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JAEA-Data/Code 2011-018

JAEA-Data/Code
３次元六角体系用中性子輸送計算コードの整備
―NSHEX、MINIHEX、MINISTRI コードの整備―
Development of Neutron Transport Calculation Codes for 3-D Hexagonal Geometry
- Development of NSHEX, MINIHEX and MINISTRI Codes 杉野和輝
Kazuteru SUGINO
原子力基礎工学研究部門
核工学・炉工学ユニット
Division of Nuclear Data and Reactor Engineering
Nuclear Science and Engineering Directorate
January 2012
Japan Atomic Energy Agency
日本原子力研究開発機構
JAEA-Data/Code
2011-018
JAEA-Data/Code 2011-018
3 ḟඖභゅయ⣔⏝୰ᛶᏊ㍺㏦ィ⟬ࢥ࣮ࢻࡢᩚഛ
NSHEXࠊMINIHEXࠊMINISTRI ࢥ࣮ࢻࡢᩚഛ
᪥ᮏཎᏊຊ◊✲㛤Ⓨᶵᵓ
ཎᏊຊᇶ♏ᕤᏛ◊✲㒊㛛
᰾ᕤᏛ࣭⅔ᕤᏛࣘࢽࢵࢺ
ᮡ㔝 ࿴㍤
(2011 ᖺ 10 ᭶ 28 ᪥ ཷ⌮)
ᐇᶵ㧗㏿⅔⅔ᚰࡸࣟࢩ࢔ࡢ BFS ⮫⏺ᐇ㦂య⣔ࡢ୰ᛶᏊ㍺㏦ィ⟬ࢆ㧗⢭ᗘ࡛⾜࠺ࡇ࡜ࡀྍ⬟
࡞Ỵᐃㄽⓗᡭἲ࡟ᇶ࡙ࡃ 3 ḟඖභゅయ⣔⏝㞳ᩓᗙᶆἲ㸦SN ἲ㸧㍺㏦ィ⟬ࢥ࣮ࢻࠊࡍ࡞ࢃࡕࠊࣀ
࣮ࢻἲ࡟ᇶ࡙ࡃ NSHEX ࢥ࣮ࢻ㸦3 ศࡢ 1 ⅔ᚰ∧: Ver. 10A.1ࠊ඲⅔ᚰ∧: Ver. 10B.1㸧ࠊභゅ࣓
ࢵࢩࣗ᭷㝈ᕪศἲ࡟ᇶ࡙ࡃ MINIHEX ࢥ࣮ࢻ㸦Ver. 2.1㸧ࠊ୕ゅ࣓ࢵࢩࣗ᭷㝈ᕪศἲ࡟ᇶ࡙ࡃ
MINISTRI ࢥ࣮ࢻ㸦Ver. 1.1㸧ࢆࡑࢀࡒࢀᩚഛࡋࡓࠋNSHEX ࡟ࡘ࠸࡚ࡣࠊ⢭ᗘྥୖࡢࡓࡵࡢ
ࣀ࣮ࢻෆከ㡯ᘧᒎ㛤ḟᩘࡢᣑᙇ࡜཰᮰ᛶᨵၿࡢࡓࡵࡢึᮇ᭷㝈ᕪศィ⟬ࡢᑟධࢆ⾜ࡗࡓࠋ
MINIHEX ࡟ࡘ࠸࡚ࡣࠊ㈇ࡢ୰ᛶᏊ᮰Ⓨ⏕᫬ࡢฎ⌮ࡢぢ┤ࡋࢆ⾜ࡗࡓࠋࡲࡓࠊMINIHEX ࡢᇶ
ᮏ࢔ࣝࢦࣜࢬ࣒ࢆኚ᭦ࡍࡿࡇ࡜࡟ࡼࡾ MINISTRI ࢆ᪂ࡓ࡟సᡂࡋࡓࠋᩚഛᚋࡢ NSHEXࠊ
MINIHEXࠊMINISTRI ࡢྛィ⟬ࢥ࣮ࢻࢆ✀ࠎࡢ㧗㏿⅔⅔ᚰయ⣔࡟㐺⏝ࡋࡓࠋࡑࡢ⤖ᯝࠊィ⟬
⢭ᗘࡢほⅬ࠿ࡽࡣ༑ศ࡞ᛶ⬟ࢆ᭷ࡍࡿࡇ࡜ࢆ☜ㄆࡋࡓࠋࡋ࠿ࡋ࡞ࡀࡽࠊྛィ⟬ࢥ࣮ࢻ࡟ඹ㏻ࡋ
ࡓၥ㢟Ⅼ࡜ࡋ࡚ࠊ㐺ษ࡞ຍ㏿ἲࡢᑟධ➼࡟ࡼࡾࠊィ⟬᫬㛫ࡢ▷⦰ࡸ཰᮰ᛶࡢᨵၿࡀᚲせ࡛࠶ࡿ
ࡇ࡜ࡀศ࠿ࡗࡓࠋ᭦࡟ࠊᦤືィ⟬➼ࡢᚋฎ⌮ࢆ⾜࠺ࡓࡵࡢᶵ⬟ࡢᩚഛࡀᮃࡲࢀࡿࠋࡑࡇ࡛ࠊィ
⟬ࢥ࣮ࢻࢆᨵၿࡍࡿୖ࡛ࡢ௒ᚋࡢ୺せㄢ㢟ࢆᩚ⌮ࡋࡓࠋ
ཎᏊຊ⛉Ꮫ◊✲ᡤ㸦㥔ᅾ㸧㸸ࠛ319-1195 Ⲉᇛ┴㑣⌃㒆ᮾᾏᮧⓑ᪉ⓑ᰿ 2-4
㼕㻌
JAEA-Data/Code 2011-018
Development of Neutron Transport Calculation Codes for 3-D Hexagonal Geometry
- Development of NSHEX, MINIHEX and MINISTRI Codes Kazuteru SUGINO
Division of Nuclear Data and Reactor Engineering,
Nuclear Science and Engineering Directorate,
Japan Atomic Energy Agency
Tokai-mura, Naka-gun, Ibaraki-ken
(Received October 28, 2011)
Deterministic discrete ordinates method (SN method) transport calculation codes
for three-dimensional hexagonal geometry have been developed: nodal calculation code
NSHEX (Ver. 10A.1 for one third core and Ver. 10B.1 for whole core), hexagonal-mesh finite
difference calculation code MINIHEX (Ver. 2.1), and triangle-mesh finite difference
calculation code MINISTRI (Ver. 1.1), which can perform neutron transport calculations
with high accuracy for cores of fast power reactors and assemblies of the Russian BFS
critical facility. NSHEX is improved by extending the polynomial expansion order of
intranode fluxes for better accuracy and adopting the initial finite difference calculation for
better convergence performance. MINIHEX is modified in the process of negative flux
fix-up. In addition, MINISTRI is newly produced by changing the basic algorithm of the
MINIHEX code. NSHEX, MINIHEX, and MINISTRI currently developed are applied to
various fast reactor cores. It is found that these codes show satisfactory performance in
terms of calculation accuracy. However, reduction of calculation time and improvement of
convergence performance are required for all the codes by such measure as introduction of
suitable acceleration technique. Further, development of post process functions is desired,
which is represented by perturbation calculation scheme. Therefore major issues are
summarized for future code development.
Keywords: NSHEX, MINIHEX, MINISTRI, Transport, Hexagonal Geometry, Nodal, Finite
Difference, Discrete Ordinates, SN
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JAEA-Data/Code 2011-018
┠
ḟ
1. ᗎㄽ -------------------------------------------------------------------------------------------------------------- 1
1.1 NSHEX ࡢᩚഛ ------------------------------------------------------------------------------------------ 1
1.2 MINIHEX ࡢᩚഛ --------------------------------------------------------------------------------------- 2
1.3 MINISTRI ࡢᩚഛ -------------------------------------------------------------------------------------- 2
1.4 ሗ࿌᭩ࡢᵓᡂ --------------------------------------------------------------------------------------------- 2
2. 3 ḟඖභゅయ⣔⏝㍺㏦ィ⟬ࢥ࣮ࢻࡢᴫせ -------------------------------------------------------------- 3
2.1 NSHEX ---------------------------------------------------------------------------------------------------- 3
2.2 MINIHEX ------------------------------------------------------------------------------------------------- 4
2.3 MINISTRI ------------------------------------------------------------------------------------------------ 5
3. 3 ḟඖභゅయ⣔⏝㍺㏦ࣀ࣮ࢻἲィ⟬ࢥ࣮ࢻ NSHEX ࡢᩚഛ -------------------------------------- 9
3.1 ࣀ࣮ࢻෆከ㡯ᘧᒎ㛤ḟᩘࡢᣑᙇ --------------------------------------------------------------------- 9
3.2 ึᮇ᭷㝈ᕪศィ⟬ࡢᑟධ ---------------------------------------------------------------------------- 11
4. 3 ḟඖභゅయ⣔⏝㍺㏦භゅ࣓ࢵࢩࣗ᭷㝈ᕪศἲィ⟬ࢥ࣮ࢻ MINIHEX ࡢᩚഛ ------------ 20
4.1 ᇶ♏ᘧࡢᑟฟ ------------------------------------------------------------------------------------------- 20
4.2 ㈇ࡢ୰ᛶᏊ᮰Ⓨ⏕᫬ࡢฎ⌮࡟㛵ࡍࡿᨵⰋ ------------------------------------------------------- 22
5. 3 ḟඖභゅయ⣔⏝㍺㏦୕ゅ࣓ࢵࢩࣗ᭷㝈ᕪศἲィ⟬ࢥ࣮ࢻ MINISTRI ࡢᩚഛ ----------- 27
5.1 ᇶ♏ᘧࡢᑟฟ ------------------------------------------------------------------------------------------- 27
5.2 ࢥ࣮ࢻࡢᩚഛ ------------------------------------------------------------------------------------------- 32
6. 3 ḟඖභゅయ⣔⏝㍺㏦ィ⟬ࢥ࣮ࢻࡢ᳨ド ------------------------------------------------------------ 36
6.1 ᳨ド᮲௳ ------------------------------------------------------------------------------------------------- 36
6.2 ᳨ド⤖ᯝ ------------------------------------------------------------------------------------------------- 37
6.2.1 KNK-II ⅔ᚰ࡟࠾ࡅࡿ᳨ド⤖ᯝ -------------------------------------------------------------- 37
6.2.2 ࠕࡶࢇࡌࡹࠖ⅔ᚰ࡟࠾ࡅࡿ᳨ド⤖ᯝ -------------------------------------------------------- 38
6.2.3 SPX ⅔ᚰ࡟࠾ࡅࡿ᳨ド⤖ᯝ ------------------------------------------------------------------- 38
6.3 ࡲ࡜ࡵ ---------------------------------------------------------------------------------------------------- 39
7. 3 ḟඖභゅయ⣔⏝㍺㏦ィ⟬ࢥ࣮ࢻࡢ㐺⏝ᛶホ౯ --------------------------------------------------- 53
7.1 ゅᗘศⅬࢭࢵࢺࡢ᮲௳タᐃ ------------------------------------------------------------------------- 53
7.2 ᳨ウ᮲௳ ------------------------------------------------------------------------------------------------- 53
7.3 ᳨ウ⤖ᯝ ------------------------------------------------------------------------------------------------- 54
7.3.1 KNK-II ⅔ᚰ࡟࠾ࡅࡿ᳨ウ⤖ᯝ -------------------------------------------------------------- 54
7.3.2 ࠕࡶࢇࡌࡹࠖ⅔ᚰ࡟࠾ࡅࡿ᳨ウ⤖ᯝ -------------------------------------------------------- 55
7.3.3 SPX ⅔ᚰ࡟࠾ࡅࡿ᳨ウ⤖ᯝ ------------------------------------------------------------------- 56
7.3.4 ࠕᖖ㝧ࠖMK-I ⅔ᚰ࡟࠾ࡅࡿ᳨ウ⤖ᯝ ------------------------------------------------------ 57
7.3.5 BFS-62-3A ⅔ᚰ࡟࠾ࡅࡿ᳨ウ⤖ᯝ ---------------------------------------------------------- 57
7.4 ࡲ࡜ࡵ ---------------------------------------------------------------------------------------------------- 58
8. ௒ᚋࡢㄢ㢟 --------------------------------------------------------------------------------------------------- 86
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JAEA-Data/Code 2011-018
9. ⤖ㄽ ------------------------------------------------------------------------------------------------------------ 87
ཧ⪃ᩥ⊩ ----------------------------------------------------------------------------------------------------------- 88
௜㘓 1 NSHEX ࡢᐇ⾜᪉ἲཬࡧධຊ࣐ࢽࣗ࢔ࣝ㸦᪥ᮏㄒ∧㸧 ------------------------------------ 90
௜㘓 2 NSHEX ࡢᐇ⾜᪉ἲཬࡧධຊ࣐ࢽࣗ࢔ࣝ㸦ⱥㄒ∧㸧 --------------------------------------- 97
௜㘓 3 MINIHEX ࡢᐇ⾜᪉ἲཬࡧධຊ࣐ࢽࣗ࢔ࣝ ------------------------------------------------- 104
௜㘓 4 MINISTRI ࡢᐇ⾜᪉ἲཬࡧධຊ࣐ࢽࣗ࢔ࣝ ------------------------------------------------ 109
௜㘓 5 NSHEX ࡟࠾ࡅࡿᚄ᪉ྥࡶࢀྲྀࡾᢅ࠸ᡭἲࡢ㑅ᐃ ---------------------------------------- 114
௜㘓 6 ゅᗘศⅬࢭࢵࢺࡢᩚ⌮ ---------------------------------------------------------------------------- 123
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JAEA-Data/Code 2011-018
Contents
1.
2.
Introduction -------------------------------------------------------------------------------------------------- 1
1.1
Development of NSHEX ------------------------------------------------------------------------------ 1
1.2
Development of MINIHEX -------------------------------------------------------------------------- 2
1.3
Development of MINISTRI -------------------------------------------------------------------------- 2
1.4
Components of the Report --------------------------------------------------------------------------- 2
Brief description of the Transport Calculation Codes for 3-dimensional Hexagonal
Geometry ---------------------------------------------------------------------------------------------------- 3
3.
2.1
NSHEX ---------------------------------------------------------------------------------------------------- 3
2.2
MINIHEX ------------------------------------------------------------------------------------------------- 4
2.3
MINISTRI ------------------------------------------------------------------------------------------------ 5
Development of the Nodal Transport Calculation Code for 3-dimensional Hexagonal
Geometry NSHEX ---------------------------------------------------------------------------------------- 9
4.
3.1
Extension of the Intranode Polynomial Expansion Order --------------------------------- 9
3.2
Adoption of the Initial Finite Difference Calculation ------------------------------------- 11
Development of the Hexagonal-mesh Finite Difference Transport Calculation Code for
3-dimensional Hexagonal Geometry MINIHEX ----------------------------------------------- 20
5.
4.1
Derivation of the Basic Formula ---------------------------------------------------------------- 20
4.2
Improvement of the Measures for Negative Flux Generation -------------------------- 22
Development of the Triangle-mesh Finite Difference Transport Calculation Code for
3-dimensional Hexagonal Geometry MINISTRI ---------------------------------------------- 27
5.1
Derivation of the Basic Formula ---------------------------------------------------------------- 27
5.2
Preparation of the Code ---------------------------------------------------------------------------- 32
6.
Verification of the Transport Calculation Codes for 3-dimensional Hexagonal Geometry
----------------------------------------------------------------------------------------------------------------- 36
6.1
Conditions for the Verification ------------------------------------------------------------------- 36
6.2
Results of the Verification ------------------------------------------------------------------------- 37
6.2.1
Verification Results for the KNK-II Core ------------------------------------------------ 37
6.2.2
Verification Results for the Monju Core ------------------------------------------------- 38
6.2.3
Verification Results for the SPX Core ---------------------------------------------------- 38
6.3
7.
Summary ------------------------------------------------------------------------------------------------ 39
Evaluation of Applicability of the Transport Calculation Codes for 3-dimensional
Hexagonal Geometry ---------------------------------------------------------------------------------- 53
7.1
Fixation of Condition of the Angular Quadrature Set ------------------------------------ 53
7.2
Condition for the Evaluation --------------------------------------------------------------------- 53
7.3
Results of the Evaluation -------------------------------------------------------------------------- 54
7.3.1
Evaluation Results for the KNK-II Core ------------------------------------------------ 54
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JAEA-Data/Code 2011-018
7.3.2
Evaluation Results for the Monju Core -------------------------------------------------- 55
7.3.3
Evaluation Results for the SPX Core ----------------------------------------------------- 56
7.3.4
Evaluation Results for the Joyo MK-I Core -------------------------------------------- 57
7.3.5
Evaluation Results for the BFS-62-3A Core -------------------------------------------- 57
7.4
Summary ------------------------------------------------------------------------------------------------ 58
8.
Future Issues ----------------------------------------------------------------------------------------------- 86
9.
Concluding Remarks ------------------------------------------------------------------------------------- 87
References -------------------------------------------------------------------------------------------------------- 88
Appendix 1
Execution Guide and Input Manual of NSHEX (Japanese Version) --------- 90
Appendix 2
Execution Guide and Input Manual of NSHEX (English Version) ----------- 97
Appendix 3
Execution Guide and Input Manual of MINIHEX ------------------------------- 104
Appendix 4
Execution Guide and Input Manual of MINISTRI ------------------------------ 109
Appendix 5
Fixation of the Treatment of the Radial Leakage in NSHEX ---------------- 114
Appendix 6
Arrangement of the Angular Quadrature Sets ----------------------------------- 123
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JAEA-Data/Code 2011-018
⾲ࣜࢫࢺ
Table 3.2-1
Comparison in calculation time among IFDC criterion for the KNK-II core
---------------------------------------------------------------------------------------------------------------- 14
Table 3.2-2
Comparison in outer iteration counts of IFDC and nodal calculation among
IFDC criterion for the KNK-II core ---------------------------------------------------------------- 14
Table 3.2-3
Comparison in calculation time among IFDC criterion for the Monju core -- 15
Table 3.2-4
Comparison in outer iteration counts of IFDC and nodal calculation among
IFDC criterion for the Monju core ------------------------------------------------------------------ 15
Table 3.2-5
Comparison in calculation time among IFDC criterion for the SPX core ----- 16
Table 3.2-6
Comparison in outer iteration counts of IFDC and nodal calculation among
IFDC criterion for the SPX core --------------------------------------------------------------------- 16
Table 4.2-1
Comparison in eigenvalue and calculation time among negative flux measures
in MINIHEX for the BFS-62-3A core -------------------------------------------------------------- 26
Table 5.1-1
Comparison in eigenvalue and calculation time among negative flux measures
in MINISTRI for the KNK-II core ------------------------------------------------------------------ 33
Table 6.1-1
Angular discretization effects in eigenvalue by NSHEX for the KNK-II core
---------------------------------------------------------------------------------------------------------------- 40
Table 6.1-2
Angular discretization effects in eigenvalue by NSHEX for the Monju core - 40
Table 6.1-3
Angular discretization effects in eigenvalue by NSHEX for the SPX core ---- 40
Table 6.1-4
Angular discretization effects in power distribution by NSHEX for the Monju
core ---------------------------------------------------------------------------------------------------------- 41
Table 6.1-5
Angular discretization effects in power distribution by NSHEX for the SPX
core ---------------------------------------------------------------------------------------------------------- 41
Table 6.1-6
Angular discretization effects in absorption reaction rate in the control rod
region by NSHEX for the KNK-II core ------------------------------------------------------------ 41
Table 6.1-7
Calculation criteria and conditions for verification tests -------------------------- 42
Table 6.2-1
Relative difference in eigenvalue and calculation time by NSHEX for the
KNK-II core ----------------------------------------------------------------------------------------------- 46
Table 6.2-2
Relative difference in eigenvalue and calculation time by MINISTRI for the
KNK-II core ----------------------------------------------------------------------------------------------- 46
Table 6.2-3
Relative difference in absorption reaction rate in the control rod region by
NSHEX for the KNK-II core ------------------------------------------------------------------------- 47
Table 6.2-4
Relative difference in absorption reaction rate in the control rod region by
MINISTRI for the KNK-II core --------------------------------------------------------------------- 47
Table 6.2-5
Relative difference in eigenvalue and calculation time by NSHEX for the
Monju core ------------------------------------------------------------------------------------------------ 48
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JAEA-Data/Code 2011-018
Table 6.2-6
Relative difference in eigenvalue and calculation time by MINISTRI for the
Monju core ------------------------------------------------------------------------------------------------ 48
Table 6.2-7
Relative difference in power distribution by NSHEX for the Monju core ----- 49
Table 6.2-8
Relative difference in power distribution by MINISTRI for the Monju core
---------------------------------------------------------------------------------------------------------------- 49
Table 6.2-9
Relative difference in eigenvalue and calculation time by NSHEX for the SPX
core ---------------------------------------------------------------------------------------------------------- 50
Table 6.2-10
Relative difference in eigenvalue and calculation time by MINISTRI for the
