.08%

• 0.21%
• 0.20% -0.21%
• 0.60%

0.08%

• 0.03%

0.17% 0.18%

• 0.04%

0.11% 0.08%

• 0.08% -0.10% -0.04%

0.12% 0.15% 0.01% 0.17% 0.14% 0.01%

• 0.03% -0.05% -0.10% -0.04%

0.08% 0.12% 0.02% 0.01% 0.00%

• 0.01% -0.02%

0.00% 0.03% 0.07% 0.05%

• 0.07% -0.20% -0.17%
• 0.80%

0.06% 0.15% 0.01% 0.10% 0.05%

• 0.12%

0.04% 0.07% 0.11% 0.09% 0.08%

• 0.07%

0.09% 0.14% 0.06% 0.11%

• 0.03% -0.08% -0.01% -0.04%

0.03% 0.08% 0.02%

• 0.01%

0.02% 0.03% 0.01%

• 0.02%

0.00% 0.06%

• 0.02% -0.10% -0.10% -0.22%
• 1.00%

0.17% 0.02% 0.04% 0.09%

• 0.12%

0.14% 0.14%

• 0.07%

0.10% 0.07% 0.02% 0.08% 0.07%

• 0.12%

0.10% 0.10% 0.01% 0.02% 0.01% 0.01% 0.07% 0.03%

• 0.22% -0.07%

0.05% 0.14% 0.12% 0.05% 0.13% 0.08% 0.08%

• 0.01%

0.03% 0.02% 0.11% 0.10% 0.13% 0.08% 0.15% 0.14%

• 0.03% -0.07%

0.05%

• 0.04%

0.08% 0.15% 0.09% 0.02% 0.07% 0.08% 0.04% 0.03% 0.08% 0.08% 0.07%

• 0.09% -0.08% -0.17%

0.08% 0.00% 0.09% 0.05% 0.05% 0.11% 0.17% 0.10% 0.17% 0.12% 0.08% 0.08% 0.13% 0.05% 0.07% 0.03% 0.08% 0.02% 0.09% 0.11% 0.02% 0.04%

