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, 2018Multi-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

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

4https://www.casl.gov/

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

6B. Zhang et al., “Heterogeneous Neutron Leakage Model for PWR Pin-by-pin Calculation,” Ann. Nucl. Energy, 110, 443 (2017).

Recent trends (EU)

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

7D. Schneider et al., “APOLLO3: CEA/DEN Deterministic Multi-Purpose Code for Reactor Physics Analysis,” Proc. PHYSOR2016

Outline of the GENESIS code

8

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

LEAF method

11

z

x

y

x

y

z

x

y

z

s

LEAF method

12

LEAF method

13

ss

z

z

s

z

𝜓 , 𝑧

𝜓 , 𝑠

𝜓 , 𝑧

𝜓 , 𝑠

𝑞 𝑠, 𝑧

Planar MOC vs LEAF

14

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

z

x

yz

s

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

LEAFNo approximation

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.htmlhttp://neutron.snu.ac.kr/node/7

BWR – 3x3 fuel assemblies

BWR – flux regions

BWR – 3x3 fuel assemblies

KAIST benchmark problem (Cho et al.)

C5G7 hexagonal benchmark (Joo et al.)

PWR – 4 loop type, full core with baffle reflector

Seed – blanket fuel

CANDU

25

Large FBR

26

FBR fuel assembly with wrapper tube

Verification calculations

27

C5G7 3D benchmark problem

28

Rodded A, Rodded B

Rodded B

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

RM

S di

ffer

ence

(%

)

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

C5G7 3D void benchmark problem

30

Void-A Void-B

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%

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

Abso

lute

ave

rage

diff

. (%

)

Average absolute difference of pin-wise fission rate

C5G7 3D hexagonal benchmark problem

34

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

RM

S di

ffer

ence

(%

)

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 /𝑠

Σt

1/cm

Set i Set ii

Σs

1/cm

Σs

1/cm

Source 1 10 1 0 5 10 2

Void 0 10 4 0 5 10 5

Shield 0 10 1 0 5 10 2

K. Kobayashi et al, 3-D RADIATION TRANSPORT BENCHMARK PROBLEMS AND RESULTS FOR SIMPLEGEOMETRIES WITH VOID REGIONS2000, OECD/NEA

Results (Prob.3,without scattering)

371.0E‐06

1.0E‐05

1.0E‐04

0 10 20 30 40 50 60

Neu

tron 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%

0 10 20 30 40 50 60

Difference of Neu

tron 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

0 10 20 30 40 50 60

Neu

tron

Sca

lar

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%

0 10 20 30 40 50 60

Diff

eren

ce o

f N

eutr

on F

lux

[-]

Position [cm]

Azi 120, Pol 60

Azi 96, Pol 48

Azi 72, Pol 36

Azi 48, Pol 24

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

0 2 4 6 8 10 12 14 16

Residual of scalar flux

Number of transport sweeps

Summary and future tasks

40

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