SPX core --------------------------------------------------------------------------------------------------- 50
Table 6.2-11
Relative difference in power distribution by NSHEX for the SPX core ------ 51
Table 6.2-12
Relative difference in power distribution by MINISTRI for the SPX core -- 51
Table 7.1-1
Relative difference of the flux and absorption reaction rate in the control rod
region due to the change of the angular quadrature set and maximum polynomial
order in NSHEX for "Rods half-in" case of the KNK-II core -------------------------------- 59
Table 7.1-2
Relative difference of the flux and absorption reaction rate in the control rod
region due to the change of the angular quadrature set and radial mesh width in
MINISTRI for "Rods half-in" case of the KNK-II core ---------------------------------------- 59
Table 7.2-1
Calculation criteria and conditions for the reference scheme -------------------- 62
Table 7.2-2
Comparison in effective radial mesh sizes among various cores ---------------- 63
Table 7.3-1
Relative difference in eigenvalue and calculation time by NSHEX and
MINISTRI with the standard calculation condition for the KNK-II core --------------- 66
Table 7.3-2
Relative difference in eigenvalue and calculation time by NSHEX and
MINISTRI with the standard calculation condition for the Monju core ----------------- 67
Table 7.3-3
Relative difference in power distribution by NSHEX and MINISTRI with the
standard calculation condition for the Monju core -------------------------------------------- 67
Table 7.3-4
Relative difference in eigenvalue and calculation time by NSHEX and
MINISTRI with the standard calculation condition for the SPX core -------------------- 68
Table 7.3-5
Relative difference in power distribution by NSHEX and MINISTRI with the
standard calculation condition for the SPX core ----------------------------------------------- 68
Table 7.3-6
Relative difference in eigenvalue and calculation time by NSHEX and
MINISTRI with the standard calculation condition for the Joyo MK-I core ----------- 69
Table 7.3-7
Relative difference in power distribution by NSHEX and MINISTRI with the
standard calculation condition for the Joyo MK-I core --------------------------------------- 69
Table 7.3-8
Relative difference in eigenvalue and calculation time by MINIHEX with the
standard calculation condition for the BFS-62-3A core -------------------------------------- 70
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JAEA-Data/Code 2011-018
ᅗࣜࢫࢺ
Fig. 2.1-1
Conceptual view of the nodal method for the 3-D hexagonal-Z geometry -------- 6
Fig. 2.1-2
Conceptual view of the transverse leakage in the 3-D hexagonal-Z geometry -- 7
Fig. 2.3-1
Triangle mesh division for the 3-D hexagonal-Z geometry ---------------------------- 8
Fig. 3.1-1
Definition of basic node parameters ------------------------------------------------------- 17
Fig. 3.2-1
Comparison in convergence performance of fission source between with and
without IFDC for "Rods half-in" case of the KNK-II core -------------------------------------- 18
Fig. 3.2-2
Comparison in convergence performance of fission source between with and
without IFDC for "MCR half-in" case of the Monju core --------------------------------------- 18
Fig. 3.2-3
Comparison in convergence performance of fission source between with and
without IFDC for " MCR half-in " case of the SPX core ---------------------------------------- 19
Fig. 4.1-1
Parameters used in the basic formula of MINIHEX ---------------------------------- 25
Fig. 5.1-1
Parameters used in the basic formula of MINISTRI ---------------------------------- 34
Fig. 5.2-1
Mesh numbering within a subassembly in MINISTRI ------------------------------- 35
Fig. 6.1-1
Layout of the KNK-II core -------------------------------------------------------------------- 43
Fig. 6.1-2
Layout of the Monju core --------------------------------------------------------------------- 44
Fig. 6.1-3
Layout of the Super Phenix (SPX) core --------------------------------------------------- 45
Fig. 6.2-1
Comparison of the 4th group neutron flux distribution calculated by NSHEX
around the control rod region for the KNK-II core ---------------------------------------------- 52
Fig. 7.1-1
Dependence of eigenvalue on three angular quadrature sets in NSHEX for
"Rods half-in" case of the KNK-II core (2nd order polynomial expansion) ---------------- 60
Fig. 7.1-2
Dependence of eigenvalue on the maximum polynomial order in NSHEX for
"Rods half-in" case of the KNK-II core (Angular quadrature set of S4) -------------------- 60
Fig. 7.1-3
Dependence of eigenvalue on three angular quadrature sets in MINISTRI for
"Rods half-in" case of the KNK-II core (Radially 24meshes/SA) ----------------------------- 61
Fig. 7.1-4
Dependence of eigenvalue on the radial mesh division in MINISTRI for "Rods
half-in" case of the KNK-II core (Angular quadrature set of S4) ----------------------------- 61
Fig. 7.2-1
Layout of the Joyo MK-I core ---------------------------------------------------------------- 64
Fig. 7.2-2
Layout of the BFS-62-3A core --------------------------------------------------------------- 65
Fig. 7.3-1
Effects of polynomial expansion and angular discretization by NSHEX for the
KNK-II core ------------------------------------------------------------------------------------------------- 71
Fig. 7.3-2
Effects of spatial mesh and angular discretization by MINISTRI for the KNK-II
core ------------------------------------------------------------------------------------------------------------ 72
Fig. 7.3-3
Effects of polynomial expansion and angular discretization by NSHEX for the
Monju core -------------------------------------------------------------------------------------------------- 73
Fig. 7.3-4
Effects of spatial mesh and angular discretization by MINISTRI for the Monju
core ------------------------------------------------------------------------------------------------------------ 74
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JAEA-Data/Code 2011-018
Fig. 7.3-5
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "All rods out" case of the Monju
core ------------------------------------------------------------------------------------------------------------ 75
Fig. 7.3-6
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "MCR half-in" case of the Monju
core ------------------------------------------------------------------------------------------------------------ 75
Fig. 7.3-7
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "MCR in" case of the Monju core
------------------------------------------------------------------------------------------------------------------ 76
Fig. 7.3-8
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "BCR in" case of the Monju core
------------------------------------------------------------------------------------------------------------------ 76
Fig. 7.3-9
Effects of polynomial expansion and angular discretization by NSHEX for the
SPX core ----------------------------------------------------------------------------------------------------- 77
Fig. 7.3-10
Effects of spatial mesh and angular discretization by MINISTRI for the SPX
core ------------------------------------------------------------------------------------------------------------ 78
Fig. 7.3-11
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "All rods out" case of the SPX
core ------------------------------------------------------------------------------------------------------------ 79
Fig. 7.3-12
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "MCR half-in" case of the SPX
core ------------------------------------------------------------------------------------------------------------ 79
Fig. 7.3-13
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "MCR in" case of the SPX core
------------------------------------------------------------------------------------------------------------------ 80
Fig. 7.3-14
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "BCR in" case of the SPX core
------------------------------------------------------------------------------------------------------------------ 80
Fig. 7.3-15
Effects of spatial mesh and angular discretization by MINISTRI for the Joyo
MK-I core ---------------------------------------------------------------------------------------------------- 81
Fig. 7.3-16
Percentage relative difference in radial power distribution by MINISTRI with
the standard calculation condition for "All rods out" case of the Joyo MK-I core ------- 82
Fig. 7.3-17
Percentage relative difference in radial power distribution by MINISTRI with
the standard calculation condition for "MCR half-in" case of the Joyo MK-I core ------ 82
Fig. 7.3-18
Percentage relative difference in radial power distribution by MINISTRI with
the standard calculation condition for "MCR in" case of the Joyo MK-I core ------------ 83
Fig. 7.3-19
Percentage relative difference in radial power distribution by MINISTRI with
the standard calculation condition for "BCR in" case of the Joyo MK-I core ------------- 83
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JAEA-Data/Code 2011-018
Fig. 7.3-20
Effects of spatial mesh and angular discretization by MINIHEX and
MINISTRI for the BFS-62-3A core ------------------------------------------------------------------- 84
Fig. 7.4-1
Dependence of relative difference of eigenvalue to the reference on the angular
quadrature set of S4 for the KNK-II core ----------------------------------------------------------- 85
㼤㼕㻌
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JAEA-Data/Code 2011-018
1. ᗎㄽ
㧗㏿⅔⅔ᚰࡢヲ⣽࡞᰾≉ᛶゎᯒ࡛ࡣࠊ୰ᛶᏊ㍺㏦⌮ㄽ࡟ᇶ࡙ࡃィ⟬ࢥ࣮ࢻࡢ㐺⏝ࡀ୙ྍḞ࡛
࠶ࡿࠋ㧗㏿⅔ࡢ୰࡛ࠊᐇᶵࣉࣛࣥࢺࡸ୍㒊ࡢ⮫⏺ᐇ㦂⿦⨨ࡢ⅔ᚰࡣࠊභゅ᱁Ꮚ㓄ิࡢ⇞ᩱ㞟ྜ
యࡸ⇞ᩱせ⣲࡛ᵓᡂࡉࢀ࡚࠸ࡿࠋ୍᪉ࠊࡑࢀࡽභゅ᱁Ꮚ㓄ิࢆ┤᥋ྲྀࡾᢅ࠺ࡇ࡜ࡢ࡛ࡁࡿ 3 ḟ
ඖභゅయ⣔⏝ࡢỴᐃㄽⓗᡭἲ࡟ᇶ࡙ࡃ㍺㏦ィ⟬ࢥ࣮ࢻ࡟ࡘ࠸࡚ࡣࠊྠࡌ 3 ḟඖࡢ┤஺ᗙᶆయ⣔
⏝ࡢ㍺㏦ィ⟬ࢥ࣮ࢻࡢࡼ࠺࡟༑ศ࡟ᩚഛࡀ⾜ࡁᒆ࠸࡚࠸ࡿ࡜ゝࡗࡓ≧ἣ࡛ࡣ࡞࠸ࠋ௚᪉ࠊྠࡌ
ࡃ㍺㏦⌮ㄽ࡟ᇶ࡙࠸࡚࠸ࡿࣔࣥࢸ࢝ࣝࣟἲࡣཎ⌮ⓗ࡟௵ពࡢయ⣔࡬ࡢ㐺⏝ࡀྍ⬟࡛࠶ࡾࠊ3 ḟ
ඖභゅయ⣔࡬ࡢ㐺⏝ࡶ౛እ࡛ࡣ࡞࠸ࡀࠊ᭱኱⥺ฟຊ➼ࡢᒁᡤⓗ࡞ฟຊศᕸࡸࠊᚤᑠ࡞཯ᛂᗘኚ
໬➼ࡢゎᯒ࡛ࡣࠊ⤫ィ⢭ᗘࡢほⅬ࠿ࡽㄢ㢟ࡀṧࡉࢀ࡚࠸ࡿࠋᚑࡗ࡚ࠊỴᐃⓗᡭἲ࡟ᇶ࡙ࡃ 3 ḟ
ඖභゅయ⣔⏝ࡢ㍺㏦ィ⟬ࢥ࣮ࢻࡢᩚഛࡣࠊ≉࡟ࡑࢀࡽࡢ᰾≉ᛶゎᯒࢆ⾜࠺ほⅬ࠿ࡽ㔜せ࡛࠶ࡿࠋ
ࡑࡢࡼ࠺࡞⫼ᬒࡢୗࠊ3 ✀㢮ࡢ 3 ḟඖභゅయ⣔⏝㍺㏦ィ⟬ࢥ࣮ࢻ NSHEXࠊMINIHEXࠊ
MINISTRI ࡢᩚഛࢆ⾜࠺ࡇ࡜࡜ࡋ࡚࠸ࡿࠋ
1.1 NSHEX ࡢᩚഛ
ືຊ⅔࣭᰾⇞ᩱ㛤Ⓨ஦ᴗᅋ㸦⌧ࠊ᪥ᮏཎᏊຊ◊✲㛤Ⓨᶵᵓ㸧࡜኱㜰኱Ꮫ࡜ࡢඹྠ◊✲࡟ࡼࡾࠊ
ᐇᶵ㧗㏿⅔⏝࡜ࡋ࡚ 3 ḟඖභゅయ⣔⏝㍺㏦ࣀ࣮ࢻἲィ⟬ࢥ࣮ࢻ NSHEX ࡢ㛤Ⓨࢆ⾜ࡗ࡚ࡁࡓ 1,
2)ࠋNSHEX
ࡣ✵㛫ⓗ࡞ィ⟬せ⣲㸦✵㛫࣓ࢵࢩࣗ࠶ࡿ࠸ࡣ✵㛫ࣀ࣮ࢻ㸧ෆࡢ୰ᛶᏊ᮰➼ࡢศᕸ
ࢆ 2 ḟࡢከ㡯ᘧᒎ㛤࡟ࡼࡾྲྀࡾᢅ࠺ࡢ࡛ࠊ1 ḟᘧ࡟ࡼࡿྲྀࡾᢅ࠸ࢆ௬ᐃࡋ࡚࠸ࡿ᭷㝈ᕪศἲ࡜
ẚ㍑ࡋ࡚ࠊィ⟬⢭ᗘࢆᦆ࡞࠺ࡇ࡜࡞ࡃ✵㛫ⓗ࡞ィ⟬せ⣲ࢆ኱ࡁࡵ࡟ྲྀࡿࡇ࡜ࡀྍ⬟࡜࡞ࡿࠋ౛
࠼ࡤࠊᐇᶵ㧗㏿⅔ࡢከࡃࡣ⇞ᩱ㞟ྜయࢧ࢖ࢬ㸦㞟ྜయ㓄ิࣆࢵࢳ㸧ࡀ 10cm ௨ୖ࠶ࡿࡢ࡛ࠊ᭷
㝈ᕪศἲࡢሙྜࡣᚄ᪉ྥ࡟㏻ᖖ 6 ಶ௨ୖࡢ୕ゅ࣓ࢵࢩࣗศ๭ࡀᚲせ࡜࡞ࡿࡀࠊNSHEX ࡛ࡣ㞟
ྜయෆࡢࣀ࣮ࢻศ๭ࡣ୙せ࡛࠶ࡿࠋ
ࡉ࡚ࠊ኱ᆺ㧗㏿⅔ࡢゎᯒ࡛᝿ᐃࡉࢀࡿࡼ࠺࡟ࢧ࢖ࢬࡢ኱ࡁ࠸⇞ᩱ㞟ྜయࢆྲྀࡾᢅ࠺ሙྜࠊィ
⟬⢭ᗘࢆ⥔ᣢࡍࡿ࡟ࡣࠊ᭷㝈ᕪศἲ࡛ࡣ⇞ᩱ㞟ྜయࢧ࢖ࢬ࡟ᛂࡌ࡚࣓ࢵࢩࣗศ๭ᩘࢆୖࡆࡿᚲ
せࡀ࠶ࡿࡢ࡛ࠊィ⟬㈇Ⲵࡣ┦ᛂ࡟ቑຍࡍࡿࠋࡑࢀ࡟ᑐࡋࠊNSHEX ࡛ࡣከ㡯ᘧᒎ㛤ḟᩘࡢᣑᙇ
࡟ࡼࡾィ⟬㈇Ⲵࢆ࡯࡜ࢇ࡝ቑຍࡉࡏࡿࡇ࡜࡞ࡋ࡟ࡼࡾ⢭ᗘࢆ㧗ࡵࡓゎᯒࡀྍ⬟࡛࠶ࡿ࡜⪃࠼ࡽ
ࢀࡿࠋࡑࡇ࡛ࠊ᪂ࡓ࡟ከ㡯ᘧᒎ㛤ࡢ᭱኱ḟᩘࢆ 6 ḟ࡟ࡲ࡛ᣑᙇࡍࡿࡇ࡜࡟ࡼࡾࠊィ⟬⢭ᗘྥୖ
࡟ࡘ࠸᳨࡚ウࢆ⾜࠺ࡇ࡜࡜ࡍࡿࠋ
ࡲࡓࠊNSHEX ࡣࣀ࣮ࢻἲࢥ࣮ࢻ࡛࠶ࡿࡇ࡜࡟㉳ᅉࡋ࡚ࠊ᭷㝈ᕪศἲィ⟬ࢥ࣮ࢻࡼࡾࡶ཰᮰
ᛶࡀᝏ࠸ࡓࡵ࡟ࠊ཰᮰ุᐃ᮲௳ࢆ㏻ᖖ㸦୰ᛶᏊ᮰ࡲࡓࡣ᰾ศ⿣୰ᛶᏊ※: 110-4ࠊᅛ᭷್: 1
10-5㸧ࡢ 5 ಸ⛬ᗘ࡜ࡋ࡚࠾ࡾࠊィ⟬⢭ᗘࡢᝏ໬ࢆᣍ࠸࡚࠸ࡓࠋࣀ࣮ࢻἲィ⟬࡟࠾ࡅࡿ཰᮰ᛶᝏ
໬ࡢཎᅉࡢ 1 ࡘ࡜ࡋ࡚ࠊึᮇ᥎ᐃ್ࡢタᐃ࡟᳨ウࡢవᆅࡀ࠶ࡿ࡜⪃࠼ࡓࠋࡑࡇ࡛ࠊ୰ᛶᏊ᮰ࡢ
ึᮇ᥎ᐃࡢࡓࡵ࡟ィ⟬ึᮇ࡟᭷㝈ᕪศἲィ⟬ࢆᑟධࡍࡿࡇ࡜࡟ࡼࡾ཰᮰ᛶࡢᨵၿ࡟ࡘ࠸᳨࡚ウ
ࢆ⾜࠺ࡇ࡜࡜ࡍࡿࠋ
㻙㻌㻝㻌㻙㻌
JAEA-Data/Code 2011-018
1.2 MINIHEX ࡢᩚഛ
ࣟࢩ࢔ゎయ᰾ฎศᨭ᥼ࢆ┠ⓗ࡜ࡋ࡚ࠊࣟࢩ࢔≀⌮໬Ꮫ࢚ࢿࣝࢠ࣮◊✲ᡤ㸦IPPE㸧࡟࠶ࡿ⮫⏺
ᐇ㦂⿦⨨ BFS-2 ࢆ⏝࠸ࡓ⅔≀⌮ᐇ㦂ࡢゎᯒࢆ⾜࠺ᚲせᛶࡀ⏕ࡌࡓ 3)ࠋBFS-2 ࡛ᵓ⠏ࡉࢀࡿ⅔ᚰ
య⣔ࡣ㓄ิࣆࢵࢳ 5.1cm ࢆ᭷ࡍࡿභゅ᱁Ꮚ࡟ࡼࡾᵓᡂࡉࢀࡿࠋࡇࡇ࡛ࠊ5.1cm ࡢ㓄ิࣆࢵࢳ࡟
ᑐࡋ࡚ࣀ࣮ࢻἲࡣ㐣ᗘ࡟ヲ⣽࡛࠶ࡿࡇ࡜࡟ຍ࠼࡚ࠊ⣙ 4,000 ಶࡢභゅ᱁Ꮚ࠿ࡽᵓᡂࡉࢀࡿయ⣔
ࢆྲྀࡾᢅࡗࡓሙྜ࡟ࡣィ⟬ᶵᐜ㔞ࡀ⭾኱࡟࡞ࡿࡇ࡜࠿ࡽࠊNSHEX ࡢ㐺⏝ࡣ⌧ᐇⓗ࡛ࡣ࡞࠿ࡗ
ࡓࠋࡑࡇ࡛ࠊ୰ᆺ㧗㏿⅔ࡢゎᯒ࡟ SN ἲ᭷㝈ᕪศἲ㍺㏦ィ⟬ࢥ࣮ࢻࢆ㐺⏝ࡍࡿሙྜ࡟ࡣࠊゅᗘ
ศⅬࢆ S4 ࡜ࡋࠊ✵㛫࣓ࢵࢩࣗᖜࢆ 5cm ⛬ᗘ࡜ࡍࢀࡤࠊゅᗘศⅬ࡜✵㛫࣓ࢵࢩࣗࡢヲ⣽໬࡟క
࠺ຠᯝࡀᡴᾘྜ࠺ࡇ࡜࡟ࡼࡾࠊ↓㝈ゅᗘศⅬཬࡧ↓㝈ᑠ✵㛫࣓ࢵࢩࣗィ⟬┦ᙜࡢ⤖ᯝࡀᚓࡽࢀ
ࡿ࡜ࡢ▱ぢ
4) ࡟ᇶ࡙࠸࡚ࠊ᪂ࡓ࡟
3 ḟඖභゅయ⣔⏝භゅ࣓ࢵࢩࣗ᭷㝈ᕪศἲィ⟬ࢥ࣮ࢻ
MINIHEX ࢥ࣮ࢻ 5)ࡀసᡂࡉࢀࡓࠋ᰾⇞ᩱࢧ࢖ࢡࣝ㛤Ⓨᶵᵓ㸦⌧ࠊ᪥ᮏཎᏊຊ◊✲㛤Ⓨᶵᵓ㸧
ࡣࠊࡇࡢ MINIHEX ࢆ BFS-2 ⮫⏺ᐇ㦂ゎᯒ࡟㐺⏝ࡍࡿࡇ࡜ࡼࡾࠊࣟࢩ࢔ゎయ᰾ฎศᨭ᥼άື
࡟኱࠸࡟㈉⊩ࡋࡓ 6)ࠋ
MINIHEX ࡟㛵ࡋ࡚ࡣࠊ᪤Ꮡࡢࡶࡢ࠿ࡽ≉࡟ᨵⰋࡣ⾜ࡗ࡚࠸࡞࠸ࡀࠊᚋ㏙ࡢ MINISTRI ࡢ
ᩚഛ࡟ྜࢃࡏ࡚ࠊ㈇ࡢ୰ᛶᏊ᮰Ⓨ⏕᫬ࡢฎ⌮ࢆぢ┤ࡍࡇ࡜࡜ࡍࡿࠋ
1.3 MINISTRI ࡢᩚഛ
NSHEX ࡣ㈗㔜࡞ 3 ḟඖභゅయ⣔⏝㍺㏦ィ⟬ࢥ࣮ࢻ࡛࠶ࡿࡇ࡜࠿ࡽࠊࡑࡢᐇᶵࣉࣛࣥࢺィ⟬
࡛ࡢ฼⏝ࡸᛂ⏝ࡀ኱࠸࡟ᮃࡲࢀ࡚࠾ࡾࠊᦤືィ⟬࡬᥋⥆ࡍࡿࡇ࡜ࡣᚲ㡲࡛࠶ࡿࠋ㍺㏦ࣀ࣮ࢻἲ
࡟ᇶ࡙ࡃᦤືィ⟬ࢆ⾜࠺࡟ࡣࠊ᭷㝈ᕪศἲ࡜␗࡞ࡾࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰ࡔࡅ࡛࡞ࡃࣀ࣮ࢻෆࡢ
୰ᛶᏊ᮰ศᕸཬࡧ㝶క୰ᛶᏊ᮰ศᕸࢆ⢭ᗘⰋࡃ෌ᵓ⠏ࡍࡿᚲせࡀ࠶ࡿࠋࡑࡢࡓࡵࠊᦤືィ⟬⏝
࡟ࣀ࣮ࢻෆࡢ୰ᛶᏊ᮰ศᕸཬࡧ㝶క୰ᛶᏊ᮰ศᕸࡢ෌ᵓ⠏ࡀヨࡳࡽࢀࡓࡀࠊཧ↷ゎ࡜࡞ࡿ┤᥋
ィ⟬࡟ࡼࡿ⤖ᯝࢆ෌⌧࡛ࡁࡿ෌ᵓ⠏ἲࢆぢฟࡍࡇ࡜ࡣ࡛ࡁ࡞࠿ࡗࡓ 7)ࠋ
ࡲࡓࠊBFS-2 ࡟ᑐࡍࡿ MINIHEX ࡢ㐺⏝ᛶ࡟㛵ࡋ࡚ࠊゅᗘศⅬ࡜✵㛫࣓ࢵࢩࣗࡢヲ⣽໬࡟క
࠺ຠᯝࡢᡴᾘࡋྜ࠸ࡢ▱ぢ࡟ࡣᇶ࡙࠸࡚࠸ࡓࡶࡢࡢࠊࡑࢀࡽࡢලయⓗ࡞᳨ウࡣ⾜ࡗ࡚࠾ࡽࡎࠊ
▱ぢᡂ❧ࡢ☜ㄆࡢࡓࡵࡢᐃ㔞ⓗ࡞ホ౯ࡀᚲせ࡛࠶ࡿࠋ
ࡑࡇ࡛ࠊNSHEX ཬࡧ MINIHEX ࡢ⿵᏶ⓗ࡞⏝㏵࡬ࡢ㐺⏝ࢆ᝿ᐃࡋ࡚ࠊ3 ḟඖභゅయ⣔⏝୕
ゅ࣓ࢵࢩࣗ᭷㝈ᕪศἲィ⟬ࢥ࣮ࢻ MINISTRI ࢆ᪂ࡓ࡟సᡂࡋࠊୖグㄢ㢟࡟ࡘ࠸᳨࡚ウࡍࡿࠋ
1.4 ሗ࿌᭩ࡢᵓᡂ
ሗ࿌᭩ࡢᵓᡂ࡜ࡋ࡚ࡣࠊ➨ 2 ❶࡟࠾࠸࡚ྛィ⟬ࢥ࣮ࢻࡢᴫせࢆ㏙࡭ࠊ➨ 3 ❶ࠊ➨ 4 ❶ࠊ➨ 5
❶࡛ࡣࡑࢀࡒࢀ NSHEXࠊMINIHEXࠊMINISTRI ࡢᩚഛ࡟ࡘ࠸࡚グ㏙ࡋࠊ➨ 6 ❶࡛ࡣ NSHEX
࡜ MINISTRI ࡢ᳨ド⤖ᯝࢆࠊ➨ 7 ❶࡛ࡣ NSHEX ࡜ MINISTRI ࡟ຍ࠼࡚ MINIHEX ࡶຍ࠼ࡓ
㐺⏝ᛶホ౯ࢆࠊ➨ 8 ❶࡛ࡣ 3 ࡘࡢࢥ࣮ࢻ࡟㛵ࡍࡿㄢ㢟ࢆࡲ࡜ࡵࠊ➨ 9 ❶࡛⤖ㄽࢆ㏙࡭ࡿࠋ
࡞࠾ࠊᮏሗࡢ௜㘓࡟ࠊNSHEXࠊMINIHEXࠊMINISTRI ࡢᐇ⾜᪉ἲ࡜ධຊ࣐ࢽࣗ࢔ࣝࢆ♧
ࡋࠊ3 ࡘࡢࢥ࣮ࢻࡢ฼⏝ᛶྥୖ࡟㈨ࡍࡿࠋ
㻙㻌㻞㻌㻙㻌
JAEA-Data/Code 2011-018
2. 3 ḟඖභゅయ⣔⏝㍺㏦ィ⟬ࢥ࣮ࢻࡢᴫせ
2.1 NSHEX
NSHEX㸦Nodal SN transport calculation code for HEXagonal-Z geometry㸧ࡣ 3 ḟඖභゅ
య⣔⏝㍺㏦ࣀ࣮ࢻἲィ⟬ࢥ࣮ࢻ࡛࠶ࡿࠋᇶ♏᪉⛬ᘧࡣࠊ㍺㏦᪉⛬ᘧ࡟ᑐࡋ࡚ᶓ᪉ྥ㸦౛࠼ࡤࠊ
X ㍈᪉ྥ࡟╔┠ࡍࡿሙྜ࡟ࡣ Y ㍈᪉ྥ࡜ Z ㍈᪉ྥ㸧࡟✚ศࢆ⾜࠺ࡇ࡜࡟ࡼࡾࠊ୰ᛶᏊࢯ࣮ࢫ㡯
࡟ᶓ᪉ྥࡶࢀ㡯ࡀຍ࠼ࡽࢀࡓ 1 ḟඖ㍺㏦᪉⛬ᘧࢆồࡵࠊࡑࡢ᪉⛬ᘧࢆゎᯒⓗ࡟ゎࡃࡇ࡜࡟ࡼࡾ
ᚓࡽࢀࡿࠋNSHEX ࡣࠊᇶ♏᪉⛬ᘧࡢゎἲࡸᶓ᪉ྥࡶࢀࡢྲྀࡾᢅ࠸࡞࡝࡟࠾࠸࡚ࠊ௨ୗࡢ≉ᚩ
ࢆ᭷ࡋ࡚࠸ࡿࠋ
ձSN ἲ࡟ࡼࡿ୰ᛶᏊ᮰ࡢゅᗘ౫Ꮡᛶࡢྲྀࡾᢅ࠸
୰ᛶᏊ᮰ࡢゅᗘ౫Ꮡᛶࡢྲྀࡾᢅ࠸ᡭἲ࡜ࡋ࡚ࠊᅜෆࡢ㧗㏿⅔ゎᯒ࡟࠾࠸࡚౑⏝ᐇ⦼ࡢ㇏ᐩ࡞
㞳ᩓᗙᶆἲ㸦SN ἲ㸧ࢆ᥇⏝ࡋ࡚࠸ࡿ 1)ࠋ࡞࠾ࠊ㠀➼᪉ᩓ஘ࢆ⪃៖ࡍࡿࡓࡵࡢ㧗ḟ PN ᐃᩘࡢྲྀ
ࡾᢅ࠸࡟ࡣᑐᛂࡋ࡚࠸࡞࠸ࠋ
ղከ㡯ᘧᒎ㛤࡟ࡼࡿࣀ࣮ࢻෆ୰ᛶᏊ᮰࠾ࡼࡧࢯ࣮ࢫศᕸࡢྲྀࡾᢅ࠸
Fig. 2.1-1 ࡟♧ࡍࡼ࠺࡟ࣀ࣮ࢻෆࡢ୰ᛶᏊ᮰࠾ࡼࡧࢯ࣮ࢫศᕸࡣከ㡯ᘧᒎ㛤࡟ࡼࡾྲྀࡾᢅࢃ
ࢀࡿ 1)ࠋከ㡯ᘧᒎ㛤ࡣ᭱኱ 2 ḟࡲ࡛ྍ⬟࡛࠶ࡗࡓࡀࠊ㐺ྜᛶࡢྥୖࢆᅗࡿࡓࡵ࡟ᮏᩚഛ࡟ࡼࡾ
᭱኱ 6 ḟࡲ࡛ᣑᙇࡍࡿࠋ
ճࣀ࣮ࢻ㛫ࣃ࣓࣮ࣛࢱ᥋⥆࡟࠾ࡅࡿ SN ἲࡢ㐺⏝
NSHEX ࡢ㛤Ⓨ๓ࡣࠊࣀ࣮ࢻ㛫ࡢࣃ࣓࣮ࣛࢱࡢ᥋⥆࡜ࡋ࡚ࠊᣑᩓࣀ࣮ࢻἲࢆⓎᒎࡉࡏ࡚ࠊࢫ
࣮࢝ࣛ୰ᛶᏊ᮰࡜㒊ศ୰ᛶᏊὶࢆ⏝࠸ࡓ᪉ἲࡀሗ࿌ࡉࢀ࡚࠸ࡓ
8)ࠋNSHEX
࡛ࡣィ⟬⢭ᗘྥୖ
ࢆ┠ⓗ࡜ࡋ࡚ࠊࡼࡾᛅᐇ࡛࠶ࡿゅᗘ୰ᛶᏊ᮰ࢆ⏝࠸ࡓ᥋⥆ࠊࡍ࡞ࢃࡕࠊࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰࠾
ࡼࡧᶓ᪉ྥࡶࢀࡢゅᗘ౫Ꮡᛶࡢྲྀࡾᢅ࠸࡟ᑐࡋ࡚ࡶ SN ἲࢆ㐺⏝ࡋ࡚࠸ࡿ 1)ࠋ
մභゅ᱁Ꮚయ⣔⏝ࡢ⊂⮬ࡢᶓ᪉ྥࡶࢀࡢྲྀࡾᢅ࠸ᡭἲ
භゅ᱁Ꮚ࡟ᑐࡋ࡚ࣀ࣮ࢻἲࢆ㐺⏝ࡍࡿሙྜࠊFig. 2.1-2 ࡟♧ࡍࡼ࠺࡟ࠊᚄ᪉ྥ㸦౛࠼ࡤ X ㍈
᪉ྥ㸧࡬ࡢ㐺⏝࡜㍈᪉ྥ㸦Z ㍈᪉ྥ㸧࡬ࡢ㐺⏝࡜࡛ࠊᶓ᪉ྥࡶࢀࡢᙧែࡀ␗࡞ࡗ࡚࠸ࡿࡓࡵ࡟ࠊ
ྲྀࡾᢅ࠸᪉ἲࡶ␗࡞ࡿࠋ㍈᪉ྥ࡟ࣀ࣮ࢻἲࢆ㐺⏝ࡍࡿሙྜ࡟ࡣࠊᶓ᪉ྥࡶࢀࡣᚄ᪉ྥ㸦X ㍈ࠊ
U ㍈ࠊV ㍈᪉ྥ㸧ࡢࡳ࡞ࡢ࡛ࠊᐃᘧ໬ࡣ┤஺ᗙᶆయ⣔⏝ࡢࣀ࣮ࢻἲ࡜ྠࡌ࡛࠶ࡾࠊ┤஺ᗙᶆయ
⣔⏝ࣀ࣮ࢻἲ୍࡛⯡࡟᥇⏝ࡉࢀ࡚࠸ࡿ 2 ḟከ㡯ᘧ㏆ఝࢆ᥇⏝ࡋ࡚࠸ࡿ 1)ࠋࡑࢀ࡟ᑐࡋࠊᚄ᪉ྥ
㸦౛࠼ࡤ X ㍈᪉ྥ㸧࡟ࣀ࣮ࢻἲࢆ㐺⏝ࡍࡿሙྜ࡟ࡣࠊᶓ᪉ྥࡶࢀࡣ㍈᪉ྥ㸦Z ㍈᪉ྥ㸧࡜ᚄ᪉
ྥ㸦U ㍈ࠊV ㍈᪉ྥ㸧࡟ࡑࢀࡒࢀᏑᅾࡍࡿࠋ
㍈᪉ྥࡶࢀ࡟ࡘ࠸࡚ࡣࠊࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰ࡢ㍈᪉ྥෆᤄࢆ฼⏝ࡋࡓ᪉ἲࢆ᥇⏝ࡋ࡚࠸ࡿ 2)ࠋ
ᚄ᪉ྥࡶࢀ࡟ᑐࡋ࡚ࡣࠊᗄఱᏛⓗᙧ≧࠿ࡽ௚ࡢࡶࢀࡢࡼ࠺࡟㛵ᩘࢆࣇ࢕ࢵࢸ࢕ࣥࢢࡍࡿࡼ࠺
࡞⡆༢࡞᪉ἲ࡛ྲྀࡾᢅ࠺ࡇ࡜ࡣ୙ྍ⬟࡛࠶ࡿࠋᚑࡗ࡚ࠊNSHEX ࡛ࡣࣀ࣮ࢻࡢ㡬Ⅼ㸦ࢥ࣮ࢼ࣮㸧
ࡢ୰ᛶᏊ᮰ࢆࡑࡢ࿘ᅖࡢࣃ࣓࣮ࣛࢱ࠿ࡽࡢ㏆ఝ࡟ࡼࡾồࡵࠊᚓࡽࢀࡓࣀ࣮ࢻ㡬Ⅼ୰ᛶᏊ᮰ࢆ฼
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⏝ࡋ࡚ࡶࢀࡢ⟬ฟࢆ⾜ࡗ࡚࠸ࡿ 9)ࠋ࡞࠾ࠊᩥ⊩ 9)࡛ࡣ 2 ḟከ㡯ᘧᒎ㛤࡟ࡼࡿྲྀࡾᢅ࠸ࢆ♧ࡋ࡚
࠸ࡿࡀࠊᮏሗࡢ௜㘓 5 ࡟♧ࡍࡼ࠺࡟ࠊᚄ᪉ྥࡶࢀࡢྲྀࡾᢅ࠸࡟㛵ࡍࡿࢧ࣮࣋࢖ࢆ⾜࠸ࠊ1 ḟከ
㡯ᘧᒎ㛤ࡀ᭱㐺࡜ุ᩿ࡋࡓࠋ
յ཰᮰ᛶྥୖࡢࡓࡵࡢึᮇ᭷㝈ᕪศἲィ⟬
ᮏሗࡢ➨ 3 ❶࡛♧ࡍࡼ࠺࡟ࠊࣀ࣮ࢻἲィ⟬ࡢ཰᮰ᛶࢆᨵၿࡍࡿࡓࡵ࡟ึᮇ୰ᛶᏊ᮰ࡢ᥎ᐃ࡜
ࡋ࡚ึᮇ᭷㝈ᕪศἲィ⟬ࢆᑟධࡍࡿࠋࡍ࡞ࢃࡕࠊࣀ࣮ࢻἲィ⟬࡟ඛ❧ࡕࠊ1 ࣀ࣮ࢻࢆ 1 ࣓ࢵࢩ
ࣗ࡜ࡍࡿ᭷㝈ᕪศἲィ⟬࡟ࡼࡾࠊึᮇ᰾ศ⿣୰ᛶᏊ※ศᕸࢆ୚࠼ࠊ཰᮰ᛶࡢᨵၿࢆᅗࡿࠋ࡞࠾ࠊ
࣮ࣘࢨ࣮ࡢ฼౽ࢆ⪃࠼ࠊᙜィ⟬ฎ⌮ࡢᑟධ࡟㝿ࡋ࡚ࡣࠊࢃࡎ࠿࡞ධຊࡢኚ᭦ࡢࡳ࡛῭ࡴࡼ࠺࡟
ࡍࡿࠋ
ຍ㏿ἲ࡜ࡋ࡚ࡣࠊෆഃ཯᚟ィ⟬࡟࠾࠸࡚ࣀ࣮ࢻ༢఩ࡢࣜࣂࣛࣥࢫἲࡢ㐺⏝ࡀྍ⬟࡛࠶ࡿࠋ
NSHEX ࡟㛵ࡋ࡚ࡣࠊࡇࢀࡲ࡛ࠊῶ㏿ᮦ௜ᑠᆺ㧗㏿⅔⅔ᚰ KNK-IIࠊ୰ᆺ㧗㏿⅔⅔ᚰࠕࡶࢇ
ࡌࡹࠖࠊ኱ᆺ㧗㏿⅔⅔ᚰࠕࢫ࣮ࣃ࣮ࣇ࢙ࢽࢵࢡࢫࠖࢆᑐ㇟࡟᳨ドࡀ⾜ࢃࢀ࡚࠸ࡿ 1, 2, 10)ࠋᮏሗ࡛
ࡣࡑࢀࡽ࡟㛵㐃ࡍࡿ NSHEX ࡢᩚഛ࡟ࡼࡿຠᯝࡢヲ⣽ࢆ♧ࡍ࡜ඹ࡟ࠊᐇ⏝ᛶࢆ㔜どࡋࡓ㐺⏝ᛶ
ホ౯࡟ࡶゝཬࡍࡿࠋ
2.2 MINIHEX
MINIHEX 㸦 Transport calculation code for reactor cores with MINI-HEXagonal-Z
geometry㸧ࡣ 3 ḟඖභゅయ⣔⏝㍺㏦භゅ࣓ࢵࢩࣗ᭷㝈ᕪศἲィ⟬ࢥ࣮ࢻ࡛࠶ࡿ 5)ࠋභゅ᱁Ꮚ࡛
ᙧᡂࡉࢀࡿᚄ᪉ྥ࡟㛵ࡋ࡚ࡣࠊ1 ᱁Ꮚࡀ 1 ࣓ࢵࢩࣗ࡟┦ᙜࡋࠊࡑࢀ௨ୖࡢ࣓ࢵࢩࣗࡢ⣽ศ໬࡟
ࡣᑐᛂࡋ࡚࠸࡞࠸ࠋ㍈᪉ྥ࡟ࡣ௵ព࡟࣓ࢵࢩࣗࡢศ๭ࡀྍ⬟࡛࠶ࡿࠋ୰ᛶᏊ᮰ࡢゅᗘ౫Ꮡᛶࡢ
ྲྀࡾᢅ࠸࡟ࡣ NSHEX ࡜ྠᵝ࡟ SN ἲࢆ⏝࠸࡚࠸ࡿࠋྠࡌࡃࠊ㠀➼᪉ᩓ஘ࢆ⪃៖ࡍࡿࡓࡵࡢ㧗
ḟ PN ᐃᩘࡢྲྀࡾᢅ࠸࡟ࡣᑐᛂࡋ࡚࠸࡞࠸ࠋຍ㏿ἲ࡜ࡋ࡚ࡣࠊእഃ཯᚟ィ⟬࡟࠾࠸࡚ࠊ୰ᛶᏊ
※እᤄἲࡢ㐺⏝ࡀྍ⬟࡛࠶ࡿࠋ
MINIHEX ࡣභゅ᱁Ꮚࡢ㓄ิࣆࢵࢳࡀ 5.1cm ࡛࠶ࡿࣟࢩ࢔ࡢ≀⌮⛉Ꮫ࢚ࢿࣝࢠ࣮◊✲ᡤ
㸦IPPE㸧࡟࠶ࡿ⮫⏺ᐇ㦂⿦⨨ BFS-2 ࢆ⏝࠸࡚⾜ࢃࢀࡓ⮫⏺ᐇ㦂ࡢゎᯒ
6)ࢆ᝿ᐃࡋ࡚సᡂࡉࢀ
ࡓࢥ࣮ࢻ࡛࠶ࡿࠋ୰ᆺ㧗㏿⅔ࡢゎᯒ࡟ SN ἲ᭷㝈ᕪศἲ㍺㏦ィ⟬ࢥ࣮ࢻࢆ㐺⏝ࡍࡿሙྜ࡟ࡣࠊ
ゅᗘศⅬࢆ S4 ࡜ࡋࠊ✵㛫࣓ࢵࢩࣗᖜࢆ 5cm ⛬ᗘ࡜ࡍࢀࡤࠊゅᗘศⅬ࡜✵㛫࣓ࢵࢩࣗࡢヲ⣽໬
࡟ຠᯝࡀᡴᾘྜ࠺ࡇ࡜࡟ࡼࡾ㸦ヲ⣽ࡣ➨ 6 ❶ཧ↷㸧ࠊ↓㝈ゅᗘศⅬཬࡧ↓㝈ᑠ✵㛫࣓ࢵࢩࣗィ
⟬┦ᙜࡢ⤖ᯝࡀᚓࡽࢀࡿ࡜ࡢ▱ぢ࡟ᇶ࡙࠸࡚ 4)ࠊMINIHEX ࡀసᡂࡉࢀࡓࠋ
ࡋ࠿ࡋ࡞ࡀࡽࠊᙜ᫬ࡢࡇࡢ▱ぢࡣࠊ2 ḟඖ RZ య⣔ィ⟬࡟࠾࠸࡚ぢฟࡉࢀࡓࡶࡢ࡛࠶ࡾࠊ3
ḟඖභゅయ⣔࡟ᑐࡋ࡚ࡢጇᙜᛶࡢ☜ㄆࡀᮃࡲࡋ࠸≧ἣ࡛࠶ࡿࠋࡑࡇ࡛ࠊᮏሗ࡛ࡣࠊMINIHEX
ࡢ㐺⏝ᛶ࡟ຍ࠼࡚ࠊḟ࡟⤂௓ࡍࡿ MINISTRI ࡟ࡼࡿゎᯒ࡜⤌ྜࡏࡿࡇ࡜࡟ࡼࡾࠊ3 ḟඖභゅయ
⣔࡛࠶ࡿ BFS-2 ࡟ᑐࡍࡿࡑࡢ▱ぢࡢጇᙜᛶホ౯࡟ࡘ࠸࡚ࡶゐࢀࡿࠋ
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2.3 MINISTRI
MINISTRI㸦Transport calculation code for reactor cores with hexagonal-Z geometry by
treating MINced InSide TRIangle-Z meshes㸧ࡣ 3 ḟඖභゅయ⣔⏝㍺㏦୕ゅ࣓ࢵࢩࣗ᭷㝈ᕪศ
ἲィ⟬ࢥ࣮ࢻ࡛࠶ࡿࠋභゅ᱁Ꮚ࡛ᙧᡂࡉࢀࡿᚄ᪉ྥ࡟㛵ࡋ࡚ࡣࠊ1 ᱁Ꮚࢆ 6ࠊ24ࠊ54ࠊ96 ಶࡢ
୕ゅ࣓ࢵࢩࣗ࡟ศ๭ࡋ࡚ィ⟬ࢆ⾜࠺ࡇ࡜ࡀ࡛ࡁࡿ㸦≀㉁㸦᩿㠃✚㸧ࡢᣦᐃࡣභゅ᱁Ꮚ༢఩࡛࠶
ࡾࠊ୕ゅ࣓ࢵࢩࣗ༢఩࡛ࡢᣦᐃࡣ୙ྍ⬟㸧ࠋලయ౛࡜ࡋ࡚ࠊFig. 2.3-1 ࡟ࡣ 1 ࡘࡢභゅ᱁Ꮚ㸦⇞
ᩱ㞟ྜయ㸧ࢆ 6 ಶཬࡧ 24 ಶࡢ୕ゅ࣓ࢵࢩࣗ࡟ศ๭ࡋࡓᵝᏊࢆ♧ࡋ࡚࠸ࡿࠋ㍈᪉ྥ࡟ࡣ௵ព࡟
࣓ࢵࢩࣗࡢศ๭ࡀྍ⬟࡛࠶ࡿࠋ୰ᛶᏊ᮰ࡢゅᗘ౫Ꮡᛶࡢྲྀࡾᢅ࠸࡟ࡣ NSHEX ࡸ MINIHEX ࡜
ྠᵝ࡟ SN ἲࢆ⏝࠸࡚࠸ࡿࠋྠࡌࡃࠊ㠀➼᪉ᩓ஘ࢆ⪃៖ࡍࡿࡓࡵࡢ㧗ḟ PN ᐃᩘࡢྲྀࡾᢅ࠸࡟ࡣ
ᑐᛂࡋ࡚࠸࡞࠸ࠋຍ㏿ἲ࡜ࡋ࡚ࡣࠊෆഃཬࡧእഃ཯᚟ィ⟬ࡢࡑࢀࡒࢀ࡟࠾࠸࡚ࠊ୰ᛶᏊ※እᤄ
ἲཬࡧ⢒࣓ࢵࢩࣗࣜࣂࣛࣥࢫἲࡢ཮᪉ࡢ㐺⏝ࡀྍ⬟࡛࠶ࡿࠋ
3 ḟඖ SN ἲ㍺㏦୕ゅ࣓ࢵࢩࣗィ⟬ࢥ࣮ࢻ࡜ࡋ࡚ࡣࠊENSEMBLE-TRIZ ࡀ᪤࡟Ꮡᅾࡍࡿࡀ
11-13) ࠊබ㛤ࡸ୍⯡ඹ⏝ࡣࡉࢀ࡚࠸࡞࠸ࠋᚑࡗ࡚ࠊENSEMBLE-TRIZ
࡜ྠᵝࡢᶵ⬟ࢆ᭷ࡋࠊ
NSHEX ࡢ⿵᏶ⓗ࡞఩⨨࡙ࡅ࡜ࡋ࡚ࠊMINISTRI ࢆ᪂ࡓ࡟సᡂࡋࡓࠋᮏሗ࡛ࡣࠊMINISTRI
ࡢᩚഛࠊNSHEX ࡜ࡢẚ㍑ࢆྵࡵࡓ᳨ドࡸ㐺⏝ᛶホ౯࡟ࡘ࠸࡚グ㏙ࡍࡿࠋࡲࡓࠊඛ࡟㏙࡭ࡓ
MINIHEX ࢥ࣮ࢻࡢ㐺⏝ᛶホ౯࡟㈨ࡍࡿࡓࡵ࡟ᚄ᪉ྥ࣓ࢵࢩࣗศ๭ຠᯝࡢホ౯⤖ᯝ࡟ࡘ࠸࡚ࡶ
♧ࡍࠋ
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Fig. 2.1-1
Conceptual view of the nodal method for the 3-D hexagonal-Z geometry
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Fig. 2.1-2
Conceptual view of the transverse leakage in the 3-D hexagonal-Z geometry
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(6 meshes per subassembly in the radial direction)
(24 meshes per subassembly in the radial direction)
Fig. 2.3-1
Triangle mesh division for the 3-D hexagonal-Z geometry
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3. 3 ḟඖභゅయ⣔⏝㍺㏦ࣀ࣮ࢻἲィ⟬ࢥ࣮ࢻ NSHEX ࡢᩚഛ
ᮏ❶࡛ࡣࠊNSHEX㸦3 ศࡢ 1 ⅔ᚰ∧: Ver. 10A.1ࠊ඲⅔ᚰ∧: Ver. 10B.1㸧ࡢᩚഛ࡜ࡋ࡚ࠊࣀ
࣮ࢻෆከ㡯ᘧᒎ㛤ḟᩘࡢᣑᙇ࡜ึᮇ᭷㝈ᕪศィ⟬ࡢᑟධ࡟ࡘ࠸࡚㏙࡭ࡿࠋ
3.1 ࣀ࣮ࢻෆከ㡯ᘧᒎ㛤ḟᩘࡢᣑᙇ
NSHEX ࡛ࡣࠊࣀ࣮ࢻෆࡢ୰ᛶᏊ᮰ศᕸࢆከ㡯ᘧᒎ㛤࡟ࡼࡾྲྀࡾᢅ࠺ࡀࠊᚑ᮶ࡢ NSHEX ࡛
ࡣ᭱኱ 2 ḟࡲ࡛ࡢྲྀࡾᢅ࠸࡛࠶ࡗࡓࠋNSHEX ࡢ㐺⏝ᛶྥୖࢆ⪃࠼ࡓሙྜࠊ≉࡟኱ᆺ⅔ᚰࡢࡼ
࠺࡞኱ᆺ⇞ᩱ㞟ྜయࢆ᭷ࡍࡿ⅔ᚰࡢゎᯒ࡛ࡣࠊ2 ḟࡢከ㡯ᘧᒎ㛤࡛ࡣࣀ࣮ࢻෆࡢ୰ᛶᏊ᮰ࢆ㐺
ษ࡟⾲⌧࡛ࡁࡎࠊィ⟬⢭ᗘࡀ୙༑ศ࡛࠶ࡿࡇ࡜ࡀᠱᛕࡉࢀࡿࠋࡑࡇ࡛ࠊࡑࡢࡼ࠺࡞኱ᆺ⇞ᩱ㞟
ྜయࢆ᭷ࡍࡿ⅔ᚰࡢゎᯒ࡟࠾࠸࡚ࡶࠊ༑ศ࡞⢭ᗘࢆ☜ಖࡍࡿࡓࡵ࡟ࠊࣀ࣮ࢻෆࡢ୰ᛶᏊ᮰ࢆ᭱
኱࡛ 6 ḟࡢከ㡯ᘧᒎ㛤࡟ࡼࡾྲྀࡾᢅ࠸ྍ⬟࡜࡞ࡿࡼ࠺࡟ᶵ⬟ᣑᙇࢆ⾜࠺ࠋ
௒ࠊḟࡢ㞳ᩓᗙᶆἲ㸦SNἲ㸧࡟ᇶ࡙ࡃ3ḟඖ୰ᛶᏊ㍺㏦᪉⛬ᘧࢆᢅ࠺ࠋ
&m
: \
m
x, y, z 6t\ m x, y, z Q x, y , z .