• 0.08%

0.04% 0.02% 0.08% 0.08%

• 0.03%

0.00%

• 0.09%
• 0.02% -0.06%

0.04% 0.08% 0.10% 0.02% 0.14% 0.12% 0.04% 0.13% 0.14% 0.08% 0.00% 0.01% 0.00%

• 0.14%

0.04% 0.03%

• 0.01%
• 0.02% -0.02%
• 0.01% -0.01%

0.00% 0.02% 0.00%

• 0.22% -0.08%
• 0.05%

0.07%

• 0.09%

0.02% 0.12%

• 0.03%

0.11% 0.00% 0.15%

• 0.01%

0.10% 0.02% 0.13% 0.05%

• 0.01%

0.09% 0.00%

• 0.06%

0.11%

• 0.14%

0.06% 0.07%

• 0.06% -0.04% -0.05% -0.04% -0.06%

0.01%

• 0.02%

0.05% 0.08%

• 0.13%

0.03%

• 0.10%
• 0.09% -0.06% -0.04%

0.05%

• 0.09%

0.07%

• 0.07% -0.04%

0.00%

• 0.03% -0.05%

0.07%

• 0.03%

0.07% 0.00% 0.00%

• 0.04% -0.02% -0.06%

0.00% 0.01%

• 0.05%

0.04%

• 0.05% -0.04% -0.05% -0.03% -0.05%

0.02%

• 0.01%

0.01% 0.01%

• 0.08% -0.12%
• 0.10% -0.05% -0.04% -0.02% -0.11%

0.03%

• 0.09% -0.06% -0.07% -0.06% -0.09%

0.07%

• 0.08%

0.03%

• 0.01% -0.05% -0.01% -0.05% -0.03% -0.02%

0.01%

• 0.03%

0.03%

• 0.02% -0.02% -0.02% -0.02% -0.03%

0.02%

• 0.03%

0.01%

• 0.02% -0.02% -0.03%
• 0.13%

0.08%

• 0.21% -0.01% -0.06% -0.22% -0.06% -0.14% -0.09% -0.10% -0.02% -0.12%

0.04% 0.08%

• 0.14%

0.10%

• 0.05% -0.02%

0.03%

• 0.05% -0.01%

0.05%

• 0.02%

0.03%

• 0.01%

0.05%

• 0.02%

0.02%

• 0.02%

0.01%

• 0.01% -0.03%

0.00%

• 0.01%

0.02%

• 0.16%

0.00%

• 0.06% -0.15%
• 0.11% -0.04%
• 0.04% -0.04%
• 0.05%

0.02% 0.05%

• 0.14%

0.00%

• 0.01% -0.04%

0.00% 0.01% 0.03% 0.00% 0.04% 0.04%

• 0.02%

0.02% 0.01% 0.00% 0.00%

• 0.02%

0.02% 0.02% 0.04% 0.02% 0.00%

• 0.03%

0.08%

• 0.20%

0.07% 0.02% 0.09% 0.08% 0.03% 0.06% 0.01% 0.02% 0.00% 0.02%

• 0.01%

0.00% 0.03% 0.04% 0.03% 0.05% 0.03% 0.01% 0.00% 0.02% 0.01% 0.03% 0.04% 0.10% 0.02% 0.04% 0.06% 0.04% 0.08% 0.09% 0.12% 0.12% 0.08% 0.10% 0.15% 0.09%

• 0.01%

0.07%

• 0.05% -0.02%

0.05% 0.03%

• 0.01%

0.02% 0.01% 0.01%

• 0.01% -0.01% -0.01%

0.03% 0.02% 0.02% 0.01% 0.03% 0.03% 0.06% 0.04% 0.04% 0.06% 0.01%

• 0.04%

0.01% 0.02% 0.02% 0.10% 0.11%

• 0.05%

0.04% 0.03%

• 0.01%

0.00% 0.01%

• 0.05%

0.03% 0.03%

• 0.03%

0.03% 0.01% 0.02% 0.06%

• 0.02% -0.03% -0.01% -0.02% -0.06% -0.06% -0.04% -0.03%

0.05% 0.01%

• 0.02%

0.00% 0.02% 0.02%

• 0.02% -0.04% -0.05% -0.02%

0.03% 0.00% 0.04% 0.02%

• 0.04%

0.01% 0.03% 0.04% 0.02% 0.03%

• 0.01%

0.03% 0.03% 0.02% 0.05% 0.04%

• 0.02%

0.01%

• 0.03% -0.03%

0.01%

• 0.03%

0.00%

• 0.02% -0.01%

0.00% 0.01% 0.02% 0.07% 0.03%

• 0.02% -0.05% -0.04% -0.02% -0.02%

0.04% 0.05% 0.00% 0.03% 0.02%

• 0.02% -0.03% -0.02%

0.04% 0.05%

• 0.01%

0.05% 0.05% 0.02% 0.06%

• 0.03%

0.00%

• 0.04% -0.03%
• 0.03% -0.04%
• 0.02%

0.03% 0.08%

• 0.08%
• 0.04% -0.05% -0.02%

0.05% 0.03% 0.00% 0.04%

• 0.03%
• 0.02%

0.04% 0.01% 0.02% 0.07% 0.07%

• 0.02% -0.04% -0.02% -0.02% -0.03% -0.04% -0.01% -0.05%

0.00%

• 0.03%

0.01% 0.01% 0.05% 0.04% 0.00%

• 0.06% -0.03% -0.02% -0.03%

0.04% 0.05%

• 0.01%

0.04% 0.03%

• 0.01% -0.02%

0.00% 0.03% 0.04% 0.00% 0.05% 0.05% 0.01% 0.05%

• 0.04% -0.01% -0.02% -0.03% -0.04% -0.04% -0.06% -0.02%

0.05% 0.00%

• 0.02%

0.01% 0.03% 0.02%

• 0.01%

0.01%

• 0.06% -0.03%

0.03% 0.00% 0.02% 0.03%

• 0.03%

0.02% 0.03% 0.04% 0.03% 0.03% 0.00% 0.04% 0.04% 0.02% 0.04% 0.05% 0.02% 0.01% 0.02% 0.00%

• 0.04%

0.02% 0.03% 0.00% 0.08% 0.08%

• 0.01%

0.03% 0.02%

• 0.02%
• 0.01%

0.02%

• 0.01%

0.03% 0.04%

• 0.01%

0.04% 0.02% 0.03% 0.06% 0.03% 0.01%

• 0.01%

0.02%

• 0.01%

0.01% 0.04% 0.04% 0.08% 0.07% 0.06% 0.07% 0.08% 0.08% 0.00% 0.05%

• 0.01% -0.03%

0.02% 0.03% 0.01% 0.03% 0.03% 0.03% 0.00% 0.02% 0.02% 0.03% 0.03% 0.04% 0.03% 0.04% 0.04% 0.05%

• 0.03%

0.00%

• 0.03%
• 0.01% -0.06% -0.06%

0.02%

• 0.21%

0.04%

• 0.02%

0.03% 0.06% 0.03% 0.09% 0.01% 0.02% 0.00% 0.01% 0.02% 0.02% 0.04% 0.05% 0.04% 0.05% 0.04% 0.02% 0.03% 0.04% 0.02% 0.04%