(3.1-1)
ࡇࡇ࡛ࠊ
&m
: : ୰ᛶᏊ᪉ྥవᘻ࣋ࢡࢺࣝ㸦
P
m
,K m , [ m 㸧
m : ゅᗘศⅬኚᩘ
\ m : ゅᗘศⅬ m ࡢゅᗘ୰ᛶᏊ᮰
6t : ඲᩿㠃✚
Q : ୰ᛶᏊ※㸦➼᪉㸧
ࡇࢀ࠿ࡽᑐ㇟࡜ࡍࡿࡢࡣࠊᚄ᪉ྥ㸦X㍈᪉ྥ㸧ࡢᑐ㠃㛫㊥㞳 d r ࠊ㍈᪉ྥ㸦Z㍈᪉ྥ㸧ࡢᖜ d z ࢆ
᭷ࡍࡿභゅᰕ≧ࡢࣀ࣮ࢻ࡛࠶ࡿࠋFig. 3.1-1࡟♧ࡍࡼ࠺࡟XࠊYࠊZ㍈ࡢྛ᪉ྥࡢᗙᶆࡣᑐ㠃㛫㊥
㞳 d r ࡜㍈᪉ྥࣀ࣮ࢻᖜ d z ࡟ࡼࡗ࡚ࡑࢀࡒࢀつ᱁໬ࡉࢀ࡚࠸ࡿࠋ(3.1-1)ᘧࢆX㍈᪉ྥ࡟ᑐࡍࡿᶓ
᪉ྥ㸦ᆶ┤᪉ྥ㸧ࠊࡍ࡞ࢃࡕࠊY㍈᪉ྥ࡜Z㍈᪉ྥ࡟ࡑࢀࡒࢀࠊ y s x y y s x ࠊཬࡧࠊ
1 2 z 1 2 ࡢ༊㛫࡟ࢃࡓࡗ࡚✚ศࡍࡿࡇ࡜࡟ࡼࡾࠊḟࡢX㍈᪉ྥࡢ1ḟඖࡢ㍺㏦᪉⛬ᘧࢆᚓ
ࡿࠋ
Pm d
dr
^y x \ x ` 6 y x \ x dx
ࡇࡇ࡛ࠊ\
m
s
m
m
t
x s
^
`
y s x Q x Lmz x Lmr x .
ࡣḟᘧ࡛ᐃ⩏ࡉࢀࡿX㍈᪉ྥࡢ1ḟඖࡢゅᗘ୰ᛶᏊ᮰࡛࠶ࡿࠋ
㻙㻌㻥㻌㻙㻌
(3.1-2)
JAEA-Data/Code 2011-018
12
\
m
³
x 1 2
dz ³
ys x ys x 12
³
1 2
dy\ m x, y, z dz ³
ys x ys x .
(3.1-3)
dy
ࡑࡋ࡚ࠊ ys x ࡣḟᘧ࡛ᐃ⩏ࡉࢀࡿ㛵ᩘ࡛࠶ࡿࠋ
ys x 1 x
.
3
(3.1-4)
ྠᵝ࡟ࡋ࡚ࠊZ㍈᪉ྥࡢ1ḟඖ㍺㏦᪉⛬ᘧࡣࠊ(3.1-1)ᘧࢆZ㍈᪉ྥ࡟ᑐࡍࡿᶓ᪉ྥࠊࡍ࡞ࢃࡕࠊ
Y㍈᪉ྥ࡜X㍈᪉ྥ࡟ࡑࢀࡒࢀࠊ y s x y y s x ࡜ 1 2 x 1 2 ࡢ༊㛫࡟ࢃࡓࡗ࡚✚ศࡍࡿ
ࡇ࡜࡟ࡼࡾࠊḟࡢ㏻ࡾᚓࡽࢀࡿࠋ
[m d
d z dz
\ m z 6 t\ m z Qz Lmr z .
ࡇࡇ࡛ࠊ\
m
z 12
\
m
³
z 1 2
(3.1-5)
ࡣḟᘧ࡛୚࠼ࡽࢀࡿZ㍈᪉ྥࡢ1ḟඖࡢゅᗘ୰ᛶᏊ᮰࡛࠶ࡿࠋ
dx ³
ys x ys x 12
³
1 2
dy\ m x, y, z dx ³
ys x ys x .
(3.1-6)
dy
(3.1-2)ᘧ࡜(3.1-5)ᘧ࡟࠶ࡿ Lz x ࠊ Lr x ࠊ Lr z ࡣᶓ᪉ྥࡶࢀ࡛࠶ࡾࠊヲ⣽ࡣᩥ⊩1)ࢆཧ↷
m
m
m
ࡉࢀࡓ࠸ࠋ(3.1-2)ᘧ࡜(3.1-5)ᘧࢆゎࡃࡇ࡜࡟ࡼࡾࠊࣀ࣮ࢻෆ୰ᛶᏊ᮰\
m
x ཬࡧ\ m z ࡀᚓࡽ
ࢀࡿࡀࠊヲ⣽ࡣྠࡌࡃᩥ⊩1)ࢆཧ↷ࡉࢀࡓ࠸ࠋ
NSHEX࡛ࡣX㍈᪉ྥࡢࣀ࣮ࢻෆゅᗘ୰ᛶᏊ᮰ࡣḟࡢከ㡯ᘧᒎ㛤࡟ࡼࡾᢅࢃࢀࡿࠋ
\
N
m
x ¦\ xm,i hi x .
(3.1-7)
i 0
ࡇࡇ࡛ࠊ N ࡣከ㡯ᘧᒎ㛤ḟᩘ࡛࠶ࡿࠋࡲࡓࠊ hi x ࡣභゅᗙᶆ࡟࠾ࡅࡿ┤஺㛵ᩘ⣔࡛࠶ࡾࠊḟ
ᘧࢆ‶ࡓࡍࠋ
12
³
1 2
dxhi x h j x y s x v G ij .
(3.1-8)
ྠᵝ࡟ࡋ࡚ࠊZ㍈᪉ྥࡢࣀ࣮ࢻෆゅᗘ୰ᛶᏊ᮰ࡣḟᘧࡢ㏻ࡾᢅࢃࢀࡿࠋ
\ m z N
¦\
m
z ,i
f i z ,
(3.1-9)
i 0
㻙㻌㻝㻜㻌㻙㻌
JAEA-Data/Code 2011-018
ࡇࡇ࡛ࠊ f i z ࡣXYZᗙᶆ㸦┤⾜ᗙᶆ㸧࡟࠾ࡅࡿ┤஺㛵ᩘ⣔࡛࠶ࡾࠊḟᘧࢆ‶ࡓࡍࠋ
12
³
1 2
dzf i z f j z v G ij .
(3.1-10)
ࡇࢀࡲ࡛ࡢNSHEX࡛ࡣ᭱኱2ḟࡢከ㡯ᘧᒎ㛤࡟ࡼࡿᢅ࠸࡛࠶ࡗࡓࡀࠊࡇࡇ࡛ࡣィ⟬⢭ᗘྥୖ
ࡢࡓࡵ࡟᭱኱6ḟࡲ࡛ᣑᙇࡍࡿࠋ
ᚄ᪉ྥ㸦X㍈᪉ྥ㸧ࡢ┤஺㛵ᩘ⣔ hi x ࡣḟࡢ㏻ࡾᐃ⩏ࡉࢀࡿࠋ
h0 x °h x ° 1
° h x ° 2
°
°° h3 x ®
° h x ° 4
°
°h5 x °
°h6 x °¯
1
x
5
72
7
3
x x
50
.
725 2
631
4
x x 3556
142240
1015 3
5693
5
x x x
3786
424032
2517805 4 13769 2
1425815
x6 x x 7607512
524656
5112248064
x2 (3.1-11)
ࡲࡓࠊ㍈᪉ྥ㸦Z㍈᪉ྥ㸧ࡢ┤஺㛵ᩘ⣔ f i z ࡣḟᘧࡢ㏻ࡾᐃ⩏ࡉࢀࡿࠋ
f 0 z ° f z ° 1
° f z ° 2
°
° f 3 z ®
° f 4 z °
°
° f 5 z °
° f 6 z ¯
1
z
1
12
3
3
z z
20
.
3 2
3
4
z z 14
560
5 3
5
5
z z z
18
336
15 4
5 2
5
z6 z z 44
176
14784
z2 (3.1-12)
(3.1-11)ᘧཬࡧ(3.1-12)ᘧࡢ3ḟ࠿ࡽ6ḟࡲ࡛ࡀᣑᙇ㒊ศ࡛࠶ࡿࠋ
ࣀ࣮ࢻෆከ㡯ᘧᒎ㛤ḟᩘࢆ 2 ḟ࠿ࡽ 6 ḟ࡟ᣑᙇࡋࡓࡇ࡜࡟ࡼࡿຠᯝ࡟ࡘ࠸࡚ࡣࠊ➨ 4 ❶ཬࡧ
➨ 5 ❶࡛ゝཬࡍࡿࠋ
3.2 ึᮇ᭷㝈ᕪศィ⟬ࡢᑟධ
ࡇࢀࡲ࡛ࡢ⤒㦂࠿ࡽࠊึᮇ᰾ศ⿣୰ᛶᏊ※ࡢ୚࠼᪉࡟ࡼࡗ࡚ࠊィ⟬ࡢ཰᮰ᛶࡀ␗࡞ࡿࡇ࡜ࡀ
ศ࠿ࡗ࡚࠸ࡓࡀࠊࡑࡢせᅉࡢ 1 ࡘ࡜ࡋ࡚ࠊ㍺㏦ࣀ࣮ࢻἲ࡛ࡣィ⟬ࣃ࣓࣮ࣛࢱࡀ᭷㝈ᕪศἲ➼ࡢ
୍⯡ࡢィ⟬ἲ࡜ẚ㍑ࡋ࡚ẚ㍑ⓗከ࠸ࡇ࡜ࡀᣲࡆࡽࢀࡿࠋࡍ࡞ࢃࡕࠊ୙㐺ษ࡞ึᮇ୰ᛶᏊ※ࡢୗ
㻙㻌㻝㻝㻌㻙㻌
JAEA-Data/Code 2011-018
࡛ࡣ୙㐺ษ࡞㧗ḟ࣮࣓ࣔࣥࢺࡀㄏ㉳ࡉࢀࠊ཰᮰ᛶࡀᦆ࡞ࢃࢀࡿࡶࡢ࡜⪃࠼ࡽࢀࡿࠋࡑࡇ࡛ࠊࣀ
࣮ࢻἲィ⟬๓࡟ึᮇ᭷㝈ᕪศィ⟬㸦IFDC: Initial Finite Difference Calculation㸧ࢆᑟධࡍࡿ
ࡇ࡜࡟ࡼࡾࠊࣀ࣮ࢻἲィ⟬ࡢࡓࡵࡢࡼࡾ㐺ษ࡞ึᮇ᰾ศ⿣୰ᛶᏊ※ࡢ᥎ᐃࢆヨࡳࡓࠋ
IFDC ࡣࠊ㐺ษ࡞ึᮇ᰾ศ⿣୰ᛶᏊ※ࢆᚓࡿほⅬ࠿ࡽࡣ࠶ࡿ㐺ᗘࡢ཯᚟ィ⟬ࡀᚲせ࡛࠶ࡿࡀࠊ
ࣀ࣮ࢻἲィ⟬ࡶྜࢃࡏࡓ඲ィ⟬᫬㛫▷⦰ࡢほⅬ࠿ࡽࡣᑡ࡞࠸࡟㉺ࡋࡓࡇ࡜ࡣ࡞࠸ࠋᚑࡗ࡚ࠊࣀ
࣮ࢻἲィ⟬ࡢ཰᮰ᛶྥୖ࡜ィ⟬᫬㛫ࡢ▷⦰࠿ࡽ᭱㐺࡞཯᚟ィ⟬᮲௳ࡸᅇᩘࡀᏑᅾࡍࡿࡶࡢ࡜⪃
࠼ࡽࢀࡿࠋࡑࡇ࡛ࠊIFDC ࡟࠾ࡅࡿ᰾ศ⿣୰ᛶᏊ※ࡢ཰᮰ุᐃ᮲௳ࢆࣃ࣓࣮ࣛࢱ࡟ࡋ࡚ࠊ཯᚟
ィ⟬᮲௳࡟㛵ࡍࡿࢧ࣮࣋࢖ࢆ⾜࠺ࡇ࡜࡜ࡋࡓࠋィ⟬ᑐ㇟య⣔࡜ࡋ࡚ࡣࠊ➨ 4 ❶࡛⤂௓ࡍࡿ
KNK-II ⅔ᚰࠊ
ࠕࡶࢇࡌࡹࠖ⅔ᚰࠊࢫ࣮ࣃ࣮ࣇ࢙ࢽࢵࢡࢫ㸦SPX㸧⅔ᚰࡢྛไᚚᲬᤄධ≧ែ࡜ࡋ
ࡓࠋࡲࡓࠊࣀ࣮ࢻἲィ⟬࡟࠾ࡅࡿ཰᮰ุᐃ᮲௳ࡣࠊ➨ 4 ❶ཬࡧ➨ 5 ❶࡛㏙࡭ࡿィ⟬᮲௳࡜ྠᵝ
࡟᰾ศ⿣୰ᛶᏊ※࡟ࡘ࠸࡚ࡣ 110-4 ࡜ࠊᅛ᭷್࡟ࡘ࠸࡚ࡣ 110-5 ࡜ࡋࡓࠋࡲࡓࠊィ⟬࡟ࡣ
Linux ࣮࣡ࢡࢫࢸ࣮ࢩࣙࣥ Precision 690㸦CPU: Core2 Duoࠊࢡࣟࢵࢡ࿘Ἴᩘ 3.0GHz㸧ࢆ౑
⏝ࡋࡓࠋ
(1) KNK-II ⅔ᚰ
IFDC ࡟࠾ࡅࡿ᰾ศ⿣୰ᛶᏊ※ࡢ཰᮰ุᐃ᮲௳ࢆࣃ࣓࣮ࣛࢱ࡟ࡋࡓሙྜࡢࠊィ⟬᫬㛫㸦IFDC
࡜ࣀ࣮ࢻἲィ⟬ࡢྜィ㸧ࡢẚ㍑ࢆ Table 3.2-1 ࡟ࠊIFDC ࡜ࣀ࣮ࢻἲィ⟬ྛࠎࡢእഃ཯᚟ᅇᩘࡢ
ẚ㍑ࢆ Table 3.2-2 ࡟ࡑࢀࡒࢀ♧ࡍࠋ
KNK-II ⅔ᚰ࡟㛵ࡋ࡚ࡣࠊ"All rods out"㸦඲ไᚚᲬᘬᢤࠊRod ࡣไᚚᲬࡢព㸧ࡢࢣ࣮ࢫ࡛ࡣ
IFDC ࡢ㐺⏝࡞ࡋ࡛ࡶ཰᮰ࡀᚓࡽࢀ࡚࠸ࡿࠋࡑࢀ࡟ᑐࡋࠊ"Rods half-in"㸦ไᚚᲬ༙ᤄධ㸧࡜"Rods
in"㸦ไᚚᲬ඲ᤄධ㸧ࡢࢣ࣮ࢫ࡟ࡘ࠸࡚ࡣࠊIFDC ࡢ㐺⏝࡞ࡋ࡛ࡣ཰᮰ࡀᚓࡽࢀࡎࠊIFDC ࡢ㐺
⏝ࡀ୙ྍḞ࡛࠶ࡿࡇ࡜ࡀศ࠿ࡿࠋ"Rods half-in"ࡢࢣ࣮ࢫ࡟࠾ࡅࡿࣀ࣮ࢻἲィ⟬ࡢ᰾ศ⿣୰ᛶᏊ
※ࡢ཰᮰≧ἣࡢẚ㍑ࢆ Fig.3.2-1 ࡟♧ࡍࠋᅗ࠿ࡽࠊIFDC ࢆ㐺⏝ࡋ࡞࠸ሙྜ࡟ࡣࠊ᰾ศ⿣୰ᛶᏊ
※ࡣ୍᪦ 110-3 ⛬ᗘࡲ࡛ࡣ཰᮰ࡍࡿࡀࠊุᐃ᮲௳࡛࠶ࡿ 110-4 ࡲ࡛࡟ࡣ཯᚟ㄗᕪࡣῶᑡࡏࡎ
࡟㏫࡟ቑຍ࡟㌿ࡌ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋ
ḟ࡟ࠊIFDC ࢆ㐺⏝ࡋࡓሙྜࡢィ⟬᫬㛫ࡢẚ㍑࡟ࡘ࠸࡚ࠊIFDC ࡢ཰᮰ุᐃ᮲௳ࢆ 0.1 ࠿ࡽ
0.05ࠊ0.04 ࡜ཝࡋࡃࡍࡿ࡟ᚑ࠸ࠊࢃࡎ࠿࡞ࡀࡽィ⟬᫬㛫ࡢቑຍࡀぢࡽࢀࡿࡇ࡜ࡀศ࠿ࡿࠋࡇࢀ
ࡣࠊIFDC ࡢ཰᮰ุᐃ᮲௳ࢆཝࡋࡃࡋࡓሙྜࠊ࡯ࡰ༢⣧࡟ IFDC ࡢ཯᚟ᅇᩘ㸦ィ⟬᫬㛫㸧ࡀቑ
ຍࡍࡿࡔࡅ࡛ࠊࣀ࣮ࢻἲࡢ཯᚟ᅇᩘ㸦ィ⟬᫬㛫㸧ࡀ࡯࡜ࢇ࡝▷⦰ࡉࢀ࡞࠸ࡓࡵ࡛࠶ࡿࠋࡇࡢࡼ
࠺࡟ࠊKNK-II ⅔ᚰ࡟ᑐࡋ࡚ࡣࠊIFDC ࡣ㠀ᖖ࡟᭷ຠ࡛࠶ࡾࠊIFDC ࡢ཰᮰ุᐃ᮲௳ࡣ IFDC ࡢ
እഃ཯᚟ィ⟬ 2㹼4 ᅇ࡟┦ᙜࡍࡿ 0.1 ⛬ᗘ࡛༑ศ࡛࠶ࡿࡇ࡜ࡀศ࠿ࡗࡓࠋ
(2) ࠕࡶࢇࡌࡹࠖ⅔ᚰ
ィ⟬᫬㛫ࡢẚ㍑ࢆ Table 3.2-3 ࡟ࠊIFDC ࡜ࣀ࣮ࢻἲィ⟬ྛࠎࡢእഃ཯᚟ᅇᩘࡢẚ㍑ࢆ Table
3.2-4 ࡟ࡑࢀࡒࢀ♧ࡍࠋ
ࠕࡶࢇࡌࡹࠖ⅔ᚰ࡟ࡘ࠸࡚ࡣࠊ"All rods out"ࠊ"MCR half-in"㸦MCR ࡣ୺ㄪᩚᲬࡢព㸧ࠊ"MCR
in"ࠊ"BCR in"㸦BCR ࡣᚋഛ⅔೵ṆᲬࡢព㸧ࡢ඲࡚ࡢࢣ࣮ࢫ࡟ᑐࡋ࡚ IFDC ࡞ࡋ࡛ࡣ཰᮰ࡀᚓ
ࡽࢀ࡚࠸࡞࠸ࠋ"MCR half-in"ࡢࢣ࣮ࢫ࡟࠾ࡅࡿࣀ࣮ࢻἲィ⟬ࡢ᰾ศ⿣୰ᛶᏊ※ࡢ཰᮰≧ἣࡢ
㻙㻌㻝㻞㻌㻙㻌
JAEA-Data/Code 2011-018
ẚ㍑ࢆ Fig.3.2-2 ࡟♧ࡍࠋᅗ࠿ࡽࠊIFDC ࢆ㐺⏝ࡋ࡞࠸ሙྜ࡟ࡣࠊ᰾ศ⿣୰ᛶᏊ※ࡣ୍᪦ 510-4
⛬ᗘࡲ࡛ࡣ཰᮰ࡍࡿࡀࠊุᐃ᮲௳࡛࠶ࡿ 110-4 ࡲ࡛࡟ࡣ཯᚟ㄗᕪࡣῶᑡࡏࡎ࡟㏫࡟ቑຍ࡟㌿
ࡌ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿࠋ
IFDC ࢆ㐺⏝ࡋࡓሙྜ࡟ࡣࠊ඲࡚ࡢሙྜ࡟ࡘ࠸࡚ィ⟬ࡢ཰᮰ࡀᚓࡽࢀ࡚࠸ࡿࠋィ⟬᫬㛫࡟㛵
ࡋ࡚ࡣࠊIFDC ࡢ཰᮰ุᐃ᮲௳ࢆ 0.02 ⛬ᗘ࡜ࡋࡓሙྜ࡟᭱ࡶ▷⦰ࡉࢀࡿࡇ࡜ࡀศ࠿ࡿࠋࡇࢀࡣࠊ
IFDC ࡢ཰᮰ุᐃ᮲௳ࢆཝࡋࡃࡍࡿ࡜ࠊIFDC ࡢ཯᚟ᅇᩘࡢቑຍࡣぢࡽࢀࡿࡶࡢࡢࠊ཰᮰ุᐃ
᮲௳ࢆ 0.02 ⛬ᗘ࡜ཝࡋࡃࡍࡿࡲ࡛ࡣࣀ࣮ࢻἲィ⟬ࡢ཯᚟ᅇᩘࡀ኱ᖜ࡟ῶᑡࡋ࡚࠸ࡿࡓࡵ࡛࠶
ࡿࠋ
(3) ࢫ࣮ࣃ࣮ࣇ࢙ࢽࢵࢡࢫ㸦SPX㸧⅔ᚰ
ィ⟬᫬㛫ࡢẚ㍑ࢆ Table 3.2-5 ࡟ࠊIFDC ࡜ࣀ࣮ࢻἲィ⟬ྛࠎࡢእഃ཯᚟ᅇᩘࡢẚ㍑ࢆ Table
3.2-6 ࡟ࡑࢀࡒࢀ♧ࡍࠋ
SPX ⅔ᚰ࡟ࡘ࠸࡚ࡶࠕࡶࢇࡌࡹࠖ⅔ᚰ࡜ྠᵝ࡟"All rods out"ࠊ"MCR half-in"ࠊ"MCR in"ࠊ
"BCR in"ࡢ඲࡚ࡢࢣ࣮ࢫ࡟ᑐࡋ࡚ IFDC ࡞ࡋ࡛ࡣ཰᮰ࡀᚓࡽࢀ࡞࠿ࡗࡓࠋ"MCR half-in"ࡢࢣ
࣮ࢫ࡟࠾ࡅࡿࣀ࣮ࢻἲィ⟬ࡢ᰾ศ⿣୰ᛶᏊ※ࡢ཰᮰≧ἣࡢẚ㍑ࢆ Fig. 3.2-3 ࡟♧ࡍࠋᅗ࠿ࡽࠊ
IFDC ࢆ㐺⏝ࡋ࡞࠸ሙྜ࡟ࡣࠊ࡯࡜ࢇ࡝཰᮰ࡀᚓࡽࢀࡎ࡟ࡍࡄ࡟Ⓨᩓࡋ࡚࠸ࡿᵝᏊࡀศ࠿ࡿࠋ
IFDC ࢆ㐺⏝ࡋࡓሙྜ࡟ࡣࠊIFDC ࡢ཰᮰ุᐃ᮲௳ࢆ 0.05 ࡼࡾࡶཝࡋࡃࡍࡿࡇ࡜࡟ࡼࡾ୍㒊
ࢆ㝖࠸࡚ィ⟬ࡢ཰᮰ࡀᚓࡽࢀࡓࠋィ⟬᫬㛫࡟㛵ࡋ࡚ࡣࠊIFDC ࡢ཰᮰ุᐃ᮲௳ࢆ 0.01 ௜㏆࡜ࡋ
ࡓሙྜ࡟᭱ࡶ▷⦰ࡉࢀࡿࡇ࡜ࡀศ࠿ࡿࡀࠊ"All rods out"ࡢࢣ࣮ࢫ࡛ࡣⓎᩓࡀぢࡽࢀ࡚࠾ࡾࠊ
0.02 ࡜ࡋࡓሙྜࡣ཰᮰ࡀᚓࡽࢀ࡚࠸ࡿࡶࡢࡢィ⟬᫬㛫ࡀ኱ᖜ࡟ቑຍࡋ࡚࠸ࡿࠋ
(4) ࡲ࡜ࡵ
IFDC ࡟㛵ࡍࡿ᳨ウ࠿ࡽࠊึᮇ᰾ศ⿣୰ᛶᏊ※ศᕸ࡟ࡣࣀ࣮ࢻἲィ⟬࡟࠾ࡅࡿ཰᮰ࡢチᐜ⠊
ᅖࡀ࠶ࡾࠊ㐺ษ࡞ IFDC ࡢ㐺⏝࡟ࡼࡾึᮇ᰾ศ⿣୰ᛶᏊ※ศᕸࢆ཰᮰ࡢチᐜ⠊ᅖእ࠿ࡽチᐜ⠊
ᅖෆ࡬࡜᥎⛣ࡉࡏࡿࡇ࡜ࡀྍ⬟࡛࠶ࡿࡇ࡜ࡀศ࠿ࡗࡓࠋ཯㠃ࠊIFDC ࡢ㐺⏝࡟ࡼࡾィ⟬ࡀⓎᩓ
ࡍࡿሙྜࡶぢࡽࢀࡿࡇ࡜ࡀศ࠿ࡗࡓࠋࡇࡢሙྜࡣࠊ⌧≧࡛ࡣ IFDC ࡢ཰᮰ุᐃ᮲௳ࢆኚ᭦ࡋࡓ
෌ィ⟬ࡋ࠿ᑐᛂ⟇ࡣぢฟࡏ࡚࠸࡞࠸ࠋ
௨ୖࡢࡼ࠺࡟ࠊ☜ᐇ࡟ࣀ࣮ࢻἲィ⟬ࢆ཰᮰ࡉࡏࡿ IFDC ࡢ᮲௳ࡣぢฟࡏ࡞࠿ࡗࡓࡀࠊ௒ᅇࡢ
᳨ウ⤖ᯝ࠿ࡽࡣ཰᮰ุᐃ᮲௳࡜ࡋ࡚ 0.02㹼0.03 ࡀ᥎ዡࡉࢀࡿࠋࡑࡢ᮲௳࡛ィ⟬ࡀⓎᩓࡋࡓሙྜ
࡟ࡣࠊ0.05 ࡟⦆ࡵࡿࠊ࠶ࡿ࠸ࡣࠊ0.005 ࡟ཝࡋࡃࡍࡿࡇ࡜ࡀ᥎ዡࡉࢀࡿࠋ
㻙㻌㻝㻟㻌㻙㻌
JAEA-Data/Code 2011-018
Table 3.2-1
Comparison in calculation time among IFDC criterion for the KNK-II core
Convergence
All rods out
Rods half-in
Rods in
(No IFDC)
89*1
NC*2
NC*2
0.100
89
159*1
103*1
0.050
88
161
102
0.040
88
157
101
0.030
90
161
107
0.020
90
160
103
0.010
91
163
104
0.005
94
164
108
criterion
*1: Calculation time [s]
*2: Not converged
Table 3.2-2
Comparison in outer iteration counts of IFDC and nodal calculation among
IFDC criterion for the KNK-II core
All rods out
Convergence
Rods half-in
Rods in
criterion
IFDC
Nodal
IFDC
Nodal
IFDC
Nodal
(No IFDC)
0
39
0
NC*1
0
NC*1
0.100
3
31
4
43
2
37
0.050
4
30
4
43
4
35
0.040
4
30
6
38
4
35
0.030
6
30
7
42
5
35
0.020
7
30
8
41
6
35
0.010
8
29
11
41
7
34
0.005
11
29
14
40
11
34
*1: Not converged
㻙㻌㻝㻠㻌㻙㻌
JAEA-Data/Code 2011-018
Table 3.2-3
Comparison in calculation time among IFDC criterion for the Monju core
Convergence
All rods out
MCR half-in
MCR in
BCR in
(No IFDC)
NC*2
NC*2
NC*2
NC*2
0.100
120*1
118*1
110*1
113*1
0.050
110
105
84
111
0.040
109
115
84
110
0.030
98
85
84
88
0.020
76
87
79
84
0.010
78
86
81
90
0.005
79
88
82
87
criterion
*1: Calculation time [min]
*2: Not converged
Table 3.2-4
Comparison in outer iteration counts of IFDC and nodal calculation among
IFDC criterion for the Monju core
All rods out
Convergence
MCR half-in
MCR in
BCR in
criterion
IFDC
Nodal
IFDC
Nodal
IFDC
Nodal
IFDC
Nodal
(No IFDC)
0
NC*1
0
NC*1
0
NC*1
0
NC*1
0.100
4
108
6
105
5
106
6
106
0.050
10
104
10
103
10
102
11
103
0.040
11
104
12
102
11
101
12
102
0.030
32
93
30
88
12
100
13
101
0.020
39
73
36
85
37
88
39
89
0.010
48
73
45
83
46
84
48
87
0.005
56
71
54
80
54
86
56
87
*1: Not converged
㻙㻌㻝㻡㻌㻙㻌
JAEA-Data/Code 2011-018
Table 3.2-5
Comparison in calculation time among IFDC criterion for the SPX core
Convergence
All rods out
MCR half-in
MCR in
BCR in
(No IFDC)
NC*2
DIV*3
NC*2
NC*2
0.100
DIV*3
NC*2
280*1
261*1
0.050
158*1
NC
201
200
0.040
153
217*1
174
198
0.030
157
237
174
195
0.020
248
204
215
175
0.010
DIV
195
209
172
0.005
148
206
243
174
criterion
*1: Calculation time [min]
*2: Not converged
*3: Diverged
Table 3.2-6
Comparison in outer iteration counts of IFDC and nodal calculation among
IFDC criterion for the SPX core
All rods out
Convergence
criterion
IFDC
Nodal
*1
MCR half-in
IFDC
Nodal
MCR in
IFDC
BCR in
Nodal
0
DIV
*2
0
NC
*1
IFDC
Nodal
0
NC*1
(No IFDC)
0
NC
0.100
15
DIV*2
6
NC*1
6
150
4
153
0.050
40
96
36
NC
33
94
39
120
0.040
43
87
39
109
36
95
42
116
0.030
46
87
42
115
40
92
45
119
0.020
50
141
48
110
44
102
48
99
0.010
55
DIV
58
102
52
110
54
100
0.005
62
80
65
108
71
129
62
97
*1: Not converged
*2: Diverged
㻙㻌㻝㻢㻌㻙㻌
JAEA-Data/Code 2011-018
y
z
ȯm(x)
1
2
ys(x)
ȯm(z)
z
-1
2
0
1
2
x
x
x
-1
2
z
y
m
Ȟ
Ѝ
Ȑm
m
Ѝm
Ȑ
0
ȣm
ȥ
0
ȣm
x
(Radial view)
Fig. 3.1-1
(Axial view)
Definition of basic node parameters
㻙㻌㻝㻣㻌㻙㻌
x
JAEA-Data/Code 2011-018
Maximum iteration error
1E+0
1E-1
Without IFDC
1E-2
1E-3
With IFDC under
condition of 0.002
1E-4
Convergence criterion
1E-5
0
10
20
30
40
50
Outer iteration count of nodal calculation
Fig. 3.2-1
Comparison in convergence performance of fission source between with and
without IFDC for "Rods half-in" case of the KNK-II core
Maximum iteration error
1E+0
1E-1
Without IFDC
1E-2
1E-3
With IFDC under
condition of 0.02
1E-4
Convergence criterion
1E-5
0
20
40
60
80
100
Outer iteration count of nodal calculation
Fig. 3.2-2
Comparison in convergence performance of fission source between with and
without IFDC for "MCR half-in" case of the Monju core
㻙㻌㻝㻤㻌㻙㻌
JAEA-Data/Code 2011-018
Maximum iteration error
1E+0
1E-1
Without IFDC
1E-2
With IFDC under
condition of 0.02
1E-3
1E-4
Convergence criterion
1E-5
0
20
40
60
80
100
Outer iteration count of nodal calculation
Fig. 3.2-3
Comparison in convergence performance of fission source between with and
without IFDC for "MCR half-in" case of the SPX core
㻙㻌㻝㻥㻌㻙㻌
JAEA-Data/Code 2011-018
4. 3 ḟඖභゅయ⣔⏝㍺㏦භゅ࣓ࢵࢩࣗ᭷㝈ᕪศἲィ⟬ࢥ࣮ࢻ MINIHEX ࡢᩚഛ
ᮏ❶࡛ࡣࠊMINIHEX㸦Ver. 2.1㸧ࡢᩚഛ࡜ࡋ࡚ࠊᇶ♏ᘧࡢᑟฟ㸦ཧ⪃⏝㸧࡜㈇ࡢ୰ᛶᏊ᮰Ⓨ
⏕᫬ࡢฎ⌮࡟㛵ࡍࡿᨵⰋ࡟ࡘ࠸࡚㏙࡭ࡿࠋ
4.1 ᇶ♏ᘧࡢᑟฟ
ࡇࡇ࡛ࡣࠊ༢఩⇞ᩱ㞟ྜయࢆ᝿ᐃࡋࡓṇභゅᙧయ⣔㸦ᑐ㎶㛫㊥㞳 hr 㸧ࢆྲྀࡾᢅ࠺ࠋࡲࡓࠊ⡆
༢ࡢࡓࡵ࡟୰ᛶᏊ᮰ࡢ㍈᪉ྥ㸦Z ㍈᪉ྥ㸧ࡢࢫࢺ࣮࣑ࣜࣥࢢࡢྲྀࡾᢅ࠸࡟ࡘ࠸࡚ࡣ┬␎ࡍࡿࠋ
ࡉ࡚ࠊࡲࡎࡣḟࡢ SN ἲ࡟ᇶ࡙ࡃ 2 ḟඖ㍺㏦᪉⛬ᘧ㸦X-Y ㍈᪉ྥ㸧ࢆᇶᮏ࡟ࡍࡿࠋ
P m w\ m x, y K m w\ m x, y hr
wx
hr
wy
6 t\ m x, y Q x, y .
(4.1-1)
ࡇࡇ࡛ࠊ
P m : ୰ᛶᏊ᪉ྥవᘻ㸦ゅᗘศⅬ m 㸧ࡢX㍈᪉ྥᡂศ
K m :୰ᛶᏊ᪉ྥవᘻ㸦ゅᗘศⅬ m 㸧ࡢY㍈᪉ྥᡂศ
m : ゅᗘศⅬኚᩘ
\ m : ゅᗘศⅬ m ࡢゅᗘ୰ᛶᏊ᮰
6t : ඲᩿㠃✚
Q : ୰ᛶᏊ※㸦➼᪉㸧
௒ࠊFig. 4.1-1 ࡟♧ࡍභゅ࣓ࢵࢩࣗࢆᑐ㇟࡜ࡍࡿࠋFig. 4.1-1 ୰࡟࠶ࡿ㛵ᩘ ys x ࡣḟࡢ㏻ࡾ
ᐃ⩏ࡉࢀࡿࠋ
ys x 1 x
3
.
(4.1-2)
ࡲࡎࠊ༢఩ṇභゅᙧ࣓ࢵࢩࣗࡢ✚ศ࡟ࡼࡾࣂࣛࣥࢫᘧࢆᚓࡿࠋ
(4.1-1)ᘧࡢᕥ㎶➨ 1 㡯࡟ࡘ࠸࡚ࠊ
㻙㻌㻞㻜㻌㻙㻌
JAEA-Data/Code 2011-018
Pm
12
³
1 2
hr
Pm
dx ³
ys x dy
ys x w\ m x, y wx
d ys x w ys x dy ½
dx ® ³
dy\ m x, y ³
dy\ m x, y ¾
wy ys x hr 1 2 ¯ dx ys x dx ¿
m
P 12
d ys x dx
dy\ m x, y ³
³
1
2
y
x
hr
dx s
12
³
.
dy x d ys x ½

dx ®\ m x, y s x s \ m x, y s x ¾
³
1
2
hr
dx
dx
¯
¿
Pm
12
Pm ª
m
12
m
º P
\
dy
x
,
y
»¼ 1 2
hr «¬ ³ ys x 3hr
ys x Pm
\
3hr
m
x
\ xm Pm
2 3hr
\
m
u
12
³
1 2
^
`
dx sign x \ m x, y s x \ m x, y s x \ vm \ vm \ um
(4.1-3)
(4.1-1)ᘧࡢᕥ㎶➨ 2 㡯࡟ࡘ࠸࡚ࠊ
Km
hr
12
dx ³
³
ys x 1 2
Km
2hr
ys x \
m
u
\
w\ m x, y K m
wy
hr
dy
m
v
\
m
v
\
m
u
12
³
1 2
^
`
dx \ m x, y s x \ m x, ys x .
(4.1-4)
(4.1-1)ᘧࡢᕥ㎶➨ 1 㡯࡜➨ 2 㡯࡟ࡘ࠸࡚ࡣࠊ௨ୗࡢ㏻ࡾኚᙧࡉࢀࡿࠋ
Pm
hr
12
³
1 2
Pm
3hr
Pm
3hr
1
3hr
dx ³
ys x dy
ys x w\ m x, y K m
wx
hr
\
m
x
\ xm \
m
x
\
m
x
Pm
2 3hr
\
m
u
12
³
1 2
dx ³
ys x ys x dy
w\ m x, y wy
\ vm \ vm \ um Km
2hr
\
m
u
\ vm \ vm \ um
.
§1 m
3 m· m
1
¨ P K ¸¸ \ u \ um ¨2
2
3hr
©
¹
§ 1 m
3 m· m
¨ P K ¸¸ \ v \ vm
¨ 2
2
©
¹
(4.1-5)
ࡇࡇ࡛ࠊḟᘧ࡛⾲ࡉࢀࡿභゅయ⣔⏝ࡢ᪉ྥవᘻࢆᐃ⩏ࡍࡿࠋ

° P xm
°°
m
®Pu
°
°P m
° v
¯
Pm
1 m
P 2
1 m
P 2
3 m
K .
2
3 m
K
2
(4.1-6)
㻙㻌㻞㻝㻌㻙㻌
JAEA-Data/Code 2011-018
ࡍࡿ࡜ࠊ(4.1-5)ᘧࡣ௨ୗࡢࡼ࠺࡟ኚᙧࡉࢀࡿࠋ
Pm
hr
12
³
1 2
dx ³
ys x ys x dy
w\ m K m
hr
wx
12
³
1 2
dx ³
ys x ys x dy
w\ m
wy
.
(4.1-7)
1
^P xm \ xm \ xm Pum \ um \ um Pvm \ vm \ vm `
3hr
(4.1-1)ᘧࡢᕥ㎶➨ 3 㡯࡜ྑ㎶࡟ࡘ࠸࡚ࡣᖹᆒฎ⌮࡟ࡼࡾࠊᇶᮏⓗ࡟ṇ୕ゅᙧࡢ㠃✚ࡢಀᩘ
3
ࢆ஌ࡌࡓᶆグ࡜࡞ࡾࠊ⤖ᒁࠊ࣓ࢵࢩࣗࣂࣛࣥࢫᘧࡣ௨ୗࡢ㏻ࡾ࡜࡞ࡿࠋ
2
^ `
1
3
6 t\
P xm \ xm \ xm Pum \ um \ um Pvm \ vm \ vm 2
3hr
m
3
Q . (4.1-8)
2
ࡍ࡞ࢃࡕ
^ `
2
P xm \ xm \ xm Pum \ um \ um P vm \ vm \ vm 6 t\
3hr
m
Q.
(4.1-9)
ḟ࡟ࠊ࣓ࢵࢩࣗෆ࡛ࡣ୰ᛶᏊ᮰ࡀ⥺ᙧ࡟ኚ໬ࡍࡿ࡜௬ᐃࡋࠊḟࡢ⥺ᙧᕪศᘧࢆྲྀࡾධࢀࡿࠋ
\
m
1 m
\ x \ xm
2
1 m
\ u \ um
2
1 m
\ v \ vm .
2
(4.1-10)
m
(4.1-10)ᘧࢆ⏝࠸ࡿࡇ࡜࡟ࡼࡾࠊ࣓ࢵࢩࣗὶฟ୰ᛶᏊ᮰\ x
ࠊ\ um ࠊ\ vm ࢆࡑࢀࡒࢀ௨ୗࡢ㏻
ࡾ⾲ࡍࡇ࡜ࡀ࡛ࡁࡿࠋ
\ xm
° m
®\ u °\ m
¯ v
2\
m
\ xm
2\
m
\ um .
2\
m
\
(4.1-11)
m
v
(4.1-11)ᘧࢆ(4.1-9)ᘧ࡟௦ධࡍࡿࡇ࡜࡟ࡼࡾࠊ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰\
m
ࡣ᪤▱ࡢ࣓ࢵࢩࣗධ
m
ᑕ୰ᛶᏊ᮰\ x
ࠊ\ um ࠊ\ vm ࡜୰ᛶᏊ※ Q ࠿ࡽḟࡢࡼ࠺࡟ᚓࡿࡇ࡜ࡀ࡛ࡁࡿࠋ
\
m
4 P xm\ xm Pum\ um Pvm\ vm
Q
3hr
.
4 P xm Pum Pvm
6t
3hr
(4.1-12)
4.2 ㈇ࡢ୰ᛶᏊ᮰Ⓨ⏕᫬ࡢฎ⌮࡟㛵ࡍࡿᨵⰋ
ᚑ᮶ࡢ MINIHEX ࡛ࡣ㈇ࡢὶฟ୰ᛶᏊ᮰ࡀ⏕ࡌࡓሙྜ࡟ࡣࠊ༢࡟ᙜヱࡢὶฟ୰ᛶᏊ᮰ࢆࢮࣟ
࡟ࢭࢵࢺࡍࡿࡔࡅ࡛࠶ࡗࡓࠋ㏻ᖖࡢ᰾≉ᛶゎᯒ⏝ࡢ㍺㏦ィ⟬ࢥ࣮ࢻ࡛ࡣ"Set flux to zero and
㻙㻌㻞㻞㻌㻙㻌
JAEA-Data/Code 2011-018
correct (Flux fix-up)"࡜࿧ࡤࢀࡿฎ⌮ࡀ⾜ࢃࢀ࡚࠾ࡾࠊMINIHEX ࡟ᑐࡋ࡚ࡶᙜฎ⌮ࢆ⾜࠺ࡇ
࡜ࡀ᭱ࡶ㐺ษ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋࡋ࠿ࡋ࡞ࡀࡽࠊMINIHEX ࡟㛵ࡋ࡚ࡣࠊ௒ᚋ౑⏝⤒㦂ࡢ⵳
✚࡟ࡼࡾ཰᮰ᛶࢆᦆ࡞ࢃࡎ࡟࠿ࡘィ⟬⢭ᗘࢆᝏ໬ࡉࡏ࡞࠸᪉ἲࢆぢฟࡍࡇ࡜ࢆ᝿ᐃࡋ࡚ࠊ௨ୗ
ࡢ 5 ✀㢮ࡢ᪉ἲࢆ㑅ᢥ࡛ࡁࡿࡼ࠺࡟ࡋࡓࠋ
1 ࡘ┠ࡣࠊ㈇ࡢὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋ࡞࠸᪉ἲ࡛࠶ࡿ㸦"No operation"㸧ࠋ
2 ࡘ┠ࡣࠊ㈇ࡢὶฟ୰ᛶᏊ᮰ࢆ༢࡟ࢮࣟ࡟ࢭࢵࢺࡍࡿ᪉ἲ࡛࠶ࡿ㸦"Set to zero"㸧ࠋ
3 ࡘ┠ࡣࠊ㈇ࡢὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋࠊ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࢆ෌ィ⟬ࡍࡿ᪉ἲ࡛
࠶ࡿ㸦"Set to zero and correct average"㸧ࠋࡍ࡞ࢃࡕࠊὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋࠊ(4.1-9)
m
ࡀ㈇࡟
ᘧ࡟ᚑࡗ࡚ࠊ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࢆ෌ィ⟬ࡍࡿࠋ౛࠼ࡤࠊ࣓ࢵࢩࣗὶฟ୰ᛶᏊ᮰\ x
࡞ࡗࡓሙྜࠊ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࡣḟࡢࡼ࠺࡟୚࠼ࡽࢀࡿࠋ
\
m
4 1 2 P xm\ xm Pum\ um Pvm\ vm
Q
3hr
.
4 Pum Pvm
6t
3hr
(4.1-13)
ࡲࡓࠊ඲࡚ࡢ㸦ᚄ᪉ྥ㸧࣓ࢵࢩࣗὶฟ୰ᛶᏊ᮰ࡀ㈇࡜࡞ࡗࡓሙྜࠊ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࡣ
ḟᘧ࡛⾲ࡉࢀࡿࠋ
\
m
2 P xm\ xm Pum\ um Pvm\ vm
Q
3hr
.
6t
(4.1-14)
4 ࡘ┠ࡣࠊ㈇ࡢὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋࠊ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࢆ෌ィ⟬ࡋࠊ㈇࡛࡞
࠿ࡗࡓὶฟ୰ᛶᏊ᮰ࢆ(4.1-11)ᘧࢆ⏝࠸࡚෌ィ⟬ࢆ⾜࠺᪉ἲ࡛࠶ࡿ㸦"Set to zero and correct
average and outgoing"㸧ࠋࡇࡢ᪉ἲࡀ"Set flux to zero and correct (Flux fix-up)"࡜࿧ࡤࢀࡿฎ
⌮ἲ࡛࠶ࡾࠊ᭱ࡶ㐺ษ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋ
᭱ᚋࡢ 5 ࡘ┠ࡣࠊ㈇ࡢὶฟ୰ᛶᏊ᮰ࢆ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰࡟ࢭࢵࢺࡍࡿ᪉ἲ࡛࠶ࡿ㸦"Set to
average"㸧ࠋࡇࡢ᪉ἲࡣ"Step"㏆ఝ࡜࿧ࡤࢀࡿࠋ
௨ୖᣲࡆࡓ 5 ✀㢮ࡢฎ⌮ἲ࡟ࡘ࠸࡚ࠊ➨ 7 ❶࡛ヲ⣽ࢆ♧ࡍ BFS-62-3A ⅔ᚰࢆᑐ㇟࡟ᅛ᭷್
࡜ィ⟬᫬㛫ࡢẚ㍑ࢆ⾜ࡗࡓࠋẚ㍑⤖ᯝࢆ Table 4.2-1 ࡟♧ࡍࡀࠊ"No operation"࡜"Set to
average"ࢆ㐺⏝ࡋࡓሙྜ࡟ࡣࠊ୰ᛶᏊ᮰ࡢ཰᮰ࡀᚓࡽࢀ࡞࠿ࡗࡓࠋࡲࡎࠊᅛ᭷್࡟ࡘ࠸࡚ࡣࠊ
᭱ࡶ㐺ษ࡞ฎ⌮ἲ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿ"Set to zero and correct average and outgoing"࡟ᑐࡋ
࡚ࠊ"Set to zero"ཬࡧ"Set to zero and correct average"ࡣไᚚᲬ඲ᤄධయ⣔࡟࠾࠸࡚ࡶ 0.02%
ࡢᕪ␗࡟␃ࡲࡗ࡚࠾ࡾࠊ≉࡟ၥ㢟ࡣぢࡽࢀ࡞࠸ࡇ࡜ࡀศ࠿ࡿࠋḟ࡟ࠊィ⟬᫬㛫ࡢẚ㍑࡟ࡘ࠸࡚
ࡣࠊ"Set to zero and correct average and outgoing"ࢆ㐺⏝ࡋࡓሙྜࢆᇶ‽࡟ࡍࡿ࡜ࠊ"Set to
zero and correct average"ࢆ㐺⏝ࡋࡓሙྜ࡟ࡣ⣙ 20%ῶ࡟␃ࡲࡗ࡚࠸ࡿࡢ࡟ᑐࡋࠊ"Set to zero"
ࢆ⏝࠸ࡓሙྜ࡟ࡣ 3 ศࡢ 1 ⛬ᗘ࡟ࡲ࡛▷⦰ࡉࢀ࡚࠸ࡿࠋࡇࡢࡼ࠺࡟ࠊBFS-62-3A ⅔ᚰ࡟ᑐࡍࡿ
ẚ㍑⤖ᯝ࠿ࡽࡣࠊ㈇ࡢ୰ᛶᏊ᮰Ⓨ⏕᫬ࡢฎ⌮ἲ࡜ࡋ࡚ࠊィ⟬⢭ᗘ㠃࡟ຍ࠼࡚≉࡟ィ⟬᫬㛫ࡢ▷
⦰ࡢほⅬ࠿ࡽ"Set to zero"ࡀ᥎ዡࡉࢀࠊḟ࠸࡛"Set to zero and correct average"ࡀᣲࡆࡽࢀࡿࠋ
㻙㻌㻞㻟㻌㻙㻌
JAEA-Data/Code 2011-018
ཧ⪃ࡲ࡛࡟ࠊ"No operation"࡜"Set to average"࡟㛵ࡋ࡚ࠊ➨ 6 ❶࡛ヲ⣽ࢆ♧ࡍ KNK-II ⅔ᚰࡢ
ィ⟬࡟࠾࠸࡚ࡶ୧⪅ࡢ㐺⏝ࢆヨࡳࡓࡀࠊBFS-62-3A ࡬ࡢ㐺⏝ࡢሙྜ࡜ྠᵝ࡟୰ᛶᏊ᮰ࡢ཰᮰ࡀ
ᚓࡽࢀ࡞࠿ࡗࡓࡇ࡜࠿ࡽࠊMINIHEX ࢆ⏝࠸ࡓィ⟬࡛ࡣ୧⪅ࡢ㐺⏝ࡣ᥎ዡ࡛ࡁ࡞࠸࡜⪃࠼ࡽࢀ
ࡿࠋ
㻙㻌㻞㻠㻌㻙㻌
JAEA-Data/Code 2011-018
y
\ um
\ vm
\ xm
yS x \
1
2
\ xm
m
1
2
0
x
\ um
\ vm
Fig. 4.1-1
Parameters used in the basic formula of MINIHEX
㻙㻌㻞㻡㻌㻙㻌
JAEA-Data/Code 2011-018
Table 4.2-1
Comparison in eigenvalue and calculation time among negative flux measures
in MINIHEX for the BFS-62-3A core
Central
Off-center
MCR in
MCR in
NC*2
NC*2
NC*2
NC*2
-
+0.022*1
+0.022*1
+0.023*1
+0.023*1
228
+0.022
+0.024
+0.023
+0.023
486
NC*2
NC*2
NC*2
NC*2
-
0.99060
0.98665
0.98771
0.98496
605
Measure
All rods out
No operation
Set to zero
Set to zero and
correct average
Set to average
1 BCR in
Average
time [min]
Set to zero and
correct average
and outgoing
(Ref.)
*1: Relative difference to the reference [%]
*2: Not converged
㻙㻌㻞㻢㻌㻙㻌
JAEA-Data/Code 2011-018
5. 3 ḟඖභゅయ⣔⏝㍺㏦୕ゅ࣓ࢵࢩࣗ᭷㝈ᕪศἲィ⟬ࢥ࣮ࢻ MINISTRI ࡢᩚഛ
ᮏ❶࡛ࡣࠊMINISTRI㸦Ver. 1.1㸧ࡢᩚഛ࡜ࡋ࡚ࠊᇶ♏ᘧࡢᑟฟ࡜ࢥ࣮ࢻࡢᩚഛ࡟ࡘ࠸࡚㏙࡭
ࡿࠋ
5.1 ᇶ♏ᘧࡢᑟฟ
ࡇࡇ࡛ࡣࠊ༢఩⇞ᩱ㞟ྜయࢆ᝿ᐃࡋࡓṇභゅᙧయ⣔㸦ᑐ㎶㛫㊥㞳 hr 㸧ࢆᚄ᪉ྥ࡟ 6 ศ๭ࡍࡿ
ࡇ࡜࡟ࡼࡾ⏕ࡌࡿṇ୕ゅᙧ࣓ࢵࢩࣗ࡟ࡘ࠸࡚ྲྀࡾᢅ࠺ࠋࡑࢀ௨ୖࡢ⣽ศ໬ࢆ⾜ࡗࡓሙྜࡢᐃᘧ
໬ࡣࠊኚᩘ hr ࢆㄪᩚࡍࡿࡇ࡜࡛ᐜ᫆࡟ᑐᛂྍ⬟࡛࠶ࡿࠋࡲࡓࠊ⡆༢ࡢࡓࡵ࡟୰ᛶᏊ᮰ࡢ㍈᪉ྥ
㸦Z ㍈᪉ྥ㸧ࡢࢫࢺ࣮࣑ࣜࣥࢢࡢྲྀࡾᢅ࠸࡟ࡘ࠸࡚ࡣ┬␎ࡍࡿࠋ
ࡉ࡚ࠊࡲࡎࡣḟࡢ SN ἲ࡟ᇶ࡙ࡃ 2 ḟඖ㍺㏦᪉⛬ᘧ㸦X-Y ㍈᪉ྥ㸧ࢆᇶᮏ࡟ࡍࡿࠋ
P m w\ m x, y K m w\ m x, y hr
wx
hr
wy
6 t\ m x, y Q x, y .
(5.1-1)
ࡇࡇ࡛ࠊ
P m : ୰ᛶᏊ᪉ྥవᘻ㸦ゅᗘศⅬ m 㸧ࡢX㍈᪉ྥᡂศ
K m :୰ᛶᏊ᪉ྥవᘻ㸦ゅᗘศⅬ m 㸧ࡢY㍈᪉ྥᡂศ
m : ゅᗘศⅬኚᩘ
\ m : ゅᗘศⅬ m ࡢゅᗘ୰ᛶᏊ᮰
6t : ඲᩿㠃✚
Q : ୰ᛶᏊ※㸦➼᪉㸧
௒ࠊFig. 5.1-1 ࡟♧ࡍ 2 ࡘࡢ୕ゅ࣓ࢵࢩࣗ D ཬࡧ E ࢆᑐ㇟࡜ࡍࡿࠋ୕ゅ࣓ࢵࢩࣗయ⣔࡟࠾ࡅ
ࡿ࠶ࡿゅᗘศⅬࡢゅᗘ୰ᛶᏊ᮰ࡢ✵㛫ࢫ࢘࢕࣮ࣉࢆ⪃࠼ࡓሙྜࠊධᑕ୰ᛶᏊ᮰ᩘ 2㸦᪤▱㸧࡛
ὶฟ୰ᛶᏊ᮰ᩘ 1㸦ᮍ▱㸧࡜࡞ࡿ࣓ࢵࢩࣗ㸦࣓ࢵࢩࣗ D 㸧࡜ࠊ㏫࡟ධᑕ୰ᛶᏊ᮰ᩘ 1㸦᪤▱㸧
࡛ὶฟ୰ᛶᏊ᮰ᩘ 2㸦ᮍ▱㸧࡜࡞ࡿ࣓ࢵࢩࣗ㸦࣓ࢵࢩࣗ E 㸧ࡀᏑᅾࡍࡿࡇ࡜࡟࡞ࡿࠋࡑࡇ࡛ࠊ
௨㝆ࡣ 2 ✀㢮ࡢ୕ゅ࣓ࢵࢩࣗ D ࡜ E ࡑࢀࡒࢀ࡟ࡘ࠸࡚ࠊᐃᘧ໬ࢆ⾜࠺ࡇ࡜࡜ࡍࡿࠋ
ࡲࡓࠊFig. 5.1-1 ୰࡟࠶ࡿ㛵ᩘ ys x ࡣḟࡢ㏻ࡾᐃ⩏ࡉࢀࡿࠋ
ys x x
3
.
(5.1-2)
ࡲࡎࠊ࣓ࢵࢩࣗ D㸦xӍ0㸧࡟ࡘ࠸࡚ࠊ༢఩ṇ୕ゅᙧ࣓ࢵࢩࣗࡢ✚ศ࡟ࡼࡾࣂࣛࣥࢫᘧࢆᚓࡿࠋ
(5.1-1)ᘧࡢᕥ㎶➨ 1 㡯࡟ࡘ࠸࡚ࠊ
㻙㻌㻞㻣㻌㻙㻌
JAEA-Data/Code 2011-018
Pm
hr
12
³
ys x dy
ys x 0
w\ m x, y wx
d ys x dy x ½
w ys x m
\
dx
dy
x
,
y
dy\ m x, y s ¾
®
³
³
³
y
x
y
x
0
wy s
hr
dx ¿
¯ dx s
.
m
12
12
dy
x
d
y
x
P m ª ys x P

½
s
dy\ m x, y º dx ®\ m x, y s x s \ m y s x ¾
»¼ 0
hr «¬ ³ ys x hr ³0
dx
dx
¯
¿
Pm
dx ³
12
Pm
3hr
\ xm Pm
2 3hr
\
m
v
\ um
(5.1-3)
(5.1-1)ᘧࡢᕥ㎶➨ 2 㡯࡟ࡘ࠸࡚ࠊ
Km
hr
12
³
2hr
ys x ys x 0
Km
dx ³
\
\
m
v
dy
m
u
w\ m x, y K m
hr
wy
12
³
0
dx^\ m ys x \ m ys x `
.
(5.1-4)
(5.1-1)ᘧࡢᕥ㎶➨ 1 㡯࡜➨ 2 㡯࡟ࡘ࠸࡚ࡣࠊ௨ୗࡢ㏻ࡾኚᙧࡉࢀࡿࠋ
Pm
hr
12
³
0
Pm
3hr
Pm
3hr
dx ³
ys x ys x \ xm dy
w\ m x, y K m
wx
hr
Pm
2 3hr
\ xm 1
3hr
\
m
v
\ um 12
³
dx ³
Km
\
ys x ys x 0
2hr
m
v
dy
\ um
w\ m x, y wy
.
(5.1-5)
§ Pm
3K m · m
3K m · m
1 § Pm
¨
¸\ u ¨
¸\ v ¨ 2
¸
¨ 2
¸
2
2
h
3
r ©
©
¹
¹
ࡇࡇ࡛ࠊḟᘧ࡛⾲ࡉࢀࡿභゅయ⣔⏝ࡢ᪉ྥవᘻࢆᐃ⩏ࡍࡿࠋ

° P xm
°°
m
®Pu
°
°P m
° v
¯
Pm
1 m
P 2
1 m
P 2
3 m
K .
2
3 m
K
2
(5.1-6)
ࡍࡿ࡜ࠊ(5.1-5)ᘧࡣ௨ୗࡢࡼ࠺࡟ኚᙧࡉࢀࡿࠋ
Pm
hr
12
³
0
dx ³
ys x ys x dy
w\ m K m
wx
hr
12
³
0
dx ³
ys x ys x dy
w\ m
wy
1
P xm\ xm P um\ um P vm\ vm .
3hr
(5.1-7)
(5.1-1)ᘧࡢᕥ㎶➨ 3 㡯࡜ྑ㎶࡟ࡘ࠸࡚ࡣᖹᆒฎ⌮࡟ࡼࡾࠊᇶᮏⓗ࡟ṇ୕ゅᙧࡢ㠃✚ࡢಀᩘ
㻙㻌㻞㻤㻌㻙㻌
JAEA-Data/Code 2011-018
1
ࢆ஌ࡌࡓᶆグ࡜࡞ࡾࠊ⤖ᒁࠊ࣓ࢵࢩࣗࣂࣛࣥࢫᘧࡣ௨ୗࡢ㏻ࡾ࡜࡞ࡿࠋ
4 3
1
1
P xm\ x Pum\ u Pvm\ v 6 t\ Dm
3hr
4 3
1
4 3
QD .
(5.1-8)
ࡍ࡞ࢃࡕࠊ࣓ࢵࢩࣗ D ࡢࣂࣛࣥࢫᘧࡣḟࡢ㏻ࡾ⾲グࡉࢀࡿࠋ
4 m
P x \ x Pum\ u P vm\ v 6 t\ Dm
hr
QD .
(5.1-9)
ྠᵝ࡟ᘧࡢኚᙧࢆ⾜࠺ࡇ࡜࡟ࡼࡾࠊ࣓ࢵࢩࣗ E㸦xӌ0㸧࡟ࡘ࠸࡚ࡶࠊ௨ୗࡢ㏻ࡾ⾲グ࡛ࡁࡿࠋ
4
P xm\ xm Pum\ um P vm\ vm 6 t\ Em
hr
QE .
(5.1-10)
ḟ࡟ࠊ࣓ࢵࢩࣗෆ࡛ࡣ୰ᛶᏊ᮰ࡀ⥺ᙧ࡟ኚ໬ࡍࡿ࡜௬ᐃࡋࠊྛࠎࡢ࣓ࢵࢩࣗෆࡢᕪศᘧࢆྲྀ
ࡾධࢀࡿࠋ࣓ࢵࢩࣗ D ࡟ࡘ࠸࡚ࡣࠊ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ \ Dm ࡜࣓ࢵࢩࣗධᑕ୰ᛶᏊ᮰\ um ཬ
ࡧ\ vm ࡜࣓ࢵࢩࣗ㡬Ⅼ୰ᛶᏊ᮰\ Dm,U ཬࡧ\ Dm,V ࡟㛵ࡋ࡚ࠊḟࡢ⥺ᙧᕪศᘧࢆྲྀࡾධࢀࡿࠋ
\ Dm
1
2\ um \ Dm,U
3
1
2\ vm \ Dm,V .
3
(5.1-11)
m
ࡲࡓࠊ࣓ࢵࢩࣗὶฟ୰ᛶᏊ᮰\ x
࡜࣓ࢵࢩࣗ㡬Ⅼ୰ᛶᏊ᮰\ Dm,U ཬࡧ\ Dm,V ࡟㛵ࡋ࡚ࠊḟࡢ⥺ᙧ
ᕪศᘧࢆྲྀࡾධࢀࡿࠋ
\ x
m
1 m
\ D ,U \ Dm,V .
2
(5.1-12)
m
(5.1-11)ᘧཬࡧ(5.1-12)ᘧࢆ⏝࠸ࡿࡇ࡜࡟ࡼࡾࠊ࣓ࢵࢩࣗὶฟ୰ᛶᏊ᮰\ x
ࢆ௨ୗࡢ㏻ࡾ⾲ࡍ
ࡇ࡜ࡀ࡛ࡁࡿࠋ
\ xm
3\ Dm \ um \ vm .
(5.1-13)
(5.1-13)ᘧࢆ(5.1-9)ᘧ࡟௦ධࡍࡿࡇ࡜࡟ࡼࡾࠊ࣓ࢵࢩࣗ D ࡢ୰ᛶᏊ᮰ࡣ᪤▱ࡢ࣓ࢵࢩࣗධᑕ
୰ᛶᏊ᮰\ um ཬࡧ\ vm ࡜୰ᛶᏊ※ QD ࠿ࡽḟࡢࡼ࠺࡟ᚓࡿࡇ࡜ࡀ࡛ࡁࡿࠋ
\ Dm
4 P xm Pum \ um 4 P xm P vm \ vm
QD
hr
.
12P xm
6t
hr
(5.1-14)
௚᪉ࠊ࣓ࢵࢩࣗ E ࡟ࡘ࠸࡚ࡣࠊ୚࠼ࡽࢀࡓ᮲௳ᘧࡢᩘࡀ࣓ࢵࢩࣗ D ࡜ྠࡌ࡛ࡶᮍ▱ᩘࡀ 1 ࡘ
ከ࠸ࡓࡵ࡟ࠊྠᵝࡢ᪉ἲ࡛ࡣ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࢆᚓࡿࡇ࡜ࡣ࡛ࡁ࡞࠸ࠋࡑࡇ࡛ࠊ㞄᥋ࡍࡿ
࣓ࢵࢩࣗ J ࡢ᝟ሗ㸦᪤▱㸧ࢆ฼⏝ࡍࡿࡇ࡜࡜ࡍࡿࠋࡲࡎࠊ࣓ࢵࢩࣗ J ෆࡢ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ
㻙㻌㻞㻥㻌㻙㻌
JAEA-Data/Code 2011-018
᮰ \ Jm ࡜࣓ࢵࢩࣗධᑕ୰ᛶᏊ᮰ \ Jm,v ཬࡧ \ Jm,u ࡜࣓ࢵࢩࣗ㡬Ⅼ୰ᛶᏊ᮰ \ Em,U ཬࡧ \ Em,V ࡟㛵ࡍ
ࡿḟࡢ⥺ᙧᕪศᘧࢆྲྀࡾධࢀࡿࠋ
\J
m
1
2\ Jm,v \ Em,U
3
1
2\ Jm,u \ Em,V .
3
(5.1-15)
(5.1-15)ᘧ࠿ࡽ࣓ࢵࢩࣗ㡬Ⅼ୰ᛶᏊ᮰\ Em,U ཬࡧ\ Em,V ࡣḟࡢࡼ࠺࡟୚࠼ࡽࢀࡿࠋ
°\ Em,U
m
°̄\ E ,V
3\ Jm 2\ Jm,v ®
(5.1-16)
3\ Jm 2\ Jm,u ᭦࡟ࠊ࣓ࢵࢩࣗ E ෆࡢ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰\ Em ࡜࣓ࢵࢩࣗὶฟ୰ᛶᏊ᮰ \ u ཬࡧ \ v ࡜࣓
m
m
ࢵࢩࣗ㡬Ⅼ୰ᛶᏊ᮰\ Em,U ཬࡧ\ Em,V ࡟㛵ࡍࡿḟࡢ⥺ᙧᕪศᘧࢆྲྀࡾධࢀࡿࠋ
\ Em
1
2\ um \ Em,U
3
1
2\ vm \ Em,V .
3
(5.1-17)
(5.1-17)ᘧࡼࡾࠊ࣓ࢵࢩࣗ E ࠿ࡽࡢὶฟ୰ᛶᏊ᮰\ um ཬࡧ\ vm ࡣḟࡢࡼ࠺࡟୚࠼ࡽࢀࡿࠋ
m
°\ u ®
°\ vm
¯
1
3\ Em \ Em,U
2
.
1
m
m
3\ E \ E ,V
2
(5.1-18)
(5.1-18)ᘧࢆ(5.1-10)ᘧ࡟௦ධࡍࡿࡇ࡜࡟ࡼࡾࠊ࣓ࢵࢩࣗ E ࡢᖹᆒ୰ᛶᏊ᮰\ Em ࡣ᪤▱ࡢ࣓ࢵ
m
࡜࣓ࢵࢩࣗ㡬Ⅼ୰ᛶᏊ᮰\ Em,U ཬࡧ\ Em,V ࡜୰ᛶᏊ※ QE ࠿ࡽḟࡢ㏻ࡾ⾲グ
ࢩࣗධᑕ୰ᛶᏊ᮰\ x
࡛ࡁࡿࠋ
\ Em
4 P xm\ xm 2 P um\ Em,U 2 P vm\ Em,V
QE
hr
.