• 0.05% -0.21% -0.10% -0.12% -0.18%
• 0.16% -0.09%
• 0.08% -0.09%
• 0.09% -0.03%

0.00%

• 0.13%

0.01%

• 0.02% -0.02%

0.01% 0.03% 0.04% 0.03% 0.05% 0.05% 0.03% 0.04% 0.04% 0.03% 0.02% 0.03%

• 0.21% -0.13% -0.32% -0.14% -0.20% -0.32% -0.17% -0.24% -0.19% -0.20% -0.11% -0.21% -0.08% -0.01% -0.21%

0.03%

• 0.07% -0.01%

0.01% 0.00% 0.02% 0.04% 0.02% 0.05% 0.02% 0.07% 0.02% 0.04% 0.02% 0.03% 0.02% 0.03% 0.03% 0.04%

• 0.30% -0.23% -0.24% -0.22% -0.27% -0.15% -0.25% -0.20% -0.21% -0.18% -0.21% -0.07% -0.17% -0.09% -0.07% -0.10% -0.11% -0.02%

0.01%

• 0.01%

0.03% 0.06% 0.07% 0.05% 0.07% 0.07% 0.07% 0.05% 0.06% 0.06% 0.03% 0.03% 0.04% 0.03%

Absolute error of pin-by-pin fission rate in Void-A condition (axially integrated) 1.0%

• 1.0%

SLIDE 17

C5G7 3D void benchmark problem

33

0.14 0.18 0.16 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 No void Void-A Void-B Absolute average diff. (%)

Average absolute difference of pin-wise fission rate

C5G7 3D hexagonal benchmark problem

34

SLIDE 18

C5G7 3D hexagonal benchmark problem

35

0.10 0.49 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Genesis nTracer RMS difference (%)

RMS difference of pin-by-pin fission rate (Rodded-B)

Kobayashi 3D transport benchmark: geometry and XS

36

Problem 3 Void Source Shield

Region S

n/cm3 /𝑡

Σt

1/cm

Set i Set ii

Σs

1/cm

Σs

1/cm

Source 1 101 5 102 Void 104 5 105 Shield 101 5 102

• K. Kobayashi et al, 3-D RADIATION TRANSPORT BENCHMARK PROBLEMS AND RESULTS FOR SIMPLE

GEOMETRIES WITH VOID REGIONS2000, OECD/NEA

SLIDE 19

Results (Prob.3, without scattering)

37

1.0E‐06 1.0E‐05 1.0E‐04 10 20 30 40 50 60 Neutron Scalar Flux [1/cm^2/s] Position [cm] Reference Azi 120, Pol 60 Azi 96, Pol 48 Azi 72, Pol 36 Azi 48, Pol 24 ‐30% ‐20% ‐10% 0% 10% 20% 30% 40% 10 20 30 40 50 60 Difference of Neutron Flux [‐] Position [cm] Azi 120, Pol 60 Azi 96, Pol 48 Azi 72, Pol 36 Azi 48, Pol 24

Results (Prob.3, with scattering)

38

1.0E-05 1.0E-04 1.0E-03 10 20 30 40 50 60 Neutron Scalar Flux [1/cm^2/s] Position [cm] Reference Azi 120, Pol 60 Azi 96, Pol 48 Azi 72, Pol 36 Azi 48, Pol 24

• 10%
• 8%
• 6%
• 4%
• 2%

0% 2% 4% 6% 8% 10% 10 20 30 40 50 60 Difference of Neutron Flux [-] Position [cm] Azi 120, Pol 60 Azi 96, Pol 48 Azi 72, Pol 36 Azi 48, Pol 24

SLIDE 20

Convergence stability

 Residual of scalar flux (with scattering) 39

1.0E‐06 1.0E‐05 1.0E‐04 1.0E‐03 1.0E‐02 1.0E‐01 1.0E+00 1.0E+01 2 4 6 8 10 12 14 16 Residual of scalar flux Number of transport sweeps

Summary and future tasks

40

SLIDE 21

Summary and future tasks

 Introduce development status of GENESIS, which is a

multigroup neutron/photon transport calculation code

 Calculation capabilities are almost implemented.

Released to Japanese users at June 2018.

 Contact to authors for detail  Search “中性子輸送計算コ

ード GENESIS”

 Further developments on calculation efficiency,

extension of available cross section formats

 Expect wide use of GENESIS in Japan as a cutting-

edge transport calculation code

41