6 Pum P vm
6t
hr
(5.1-19)
㈇ࡢὶฟ୰ᛶᏊ᮰ࡀ⏕ࡌࡓሙྜࡢฎ⌮ࡣࠊMINIHEX ࡜ྠᵝ࡟ MINISTRI ࡛ࡣ௨ୗࡢ 5 ✀
㢮ࡢ᪉ἲࢆ㑅ᢥ࡛ࡁࡿࡼ࠺࡟ࡋ࡚࠸ࡿࠋ
1 ࡘ┠ࡣࠊ㈇ࡢὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋ࡞࠸᪉ἲ࡛࠶ࡿ㸦"No operation"㸧ࠋ
2 ࡘ┠ࡣࠊ㈇ࡢὶฟ୰ᛶᏊ᮰ࢆ༢࡟ࢮࣟ࡟ࢭࢵࢺࡍࡿ᪉ἲ࡛࠶ࡿ㸦"Set to zero"㸧ࠋ
3 ࡘ┠ࡣࠊ㈇ࡢὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋࠊ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࢆ෌ィ⟬ࡍࡿ᪉ἲ࡛
࠶ࡿ㸦"Set to zero and correct average"㸧ࠋࡍ࡞ࢃࡕࠊὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋࠊ(5.1-9)
㻙㻌㻟㻜㻌㻙㻌
JAEA-Data/Code 2011-018
ᘧཬࡧ(5.1-10)ᘧ࡟ᚑࡗ࡚ࠊ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࢆ෌ィ⟬ࡍࡿࠋᮏሗ࿌࡛ࡣࡇࡢ᪉ἲࢆ᥇⏝
ࡋ࡚࠸ࡿࠋලయⓗ࡟ᩘᘧࢆ⏝࠸࡚♧ࡍࡇ࡜࡜ࡍࡿࠋ
ࡲࡎࠊ࣓ࢵࢩࣗ D ࡟ࡘ࠸࡚ࡣḟࡢ㏻ࡾ࡜࡞ࡿࠋ
\ Dm
4Pum\ um 4Pvm\ vm
QD
hr
.
6t
(5.1-20)
ࡲࡓࠊ࣓ࢵࢩࣗ E ࡟ࡘ࠸࡚ࠊ୍᪉ࡢὶฟ୰ᛶᏊ᮰ࡢࡳ㸦౛࠼ࡤࠊ\ um 㸧ࡀ㈇࡜࡞ࡗࡓሙྜࠊ
࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࡣḟᘧ࡛⾲ࡉࢀࡿࠋ
\ Em
4 P xm\ xm 2 P vm\ Em,V
QE
hr
.
6 P vm
6t
hr
(5.1-21)
᭦࡟ࠊ࣓ࢵࢩࣗ E ࡟ࡘ࠸࡚ࠊ཮᪉ࡢὶฟ୰ᛶᏊ᮰ࡀ㈇࡜࡞ࡗࡓሙྜࡣḟࡢ㏻ࡾ࡜࡞ࡿࠋ
\ Em
4P xm\ xm
QE
hr
.
6t
(5.1-22)
4 ࡘ┠ࡣࠊ࣓ࢵࢩࣗ E ࡟ࡘ࠸࡚ࠊ୍᪉ࡢὶฟ୰ᛶᏊ᮰ࡢࡳࡀ㈇࡜࡞ࡗࡓሙྜ࡟㝈ࡽࢀࡿࡀࠊ
㈇ࡢὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋࠊ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࢆ෌ィ⟬ࡋࠊ㈇࡛࡞࠿ࡗࡓὶฟ୰
ᛶᏊ᮰ࢆ(5.1-18)ᘧࢆ⏝࠸࡚෌ィ⟬ࢆ⾜࠺᪉ἲ࡛࠶ࡿ㸦"Set to zero and correct average and
outgoing"㸧ࠋࡇࡢ᪉ἲࡀ"Set flux to zero and correct (Flux fix-up)" ࡜࿧ࡤࢀࡿฎ⌮ἲ࡛࠶ࡾࠊ
᭱ࡶ㐺ษ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋ
᭱ᚋࡢ 5 ࡘ┠ࡣࠊ㈇ࡢὶฟ୰ᛶᏊ᮰ࢆ࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰࡟ࢭࢵࢺࡍࡿ᪉ἲ࡛࠶ࡿ㸦"Set to
average"㸧ࠋࡇࡢ᪉ἲࡣ"Step"㏆ఝ࡜࿧ࡤࢀࡿࠋ
࡞࠾ࠊ࣓ࢵࢩࣗ㡬Ⅼ୰ᛶᏊ᮰ࡀ㈇࡟࡞ࡗࡓሙྜࡢฎ⌮࡜ࡋ࡚ࠊࢮࣟ࡟ࡣࢭࢵࢺࡍࡿࡀࠊ࣓ࢵ
ࢩࣗᖹᆒ୰ᛶᏊ᮰ࡢ෌ィ⟬ࡣ⾜ࢃࡎࠊ࣓ࢵࢩࣗቃ⏺୰ᛶᏊ᮰ࡢ෌ィ⟬⤖ᯝ࡟ྜࢃࡏ࡚ࠊ㈇࡟࡞
ࡽ࡞࠿ࡗࡓഃࡢ࣓ࢵࢩࣗ㡬Ⅼ୰ᛶᏊ᮰ࢆ(5.1-12)ᘧ࡟ࡼࡾ෌ィ⟬ࡍࡿࠋ
௨ୖᣲࡆࡓ 5 ✀㢮ࡢฎ⌮ἲ࡟ࡘ࠸࡚ࠊ➨ 6 ❶࡛ヲ⣽ࢆ♧ࡍ KNK-II ⅔ᚰࢆᑐ㇟࡟ᅛ᭷್࡜ィ
⟬᫬㛫ࡢẚ㍑ࢆ⾜ࡗࡓࠋẚ㍑⤖ᯝࢆ Table 5.1-1 ࡟♧ࡍࠋᅛ᭷್࡟ࡘ࠸࡚ࡣࠊ᭱ࡶ㐺ษ࡞ฎ⌮
ἲ ࡛ ࠶ ࡿ ࡜ ⪃ ࠼ ࡽ ࢀ ࡿ "Set to zero and correct average and outgoing" ࡟ ᑐ ࡋ ࡚ ࠊ "No
operation"࡜"Set to average"ࢆ᥇⏝ࡋࡓሙྜ࡟ࡣࠊไᚚᲬ඲ᤄධయ⣔࡟࠾࠸࡚ࡑࢀࡒࢀ 0.06%ࠊ
0.10%࡜ẚ㍑ⓗ኱ࡁ࡞ᕪ␗ࡀぢࡽࢀࠊ᰾≉ᛶィ⟬ࡢᐇ⏝ୖࡣၥ㢟࡜࡞ࡿྍ⬟ᛶࡢ࠶ࡿࡇ࡜ࡀศ
࠿ࡿࠋࡑࢀ࡟ᑐࡋࠊ"Set to zero"ཬࡧ"Set to zero and correct average"ࡣไᚚᲬ඲ᤄධయ⣔࡟
࠾࠸࡚ࡶࡑࢀࡒࢀ 0.03%ࠊ0.02%ࡢᕪ␗࡟␃ࡲࡗ࡚࠾ࡾࠊ≉࡟ၥ㢟ࡣぢࡽࢀ࡞࠸ࡇ࡜ࡀศ࠿ࡿࠋ
࡞࠾ࠊィ⟬᫬㛫ࡢẚ㍑࡟ࡘ࠸࡚ࡣ 5 ✀㢮ࡢฎ⌮ἲ㛫࡛≉࡟ᕪࡣぢࡽࢀ࡞࠸ࠋࡇࡢࡼ࠺࡟ࠊKNK-II
⅔ᚰ࡟ᑐࡍࡿẚ㍑⤖ᯝ࠿ࡽࡣࠊ㈇ࡢ୰ᛶᏊ᮰Ⓨ⏕᫬ࡢฎ⌮࡜ࡋ࡚ࠊ"Set to zero and correct
average and outgoing"ࡀ᭱㐺࡛࠶ࡿࡀࠊ"Set to zero and correct average"ࡸ"Set to zero"ࢆ㐺
㻙㻌㻟㻝㻌㻙㻌
JAEA-Data/Code 2011-018
⏝ࡋ࡚ࡶ≉࡟ၥ㢟ࡣ࡞࠸࡜ゝ࠼ࡿࠋ
5.2 ࢥ࣮ࢻࡢᩚഛ
ᇶᮏⓗ࡟ࡣ MINIHEX ࢥ࣮ࢻࢆ࣮࣋ࢫ࡟᭷㝈ᕪศἲィ⟬㒊ศࢆࠊඖࠎࡢභゅ-Z య⣔⏝ࡢฎ⌮
࠿ࡽ୕ゅ-Z య⣔⏝࡟ኚ᭦ᨵⰋࡍࡿࡇ࡜࡟ࡼࡾ MINISTRI ࡢసᡂࢆ⾜ࡗࡓࠋ㞟ྜయෆࡢ୕ゅ࣓
ࢵࢩࣗ࡟ࡼࡿᚄ᪉ྥศ๭ᩘࡣ 6ࠊ24ࠊ54ࠊ96 ࡟ᑐᛂࡉࡏࡓࠋ㞟ྜయෆࡢ࣓ࢵࢩࣗ␒ྕࡣ Fig. 5.2-1
࡟♧ࡍ㏻ࡾ㞟ྜయ୰ᚰ࠿ࡽ⼺᪕≧࡟ࡘࡅࠊᚄ᪉ྥࡢ✵㛫ࢫ࢘࢕࣮ࣉࡸ࣓ࢵࢩࣗ㛫ࡢࢹ࣮ࢱࡢཷ
ࡅΏࡋࡣࠊ6ࠊ24ࠊ24ࠊ96 ࣓ࢵࢩࣗศ๭᫬ࡢࡒࢀࡒࢀࡢ࣓ࢵࢩࣗ␒ྕ⾲࡟ࡼࡾ⟶⌮ࡍࡿࡇ࡜࡜
ࡋࡓࠋ
㻙㻌㻟㻞㻌㻙㻌
JAEA-Data/Code 2011-018
Table 5.1-1
Comparison in eigenvalue and calculation time among negative flux measures
in MINISTRI for the KNK-II core
Rods
Average
Measure
All rods out
No operation
+0.000*1
+0.044*1
+0.103*1
10
Set to zero
+0.000
+0.018
+0.026
11
+0.000
+0.014
+0.021
11
-0.000
+0.029
+0.055
10
1.09451
0.98283
0.87960
11
Set to zero and
correct average
Set to average
Rods in
half-in
time [min]
Set to zero and
correct average
and outgoing
(Ref.)
*1: Relative difference to the reference [%]
㻙㻌㻟㻟㻌㻙㻌
JAEA-Data/Code 2011-018
y
Mesh D
Mesh E
\ Dm,U
\
\ um
\ Em,V
m
J ,v
yS x \ J \ xm
m
\
m
J ,u
Mesh J
Fig. 5.1-1
1
2
\ Em
0
\ vm
\ vm
\ xm
\D
m
\
m
u
\ Em,U
1
2
x
\ Dm,V
Parameters used in the basic formula of MINISTRI
㻙㻌㻟㻠㻌㻙㻌
JAEA-Data/Code 2011-018
㻟㻡㻟㻠
㻟㻣㻟㻢
㻟㻥㻟㻤
㻠㻜
㻝㻟㻝㻞
㻝㻡㻝㻠
㻝㻢
㻟㻞
㻠
㻝㻤
㻝
㻥
㻝㻤
㻟㻞
㻠㻟㻝㻤
㻣
㻥㻞㻤
㻡㻢
㻠㻡㻠㻢
㻣㻞㻢
㻞㻝㻞㻞
㻡㻝㻡㻞
㻞㻝㻞㻞
㻠㻥㻡㻜
㻔㻢㻌㼙㼑㼟㼔㼑㼟㻌㼜㼑㼞㻌㻿㻭㻕
㻔㻞㻠㻌㼙㼑㼟㼔㼑㼟㻌㼜㼑㼞㻌㻿㻭㻕
㻔㻡㻠㻌㼙㼑㼟㼔㼑㼟㻌㼜㼑㼞㻌㻿㻭㻕
㻢㻥㻢㻤
㻣㻡㻣㻠
㻣㻢
㻟㻣㻟㻢
㻟㻥㻟㻤
㻣㻣㻠㻜
㻣㻤
㻝㻝㻝㻜
㻝㻣㻠
㻤㻝㻠㻠
㻤㻟㻤㻠
㻞㻣㻡㻤
㻞㻟㻞㻠
㻠㻣㻠㻤
㻡㻣
㻞㻡㻡㻢
㻡㻟㻡㻠
㻡㻝㻡㻞
㻠㻥㻡㻜
㻤㻣㻤㻤
㻡㻥
㻣㻞㻢
㻞㻝㻞㻞
㻤㻡㻤㻢
㻞㻥㻢㻜
㻝㻤
㻝㻥㻞㻜
㻢㻝
㻥㻞㻤
㻡㻢
㻠㻡㻠㻢
㻢㻟㻢㻞
㻟㻝㻟㻜
㻟㻞
㻠㻟㻝㻤
㻤㻞
㻟㻟㻟㻞
㻝㻡㻝㻠
㻣㻥㻠㻞
㻢㻡㻢㻠
㻝㻟㻝㻞
㻠㻝㻝㻢
㻤㻜
㻢㻣㻢㻢
㻟㻡㻟㻠
㻡㻡
㻥㻡㻥㻢
㻥㻟㻥㻠
㻥㻝㻥㻞
㻤㻥㻥㻜
㻔㻥㻢㻌㼙㼑㼟㼔㼑㼟㻌㼜㼑㼞㻌㻿㻭㻕
Fig. 5.2-1
Mesh numbering within a subassembly in MINISTRI
㻙㻌㻟㻡㻌㻙㻌
㻞㻡
㻡㻟㻡㻠
㻡㻢
㻣㻟㻣㻞
㻞㻣
㻞㻟㻞㻠
㻠㻣㻠㻤
㻣㻝㻣㻜
㻞㻥
㻝㻤
㻝㻥㻞㻜
㻞㻟㻞㻠
㻟㻝㻟㻜
㻝㻝㻝㻜
㻝㻣㻠
㻠㻠
㻡㻢
㻝㻥㻞㻜
㻝㻡㻝㻠
㻠㻞
㻟㻞
㻝㻣㻠
㻝㻟㻝㻞
㻠㻝㻝㻢
㻝㻝㻝㻜
㻟㻟㻟㻞
JAEA-Data/Code 2011-018
6. 3 ḟඖභゅయ⣔⏝㍺㏦ィ⟬ࢥ࣮ࢻࡢ᳨ド
6.1 ᳨ド᮲௳
᳨ドࡣࠊゅᗘศⅬࢭࢵࢺཬࡧ✵㛫࣓ࢵࢩࣗ㸦ከ㡯ᘧᒎ㛤㸧ࢆࡑࢀࡒࢀ᭱኱㝈࡟ヲ⣽࡟ࡋࡓሙ
ྜ┦ᙜ࡜࡞ࡿࡼ࠺࡟༑ศ࡟ヲ⣽࡞᮲௳࡛⾜࠺ࠋᚑࡗ࡚ࠊ㍈᪉ྥ࡟ຍ࠼࡚ᚄ᪉ྥ࡟ᑐࡋ࡚ࡶ୰ᛶ
Ꮚ᮰ࡢ✵㛫ศᕸࢆヲ⣽࡟ྲྀࡾᢅ࠺ࡇ࡜ࡀྍ⬟࡞ NSHEX ཬࡧ MINISTRI ࡢ᳨ドࢆ⾜࠺ࡇ࡜࡜
ࡍࡿࠋMINIHEX ࡣᚄ᪉ྥ࣓ࢵࢩࣗࡢ⣽ศ໬ࡀ୙ྍ⬟࡛࠶ࡿࡓࡵࠊḟ❶࡛♧ࡍ㐺⏝ᛶホ౯ࡢࡳ
ࡢᑐ㇟࡜ࡍࡿࠋ᳨ド࡟࠾ࡅࡿཧ↷ゎࡣࠊྠࡌ᩿㠃✚ࢆ⏝࠸ࡓከ⩌ࣔࣥࢸ࢝ࣝࣟἲィ⟬ࢥ࣮ࢻ
GMVP22)࡟ࡼࡿィ⟬⤖ᯝ࡜ࡍࡿࠋ
(1) ィ⟬య⣔
ィ⟬య⣔࡜ࡋ࡚ࡣࠊFig. 6.1-1 ࡟♧ࡍᑠᆺ⅔ᚰ KNK-II14)ࠊFig. 6.1-2 ࡟♧ࡍ୰ᆺ⅔ᚰࠕࡶࢇ
ࡌࡹࠖ㸦Monju㸧15, 16)ࠊFig. 6.1-3 ࡟♧ࡍ኱ᆺ⅔ᚰࠕࢫ࣮ࣃ࣮ࣇ࢙ࢽࢵࢡࢫࠖ㸦SPX㸧17, 18)ࢆᑐ
㇟࡜ࡍࡿࠋไᚚᲬᤄධ≧ែ࡜ࡋ࡚ࡣࠊ㏻ᖖࡢฟຊ㐠㌿≧ែࢆ᝿ᐃࡋ࡚ࠊ⇞↝ᮎᮇࢆᶍᨃࡋࡓไ
ᚚᲬ඲ᘬᢤ㸦"All rods out"㸧࡜⇞↝ึᮇࢆᶍᨃࡋࡓไᚚᲬ༙ᤄධ㸦"Rods half-in"ࡲࡓࡣ"MCR
half-in"ࠊ"MCR"ࡣ"Main Control rod"㸦୺ㄪᩚᲬࡢ␎㸧㸧ࠊཬࡧࠊ⅔ᚰࡢ೵Ṇ≧ែ࡛࠶ࡿไᚚᲬ
඲ᤄධ㸦"Rods in"ࡲࡓࡣ"MCR in"࠶ࡿ࠸ࡣ"BCR in"ࠊ"BCR"ࡣ"Backup Control rod"㸦ᚋഛ
ࠕࡶࢇࡌࡹࠖࡣ MCR ࡀ 40%
⅔೵ṆᲬࡢ␎㸧㸧࡛࠶ࡿࠋไᚚᲬࡢ 10B ⃰⦰ᗘࡣࠊKNK-II ࡣ 40%ࠊ
࡛ BCR ࡀ 90%ࠊSPX ࡣ MCR ࡜ BCR ࡢ཮᪉࡜ࡶ 90%࡛࠶ࡾࠊゎᯒୖࡶᶍᨃࡋ࡚࠸ࡿࠋ
(2) ィ⟬ᑐ㇟᰾≉ᛶ
ホ౯ᑐ㇟ࡢ᰾≉ᛶ࡜ࡋ࡚ࡣࠊ3 ࡘ඲࡚ࡢ⅔ᚰࡢᅛ᭷್㸦ᐇຠቑಸ⋡㸧࡜ࠕࡶࢇࡌࡹࠖཬࡧ SPX
ࡢ⅔ᚰ㡿ᇦ࡟࠾ࡅࡿ㞟ྜయẖฟຊศᕸ࡜ࡍࡿࠋᅛ᭷್ཬࡧ㞟ྜయẖฟຊศᕸࡢ┠ᶆ⢭ᗘࡣࠊ⡿
ᅜ࡟࠾ࡅࡿ᳨ウ⤖ᯝ
19)ࠊFBR
ࢧ࢖ࢡࣝᐇ⏝໬ᡓ␎ㄪᰝ◊✲࡟࠾ࡅࡿ᳨ウ⤖ᯝ
20)ࢆᇶ࡟ࠊ᩿㠃
✚㉳ᅉㄗᕪࡢホ౯⤖ᯝ 21)ࢆᕪࡋᘬࡃࡇ࡜࡟ࡼࡾゎᯒᡭἲ࡟ಀࡿ⢭ᗘ࡜ࡋ࡚タᐃࡍࡿࠋ᳨ウ⤖ᯝ
ࢆཧ↷ࡋࡓ⤖ᯝࠊᅛ᭷್ࡣ 0.1%࡟ࠊ㞟ྜయẖฟຊศᕸࡣ 2%࡟ࡑࢀࡒࢀタᐃࡍࡿࡇ࡜࡜ࡋࡓࠋ
࡞࠾ࠊ㞟ྜయẖฟຊศᕸࡢ┠ᶆ⢭ᗘࡣࠊ㏻ᖖࡢฟຊ㐠㌿≧ែࠊࡍ࡞ࢃࡕࠊไᚚᲬ඲ᘬᢤࡲࡓࡣ
ไᚚᲬ༙ᤄධ≧ែࡢࡳ࡟ᑐࡋ࡚㐺⏝ࡍࡿࡇ࡜࡜ࡋࠊฟຊࡀ࡯ࡰࢮ࡛ࣟ࠶ࡿไᚚᲬ඲ᤄධ≧ែ࡟
ᑐࡋ࡚ࡣࠊཧ⪃ᢅ࠸࡜ࡍࡿࠋຍ࠼࡚ࠊィ⟬᮲௳ࡢ㐪࠸࡟ࡼࡿᅛ᭷್ࡢኚ໬ࡢཎᅉࢆศᯒࡍࡿࡓ
ࡵ࡟ࠊKNK-II ⅔ᚰࢆᑐ㇟࡟ไᚚᲬᤄධ≧ែ࡟࠾ࡅࡿไᚚᲬ㡿ᇦࡢ୰ᛶᏊ᮰ࢆほᐹࡍࡿࡇ࡜࡜
ࡍࡿࠋ
(3) ィ⟬᮲௳
MINISTRI ࡟࠾ࡅࡿ㈇ࡢ୰ᛶᏊ᮰Ⓨ⏕᫬ࡢฎ⌮ࡣ㈇࡜࡞ࡗࡓ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋࠊࡑ
ࡢ᮲௳࡛࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࢆ෌ィ⟬ࡍࡿ᪉ἲ࡜ࡋࡓࠋࡲࡓࠊᇶᮏⓗ࡟ຍ㏿ἲࢆ㐺⏝ࡋ࡞࠿
ࡗࡓࡀࠊMINISTRI ࡟ࡼࡿ SPX ⅔ᚰࡢゎᯒ࡟ࡘ࠸࡚ࡢࡳࡣࠊ཰᮰ᛶࡀⰋࡃ࡞࠿ࡗࡓࡢ࡛ࠊእ
ഃ཯᚟࡟࠾࠸࡚ࢳ࢙ࣅࢩ࢙ࣇຍ㏿ἲࢆ㐺⏝ࡍࡿࡇ࡜࡜ࡋࡓࠋ
ࡲࡎࡣࠊྛ⅔ᚰయ⣔ࢆᑐ㇟࡟ࡋ࡚ࠊゅᗘศⅬࢭࢵࢺࡢタᐃ࡟㛵ࡍࡿࢧ࣮࣋࢖ࢆᐇ᪋ࡋࡓࠋィ
㻙㻌㻟㻢㻌㻙㻌
JAEA-Data/Code 2011-018
⟬⤖ᯝࡢゅᗘศⅬࢭࢵࢺ౫Ꮡᛶࢧ࣮࣋࢖࡛ࡣࣀ࣮ࢻෆࢆ 2 ḟከ㡯ᘧᒎ㛤࡜ࡋࡓ NSHEX ࢆ୺࡟
⏝࠸ࡓࡀ MINISTRI ࡟ࡼࡿィ⟬࡜ࡢẚ㍑ࡶ⾜࠺ࠋ⤖ᯝࡣ඲࡚ S12 ィ⟬⤖ᯝࢆᇶ‽࡜ࡋࡓᕪ␗࡜
ࡋ࡚ࡲ࡜ࡵࡿࠋ
ࡲࡎࠊᅛ᭷್࡟㛵ࡍࡿࢧ࣮࣋࢖⤖ᯝࢆ KNK-II ⅔ᚰࠊࠕࡶࢇࡌࡹࠖ⅔ᚰࠊSPX ⅔ᚰࡑࢀࡒࢀ
࡟ࡘ࠸࡚ࠊTable 6.1-1㹼6.1-3 ࡟♧ࡍࠋS4 ィ⟬࡛ࡣ᭱኱࡛ 0.14%࡜┠ᶆ⢭ᗘࢆ㉸࠼ࡿᕪ␗ࡀぢ
ࡽࢀ࡚࠾ࡾࠊ୙༑ศ࡛࠶ࡿࡇ࡜ࡀศ࠿ࡿࠋS8 ィ⟬࡛ࡣ᭱኱࡛ 0.02%ࡢᕪ␗࡟ࡲ࡛పୗࡋ࡚࠾ࡾࠊ
S12 ィ⟬ࡣࢧ࣮࣋࢖⏝ᇶ‽ィ⟬᮲௳࡜ࡋ࡚༑ศヲ⣽࡛࠶ࡿࡇ࡜࡜ࠊS8 ᮲௳࡜ࡍࢀࡤ┠ᶆ⢭ᗘ
0.1%࡛ࡣ᳨ドࡣ༑ศ࡛࠶ࡿࡇ࡜ࡀศ࠿ࡿࠋ࡞࠾ࠊලయⓗ࡟ࡣ♧ࡋ࡚࠸࡞࠸ࡀࠊᚄ᪉ྥ㞟ྜయෆ
ࢆ 6 ࣓ࢵࢩࣗศ๭ࡋࡓ᮲௳࡛ࡢ MINISTRI ࡟ࡼࡿィ⟬⤖ᯝࡶ࡯ࡰྠᵝࡢഴྥࢆ♧ࡋ࡚࠸ࡓࠋ
ḟ࡟ࠊ
ࠕࡶࢇࡌࡹࠖ⅔ᚰ࡜ SPX ⅔ᚰࡢ㞟ྜయẖฟຊศᕸ࡟㛵ࡍࡿࢧ࣮࣋࢖⤖ᯝࢆ Table 6.1-4ࠊ
6.1-5 ࡟♧ࡍࠋࠕࡶࢇࡌࡹࠖ⅔ᚰࡢ㞟ྜయẖฟຊศᕸ࡟ࡘ࠸࡚ࡣ S4 ィ⟬࡜ S8 ィ⟬ࡢ཮᪉࡜ࡶᕪ
␗ࡣ 0.2%௨ୗ࡜࡯࡜ࢇ࡝ぢࡽࢀ࡞࠸ࠋSPX ⅔ᚰࡢ㞟ྜయẖฟຊศᕸ࡛ࡣࠊ"All rods out"ࢣ࣮
ࢫࡢࡼ࠺࡟ S8 ィ⟬࡛ࡣᕪ␗ࡀ࡯࡜ࢇ࡝ぢࡽࢀ࡞࠸ࡀ S4 ィ⟬࡛ࡣ᭱኱ᕪ␗ࡀ 0.8%࡟ཬࢇࡔࡾࠊ
"MCR in"ࢣ࣮ࢫࡢࡼ࠺࡟ S4 ィ⟬࡜ S8 ィ⟬ࡢ཮᪉࡜ࡶ᭱኱ᕪ␗ࡀ 0.6%๓ᚋぢࡽࢀࡓࡾࡍࡿሙ
ྜࡀ࠶ࡾࠊS12 ィ⟬࡟ᑐࡍࡿᕪ␗ࡀࠕࡶࢇࡌࡹࠖ⅔ᚰ࡜ẚ࡭࡚኱ࡁࡃぢࡽࢀࡿࡇ࡜ࡀศ࠿ࡿࠋ
ࡋ࠿ࡋ࡞ࡀࡽࠊS8 ィ⟬࡟ࡼࡿᕪ␗ࡣ୧⅔ᚰయ⣔ࢆᑐ㇟࡜ࡋ࡚ࡶ᭱኱࡛ 0.6%࡛࠶ࡾࠊ┠ᶆ⢭ᗘ
ࡢ༙ศ௨ୗ࡛࠶ࡿࠋ
᭦࡟ࠊKNK-II ⅔ᚰࡢไᚚᲬ㡿ᇦࡢ୰ᛶᏊ᮰࡟㛵ࡍࡿࢧ࣮࣋࢖⤖ᯝࢆ Table 6.1-6 ࡟♧ࡍࠋS4
ィ⟬࡛ࡣ᭱኱࡛➨ 1 ⩌࡟࠾࠸࡚ 0.6%ࡢ㐣ᑠホ౯ࡀぢࡽࢀࡓࡀࠊS8 ィ⟬࡛ࡣ⣙ 0.1%⛬ᗘࡢ㐣ᑠ
ホ౯࡟ࡲ࡛పῶࡋ࡚࠾ࡾࠊS8 ィ⟬ࡢ⢭ᗘࡢⰋࡉࡀ☜ㄆ࡛ࡁࡓࠋ
௨ୖ࠿ࡽࠊ᳨ドィ⟬࡟࠾ࡅࡿゅᗘศⅬࡢ᮲௳ࡣ S8 ࡜タᐃࡍࡿࠋゅᗘศⅬࢭࢵࢺ௨እࡶྵࡵࡓ
᳨ド᮲௳ࢆ Table 6.1-7 ࡟♧ࡍࠋ࡞࠾ࠊNSHEX ࡟ࡼࡿ SPX ⅔ᚰࡢ"MCR in"ࢣ࣮ࢫࡢゎᯒ࡛ࡣࠊ
཰᮰ᛶࡀⰋࡃ࡞࠿ࡗࡓࡢ࡛ࠊእഃ཯᚟ẖࡢ㧗ḟ࣮࣓ࣔࣥࢺࡢ᭦᪂ࢆṆࡵࡿ᮲௳ࢆ㏻ᖖࡢ 2.0
10-4 ࠿ࡽ 4.010-4 ࡟⦆ࡵࡓࠋ
6.2 ᳨ド⤖ᯝ
6.2.1 KNK-II ⅔ᚰ࡟࠾ࡅࡿ᳨ド⤖ᯝ
ᅛ᭷್࡟ࡘ࠸࡚ࡢ᳨ド⤖ᯝࢆ NSHEX ࡜ MINISTRI ࡑࢀࡒࢀ࡟ࡘ࠸࡚ࠊTable 6.2-1 ཬࡧ
6.2-2 ࡟♧ࡍࠋNSHEX ࡟ࡘ࠸࡚ࡣࠊ4 ḟᒎ㛤௨ୖ࡜ࡍࡿࡇ࡜࡟ࡼࡾ࠸ࡎࢀࡢࢣ࣮ࢫ࡟ࡘ࠸࡚ࡶ
┠ᶆ⢭ᗘࢆ‶㊊ࡍࡿࡇ࡜ࡀศ࠿ࡿࠋMINISTRI ࡟ࡼࡿᅛ᭷್ࡣ࣓ࢵࢩࣗศ๭౫Ꮡᛶࡀ㠀ᖖ࡟኱
ࡁࡃࠊ㞟ྜయᙜࡓࡾᚄ᪉ྥ࡟ 24 ࣓ࢵࢩࣗ௨ୖ࡟ศ๭ࡋ࡞࠸࡜┠ᶆ⢭ᗘࢆ‶㊊ࡋ࡞࠸ࠋ㍈᪉ྥ
࡟ࡘ࠸࡚ࡶࠊヲ⣽࡟ศ๭ࡍࡿࡇ࡜࡟ࡼࡿຠᯝࡀ኱ࡁ࠸ࡇ࡜ࡀศ࠿ࡿࠋ࡞࠾ࠊࡣࡗࡁࡾ࡜ࡋࡓཎ
ᅉࡣ୙࡛᫂࠶ࡿࡀࠊ࣓ࢵࢩࣗࢆ࠶ࡿ⛬ᗘ⣽࠿ࡃศ๭ࡍࡿ࡜ࠊ཰᮰ࡋ࡞࠿ࡗࡓࡾࠊ㞟ྜయᙜࡓࡾ
ᚄ᪉ྥ 54 ࣓ࢵࢩ࡛ࣗ㍈᪉ྥ 2.5cm ࡜ࡋࡓሙྜࡢࡼ࠺࡟␗ᖖ࡞ィ⟬⤖ᯝࢆ♧ࡋࡓࡾࡋࡓሙྜࡀ
࠶ࡗࡓࠋ᥎ ࡛ࡣ࠶ࡿࡀࠊ㈇ࡢ୰ᛶᏊ᮰ࡢⓎ⏕㢖ᗘࡀቑຍࡋࡓࡓࡵ࡟ࠊ཯᚟ィ⟬ẖࡢᑐᛂฎ⌮
ࡢ᭷↓࡟ࡼࡿ᣺ືࡀ⏕ࡌࡓࡶࡢ࡜⪃࠼ࡽࢀࡿࠋィ⟬᫬㛫࡟㛵ࡋ࡚ࡣࠊNSHEX ࡛ࡣᒎ㛤ḟᩘ౫
Ꮡᛶࡣ࠶ࡲࡾぢࡽࢀࡎࠊ࠸ࡎࢀࡢሙྜࡶ GMVP ࡼࡾࡶ▷᫬㛫࡛ィ⟬ࡀ⤊஢ࡋ࡚࠸ࡿࡇ࡜ࡀศ
࠿ࡿࠋMINISTRI ࡟㛵ࡋ࡚ࡶ GMVP ࡼࡾࡣ▷᫬㛫࡛ィ⟬ࡀ⤊஢ࡋ࡚࠸ࡿࡀࠊ┠ᶆ⢭ᗘࢆ‶㊊
㻙㻌㻟㻣㻌㻙㻌
JAEA-Data/Code 2011-018
ࡍࡿࡶࡢྠኈ㸦NSHEX㸸4 ḟࠊMINISTRI㸸ᚄ᪉ྥ 24 ศ๭࣭㍈᪉ྥ 2.5cm ࣓ࢵࢩࣗ㸧࡛ẚ㍑
ࡍࡿ࡜ࠊ1 ࣮࢜ࢲ࣮NSHEX ࡢ᪉ࡀඃࢀ࡚࠸ࡿࠋ
ḟ࡟ࠊไᚚᲬ㡿ᇦࡢ୰ᛶᏊ᮰࡟ࡘ࠸࡚ࡢ᳨ド⤖ᯝࢆ NSHEX ࡜ MINISTRI ࡑࢀࡒࢀ࡟ࡘ࠸
࡚ࠊTable 6.2-3 ཬࡧ 6.2-4 ࡟♧ࡍࠋNSHEX ࡛ࡣ 2 ḟᒎ㛤ࢆ⏝࠸ࡓሙྜ࡟ࡣ GMVP ࡟ᑐࡋ࡚
㐣኱ホ౯ࡀぢࡽࢀࠊࡇࢀࡀ"Rods in"ࢣ࣮ࢫ࡟࠾ࡅࡿᅛ᭷್ࡢ㐣ᑠホ౯ࡢཎᅉ࡟࡞ࡗ࡚࠸ࡿ࡜⪃
࠼ࡽࢀࡿࠋ4 ḟᒎ㛤௨ୖ࡜ࡋࡓሙྜ࡟ࡣࠊ2 ḟᒎ㛤ࡢሙྜ࡟ぢࡽࢀࡓࡼ࠺࡞㐣኱ホ౯ࡣぢࡽࢀ
ࡎࠊᅛ᭷್ࡢィ⟬⤖ᯝ࡜ࡶᩚྜࡀぢࡽࢀࡿࡇ࡜ࡀศ࠿ࡿࠋไᚚᲬ㡿ᇦ௜㏆ࡢ➨ 4 ⩌୰ᛶᏊ᮰ศ
ᕸࡢẚ㍑ࢆ Fig. 6.2-1 ࡟♧ࡍࡀࠊ6 ḟᒎ㛤࡛ࡣࣀ࣮ࢻቃ⏺࡟࠾࠸࡚࡯ࡰ୰ᛶᏊ᮰ࡀ㐃⥆࡟࡞ࡗ
࡚࠸ࡿࠋࡑࢀ࡟ᑐࡋࠊ2 ḟᒎ㛤࡛ࡣ୰ᛶᏊ᮰ศᕸࡀ༑ศ࡟ྲྀࡾᢅࢃࢀ࡚࠾ࡽࡎࠊࣀ࣮ࢻቃ⏺࡛
ࡶ୙㐃⥆࡜࡞ࡗ࡚࠾ࡾࠊไᚚᲬ㡿ᇦ࡟࠾࠸࡚୰ᛶᏊ᮰ࢆࡸࡸ㐣኱ホ౯ࡋ࡚࠸ࡿᵝᏊࡀศ࠿ࡿࠋ
MINISTRI ࡟㛵ࡋ࡚ࡣࠊ㞟ྜయᙜࡓࡾᚄ᪉ྥ 6 ࣓ࢵࢩࣗࡢሙྜࡢࡼ࠺࡟࣓ࢵࢩࣗศ๭ࡀ⢒࠸ሙ
ྜ࡟ࡣࠊ኱ࡁ࡞㐣኱ホ౯ࡀぢࡽࢀࡿࡇ࡜ࡀศ࠿ࡾࠊᅛ᭷್ࡢ㐣ᑠホ౯ࡢཎᅉ࡜࡞ࡗ࡚࠸ࡿࡇ࡜
ࡀศ࠿ࡿࠋࡲࡓࠊ࣓ࢵࢩࣗศ๭ࢆ⣽࠿ࡃࡍࡿࡇ࡜࡟ࡼࡾࠊ㐣኱ホ౯ࡀゎᾘࡉࢀࡿഴྥ࡟࠶ࡿࡇ
࡜ࡀศ࠿ࡿࠋ
6.2.2 ࠕࡶࢇࡌࡹࠖ⅔ᚰ࡟࠾ࡅࡿ᳨ド⤖ᯝ
ᅛ᭷್࡟ࡘ࠸࡚ࡢ᳨ド⤖ᯝࢆ NSHEX ࡜ MINISTRI ࡑࢀࡒࢀ࡟ࡘ࠸࡚ࠊTable 6.2-5 ཬࡧ
6.2-6 ࡟♧ࡍࠋNSHEX ࡟㛵ࡋ࡚ࡣࠊᒎ㛤ḟᩘ౫Ꮡᛶࡀ࠶ࡲࡾぢࡽࢀࡎࠊ࠸ࡎࢀࡢࢣ࣮ࢫࡶ┠ᶆ
⢭ᗘࢆ‶㊊ࡋ࡚࠸ࡿࠋMINISTRI ࡟㛵ࡋ࡚ࡣࠊ㞟ྜయᙜࡓࡾᚄ᪉ྥ 6 ࣓ࢵࢩ࡛ࣗ㍈᪉ྥ 5cm
࣓ࢵࢩࣗ࡜ࡋࡓሙྜ࡟ࡣࠊ"MCR in"ཬࡧ"BCR in"ࡢࢣ࣮ࢫ࡛ࢃࡎ࠿࡟┠ᶆ⢭ᗘࢆ‶㊊ࡋ࡚࠸
࡞࠸ࠋྠࡌᚄ᪉ྥ࣓ࢵࢩ࡛ࣗ㍈᪉ྥ࣓ࢵࢩࣗࢆ 2.5cm 㛫㝸࡟ࡍࡿ࡜ࠊ┠ᶆ⢭ᗘࢆ‶㊊ࡍࡿࡀ
"BCR in"ࢣ࣮ࢫ࡟࠾࠸࡚᰾ศ⿣୰ᛶᏊ※ࡢ཰᮰ࡀᚓࡽࢀ࡞࠿ࡗࡓࠋ࡞࠾ࠊ㞟ྜయᙜࡓࡾᚄ᪉ྥ
24 ࣓ࢵࢩࣗ࡜ࡋࡓィ⟬ࡣ␗ᖖ࡞⤖ᯝ࡜࡞ࡗ࡚࠾ࡾࠊࠕࡶࢇࡌࡹࠖ⅔ᚰ࡟࠾࠸࡚ࡶ࣓ࢵࢩࣗࢆ⣽
࠿ࡃྲྀࡗࡓሙྜࡢ཰᮰ᛶࡢၥ㢟ࡀほ ࡉࢀࡓࠋィ⟬᫬㛫ࡣ NSHEX ࡟㛵ࡋ࡚ࡣ GMVP ࡜ྠ➼
࡛࠶ࡿࡀࠊMINISTRI ࡟ࡘ࠸࡚ࡣ NSHEX ࡢ 2 ಸ࡛ GMVP ࡢ 3 ಸ⛬ᗘࢆせࡋ࡚࠸ࡿࠋ
ḟ࡟ࠊ㞟ྜయẖฟຊศᕸ࡟ࡘ࠸࡚ࡢ᳨ド⤖ᯝࢆ NSHEX ࡜ MINISTRI ࡑࢀࡒࢀ࡟ࡘ࠸࡚ࠊ
Table 6.2-7 ཬࡧ 6.2-8 ࡟♧ࡍࠋ"All rods out"ཬࡧ"MCR half-in"ࡢࢣ࣮ࢫ࡟㛵ࡋ࡚ࠊNSHEX
࡛ࡣ 0.4%௨ෆ࡛ࠊMINISTRI ࡛ࡣ 0.5%௨ෆ୍࡛⮴ࡀぢࡽࢀ࡚࠾ࡾࠊ┠ᶆ⢭ᗘࢆ‶㊊ࡋ࡚࠸ࡿࠋ
࡞࠾ࠊཧ⪃ᢅ࠸࡛࠶ࡿ"MCR in"ཬࡧ"BCR in"ࡢࢣ࣮ࢫ࡟ࡘ࠸࡚ࡶࠊNSHEX ࡜ MINISTRI ࡢ
཮᪉ࡢ⤖ᯝඹ࡟┠ᶆ⢭ᗘࢆ‶㊊ࡋ࡚࠸ࡿࠋ
6.2.3 SPX ⅔ᚰ࡟࠾ࡅࡿ᳨ド⤖ᯝ
ᅛ᭷್࡟ࡘ࠸࡚ࡢ᳨ド⤖ᯝࢆ NSHEX ࡜ MINISTRI ࡑࢀࡒࢀ࡟ࡘ࠸࡚ࠊTable 6.2-9 ཬࡧ
6.2-10 ࡟♧ࡍࠋNSHEX ࡟㛵ࡋ࡚ࠊ2 ḟከ㡯ᘧᒎ㛤࡛ࡣ"MCR in"ࡢࢣ࣮ࢫ࡛┠ᶆ⢭ᗘࢆ‶㊊ࡋ
࡞࠸ࡇ࡜ࡀศ࠿ࡿࡀࠊ4 ḟ௨ୖࡢከ㡯ᘧᒎ㛤࡜ࡍࡿࡇ࡜࡟ࡼࡾࠊ࠸ࡎࢀࡢࢣ࣮ࢫࡶ‶㊊ࡍࡿࠋ
ィ⟬᫬㛫࡟㛵ࡋ࡚ࡣࠊGMVP ࡢᩘಸࢆせࡋ࡚࠾ࡾࠊຍ㏿ἲࡢᑟධ➼ࡢㄢ㢟ࡀṧࡉࢀ࡚࠸ࡿࡇ࡜
ࡀศ࠿ࡿࠋMINISTRI ࡟㛵ࡋ࡚ࡣࠊ཰᮰ᛶࡀᝏࡃࠊᅛ᭷್࡜᰾ศ⿣୰ᛶᏊ※ࡢ཮᪉ඹ࡟཰᮰ࡀ
ᚓࡽࢀࡓࡢࡣ㞟ྜయᙜࡓࡾᚄ᪉ྥ 6 ࣓ࢵࢩࣗࡢ㍈᪉ྥ 5cm ࣓ࢵࢩࣗ᮲௳࡜ࡋࡓሙྜࡢࠊ"MCR
㻙㻌㻟㻤㻌㻙㻌
JAEA-Data/Code 2011-018
half-in"࡜"MCR in"ࡢࢣ࣮ࢫࡢࡳ࡛࠶ࡿࠋ཰᮰ࡀᚓࡽࢀ࡚ࡶ"MCR in"ࡢࢣ࣮ࢫ࡛┠ᶆ⢭ᗘࢆ‶
㊊ࡋ࡚࠸࡞࠸ࠋ௒ᚋࠊ཰᮰ᛶࢆᨵၿࡍࡿᚲせࡀ࠶ࡿࠋ
ḟ࡟ࠊ㞟ྜయẖฟຊศᕸ࡟ࡘ࠸࡚ࡢ᳨ド⤖ᯝࢆ NSHEX ࡜ MINISTRI ࡑࢀࡒࢀ࡟ࡘ࠸࡚ࠊ
Table 6.2-11 ཬࡧ 6.2-12 ࡟♧ࡍࠋNSHEX ࡛ࡣᒎ㛤ḟᩘ౫Ꮡᛶࡀ࡯࡜ࢇ࡝ぢࡽࢀࡎࠊ"All rods
out"ཬࡧ"MCR half-in"ࡢࢣ࣮ࢫ࡛ࡣࠊ1.9%௨ෆ࡛ GMVP ࢆ୍⮴ࡋ࡚࠾ࡾࠊ┠ᶆ⢭ᗘࢆ‶㊊ࡋ
࡚࠸ࡿࠋMINISTRI ࡟㛵ࡋ࡚ࡣࠊ཰᮰ࡋࡓࢣ࣮ࢫ࡟ࡘ࠸࡚ࡣ┠ᶆ⢭ᗘࢆ‶㊊ࡋ࡚࠸ࡿࡇ࡜ࡀศ
࠿ࡿࠋ
6.3 ࡲ࡜ࡵ
NSHEX ࡜ MINISTRI ࢆᑐ㇟࡜ࡋࠊ୰ᛶᏊࡢゅᗘ࡜✵㛫ศᕸ࡟㛵ࡍࡿྲྀࡾᢅ࠸ࢆ༑ศ࡟ヲ⣽
࡟ࡋࡓ᮲௳᳨࡛ドࢆ⾜ࡗࡓࠋᑠᆺ⅔ᚰ KNK-IIࠊ୰ᆺ⅔ᚰࠕࡶࢇࡌࡹࠖࠊ኱ᆺ⅔ᚰࠕࢫ࣮ࣃ࣮ࣇ
࢙ࢽࢵࢡࢫࠖࢆᑐ㇟࡟᳨ドࢆ⾜ࡗࡓ⤖ᯝࠊNSHEX ࡟ࡼࡿ⤖ᯝࡣࠊ࠸ࡎࢀࡢ⅔ᚰయ⣔ࡢᅛ᭷್
ཬࡧ㞟ྜయẖฟຊศᕸ࡟ࡘ࠸࡚ࡶ┠ᶆ⢭ᗘࢆ‶㊊ࡍࡿࡇ࡜ࡀศ࠿ࡗࡓࠋࡑࢀ࡟ᑐࡋࠊMINISTRI
࡟㛵ࡋ࡚ࡣࠊKNK-II ࡛ࡣ┠ᶆ⢭ᗘࢆ‶㊊ࡋࡓࡀࠊ
ࠕࡶࢇࡌࡹࠖ⅔ᚰ࡜ࠕࢫ࣮ࣃ࣮ࣇ࢙ࢽࢵࢡࢫࠖ
⅔ᚰ࡟ᑐࡋ࡚ࡣࠊ┠ᶆ⢭ᗘࢆ‶㊊ࡍࡿ࡜᥎ᐃࡉࢀࡿ᮲௳࡛ࡣィ⟬ࡀ཰᮰ࡋ࡞࠸ሙྜࡀከࡃぢࡽ
ࢀࡿࡇ࡜ࡀศ࠿ࡗࡓࠋ
㻙㻌㻟㻥㻌㻙㻌
JAEA-Data/Code 2011-018
Table 6.1-1
Angular discretization effects in eigenvalue by NSHEX for the KNK-II core
Angular
quadrature set
All rods out
Rods
half-in
Rods in
S4
+0.012*1
+0.075*1
+0.140*1
S8
+0.004
+0.012
+0.018
S12
(Ref.)
(Ref.)
(Ref.)
*1: Relative difference to the reference [%]
Table 6.1-2
Angular discretization effects in eigenvalue by NSHEX for the Monju core
Angular
quadrature set
All rods out
MCR
half-in
MCR in
BCR in
S4
+0.023*1
+0.043*1
+0.061*1
+0.059*1
S8
+0.003
+0.005
+0.007
+0.007
S12
(Ref.)
(Ref.)
(Ref.)
(Ref.)
*1: Relative difference to the reference [%]
Table 6.1-3
Angular discretization effects in eigenvalue by NSHEX for the SPX core
Angular
quadrature set
All rods out
MCR
half-in
MCR in
BCR in
S4
+0.037*1
+0.046*1
+0.074*1
+0.029*1
S8
+0.003
+0.005
+0.020
+0.004
S12
(Ref.)
(Ref.)
(Ref.)
(Ref.)
*1: Relative difference to the reference [%]
㻙㻌㻠㻜㻌㻙㻌
JAEA-Data/Code 2011-018
Table 6.1-4
Angular discretization effects in power distribution by NSHEX for the Monju
core
Angular
quadrature set
All rods out
MCR
half-in
MCR in
BCR in
S4
0.10*1
0.12*1
0.15*1
0.18*1
S8
0.01
0.02
0.02
0.02
S12
(Ref.)
(Ref.)
(Ref.)
(Ref.)
*1: Maximum relative difference to the reference [%]
Table 6.1-5
Angular discretization effects in power distribution by NSHEX for the SPX
core
Angular
quadrature set
All rods out
MCR
half-in
MCR in
BCR in
S4
0.84*1
0.20*1
0.66*1
0.22*1
S8
0.01
0.04
0.55
0.09
S12
(Ref.)
(Ref.)
(Ref.)
(Ref.)
*1: Maximum relative difference to the reference [%]
Table 6.1-6
Angular discretization effects in absorption reaction rate in the control rod
region by NSHEX for the KNK-II core
Angular
quadrature set
All rods out
Rods
half-in
Rods in
S4
-
-0.38*1
-0.47*1
S8
-
-0.08
-0.06
S12
-
(Ref.)
(Ref.)
*1: Relative difference to the reference [%]
㻙㻌㻠㻝㻌㻙㻌
JAEA-Data/Code 2011-018
Table 6.1-7
Calculation criteria and conditions for verification tests
Criteria and conditions
Item
NSHEX
MINISTRI
Angular quadrature set
S8
Spatial treatment in the
Polynomial expansion with
radial direction
up to sixth order
Spatial treatment in the axial
Polynomial expansion with
direction
up to sixth order
Node or mesh width in the
axial direction
Fission source convergence
criteria for each node
Eigenvalue convergence
criteria
High order moments
calculation condition
Neutron energy group
Triangle mesh division (6,
24, 54, 96 meshes) within
Subassembly
Finer mesh division
Around 20cm
Around 5.0 cm or 2.5cm
Less than 1.0×10-4
Less than 1.0×10-5
Greater than 2.0×10-4
*1
4 (KNK-II), 18 (Monju and
SPX)
*1: Set 4.0×10-4 for "MCR in" case of the SPX core
㻙㻌㻠㻞㻌㻙㻌
Nothing
JAEA-Data/Code 2011-018
(Radial view)
(Axial view)
Fig. 6.1-1
Layout of the KNK-II core
㻙㻌㻠㻟㻌㻙㻌
JAEA-Data/Code 2011-018
Fig. 6.1-2
Layout of the Monju core
㻙㻌㻠㻠㻌㻙㻌
JAEA-Data/Code 2011-018
Fig. 6.1-3
Layout of the Super Phenix (SPX) core
㻙㻌㻠㻡㻌㻙㻌
JAEA-Data/Code 2011-018
Table 6.2-1
Relative difference in eigenvalue and calculation time by NSHEX for the
KNK-II core
Maximum
Average time
All rods out
Rods half-in
Rods in
2nd
+0.070*1
-0.017*1
-0.123*1
7
4th
+0.047
+0.037
+0.022
8
6th
+0.048
+0.038
+0.022
9
1.09527
0.98349
0.87966
±0.024*2
±0.026*2
±0.026*2
polynomial order
GMVP (Ref.)
[min]
287
*1: Relative difference to the reference [%]
*2: Statitical uncertainty (1) [%]
Underlined means exceeding of the target accuracy
Table 6.2-2
Relative difference in eigenvalue and calculation time by MINISTRI for the
KNK-II core
Radial
mesh
*1
Axial
mesh
*2
All rods out
Rods half-in
Rods in
Average time
[min]
6
5.0cm
-0.190*3
-0.310*3
-0.483*3
9
6
2.5cm
-0.158
-0.258
-0.455
20
24
5.0cm
-0.072
-0.123
-0.123
36
24
2.5cm
+0.042
-0.012
-0.042
71
54
5.0cm
-0.042
-0.071
-0.020
77
54
2.5cm
+1.196
NC*5
NC*5
211
96
5.0cm
-0.008
-0.041
+0.027
140
96
2.5cm
NC*5
NC
NC
-
1.09527
0.98349
0.87966
±0.024*4
±0.026*4
±0.026*4
GMVP (Ref.)
*1: Number of radial meshes per subassembly
*2: Axial mesh size
*3: Relative difference to the reference [%]
*4: Statitical uncertainty (1) [%]
*5: Not converged
Underlined means exceeding of the target accuracy
㻙㻌㻠㻢㻌㻙㻌
287
JAEA-Data/Code 2011-018
Table 6.2-3
Relative difference in absorption reaction rate in the control rod region by
NSHEX for the KNK-II core
Maximum
All rods out
Rods half-in
Rods in
2nd
-
+0.34*1
+0.86*1
4th
-
+0.01
+0.23
6th
-
+0.00
+0.22
-
0.14*2
0.10*2
polynomial order
Uncertainty of
GMVP
*1: Relative difference to the reference (GMVP) [%]
*2: Statitical uncertainty (1) [%]
Table 6.2-4
Relative difference in absorption reaction rate in the control rod region by
MINISTRI for the KNK-II core
Radial
mesh
*1
Axial
mesh*2
All rods out
Rods half-in
Rods in
6
5.0cm
-
+1.34*3
+1.65*3
6
2.5cm
-
+1.35
+1.88
24
5.0cm
-
+0.72
+0.47
24
2.5cm
-
+0.59
+0.47
54
5.0cm
-
+0.61
+0.15
54
2.5cm
-
NC*5
NC*5
96
5.0cm
-
+0.82
+0.08
96
2.5cm
-
NC
NC
-
0.14*4
0.10*4
Uncertainty of
GMVP
*1: Number of radial meshes per subassembly
*2: Axial mesh size
*3: Relative difference to the reference (GMVP) [%]
*4: Statitical uncertainty (1) [%]
*5: Not converged
㻙㻌㻠㻣㻌㻙㻌
JAEA-Data/Code 2011-018
Table 6.2-5
Relative difference in eigenvalue and calculation time by NSHEX for the
Monju core
Maximum
polynomial order
All rods out
MCR
half-in
MCR in
BCR in
Average
time [min]
2nd
+0.019*1
-0.013*1
+0.013*1
+0.009*1
329
4th
+0.016
-0.004
+0.031
+0.028
389
6th
+0.015
-0.004
+0.031
+0.028
422
1.03861
0.98551
0.93493
0.95665
±0.010*2
±0.010*2
±0.010*2
±0.010*2
GMVP (Ref.)
306
*1: Relative difference to the reference [%]
*2: Statitical uncertainty (1) [%]
Table 6.2-6
Relative difference in eigenvalue and calculation time by MINISTRI for the
Monju core
Radial
Axial
mesh*1
mesh*2
6
5.0cm
-0.039*3
6
2.5cm
24
5.0cm
GMVP (Ref.)
All rods out
MCR
Average
MCR in
BCR in
-0.093*3
-0.105*3
-0.107*3
384
+0.001
-0.057
-0.070
-0.076*5
858
+0.157*5
+0.073*5
+0.124*5
+0.130*5
-
1.03861
0.98551
0.93493
0.95665
±0.010*4
±0.010*4
±0.010*4
±0.010*4
half-in
*1: Number of radial meshes per subassembly
*2: Axial mesh size
*3: Relative difference to the reference [%]
*4: Statitical uncertainty (1) [%]
*5: Converged in eigenvalue only
Underlined means exceeding of the target accuracy
㻙㻌㻠㻤㻌㻙㻌
time [min]
306
JAEA-Data/Code 2011-018
Table 6.2-7
Relative difference in power distribution by NSHEX for the Monju core
Maximum
polynomial order
All rods out
MCR
half-in
MCR in*3
BCR in*3
2nd
0.35*1
0.42*1
0.59*1
0.55*1
4th
0.37
0.42
0.61
0.45
6th
0.37
0.42
0.61
0.45
0.21*2
0.22*2
0.23*2
0.23*2
Uncertainty of
GMVP
*1: Maximum relative difference to the reference (GMVP) [%]
*2: Statitical uncertainty (1) [%]
*3: Out of parameters for verification
Table 6.2-8
Radial
mesh
*1
Relative difference in power distribution by MINISTRI for the Monju core
Axial
mesh
*2
All rods out
MCR
half-in
MCR in*6
BCR in*6
6
5.0cm
0.34*3
0.53*3
0.63*3
0.65*3
6
2.5cm
0.31
0.51
0.79
NC*5
24
5.0cm
NC*5
NC*5
NC*5
NC*5
0.21*4
0.22*4
0.23*4
0.23*4
Uncertainty of
GMVP
*1: Number of radial meshes per subassembly
*2: Axial mesh size
*3: Maximum relative difference to the reference (GMVP) [%]
*4: Statitical uncertainty (1) [%]
*5: Not converged
*6: Out of parameters for verification
㻙㻌㻠㻥㻌㻙㻌
JAEA-Data/Code 2011-018
Table 6.2-9
Relative difference in eigenvalue and calculation time by NSHEX for the SPX
core
Maximum
polynomial order
All rods out
MCR
half-in
MCR in
BCR in
Average
time [min]
2nd
-0.005*1
-0.018*1
-0.113*1
-0.005*1
748
4th
-0.005
+0.011
-0.050
-0.001
820
6th
-0.005
+0.010
-0.050
-0.001
927
1.02256
0.97474
0.93021
1.01278
±0.005*2
±0.006*2
±0.006*2
±0.005*2
GMVP (Ref.)
269
*1: Relative difference to the reference [%]
*2: Statitical uncertainty (1) [%]
Underlined means exceeding of the target accuracy
Table 6.2-10
Relative difference in eigenvalue and calculation time by MINISTRI for the
SPX core
Radial
mesh
*1
Axial
mesh
*2
All rods out
MCR
half-in
MCR in
BCR in
Average
time [min]
6
5.0cm
-0.072*3,*5
-0.071*3
-0.156*3
-0.084*3,*5
1488
6
2.5cm
-0.057*5
-0.083*5
-0.178*5
-0.067*5
-
24
5.0cm
NC*6
NC*6
NC*6
NC*6
-
1.02256
0.97474
0.93021
1.01278
±0.005*4
±0.006*4
±0.006*4
±0.005*4
GMVP (Ref.)
*1: Number of radial meshes per subassembly
*2: Axial mesh size
*3: Relative difference to the reference [%]
*4: Statitical uncertainty (1) [%]
*5: Converged in eigenvalue only
*6: Not converged
Underlined means exceeding of the target accuracy
㻙㻌㻡㻜㻌㻙㻌
269
JAEA-Data/Code 2011-018
Table 6.2-11
Relative difference in power distribution by NSHEX for the SPX core
Maximum
polynomial order
All rods out
MCR
half-in
MCR in*3
BCR in*3
2nd
1.49*1
1.84*1
4.18*1
2.81*1
4th
1.44
1.78
4.09
2.92
6th
1.45
1.78
4.39
2.92
0.22*2
0.22*2
0.22*2
0.21*2
Uncertainty of
GMVP
*1: Maximum relative difference to the reference (GMVP) [%]
*2: Statitical uncertainty (1) [%]
*3: Out of parameters for verification
Table 6.2-12
Radial
mesh
*1
Relative difference in power distribution by MINISTRI for the SPX core
Axial
mesh
*2
All rods out
MCR
half-in
MCR in*6
BCR in*6
6
5.0cm
NC*5
0.98*3
1.55*3
NC*5
6
2.5cm
NC
NC*5
NC*5
NC
24
5.0cm
NC
NC
NC
NC
0.22*4
0.22*4
0.22*4
0.21*4
Uncertainty of
GMVP
*1: Number of radial meshes per subassembly
*2: Axial mesh size
*3: Maximum relative difference to the reference (GMVP) [%]
*4: Statitical uncertainty (1) [%]
*5: Not converged
*6: Out of parameters for verification
㻙㻌㻡㻝㻌㻙㻌
JAEA-Data/Code 2011-018
2.0E-5
2nd order
1.8E-5
6th order
Neutron flux [A.U.]
1.6E-5
1.4E-5
1.2E-5
1.0E-5
8.0E-6
Test zone
Driver with
moderator
Control rod
6.0E-6
4.0E-6
2.0E-6
0.0E+0
-1.5
-0.5
0.5
1.5
Relative radial coordinate [Subassmbly unit]
Fig. 6.2-1
Comparison of the 4th group neutron flux distribution calculated by NSHEX
around the control rod region for the KNK-II core
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JAEA-Data/Code 2011-018
7. 3 ḟඖභゅయ⣔⏝㍺㏦ィ⟬ࢥ࣮ࢻࡢ㐺⏝ᛶホ౯
7.1 ゅᗘศⅬࢭࢵࢺࡢ᮲௳タᐃ
ᐇ㝿ࡢᐇᶵゎᯒ࡬ࡢ㐺⏝࡟࠾࠸࡚ࡣࠊ➨ 6 ❶ࡢ᳨ウ࡛♧ࡋࡓࡼ࠺࡞ゅᗘศⅬ࡜ከ㡯ᘧᒎ㛤ḟ
ᩘ࠶ࡿ࠸ࡣ✵㛫࣓ࢵࢩࣗࢆ༑ศヲ⣽࡟ྲྀࡗࡓゎᯒࢆᚲࡎࡋࡶ⾜࠺ᚲせࡣ࡞࠸࡜⪃࠼ࡽࢀࡿࠋ
Fig. 7.1-1 ཬࡧ Fig. 7.1-2 ࡣࡑࢀࡒࢀ NSHEX ࡟࠾࠸࡚ゅᗘศⅬཬࡧከ㡯ᘧᒎ㛤ḟᩘࡢྲྀࡾ᪉
ࡢ㐪࠸࡟ࡼࡿᅛ᭷್ࡢィ⟬⤖ᯝࡢኚ໬ࢆ♧ࡋࡓࡶࡢ࡛ࠊྑ࡬⾜ࡃ࡟ᚑ࠸ィ⟬᮲௳ࢆ⢒ࡃࡍࡿࡇ
࡜࡜࡞ࡿࠋFig. 7.1-3 ཬࡧ Fig. 7.1-4 ࡣ MINISTRI ࡟࠾࠸࡚ྠᵝ࡟ゅᗘศⅬཬࡧ✵㛫࣓ࢵࢩࣗ
ࡢྲྀࡾ᪉ࡢ㐪࠸࡟ࡼࡿᅛ᭷್ࡢィ⟬⤖ᯝࡢኚ໬ࢆ♧ࡋࡓࡶࡢ࡛࠶ࡿࠋゅᗘศⅬ࡟㛵ࡋ࡚ࡣࠊ᏶
඲ᑐ⛠᮲௳㸦"Completely symmetric"㸧࡛సᡂࡉࢀࡓࡶࡢ࡜ࡋ࡚ࠊഅᩘ࣮࣓ࣔࣥࢺࢆಖᏑࡉࡏ
ࡿ᮲௳࡛タᐃࡉࢀࡓศⅬࢭࢵࢺ㸦௨ୗࠊ"Even condition"㸧 23)ࢆ⏝࠸ࡓሙྜࡣࡑࡢ㝈ࡾ࡛ࡣ࡞
࠸ࡀࠊTWOTRAN ࢥ࣮ࢻ
24)ࡢࢹࣇ࢛ࣝࢺ࡛୚࠼ࡽࢀ࡚࠸ࡿศⅬࢭࢵࢺ㸦௨ୗࠊ"Reference"㸧
ࡸࣞ࣋ࣝẖ࣮࣓ࣔࣥࢺಖᏑ᮲௳࡟ࡼࡾᚓࡽࢀࡿࡶࡢ㸦௨ୗࠊ"Level condition"㸧 23)ࢆ⏝࠸ࡓሙ
ྜ࡟ࡣࠊゅᗘศⅬࢆ⢒ࡃࡍࡿ࡟ᚑ࠸ࠊS4 ᮲௳ࡲ࡛ࡣᅛ᭷್ࡢቑຍࡀぢࡽࢀࡿ㸦ゅᗘศⅬࢭࢵࢺ
ࡢヲ⣽ࡣ௜㘓 6 ࢆཧ↷㸧ࠋ௚᪉ࠊከ㡯ᘧᒎ㛤ḟᩘ࠶ࡿ࠸ࡣ✵㛫࣓ࢵࢩࣗ࡟㛵ࡋ࡚ࡣࠊ⢒ࡃࡍࡿ
ࡇ࡜࡟ࡼࡾ㏫࡟ᅛ᭷್ࡢῶᑡࡀぢࡽࢀࡿࠋࡇࡢࡼ࠺࡞࣓࢝ࢽࢬ࣒ࡣ Table 7.1-1㸦NSHEX㸧ཬ
ࡧ Table 7.1-2㸦MINISTRI㸧࡟♧ࡍࡼ࠺࡟࡯ࡰไᚚᲬ㡿ᇦࡢ୰ᛶᏊ᮰ࡸ྾཰཯ᛂ⋡ࡢ┦ᑐ㛵ಀ
࡛ㄝ࡛᫂ࡁࡿࠋࡍ࡞ࢃࡕࠊไᚚᲬ㡿ᇦࡢ୰ᛶᏊ᮰ࡸ྾཰཯ᛂ⋡ࡣࠊ"Reference"ࡢゅᗘศⅬࢭࢵ
ࢺࢆ⏝࠸ࡓሙྜ࡟ゅᗘศⅬࢆ⢒ࡃࡍࡿࡇ࡜࡟ࡼࡾῶᑡࡍࡿࡀࠊከ㡯ᘧᒎ㛤ḟᩘ࠶ࡿ࠸ࡣ✵㛫࣓
ࢵࢩࣗศ๭ࢆ⢒ࡃࡋࡓሙྜ࡟ࡣ㏫࡟ቑຍࡋ࡚࠸ࡿࠋࡇࡢࡼ࠺࡟ࠊᅛ᭷್ࡸ୰ᛶᏊ᮰࡟࠾࠸࡚ࠊ
ゅᗘศⅬ࡜✵㛫࣓ࢵࢩࣗࢆࡼࡾ⢒ࡃྲྀࡿࡇ࡜࡟ࡼࡿຠᯝࡣ஫࠸࡟ᡴᾘࡋྜ࠺ࡇ࡜ࡀศ࠿ࡿࠋ
ࡇࡢ▱ぢ࠿ࡽࠊ"Reference"ࡢゅᗘศⅬࢭࢵࢺࢆ⏝࠸࡚ゅᗘศⅬ᮲௳ࢆ S4 ࡜ࡋࠊ᭱㐺࡞ከ㡯
ᘧᒎ㛤ḟᩘ࠶ࡿ࠸ࡣ✵㛫࣓ࢵࢩࣗศ๭ࢆྲྀࡿࡇ࡜࡟ࡼࡾࠊ᭱ࡶヲ⣽࡞ゅᗘศⅬཬࡧ✵㛫ศᕸྲྀ
ࡾᢅ࠸᮲௳ୗ࡛ࡢ⤖ᯝࢆ෌⌧ࡍࡿࡇ࡜ࡀண᝿࡛ࡁࡿࠋࡑࡇ࡛ࠊゅᗘศⅬ᮲௳ࢆ S4 ࡜ࡋࠊከ㡯ᘧ
ᒎ㛤ḟᩘ࠶ࡿ࠸ࡣ✵㛫࣓ࢵࢩࣗศ๭࡟㛵ࡍࡿࢧ࣮࣋࢖࡟ࡼࡾ᭱㐺࡞✵㛫ศᕸྲྀࡾᢅ࠸᮲௳ࢆぢ
ࡘࡅࠊᮏሗ࿌᭩࡛ᑐ㇟࡜ࡍࡿ㍺㏦ィ⟬ࢥ࣮ࢻࡢ㐺⏝ᛶホ౯ࢆ⾜࠺ࡇ࡜࡜ࡍࡿࠋ
7.2 ᳨ウ᮲௳
NSHEXࠊMINISTRIࠊMINIHEX ࡢ㐺⏝ᛶホ౯ࢆ⾜࠺ࠋホ౯ࡣࠊྠࡌ᩿㠃✚ࢆ⏝࠸ࡓከ⩌
ࣔࣥࢸ࢝ࣝࣟἲィ⟬ࢥ࣮ࢻ GMVP22)࡟ࡼࡿィ⟬⤖ᯝ࡜ࡢẚ㍑࡟ࡼࡾ⾜࠺ࠋ
(1) ィ⟬య⣔
ィ⟬య⣔࡜ࡋ࡚ࠊ➨ 6 ❶࡛ᑐ㇟࡜ࡋࡓࠊᑠᆺ⅔ᚰ KNK-IIࠊ୰ᆺ⅔ᚰࠕࡶࢇࡌࡹࠖࠊ኱ᆺ⅔ᚰ
ࠕࢫ࣮ࣃ࣮ࣇ࢙ࢽࢵࢡࢫࠖ
㸦SPX㸧ࡢ௚࡟ࠊFig. 7.2-1 ࡟♧ࡍᑠᆺ⅔ᚰࠕᖖ㝧ࠖMK-I㸦 Joyo MK-I㸧
25)࡜
Fig. 7.2-2 ࡟♧ࡍ୰ᆺ⅔ᚰ BFS-62-3A26)ࡶᑐ㇟࡜ࡍࡿࠋ
ࠕᖖ㝧ࠖMK-I ⅔ᚰࡢไᚚᲬᤄධ≧
ែ࡜ࡋ࡚ࡣࠊࠕࡶࢇࡌࡹࠖ⅔ᚰࡸ SPX ⅔ᚰ࡜ྠᵝ࡟ᐇ㝿ࡢไᚚᲬࡢ㐠⏝ࢆ᝿ᐃࡋ࡚ࠊ"All rods
out"ࠊ"MCR half-in"ࠊ"MCR in"ࠊ"BCR in"ࡢ 4 ࢣ࣮ࢫ࡜ࡍࡿࠋࠕᖖ㝧ࠖMK-I ⅔ᚰࡢ"MCR"
࡜"BCR"ࡣྠࡌ௙ᵝ࡛࠶ࡾࠊB-10 ⃰⦰ᗘࡣ 90%࡛࠶ࡿࠋBFS-62-3A ⅔ᚰ࡟ࡘ࠸࡚ࡣࠊ"All rods
㻙㻌㻡㻟㻌㻙㻌
JAEA-Data/Code 2011-018
out"ࡢ௚࡟ࠊไᚚᲬ౯್ ᐃᐇ㦂ࡢ 1 㒊ࢆᶍᨃࡋࡓࠊ"Central MCR in"ࠊ"Off center MCR in"ࠊ
"1 BCR in"ࢆຍ࠼ࡓ 4 ࢣ࣮ࢫࢆᑐ㇟࡜ࡍࡿࠋBFS-62-3A ⅔ᚰࡢ"MCR"࡜"BCR"࡛ࡣࠊ཮᪉ඹ࡟
ኳ↛࣍࢘⣲㸦B㸧ࡀ᥇⏝ࡉࢀ࡚࠸ࡿࡀࠊ࣍࢘⣲ࡢྵ᭷⋡ࡣ␗࡞ࡗ࡚࠾ࡾࠊ"BCR"ࡣ"MCR"ࡢ⣙
2.5 ಸ࡜࡞ࡗ࡚࠸ࡿࠋ
(2) ィ⟬ᑐ㇟᰾≉ᛶ
ホ౯ᑐ㇟ࡢ᰾≉ᛶ࡜ࡋ࡚ࡣࠊ5 ࡘ඲࡚ࡢ⅔ᚰࡢᅛ᭷್࡜ࠕࡶࢇࡌࡹࠖࠊSPXࠊࠕᖖ㝧ࠖMK-I
ࡢ⅔ᚰ㡿ᇦ࡟࠾ࡅࡿ㞟ྜయẖฟຊศᕸ࡜ࡍࡿࠋ┠ᶆ⢭ᗘ࡟ࡘ࠸࡚ࡣࠊ➨ 6 ❶࡛♧ࡋࡓ㏻ࡾᅛ᭷
್࡟ࡘ࠸࡚ࡣ 0.1%࡜ࡋࠊ㞟ྜయẖฟຊศᕸ࡟ࡘ࠸࡚ࡣ 2%࡜ࡍࡿࠋ࡞࠾ࠊ㞟ྜయẖฟຊศᕸࡢ
┠ᶆ⢭ᗘࡣࠊ㏻ᖖࡢฟຊ㐠㌿≧ែࠊࡍ࡞ࢃࡕࠊไᚚᲬ඲ᘬᢤࡲࡓࡣไᚚᲬ༙ᤄධ≧ែࡢࡳ࡟ᑐ
ࡋ࡚㐺⏝ࡍࡿࡇ࡜࡜ࡋࠊฟຊࡀ࡯ࡰࢮ࡛ࣟ࠶ࡿไᚚᲬ඲ᤄධ≧ែ࡟㛵ࡋ࡚ࡣཧ⪃ᢅ࠸࡜ࡍࡿࠋ
(3) ィ⟬᮲௳
ࡑࢀࡒࢀࡢࢥ࣮ࢻࡢゎᯒ᮲௳ࢆ Table 7.2-1 ࡟♧ࡍࠋࡲࡓࠊᮏ᳨ウ࡛ᑐ㇟࡜ࡋࡓ 5 ⅔ᚰ࡟ࡘ
࠸࡚ࠊMINISTRI ࡜ MINIHEX ࢆ㐺⏝ࡋࡓሙྜ࡟ࡘ࠸࡚ࠊ㞟ྜయ㸦ࢭࣝ㸧ෆᚄ᪉ྥ࣓ࢵࢩࣗ
ศ๭࡜ᐇຠ࣓ࢵࢩࣗᖜ㸦࣓ࢵࢩࣗ㠃✚ࡢᖹ᪉᰿㸧ࡢᑐᛂࢆ Table 7.2-2 ࡟♧ࡍࠋ
ゅᗘศⅬ᮲௳ཬࡧ✵㛫ศᕸྲྀࡾᢅ࠸᮲௳࡟㛵ࡍࡿᅛ᭷್ࡢࢧ࣮࣋࢖ィ⟬࡛ࡣࡲࡎࠊࡑࢀࡒࢀ
」ᩘࡢ᮲௳ୗࡢ⤖ᯝ࠿ࡽࠊ↓㝈ゅᗘศⅬ࠶ࡿ࠸ࡣ✵㛫ศᕸ㐃⥆ྲྀࡾᢅ࠸᮲௳㸦↓㝈኱ከ㡯ᘧᒎ
㛤ḟᩘ᮲௳ࡲࡓࡣ↓㝈ᑠ✵㛫ゅᗘ࣓ࢵࢩࣗ᮲௳㸧ࡢᅛ᭷್ࢆእᤄ࡟ࡼࡾồࡵࡿࠋᘬࡁ⥆ࡁࠊ✵
㛫ศᕸྲྀࡾᢅ࠸᮲௳ࢆ୍ᐃ࡜ࡋ࡚ࠊ࠶ࡿゅᗘศⅬ᮲௳㸦SN㸧ࡢ⤖ᯝ࡜↓㝈ゅᗘศⅬ᮲௳ࡢ⤖ᯝ
࡜ࡢᕪ㸦௨ୗࠊSN ゅᗘศⅬຠᯝ㸧ࢆồࡵࡿࠋྠᵝ࡟ࡋ࡚ࠊゅᗘศⅬ᮲௳ࢆ୍ᐃ࡜ࡋ࡚ࠊ࠶ࡿ✵
㛫ศᕸྲྀࡾᢅ࠸᮲௳ࡢ⤖ᯝ࡜✵㛫ศᕸ㐃⥆ྲྀࡾᢅ࠸᮲௳ࡢ⤖࡜ࡢᕪ㸦௨ୗࠊ✵㛫ศᕸྲྀࡾᢅ࠸
ຠᯝ㸧ࢆồࡵࡿࠋ
ࡑࡋ࡚ࠊୖグ࡟ࡼࡾᚓࡽࢀࡓィ⟬⤖ᯝ࠿ࡽࠊ✵㛫ศᕸຠᯝࡀ S4 ゅᗘศⅬຠᯝࢆᡴࡕᾘࡋࠊṧ
ࡾࡢຠᯝࡢ⤯ᑐ್ࡀ 0.1%Ǽk ௨ୗ࡜࡞ࡿࡼ࠺࡞ከ㡯ᘧᒎ㛤ḟᩘ࠶ࡿ࠸ࡣ࣓ࢵࢩࣗศ๭ࢆ㐺⏝
ᛶホ౯⏝ࡢ᮲௳࡜ࡋ࡚㑅ᐃࡍࡿࠋ࡞࠾ࠊከ㡯ᘧᒎ㛤ḟᩘ࠶ࡿ࠸ࡣ࣓ࢵࢩࣗศ๭ࡣィ⟬᫬㛫ࡸィ
⟬ᶵ౑⏝ᐜ㔞ࡢྜ⌮ⓗࡢࡓࡵ࡟࡛ࡁࡿࡔࡅ⢒ࡃྲྀࡿࡇ࡜࡜ࡍࡿࠋ
7.3 ᳨ウ⤖ᯝ
ྛ⅔ᚰ࡟㛵ࡋ࡚ࠊゅᗘศⅬ࡜✵㛫ศᕸྲྀࡾᢅ࠸࡟㛵ࡍࡿᅛ᭷್ࡢࢧ࣮࣋࢖⤖ᯝࠊᇶ‽᮲௳ࡢ
㑅ᐃࠊᇶ‽᮲௳࡛ࡢᅛ᭷್࡜㞟ྜయẖฟຊศᕸ㸦KNK-II ࡜ BFS-62-3A ࢆ㝖ࡃ㸧ࡢゎᯒ⤖ᯝࢆ
♧ࡍࡇ࡜࡜ࡍࡿࠋ࡞࠾ࠊMINISTRI ࡜ MINIHEX ࢆ⏝࠸ࡓሙྜ࡟ࡣࠊ㍈᪉ྥࡢ࣓ࢵࢩࣗศ๭
࡟ࡼࡿຠᯝࡶᏑᅾࡍࡿࡀࠊᚄ᪉ྥࡢຠᯝ࡟ẚ࡭࡚༑ศ࡟ᑠࡉ࠿ࡗࡓࡇ࡜࡜㍈᪉ྥࡢ࣓ࢵࢩࣗศ
๭ࡣ㏻ᖖᚄ᪉ྥ࡜ྠ⛬ᗘ࡟ࡍࡿࡇ࡜࠿ࡽࢧ࣮࣋࢖⤖ᯝࡢグ㍕ࢆ๭ឡࡋࡓࠋ
7.3.1 KNK-II ⅔ᚰ࡟࠾ࡅࡿ᳨ウ⤖ᯝ
ᅛ᭷್࡟㛵ࡍࡿゅᗘศⅬཬࡧ✵㛫ศᕸྲྀࡾᢅ࠸᮲௳ࡢ౫Ꮡᛶ࡟ࡘ࠸࡚ࠊNSHEX ࢆ⏝࠸ࡓሙ
ྜࡢ⤖ᯝࢆ Fig. 7.3-1 ࡟ࠊMINISTRI ࢆ⏝࠸ࡓሙྜ㸦MINIHEX ࡣ㐺⏝⠊ᅖእ㸧ࡢ⤖ᯝࢆ Fig.
㻙㻌㻡㻠㻌㻙㻌
JAEA-Data/Code 2011-018
7.3-2 ࡟ࡑࢀࡒࢀ♧ࡍࠋゅᗘศⅬ࡜✵㛫ศᕸྲྀࡾᢅ࠸࡟㛵ࡍࡿࢧ࣮࣋࢖࡛ࡣࠊS4 ゅᗘศⅬຠᯝ
ࢆᡴᾘࡍࡼ࠺࡞✵㛫ศᕸྲྀࡾᢅ࠸᮲௳ࢆ㑅ᐃࡍࡿࡇ࡜࡜࡞ࡿࡢ࡛ࠊከ㡯ᘧᒎ㛤ḟᩘࡲࡓࡣ࣓ࢵ
ࢩࣗศ๭ࡢ౫Ꮡᛶࢆ♧ࡍᅗ࡟ࡣࠊS4 ゅᗘศⅬຠᯝࢆ➢ྕ཯㌿ࡢୖࠕ㸫ࠖ༳࡛┦ᛂࡢ఩⨨࡟⾲♧
ࡉࡏࠊゅᗘศⅬຠᯝ࡜✵㛫ศᕸྲྀࡾᢅ࠸ຠᯝࡢᡴᾘࡋྜ࠸ࡢ⤖ᯝṧࡿຠᯝࢆ▮༳ࡢྥࡁ࡜㛗ࡉ
࡛♧ࡋ࡚࠸ࡿࠋලయⓗ࡟ࡣࠊNSHEX ࢆ⏝࠸ࡓሙྜ࡟ࡣࠊᶓ㍈ୖࡢ 2 ḟከ㡯ᘧᒎ㛤࡜ࡋࡓ᮲௳
ࡢ఩⨨࡟⾲♧ࡉࡏࡿࡇ࡜࡟ࡼࡾࠊ2 ḟከ㡯ᘧᒎ㛤ࡢ㐺⏝ᛶࡢ┠Ᏻ࡜ࡋ࡚࠸ࡿࠋࡲࡓࠊMINISTRI
࡜ MINIHEX ࢆ⏝࠸ࡓሙྜ࡟ࡣࠊᶓ㍈ୖ࡛ S4 ゅᗘศⅬຠᯝࢆᡴᾘࡍᚄ᪉ྥ࣓ࢵࢩࣗ᮲௳఩⨨
௜㏆࡟⾲♧ࡉࡏࡿࡇ࡜࡟ࡼࡾࠊ㐺ษ࡞࣓ࢵࢩࣗศ๭᮲௳㑅ᐃࡢ┠Ᏻ࡜ࡋ࡚࠸ࡿࠋ
NSHEX ࢆ⏝࠸ࡓሙྜ࡟ࡘ࠸࡚ࡣࠊ2 ḟከ㡯ᘧᒎ㛤࡜ࡍࡿࡇ࡜࡟ࡼࡾࠊ㐺ᗘ࡟ S4 ゅᗘศⅬຠ
ᯝࢆᡴᾘࡍᵝᏊࡀศ࠿ࡾࠊ2 ḟከ㡯ᘧᒎ㛤ࡀᇶ‽᮲௳࡜ࡋ࡚㑅ᐃ࡛ࡁࡿࠋ
MINISTRI ࡟ࡘ࠸࡚ࡣࠊ඲࡚ࡢࢣ࣮ࢫ࡟ࡘ࠸࡚ 2.5cm ࣓ࢵࢩࣗ㸦࣓ࢵࢩࣗ㠃✚ 6.1cm2㸧࡜
ࡍࡿ࡜✵㛫ศᕸྲྀࡾᢅ࠸ຠᯝࡀ S4 ゅᗘศⅬຠᯝࢆࡸࡸୖᅇࡿࡶࡢࡢ㐺ᗘ࡟ᡴᾘࡋྜ࠸ࠊṧࡾࡢ
ຠᯝࡣ┠ᶆ⢭ᗘࢆ‶㊊࡛ࡁࡿぢ㎸ࡳࡀㄞࡳྲྀࢀࡿࡢ࡛ࠊᚄ᪉ྥ࡜㍈᪉ྥඹ࡟ 2.5cm ࣓ࢵࢩࣗศ
๭ࢆᇶ‽᮲௳࡟㑅ᐃࡍࡿࠋ
ᇶ‽᮲௳࡛ࡢࠊᅛ᭷್ࡢィ⟬⤖ᯝཬࡧィ⟬᫬㛫ࢆ Table 7.3-1 ࡟♧ࡍࠋ
ᅛ᭷್࡟ࡘ࠸࡚ࡣࠊNSHEX ࡜ MINISTRI ࡢ཮᪉࡜ࡶᇶ‽᮲௳࡟࠾࠸࡚┠ᶆ⢭ᗘࢆ‶㊊ࡋ࡚
࠸ࡿࠋィ⟬᫬㛫࡟ࡘ࠸࡚ࡣࠊMINISTRI ࡣ NSHEX ࡢ⣙ 10 ಸࢆせࡋ࡚࠸ࡿࡀࠊ཮᪉࡜ࡶ GMVP
࡯࡝ࡣせࡋ࡚࠸࡞࠸ࡇ࡜ࡀศ࠿ࡿࠋ
7.3.2 ࠕࡶࢇࡌࡹࠖ⅔ᚰ࡟࠾ࡅࡿ᳨ウ⤖ᯝ
ᅛ᭷್࡟㛵ࡍࡿゅᗘศⅬཬࡧ✵㛫ศᕸྲྀࡾᢅ࠸᮲௳ࡢ౫Ꮡᛶ࡟ࡘ࠸࡚ࠊNSHEX ࢆ⏝࠸ࡓሙ
ྜࡢ⤖ᯝࢆ Fig. 7.3-3 ࡟ࠊMINISTRI ࢆ⏝࠸ࡓሙྜ㸦MINIHEX ࡣ㐺⏝⠊ᅖእ㸧ࡢ⤖ᯝࢆ Fig.
7.3-4 ࡟ࡑࢀࡒࢀ♧ࡍࠋ
NSHEX ࢆ⏝࠸ࡓሙྜ࡟ࡘ࠸࡚ࡣࠊ2 ḟከ㡯ᘧᒎ㛤࡜ࡋࡓሙྜࡢ✵㛫ศᕸྲྀࡾᢅ࠸ຠᯝࡀᑠ
ࡉࡃ S4 ゅᗘศⅬຠᯝࡢᡴᾘࡋᗘྜ࠸ࡀᑠࡉ࠸ࡶࡢࡢࠊṧࡾࡢຠᯝࡣ┠ᶆ⢭ᗘࢆ‶㊊࡛ࡁࡿࡇ࡜
ࡀㄞࡳྲྀࢀࡿࡢ࡛ࠊ2 ḟከ㡯ᘧᒎ㛤ࡀᇶ‽᮲௳࡜ࡋ࡚㑅ᐃ࡛ࡁࡿࠋ
MINISTRI ࡟ࡘ࠸࡚ࡣࠊ2.2cm ࣓ࢵࢩࣗ㸦࣓ࢵࢩࣗ㠃✚ 4.8cm2㸧࡜ࡍࡿ࡜✵㛫ศᕸྲྀࡾᢅ
࠸ຠᯝ࡜ S4 ゅᗘศⅬຠᯝࡀ࡯ࡰᡴࡕᾘࡋྜ࠺ࡀࠊ඲࡚ࡢࢣ࣮ࢫ࡟ࡘ࠸࡚ 4.4cm ࣓ࢵࢩࣗ㸦࣓
ࢵࢩࣗ㠃✚ 19cm2㸧࡜ࡋ࡚ࡶ✵㛫ศᕸྲྀࡾᢅ࠸ຠᯝࡀ S4 ゅᗘศⅬຠᯝࢆୖᅇࡿࡶࡢࡢࠊṧࡾࡢ
ຠᯝࡣ┠ᶆ⢭ᗘࢆ‶㊊࡛ࡁࡿぢ㎸ࡳࡀㄞࡳྲྀࢀࡿࡢ࡛ࠊᚄ᪉ྥ 4.4cm ࣓ࢵࢩࣗศ๭㸦㍈᪉ྥ
5.0cm ࣓ࢵࢩࣗศ๭㸧ࢆᇶ‽᮲௳࡟㑅ᐃࡍࡿࠋ
ᇶ‽᮲௳࡛ࡢࠊᅛ᭷್ࡢィ⟬⤖ᯝཬࡧィ⟬᫬㛫ࢆ Table 7.3-2 ࡟ࠊ㞟ྜయẖฟຊศᕸࡢィ⟬
⤖ᯝࢆ Fig. 7.3-5㹼8 ཬࡧ Table 7.3-3㸦᭱኱ㄗᕪࡢࡳ㸧࡟ࠊࡑࢀࡒࢀ♧ࡍࠋ
ᅛ᭷್࡟ࡘ࠸࡚ࡣࠊᇶ‽᮲௳࡟࠾࠸࡚ࠊNSHEX ࡟ࡘ࠸࡚ࡣ᭱኱ 0.07%ࡢ㐣኱ホ౯ࡀࠊ
MINISTRI ࡛ࡣ᭱኱ 0.06%ࡢ㐣ᑠホ౯ࡀࡑࢀࡒࢀぢࡽࢀࡿࡀࠊNSHEX ࡜ MINISTRI ࡢ཮᪉
࡜ࡶ┠ᶆ⢭ᗘࢆ‶㊊ࡋ࡚࠸ࡿࠋィ⟬᫬㛫࡟ࡘ࠸࡚ࡣࠊNSHEXࠊMINISTRIࠊGMVP ࡟ࡘ࠸࡚
ྠ➼࡛࠶ࡿࠋ
㞟ྜయẖฟຊศᕸ࡟ࡘ࠸࡚ࡣࠊ"All rods out"࡜"MCR half-in"ࡢࢣ࣮ࢫ࡟ࡘ࠸࡚ࠊGMVP ࡢ
㻙㻌㻡㻡㻌㻙㻌
JAEA-Data/Code 2011-018
⤫ィㄗᕪࢆୖᅇࡗ࡚࠸ࡿࡶࡢࡢࠊNSHEX ࡜ MINISTRI ࡢ཮᪉࡜ࡶ GMVP ࡜ 0.5%௨ෆ୍࡛⮴
ࡀぢࡽࢀࠊ┠ᶆ⢭ᗘࢆ༑ศ࡟‶㊊ࡋ࡚࠸ࡿࠋཧ⪃ࡲ࡛࡟ࠊไᚚᲬ඲ᤄධ≧ែ㸦"MCR in"ཬࡧ"BCR
in"㸧࡟ࡘ࠸࡚ࡣࠊ0.7%௨ෆ୍࡛⮴ࡀぢࡽࢀࠊไᚚᲬ඲ᤄධ࡟ࡼࡿ GMVP ࡜ࡢ୍⮴ᗘྜ࠸ࡢᝏ
໬ࡣ≉࡟ぢࡽࢀ࡞࠸ࠋ
7.3.3 SPX ⅔ᚰ࡟࠾ࡅࡿ᳨ウ⤖ᯝ
ᅛ᭷್࡟㛵ࡍࡿゅᗘศⅬ࡜✵㛫ศᕸྲྀࡾᢅ࠸᮲௳ࡢ౫Ꮡᛶ࡟ࡘ࠸࡚ࠊNSHEX ࢆ⏝࠸ࡓሙྜ
ࡢ⤖ᯝࢆ Fig. 7.3-9 ࡟ࠊMINISTRI ࢆ⏝࠸ࡓሙྜ㸦MINIHEX ࡣ㐺⏝⠊ᅖእ㸧ࡢ⤖ᯝࢆ Fig.
7.3-10 ࡟ࡑࢀࡒࢀ♧ࡍࠋ
NSHEX ࢆ⏝࠸ࡓሙྜ࡟ࡘ࠸࡚ࡣࠊ2 ḟከ㡯ᘧᒎ㛤࡜ࡋࡓሙྜࡢ✵㛫ศᕸྲྀࡾᢅ࠸ຠᯝࡣ S4
ゅᗘศⅬຠᯝࡼࡾࡶࡸࡸᑠࡉ࠸ࡀࠊṧࡾࡢຠᯝࡣ┠ᶆ⢭ᗘࢆ‶㊊࡛ࡁࡿࡇ࡜ࡀㄞࡳྲྀࢀࡿࡢ࡛ࠊ
2 ḟከ㡯ᘧᒎ㛤ࡀᇶ‽᮲௳࡜ࡋ࡚㑅ᐃ࡛ࡁࡿࠋ
MINISTRI ࡟ࡘ࠸࡚ࡣࠊ"All rods out"ࠊ"MCR half-in"ࠊ"BCR in"ࡢ 3 ࢣ࣮ࢫ࡟ࡘ࠸࡚ࡣ 6.8cm
࣓ࢵࢩࣗ㸦࣓ࢵࢩࣗ㠃✚ 47cm2㸧࡜ࡋ࡚ࡶࠊ✵㛫ศᕸྲྀࡾᢅ࠸ຠᯝࡣ S4 ゅᗘศⅬຠᯝࢆ኱ࡁࡃ
ୖᅇࡿࡇ࡜ࡣ࡞ࡃࠊṧࡾࡢຠᯝࡣ┠ᶆ⢭ᗘࢆ‶㊊࡛ࡁࡿぢ㏻ࡋ࡛࠶ࡿࠋ୍᪉ࠊ"MCR in"ࡢࢣ࣮
ࢫ࡛ࡣ 6.8cm ࣓ࢵࢩࣗ㸦࣓ࢵࢩࣗ㠃✚ 47cm2㸧࡜ࡋࡓሙྜ࡟ࡣࠊ✵㛫ศᕸྲྀࡾᢅ࠸ຠᯝࡀ㠀ᖖ
࡟኱ࡁࡃࠊS4 ゅᗘศⅬຠᯝ࡜ᡴᾘࡋྜࡗࡓṧࡾࡢຠᯝࡣ┠ᶆ⢭ᗘ࡜࡯ࡰྠ➼࡛࠶ࡿࠋ௚᪉ࠊ
"MCR in"ࡢࢣ࣮ࢫ࡛ 3.4cm ࣓ࢵࢩࣗ㸦࣓ࢵࢩࣗ㠃✚ 12cm2㸧᮲௳࡜ࡍࡿ࡜ࠊS4 ゅᗘศⅬຠᯝ
࡜✵㛫ศᕸྲྀࡾᢅ࠸ຠᯝࡀ࡯ࡰᡴࡕᾘࡋྜ࠺ࡇ࡜࠿ࡽࠊ"MCR in"ࡢࢣ࣮ࢫ࡛ࡣ 3.4cm ࣓ࢵࢩ
ࣗ᮲௳ࡀ㐺ษ࡛࠶ࡿࡇ࡜ࡀศ࠿ࡿࠋ඲࡚ࡢࢣ࣮ࢫ࡟ࡘ࠸࡚┠ᶆ⢭ᗘࢆ‶㊊࡛ࡁࡿࡢࡣ 3.4cm ࣓
ࢵࢩࣗ㸦࣓ࢵࢩࣗ㠃✚ 12cm2㸧᮲௳ࡔࡀࠊ"MCR in"ࡢࢣ࣮ࢫ௨እࡣ 6.8cm ࣓ࢵࢩࣗ᮲௳࡛ࡶ
┠ᶆ⢭ᗘࢆ‶㊊ࡍࡿぢ㏻ࡋ࡞ࡢ࡛ࠊᚄ᪉ྥࡣ 3.4cm ࡜ 6.8cm ࣓ࢵࢩࣗศ๭ࡢ཮᪉㸦㍈᪉ྥࡣ
5.0cm ࣓ࢵࢩࣗศ๭㸧ࢆᇶ‽᮲௳࡟㑅ᐃࡍࡿࠋ
ᇶ‽᮲௳࡛ࡢࠊᅛ᭷್ࡢィ⟬⤖ᯝཬࡧィ⟬᫬㛫ࢆ Table 7.3-4 ࡟ࠊ㞟ྜయẖฟຊศᕸࡢィ⟬
⤖ᯝࢆ Fig. 7.3-11㹼14㸦 MINISTRI ࡟㛵ࡋ࡚ࡣ 3.4cm ࣓ࢵࢩࣗࡢ⤖ᯝࢆᥖ㍕㸧ཬࡧ Table 7.3-5
㸦᭱኱ㄗᕪࡢࡳ㸧࡟ࠊࡑࢀࡒࢀ♧ࡍࠋ
ᅛ᭷್࡟ࡘ࠸࡚ࡣࠊNSHEX ࡛ࡣ᭱኱ 0.06%ࡢ㐣ᑠホ౯ࡀぢࡽࢀࡿࡀࠊ┠ᶆ⢭ᗘࢆ‶㊊ࡋ࡚
࠸ࡿࠋMINISTRI ࡛ࡣ 6.8cm ࣓ࢵࢩࣗ࡜ࡋࡓሙྜ࡟ࡣ"MCR in"ࢣ࣮ࢫ࡟ࡘ࠸࡚ࡣࢃࡎ࠿࡟┠
ᶆ⢭ᗘࢆ‶㊊ࡋ࡞࠸ࡀࠊࡑࢀ௨እࡢࢣ࣮ࢫ࡛ࡣ༑ศ࡟‶㊊ࡋ࡚࠸ࡿࠋ᭦࡟ࠊMINISTRI ࡟࠾࠸
࡚ 3.4cm ࡜ࡋࡓሙྜ࡟ࡣࠊ඲࡚ࡢࢣ࣮ࢫ࡟ࡘ࠸࡚┠ᶆ⢭ᗘࢆ༑ศ࡟‶㊊ࡋ࡚࠸ࡿࡀࠊ"MCR
half-in"ࡢࢣ࣮ࢫ࡛ࡣ᰾ศ⿣୰ᛶᏊ※ࡢ㠀཰᮰࡜ゝ࠺ၥ㢟ࡀ⏕ࡌࡓࠋィ⟬᫬㛫࡟ࡘ࠸࡚ࡣࠊ
NSHEX ࡜ MINISTRI ࡢ 6.8cm ࣓ࢵࢩࣗࡢሙྜࡣ GMVP ࡜ྠ➼࡛࠶ࡿࡀࠊMINISTRI ࡛ 3.4cm
࣓ࢵࢩࣗ࡜ࡍࡿ࡜ࠊ࣓ࢵࢩࣗᩘࡣ 4 ಸ࡜࡞ࡿࡢ࡛┦ᛂ࡟ィ⟬᫬㛫ࢆせࡋ࡚࠸ࡿࠋ
㞟ྜయẖฟຊศᕸ࡟ࡘ࠸࡚ࡣࠊNSHEX ࡛ࡣ┠ᶆ⢭ᗘࡣ‶㊊ࡋ࡚࠸ࡿࡶࡢࡢࠊ"All rods out"
ࡢࢣ࣮ࢫ࡛ࡣ 0.7%௨ෆࡢ୍⮴࡛࠶ࡿࡢ࡟ᑐࡋ࡚ࠊ"MCR half-in"ࡢࢣ࣮ࢫ࡛ࡣ 1.8%௨ෆࡢ୍⮴
࡛࠶ࡾࠊไᚚᲬࡢᤄධ࡟ࡼࡿ୍⮴ᗘྜ࠸ࡢᝏ໬ࡀぢࡽࢀ࡚࠸ࡿࠋࡲࡓࠊཧ⪃ᢅ࠸࡛࠶ࡿࡀࠊ"MCR
in"࡜"BCR in"ࡢࢣ࣮ࢫ࡛ࡣࠊGMVP ࡟ᑐࡋ࡚ࡑࢀࡒࢀ 4.2㸣ཬࡧ 3.1%࡟ཬࡪᕪ␗ࡀぢࡽࢀ࡚
࠸ࡿࠋMINISTRI ࡟㛵ࡋ࡚ࡣࠊ3.4cm ࣓ࢵࢩࣗ࡜ࡋࡓሙྜ㸦"MCR half-in"ࡢࢣ࣮ࢫࡣ㠀཰᮰㸧
㻙㻌㻡㻢㻌㻙㻌
JAEA-Data/Code 2011-018
࡟ຍ࠼࡚ࠊ6.8cm ࣓ࢵࢩࣗ࡜ࡋࡓሙྜ࡛ࡶ GMVP ࡜ 1.4%௨ෆࡢ୍⮴ࡀぢࡽࢀࠊ┠ᶆ⢭ᗘࢆ‶
㊊ࡋ࡚࠸ࡿࠋࡲࡓࠊไᚚᲬ඲ᤄධ≧ែ㸦"MCR in"࡜"BCR in"ࡢࢣ࣮ࢫ㸧࡛ࡶ GMVP ࡜ 2%௨
ෆࡢ୍⮴ࡀぢࡽࢀ࡚࠸ࡿࠋ
ࡇࡇ࡛ࠊ"MCR in"ࡢࢣ࣮ࢫ࡟࠾ࡅࡿ NSHEX ࡢ⤖ᯝࡢᕪ␗࡟㛵ࡍࡿ᳨ウ࡟ࡘ࠸࡚♧ࡍࠋࡇ
ࡢࢣ࣮ࢫࡢィ⟬࡛ࡣࠊእഃ཯᚟ẖ࡟㧗ḟ࣮࣓ࣔࣥࢺࡢ᭦᪂ࢆṆࡵࡿ᮲௳ࢆ㏻ᖖࡢ 2.010-4 ࠿
ࡽ 4.010-4 ࡟⦆ࡵࡓࡓࡵ࡟ࠊGMVP ࡜ࡢᕪ␗ࡀᣑ኱ࡍࡿ࡜ඹ࡟ MINISTRI ࡜ࡣᕪ␗ࡢ⌧ࢀ᪉
ࡢഴྥࡀ␗࡞ࡗࡓࡶࡢ࡜⪃࠼ࡽࢀࡿࠋࡑࡇ࡛ࠊNSHEX ࡢ཰᮰ᛶ࡜ィ⟬࢔ࣝࢦࣜࢬ࣒ࡢᨵⰋ࡟
ࡘ࠸᳨࡚ウࢆ⾜ࡗࡓࠋࡑࡢ⤖ᯝࠊෆഃ཯᚟ィ⟬࡟ࣜࣂࣛࣥࢫἲࢆ㐺⏝ࡋࠊ୰ᛶᏊ᮰ࡢ㧗ḟ࣮ࣔ
࣓ࣥࢺࢆィ⟬ࡢ᭱ᚋࡲ࡛እഃ཯᚟ẖ࡟᭦᪂ࡍࡿࡼ࠺࡟ኚ᭦ࡋࡓ࡜ࡇࢁࠊィ⟬᫬㛫ࡣඖࡢ⣙ 2 ಸ
ࢆせࡋࡓࡀࠊGMVP ࡜ࡢᕪ␗ࡣ᭱኱࡛ 2.4%࡟ࡲ࡛ᨵၿࡀぢࡽࢀࡓࠋࡍ࡞ࢃࡕࠊ4.3%࡟ཬࡪ
GMVP ࡜ࡢᕪ␗ࡣࠊNSHEX ࡢᇶ♏⌮ㄽࡢ୙ഛ࡟ࡼࡿࡶࡢ࡛ࡣ࡞࠸ࡇ࡜ࢆ☜ㄆࡋࡓࠋ
7.3.4 ࠕᖖ㝧ࠖMK-I ⅔ᚰ࡟࠾ࡅࡿ᳨ウ⤖ᯝ
ࡲࡎࠊNSHEX ࢆ⏝࠸ࡓሙྜ࡟ࡣࠊ඲࡚ࡢࢣ࣮ࢫ࡟࠾࠸࡚ィ⟬ࡢ཰᮰ࡀᚓࡽࢀ࡞࠿ࡗࡓࠋ࡞
࠾ࠊィ⟬ࡀ཰᮰ࡋ࡞࠿ࡗࡓཎᅉ࡜ࡋ࡚ࡣࠊ㏣ຍ᳨ウ࠿ࡽ㞟ྜయࣆࢵࢳࡀ 8.2cm ࡜ࡸࡸᑠࡉ࠸ࡇ
࡜࡜ࠊไᚚᲬ඲ᤄධ≧ែ࡟࠾࠸࡚㍈᪉ྥ࡟ 5cm ࡜ᑠࡉ࠸ࢧ࢖ࢬࡢࣀ࣮ࢻࢆྲྀࡗࡓࡇ࡜࡟࠶ࡿࡇ
࡜ࡀศ࠿ࡗࡓࠋ
MINISTRI ࢆ⏝࠸ࡓሙྜ㸦MINIHEX ࡣ㐺⏝⠊ᅖእ㸧ࡢᅛ᭷್࡟㛵ࡍࡿゅᗘศⅬ࡜✵㛫ศᕸ
ྲྀࡾᢅ࠸᮲௳ࡢ౫Ꮡᛶࢆ Fig. 7.3-15 ࡟♧ࡍࠋ1.6cm ࣓ࢵࢩࣗ㸦࣓ࢵࢩࣗ㠃✚ 2.4cm2㸧࡜ࡍࡿ
࡜✵㛫ศᕸྲྀࡾᢅ࠸ຠᯝ࡜ S4 ゅᗘศⅬຠᯝࡀ࡯ࡰᡴࡕᾘࡋྜ࠺ࡀࠊ✵㛫࣓ࢵࢩࣗຠᯝࡀࡸࡸ኱
ࡁ࠸ 3.1cm ࣓ࢵࢩࣗ㸦࣓ࢵࢩࣗ㠃✚ 9.7cm2㸧࡜ࡋ࡚ࡶࠊṧࡾࡢຠᯝࡣ┠ᶆ⢭ᗘࢆ‶㊊࡛ࡁࡿ
ぢ㎸ࡳࡀ࠶ࡿࡢ࡛ࠊᚄ᪉ྥ 3.1cm ࣓ࢵࢩࣗศ๭㸦㍈᪉ྥ 2.5cm ࣓ࢵࢩࣗศ๭㸧ࢆᇶ‽᮲௳࡟㑅
ᐃࡍࡿࠋ
ᇶ‽᮲௳࡛ࡢࠊᅛ᭷್ࡢィ⟬⤖ᯝཬࡧィ⟬᫬㛫ࢆ Table 7.3-6 ࡟ࠊ㞟ྜయẖฟຊศᕸࡢィ⟬
⤖ᯝࢆ Fig. 7.3-16㹼19 ཬࡧ Table 7.3-7㸦᭱኱ㄗᕪࡢࡳ㸧࡟ࠊࡑࢀࡒࢀ♧ࡍࠋ
ᅛ᭷್࡟ࡘ࠸࡚ࡣࠊᇶ‽᮲௳࡟࠾࠸࡚ࠊMINISTRI ࡛ࡣ 0.06㹼0.07%ࡢ㐣ᑠホ౯ࡀࡑࢀࡒࢀ
ぢࡽࢀࡿࡀࠊ┠ᶆ⢭ᗘࢆ‶㊊ࡋ࡚࠸ࡿࠋィ⟬᫬㛫࡟ࡘ࠸࡚ࡣࠊMINISTRI ࡜ GMVP ࡛ྠ➼࡛
࠶ࡿࠋ
㞟ྜయẖฟຊศᕸ࡟ࡘ࠸࡚ࡣࠊGMVP ࡢ⤫ィㄗᕪࢆ୍㒊ୖᅇࡗ࡚࠸ࡿࡶࡢࡢࠊMINISTRI
ࡣ GMVP ࡜ 0.6%௨ෆ୍࡛⮴ࡀぢࡽࢀࠊ┠ᶆ⢭ᗘࢆ༑ศ࡟‶㊊ࡋ࡚࠸ࡿࠋ
7.3.5 BFS-62-3A ⅔ᚰ࡟࠾ࡅࡿ᳨ウ⤖ᯝ
➨ 1 ❶ 1.2 ࡛㏙࡭ࡓࡼ࠺࡟ NSHEX ࡢ㐺⏝ࡣ⌧ᐇⓗ࡛ࡣ࡞࠸ࡢ࡛⾜ࢃ࡞࠸ࠋ
MINIHEX ཬࡧ MINISTRI ࢆ⏝࠸ࡓሙྜࡢᅛ᭷್࡟㛵ࡍࡿゅᗘศⅬ࡜✵㛫ศᕸྲྀࡾᢅ࠸᮲
௳ࡢ౫Ꮡᛶࢆ Fig. 7.3-20 ࡟♧ࡍࠋ඲࡚ࡢࢣ࣮ࢫ࡟㛵ࡋ࡚ 4.7cm ࣓ࢵࢩࣗ㸦࣓ࢵࢩࣗ㠃✚ 23cm2㸧
ࡀ᭱㐺࡛࠶ࡿࡇ࡜ࡀ᫂ࡽ࠿࡛࠶ࡾࠊMINISTRI ࡟ࡼࡿᚄ᪉ྥ 4.7cm ࣓ࢵࢩࣗ㸦㍈᪉ྥ 5.0cm
࣓ࢵࢩࣗศ๭㸧ࢆᇶ‽᮲௳࡟㑅ᐃࡍࡿࠋ
ᇶ‽᮲௳࡛ࡢࠊᅛ᭷್ࡢィ⟬⤖ᯝཬࡧィ⟬᫬㛫ࢆ Table 7.3-8 ࡟♧ࡍࠋGMVP ࡢ⤫ィ⢭ᗘࡣ
㻙㻌㻡㻣㻌㻙㻌
JAEA-Data/Code 2011-018
ⱝᖸୖᅇࡿࡶࡢࡢࠊMINIHEX ࡣ GMVP ࡜ 0.01%௨ෆࡢ୍⮴ࡀぢࡽࢀࠊ┠ᶆ⢭ᗘࢆ༑ศ࡟‶
㊊ࡋ࡚࠸ࡿࠋィ⟬᫬㛫࡟ࡘ࠸࡚ࡣࠊMINIHEX ࡜ GMVP ࡛ྠ➼࡛࠶ࡿࠋ
7.4 ࡲ࡜ࡵ
TWOTRAN ࢥ࣮ࢻࡢࢹࣇ࢛ࣝࢺ࡛୚࠼ࡽࢀ࡚࠸ࡿ"Reference"ゅᗘศⅬࢭࢵࢺࢆ⏝࠸ࡓሙྜ
࡟ࡣࠊゅᗘศⅬ࡜✵㛫࣓ࢵࢩࣗࡸከ㡯ᘧᒎ㛤ࢆヲ⣽࡟ࡍࡿຠᯝࡣ஫࠸࡟ᡴᾘࡋྜ࠺࡜ࡢ≉ᛶࢆ
⏕࠿ࡋ࡚ࠊゅᗘศⅬࢆ➨ 6 ❶࡛♧ࡋࡓ᳨ドィ⟬ࡢ S8 ࠿ࡽ S4 ࡟⦆ࡵࡓ᮲௳࡛㐺⏝ᛶホ౯ࢆ⾜ࡗ
ࡓࠋࡇࡢゅᗘศⅬ᮲௳ࡢ⦆࿴࡟ࡼࡾࠊ࡯ࡰ඲࡚ࡢィ⟬࡟ࡘ࠸࡚཰᮰ࡋࡓ⤖ᯝࡀᚓࡽࢀࡿࡼ࠺࡟
࡞ࡗࡓࠋ
㐺⏝ᛶホ౯ࡢ⤖ᯝࠊNSHEX ࡟ࡘ࠸࡚ࡣ 2 ḟከ㡯ᘧᒎ㛤ࡀࠊMINIHEX ࡜ MINISTRI ࡟ࡘ࠸
࡚ࡣࠊᑠᆺ⅔ᚰ࡛ࡣ 2.5cm ࣓ࢵࢩࣗࡀࠊ୰ᆺཬࡧ኱ᆺ⅔ᚰ࡛ࡣ 5.0cm ࣓ࢵࢩࣗ࡜ࡋࡓ᮲௳ࡀ┠
ᶆ⢭ᗘࡢ‶㊊࡜ィ⟬᫬㛫▷⦰ࡢほⅬ࠿ࡽ᭱㐺࡛࠶ࡿࡇ࡜ࡀศ࠿ࡗࡓࠋMINISTRI ࡜ MINIHEX
ࢆ⏝࠸ࡓ᭷㝈ᕪศἲィ⟬࡟㛵ࡍࡿ᳨ウ⤖ᯝࡣࠊḟࡢࡼ࠺࡟ᩚ⌮࡛ࡁࡿࠋ
⾲ S4 ゅᗘศⅬ᮲௳࡟࠾ࡅࡿ⅔ᚰࢧ࢖ࢬ࡜᭱㐺ᚄ᪉ྥ࣓ࢵࢩࣗࢧ࢖ࢬ࡜ࡢ㛵ಀ
⅔ᚰ䝃䜲䝈㻌
ᑠᆺ㻌
୰ᆺ㻌
ᚄ᪉ྥ䝯䝑䝅䝳䝃
㞟ྜయ㓄ิ䝢䝑
㞟ྜయෆᚄ᪉ྥ㻌
䜲䝈 [cm]
䝏 [cm]
䝯䝑䝅䝳ศ๭ᩘ㻌
KNK-II
2.5
13.0
24
Joyo MK-I
3.1
8.2
6
Monju
4.4
11.6
6
BFS-62-3A
4.7
5.1
1
⅔ᚰ㻌
6.8
኱ᆺ㻌
SPX
6
18.0
3.4
24
ࡲࡓࠊKNK-II ⅔ᚰࠊࠕࡶࢇࡌࡹࠖ⅔ᚰࠊࠕࢫ࣮ࣃ࣮ࣇ࢙ࢽࢵࢡࢫࠖ⅔ᚰ࡬ࡢ㐺⏝࡟࠾ࡅࡿィ
⟬᫬㛫ࡢẚ㍑࡛ࡣࠊNSHEX ࡢ᪉ࡀඃࢀ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡗࡓࠋ
࡞࠾ࠊ௒ᅇࡢ᳨ウ࡛ࡣࠊ"Reference"ゅᗘศⅬࢭࢵࢺ࡟㝈ᐃࡋࡓୖ࡛ࠊ✵㛫࣓ࢵࢩࣗࡸከ㡯ᘧ
ᒎ㛤ḟᩘ࡟㛵ࡍࡿࢧ࣮࣋࢖ࢆᐇ᪋ࡋࡓࡀࠊ㏫࡟ࠊ✵㛫࣓ࢵࢩࣗࡸከ㡯ᘧᒎ㛤ḟᩘࢆ⢒ࡵ࡟タᐃ
ࡋᅛᐃࡋࡓୖ࡛ࠊ᭱㐺࡞ S4 ゅᗘศⅬࢭࢵࢺࡢࢧ࣮࣋࢖ࢆ⾜࠺᪉⟇ࡶ⪃࠼ࡽࢀࡿࠋ౛࠼ࡤࠊᑠᆺ
⅔ᚰ KNK-II ࡟ᑐࡋ࡚ࠊ2.5cm ࡛ࡣ࡞ࡃ 5.0cm ✵㛫࣓ࢵࢩࣗศ๭࡜ࡋࡓ᮲௳࡛ MINISTRI ࡢ
㐺⏝ࢆ⪃࠼ࡿࠋFig. 7.4-1 ࡣࠊS4 ゅᗘศⅬࢭࢵࢺࡢ᭱ᑠ᪉ྥవᘻࢆࣃ࣓࣮ࣛࢱ࡜ࡋ࡚ࠊKNK-II
⅔ᚰ࡟࠾ࡅࡿᅛ᭷್ࡢཧ↷ゎ࡟ᑐࡍࡿ┦ᑐᕪࢆᅗ♧ࡋࡓࡶࡢ࡛࠶ࡿࠋᅛ᭷್ࡢ┦ᑐᕪࡣไᚚᲬ
ᤄධ≧ែ࡟ࡼࡗ࡚␗࡞ࡿࡀࠊ᭱ᑠ᪉ྥవᘻࢆ 0.235 ࡟タᐃࡋࡓሙྜ࡟ࠊ࠸ࡎࢀࡢไᚚᲬᤄධ≧
ែ࡟ᑐࡋ࡚ࡶ┠ᶆ⢭ᗘࢆ࡯ࡰ‶㊊࡛ࡁࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿࠋཧ⪃ࡲ࡛࡟ࠊ"Reference"ゅᗘศⅬ
ࢭࢵࢺ࡛ࡣ᭱ᑠ᪉ྥవᘻࡣ⣙ 0.3 ࡛࠶ࡾࠊࡑࢀࢆ㐺⏝ࡋࡓሙྜ࡟ࡣ 0.2㹼0.4%ࡢ㐣ᑠホ౯࡜࡞
ࡾ┠ᶆ⢭ᗘ࠿ࡽ㐓⬺ࡍࡿࡇ࡜ࡀศ࠿ࡿࠋ
㻙㻌㻡㻤㻌㻙㻌
JAEA-Data/Code 2011-018
Table 7.1-1
Relative difference of the flux and absorption reaction rate in the control rod
region due to the change of the angular quadrature set and maximum polynomial order in
NSHEX for "Rods half-in" case of the KNK-II core
Condition change
Angular quadrature set
(Even condition: S16䊻S4)
Angular quadrature set
(Reference: S16䊻S4)
Maximum polynomial order
(6th䊻2nd)
Absorption
Group 1
Group 2
Group 3
Group 4
+0.4*1
+0.2*1
+0.2*1
+0.4*1
+0.2*1
-0.6
-0.4
-0.3
-0.1
-0.4
+0.0
+0.1
+0.6
+2.0
+0.4
reaction rate
*1: Relative difference (%)
Table 7.1-2
Relative difference of the flux and absorption reaction rate in the control rod
region due to the change of the angular quadrature set and radial mesh width in
MINISTRI for "Rods half-in" case of the KNK-II core
Condition change
Angular quadrature set
(Even condition: S16䊻S4)
Angular quadrature set
(Reference: S16䊻S4)
Radial mesh width
(1.2䊻2.5cm)
Absorption
Group 1
Group 2
Group 3
Group 4
+0.5*1
+0.2*1
+0.2*1
+0.8*1
+0.3*1
-0.6
-0.4
-0.4
-0.1
-0.4
+0.3
+0.2
+0.1
+0.5
+0.2
*1: Relative difference (%)
㻙㻌㻡㻥㻌㻙㻌
reaction rate
JAEA-Data/Code 2011-018
0.985
Ref erence
Even condition
Eigenvalue
Level condition
0.984
S14
S2
(Identical)
0.983
S12
S8
S16 S10
S6
S4
0.982
0.0
Fig. 7.1-1
0.2
0.4
0.6
24 / N / (N+2)
0.8
1.0
1.2
Dependence of eigenvalue on three angular quadrature sets in NSHEX for
"Rods half-in" case of the KNK-II core (2nd order polynomial expansion)
Eigenvalue
0.985
0.984
0.983
Ref erence
Even condition
0.982
7
6
5
4
3
2
1
Maximum polynomial order
Fig. 7.1-2
Dependence of eigenvalue on the maximum polynomial order in NSHEX for
"Rods half-in" case of the KNK-II core (Angular quadrature set of S4)
㻙㻌㻢㻜㻌㻙㻌
JAEA-Data/Code 2011-018
0.984
Ref erence
Even condition
Eigenvalue
Level condition
0.983
S14
S2
(Identical)
0.982
S12
S8
S16 S10
0.981
0.0
Fig. 7.1-3
S6
0.2
0.4
S4
0.6
24 / N / (N+2)
0.8
1.0
1.2
Dependence of eigenvalue on three angular quadrature sets in MINISTRI for
"Rods half-in" case of the KNK-II core (Radially 24meshes/SA)
0.984
Ref erence
Eigenvalue
Even condition
0.983
6 meshes / SA
0.982
96 meshes / SA
54 meshes / SA
24 meshes / SA
0.981
0
1
2
3
4
5
6
7
Radial mesh area [cm^2]
Fig. 7.1-4
Dependence of eigenvalue on the radial mesh division in MINISTRI for "Rods
half-in" case of the KNK-II core (Angular quadrature set of S4)
㻙㻌㻢㻝㻌㻙㻌
JAEA-Data/Code 2011-018
Table 7.2-1
Calculation criteria and conditions for the reference scheme
Criteria and conditions
Item
NSHEX
MINIHEX or MINISTRI
Angular quadrature set
S4
Spatial treatment in the
Polynomial expansion with
radial direction
up to sixth order
Spatial treatment in the axial
Polynomial expansion with
direction
the second order
Node or mesh width in the
axial direction
Fission source convergence
criteria for each node
Eigenvalue convergence
criteria
High order moments
calculation condition
Neutron energy group
No division or triangle mesh
division (6, 24, 54, 96
meshes) within SA
Finer mesh division
Around 20cm
Around 5.0 cm or 2.5cm
Less than 1.0×10-4
Less than 1.0×10-5
Greater than 2.0×10-4
*1
4 (KNK-II), 18 (Monju, SPX,
Joyo MK-I, and BFS-62-3A)
*1: Set 4.0×10-4 for "MCR in" case of the SPX core
㻙㻌㻢㻞㻌㻙㻌
Nothing
JAEA-Data/Code 2011-018
Table 7.2-2
Core
KNK-II
Monju
SPX
Joyo
BFS
Comparison in effective radial mesh sizes among various cores
Core size
Small
Intermediate
Large
Small
Intermediate
(BFS-62-3A)
SA across flat
Number of radial
Effective radial
length [cm]
meshes per SA
mesh size [cm]
6
4.9
24
2.5
54
1.6
96
1.2
6
4.4
24
2.2
54
1.5
6
6.8
24
3.4
1
7.6
6
3.1
24
1.6
1
4.7
6
1.9
12.9900
11.5600
18.0190
8.1817
5.1000
㻙㻌㻢㻟㻌㻙㻌
JAEA-Data/Code 2011-018
Fig. 7.2-1
Layout of the Joyo MK-I core
㻙㻌㻢㻠㻌㻙㻌
JAEA-Data/Code 2011-018
Fig. 7.2-2
Layout of the BFS-62-3A core
㻙㻌㻢㻡㻌㻙㻌
JAEA-Data/Code 2011-018
Table 7.3-1
Relative difference in eigenvalue and calculation time by NSHEX and
MINISTRI with the standard calculation condition for the KNK-II core
Rods
Average
Code
All rods out
NSHEX
+0.079*1
+0.046*1
-0.001*1
2
MINISTRI (2.5)*3
-0.015
+0.023
+0.049
24
1.09527
0.98349
0.87966
±0.024*2
±0.026*2
±0.026*2
GMVP (Ref.)
Rods in
half-in
*1: Relative difference to the reference [%]
*2: Statitical uncertainty (1) [%]
*3: Radial and axial mesh sizes [cm]
㻙㻌㻢㻢㻌㻙㻌
time [min]
287
JAEA-Data/Code 2011-018
Table 7.3-2
Relative difference in eigenvalue and calculation time by NSHEX and
MINISTRI with the standard calculation condition for the Monju core
Code
All rods out
NSHEX
+0.039*1
MINISTRI (4.4)*3
GMVP (Ref.)
MCR
Average
MCR in
BCR in
+0.024*1
+0.067*1
+0.062*1
93
-0.021
-0.059
-0.053
-0.056
117
1.03861
0.98551
0.93493
0.95665
±0.010*2
±0.010*2
±0.010*2
±0.010*2
half-in
time [min]
306
*1: Relative difference to the reference [%]
*2: Statitical uncertainty (1) [%]
*3: Mesh size in the radial direction [cm] (5.0cm in the axial direction)
Table 7.3-3
Relative difference in power distribution by NSHEX and MINISTRI with the
standard calculation condition for the Monju core
Code
All rods out
NSHEX
0.33*1
MINISTRI (4.4)*3
Uncertainty of
GMVP
MCR
MCR in
BCR in
0.40*1
0.64*1
0.53*1
0.24
0.52
0.67
0.54
0.21*2
0.22*2
0.23*2
0.23*2
half-in
*1: Maximum relative difference to the reference (GMVP) [%]
*2: Statitical uncertainty (1) [%]
*3: Mesh size in the radial direction [cm] (5.0cm in the axial direction)
㻙㻌㻢㻣㻌㻙㻌
JAEA-Data/Code 2011-018
Table 7.3-4
Relative difference in eigenvalue and calculation time by NSHEX and
MINISTRI with the standard calculation condition for the SPX core
Code
All rods out
NSHEX
+0.029*1
MINISTRI (6.8)*3
MINISTRI (3.4)*3
GMVP (Ref.)
MCR
Average
MCR in
BCR in
+0.022*1
-0.059*1
+0.021*1
232
-0.018
-0.036
-0.107
-0.025
411
+0.018
-0.010*4
+0.018
+0.018
1426
1.02256
0.97474
0.93021
1.01278
±0.005*2
±0.006*2
±0.006*2
±0.005*2
half-in
time [min]
269
*1: Relative difference to the reference [%]
*2: Statitical uncertainty (1) [%]
*3: Mesh size in the radial direction [cm] (5.0cm in the axial direction)
*4: Converged in eigenvalue only
Underlined means exceeding of the target accuracy
Table 7.3-5
Relative difference in power distribution by NSHEX and MINISTRI with the
standard calculation condition for the SPX core
Code
All rods out
NSHEX
0.72*1
MINISTRI (6.8)*3
MINISTRI (3.4)*3
Uncertainty of
GMVP
MCR
MCR in
BCR in
1.82*1
4.23*1
3.11*1
0.73
1.42
1.46
1.76
0.58
NC*4
1.02
1.29
0.22*2
0.22*2
0.22*2
0.21*2
half-in
*1: Maximum relative difference to the reference (GMVP) [%]
*2: Statitical uncertainty (1) [%]
*3: Mesh size in the radial direction [cm] (5.0cm in the axial direction)
*4: Converged in eigenvalue only
㻙㻌㻢㻤㻌㻙㻌
JAEA-Data/Code 2011-018
Table 7.3-6
Relative difference in eigenvalue and calculation time by NSHEX and
MINISTRI with the standard calculation condition for the Joyo MK-I core
Code
All rods out
NSHEX
NC*4
MINISTRI (3.1)*3
GMVP (Ref.)
MCR
Average
MCR in
BCR in
NC*4
NC*4
NC*4
-
-0.062*1
-0.065*1
-0.063*1
-0.067*1
53
1.00958
0.98635
0.96253
0.91733
±0.011*2
±0.010*2
±0.011*2
±0.011*2
half-in
time [min]
118
*1: Relative difference to the reference [%]
*2: Statitical uncertainty (1) [%]
*3: Mesh size in the radial direction [cm] (2.5cm in the axial direction)
*4: Not converged
Table 7.3-7
Relative difference in power distribution by NSHEX and MINISTRI with the
standard calculation condition for the Joyo MK-I core
Code
All rods out
NSHEX
NC*4
MINISTRI (3.1)*3
Uncertainty of
GMVP
MCR
MCR in
BCR in
NC*4
NC*4
NC*4
0.35*1
0.60*1
0.54*1
0.54*1
0.18*2
0.19*2
0.19*2
0.19*2
half-in
*1: Maximum relative difference to the reference (GMVP) [%]
*2: Statitical uncertainty (1) [%]
*3: Mesh size in the radial direction [cm] (2.5cm in the axial direction)
*4: Not converged
㻙㻌㻢㻥㻌㻙㻌
JAEA-Data/Code 2011-018
Table 7.3-8
Relative difference in eigenvalue and calculation time by MINIHEX with the
standard calculation condition for the BFS-62-3A core
Central
Off-center
MCR in
MCR in
+0.001*1
+0.007*1
+0.006*1
-0.004*1
0.99081
0.98682
0.98788
0.98523
±0.003*2
±0.003*2
±0.003*2
±0.003*2
Code
All rods out
MINIHEX (4.7)*3
GMVP (Ref.)
1 BCR in
*1: Relative difference to the reference [%]
*2: Statitical uncertainty (1) [%]
*3: Mesh size in the radial direction [cm] (5.0cm in the axial direction)
㻙㻌㻣㻜㻌㻙㻌
Average
time [min]
486
1546
JAEA-Data/Code 2011-018
0.3
Angular distretization effect [%]
All rods out
Rods half -in
Rods in
S4
0.2
0.1
S16
S8
S12
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
24 / N / (N+2)
(Angular discretization effect)
Polynomial expansion effect [%]
0.1
0.0
All rods out
Rods half-in
-0.1
All rods out
Rods half -in
Rods in
Rods in
- S4 ef f ect
-0.2
6
4
2
0
Polynomial expansion order
(Distribution treatment effect)
Fig. 7.3-1
Effects of polynomial expansion and angular discretization by NSHEX for the
KNK-II core
㻙㻌㻣㻝㻌㻙㻌
JAEA-Data/Code 2011-018
0.2
S4
Angular distretization effect [%]
All rods out
Rods half -in
Rods in
0.1
S6
S8
S16
0.0
S12
-0.1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
24 / N / (N+2)
(Angular discretization effect)
0.1
2.5cm mesh
Spatial mesh effect [%]
1.2cm mesh
All rods out
0.0
Rods half-in
-0.1
All rods out
Rods half -in
Rods in
1.6cm
mesh
Rods in
- S4 ef f ect
-0.2
0
1
2
3
4
5
6
7
Mesh area [cm^2]
(Distribution treatment effect)
Fig. 7.3-2
Effects of spatial mesh and angular discretization by MINISTRI for the KNK-II
core
㻙㻌㻣㻞㻌㻙㻌
JAEA-Data/Code 2011-018
0.2
Angular distretization effect [%]
All rods out
MCR half -in
MCR in
BCR in
0.1
S4
S16
S8
S12
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
24 / N / (N+2)
(Angular discretization effect)
0.1
Polynomial expansion effect [%]
All rods out
MCR half -in
MCR in
BCR in
- S4 ef f ect
0.0
All rods out
MCR half-in
MCR in, BCR in
-0.1
6
4
2
0
Polynomial expansion order
(Distribution treatment effect)
Fig. 7.3-3
Effects of polynomial expansion and angular discretization by NSHEX for the
Monju core
㻙㻌㻣㻟㻌㻙㻌
JAEA-Data/Code 2011-018
0.2
Angular distretization effect [%]
All rods out
MCR half -in
MCR in
BCR in
0.1
S4
S8
S12
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
24 / N / (N+2)
(Angular discretization effect)
0.0
All rods out
Spatial mesh effect [%]
MCR half-in
1.5cm
mesh
MCR in, BCR in
2.2cm mesh
-0.1
All rods out
MCR half -in
MCR in
4.4cm mesh
BCR in
- S4 ef f ect
-0.2
0
5
10
15
20
25
Mesh area [cm^2]
(Distribution treatment effect)
Fig. 7.3-4
Effects of spatial mesh and angular discretization by MINISTRI for the Monju
core
㻙㻌㻣㻠㻌㻙㻌
JAEA-Data/Code 2011-018
-0.3
-0.2
-0.2
-0.2
-0.0
-0.1
-0.1
-0.2
-0.3
NSHEX
-0.0
-0.1
-0.1
-0.0
+0.1
+0.0
+0.0
-0.0
-0.0
MINISTRI
-0.2
-0.3
-0.0
-0.1
+0.0
-0.0
+0.2
-0.1
-0.2
-0.2
-0.2
-0.0
-0.1
+0.0
+0.0
+0.2
-0.1
-0.0
-0.0
+0.1
-0.1
-0.0
CRP
+0.2
+0.1
+0.0
+0.1
-0.1
+0.2
+0.0
-0.0
+0.0
-0.1
-0.1
+0.0
+0.1
+0.1
-0.1
-0.0
+0.1
+0.1
CRP
+0.1
-0.0
-0.0
-0.0
-0.0
-0.1
+0.2
+0.1
+0.2
+0.1
+0.1
+0.0
-0.0
+0.1
+0.1
+0.0
+0.1
-0.0
CRP
+0.0
+0.1
+0.0
+0.0
+0.1
+0.0
+0.1
CRP
+0.1
+0.0
+0.2
+0.1
+0.1
-0.0
-0.0
+0.1
+0.1
-0.0
+0.1
+0.1
-0.0
-0.1
+0.1
+0.1
+0.1
+0.0
+0.1
+0.1
-0.0
+0.1
+0.0
CRP
-0.1
-0.0
+0.1
+0.2
-0.1
-0.2
-0.1
+0.0
+0.2
+0.0
+0.1
+0.0
-0.0
-0.0
-0.0
+0.1
-0.0
-0.1
-0.1
-0.1
CRP
-0.0
-0.1
-0.2
-0.1
-0.1
+0.0
CRP
Fig. 7.3-5
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "All rods out" case of the Monju core
-0.2
+0.0
+0.1
-0.3
+0.2
-0.3
-0.2
-0.0
-0.1
-0.1
+0.0
+0.1
+0.0
+0.0
+0.3
+0.1
+0.0
NSHEX
+0.2
MINISTRI
+0.1
-0.2
-0.2
-0.4
-0.1
+0.1
+0.2
-0.2
-0.1
+0.1
-0.1
-0.3
-0.5
-0.1
+0.1
+0.1
-0.1
+0.1
+0.1
-0.1
+0.0
-0.0
CR
-0.2
-0.1
-0.0
-0.0
-0.1
+0.0
+0.0
-0.1
-0.2
-0.0
+0.2
+0.1
+0.0
+0.1
+0.0
+0.1
+0.2
CR
+0.2
-0.1
+0.1
-0.1
+0.1
CR
+0.1
+0.1
+0.1
-0.2
-0.0
-0.0
+0.3
+0.0
-0.0
-0.1
+0.2
-0.1
-0.1
+0.0
+0.2
+0.1
+0.1
+0.1
+0.2
-0.1
CR
+0.0
-0.1
-0.1
-0.0
+0.1
+0.2
+0.2
+0.0
+0.0
-0.0
+0.1
+0.2
+0.1
+0.0
+0.0
-0.1
-0.0
-0.1
+0.1
+0.1
-0.1
CRP
+0.0
+0.1
+0.2
-0.1
-0.1
+0.0
+0.2
+0.1
-0.1
-0.1
+0.0
+0.2
+0.2
+0.1
-0.1
+0.0
-0.1
CRP
-0.2
-0.0
-0.1
-0.1
-0.1
-0.0
+0.1
-0.0
-0.1
-0.0
-0.0
+0.0
CR
Fig. 7.3-6
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "MCR half-in" case of the Monju core
㻙㻌㻣㻡㻌㻙㻌
JAEA-Data/Code 2011-018
-0.4
-0.4
-0.3
-0.5
-0.3
-0.1
-0.1
+0.2
+0.4
NSHEX
+0.0
-0.1
-0.3
-0.2
-0.2
-0.1
+0.2
+0.3
+0.5
MINISTRI
-0.0
-0.1
-0.2
-0.3
-0.1
+0.2
+0.5
+0.0
+0.1
-0.1
-0.0
-0.3
-0.5
+0.0
+0.1
+0.2
+0.3
+0.4
-0.2
-0.1
-0.2
-0.3
CR
-0.1
+0.1
+0.0
+0.3
+0.6
+0.4
-0.3
-0.2
-0.0
+0.2
+0.5
+0.7
-0.2
-0.1
+0.1
-0.1
-0.1
-0.1
-0.1
-0.2
CR
+0.2
+0.0
+0.2
+0.4
+0.0
+0.0
+0.1
+0.4
+0.1
-0.4
-0.2
+0.2
-0.0
+0.1
-0.0
-0.4
-0.3
+0.0
+0.1
+0.1
-0.1
CR
-0.1
+0.0
CR
+0.3
+0.1
+0.4
-0.4
-0.0
+0.3
+0.0
+0.0
+0.4
+0.0
-0.4
-0.0
+0.0
+0.1
+0.1
+0.2
+0.3
-0.3
-0.1
+0.0
-0.2
-0.2
-0.2
CRP
-0.1
+0.3
+0.0
+0.1
-0.0
+0.1
+0.1
+0.2
+0.0
-0.2
-0.2
-0.0
-0.1
-0.1
-0.2
-0.3
-0.2
+0.0
CRP
+0.1
+0.2
+0.1
-0.2
-0.0
-0.1
-0.1
+0.2
CR
Fig. 7.3-7
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "MCR in" case of the Monju core
+0.3
+0.4
+0.5
-0.2
+0.5
+0.1
+0.2
+0.2
+0.2
-0.4
+0.2
+0.1
-0.0
+0.2
+0.2
+0.3
-0.2
NSHEX
+0.4
MINISTRI
-0.0
+0.2
+0.2
-0.4
+0.2
+0.0
-0.0
+0.2
-0.0
+0.4
+0.2
-0.1
-0.1
+0.1
-0.0
+0.2
+0.1
+0.1
+0.4
-0.2
+0.2
+0.1
CRP
+0.1
-0.1
+0.1
+0.4
-0.2
+0.2
-0.0
+0.0
-0.0
-0.1
-0.3
-0.2
+0.2
+0.0
+0.0
-0.0
+0.0
CRP
-0.1
+0.1
+0.2
+0.0
-0.1
CRP
-0.4
-0.1
-0.1
+0.2
-0.1
+0.3
-0.5
-0.1
+0.1
-0.1
-0.2
-0.3
-0.0
+0.3
+0.1
-0.1
-0.3
-0.1
-0.2
+0.1
CRP
-0.3
+0.3
-0.0
+0.3
+0.2
-0.3
-0.5
+0.0
+0.1
-0.1
+0.3
-0.1
-0.4
-0.4
-0.3
-0.0
+0.2
+0.3
-0.2
-0.3
-0.2
-0.3
-0.3
-0.2
CR
-0.2
-0.4
-0.4
+0.0
-0.2
-0.4
+0.1
-0.4
-0.3
-0.3
-0.4
-0.1
-0.3
-0.0
-0.3
-0.3
CR
+0.5
-0.0
+0.3
+0.5
-0.2
+0.5
+0.3
-0.1
+0.3
+0.4
CRP
Fig. 7.3-8
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "BCR in" case of the Monju core
㻙㻌㻣㻢㻌㻙㻌
JAEA-Data/Code 2011-018
0.2
Angular distretization effect [%]
All rods out
MCR half -in
MCR in
BCR in
S4
0.1
S8
S12
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
24 / N / (N+2)
(Angular discretization effect)
Polynomial expansion effect [%]
0.1
All rods out
MCR half -in
MCR in
BCR in
- S4 ef f ect
0.0
BCR in
All rods out
MCR half-in
MCR in
-0.1
6
4
2
0
Polynomial expansion order
(Distribution treatment effect)
Fig. 7.3-9
Effects of polynomial expansion and angular discretization by NSHEX for the
SPX core
㻙㻌㻣㻣㻌㻙㻌
JAEA-Data/Code 2011-018
Angular distretization effect [%]
0.2
All rods out
MCR half -in
MCR in
BCR in
S4
0.1
S8
S12
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
24 / N / (N+2)
(Angular discretization effect)
0.0
Spatial mesh effect [%]
All rods out, BCR in
MCR half-in
MCR in
3.4cm mesh
-0.1
All rods out
MCR half -in
MCR in
BCR in
- S4 ef f ect
6.8cm mesh
-0.2
0
10
20
30
40
50
Mesh area [cm^2]
(Distribution treatment effect)
Fig. 7.3-10
Effects of spatial mesh and angular discretization by MINISTRI for the SPX
core
㻙㻌㻣㻤㻌㻙㻌
JAEA-Data/Code 2011-018
+0.0
-0.2
-0.2
-0.3
+0.1
+0.5
+0.2
+0.2
NSHEX
+0.5
+0.2
-0.1
+0.2
+0.6
+0.7
+0.6
+0.7
MINISTRI
-0.2
-0.1
+0.1
-0.2
-0.0
+0.4
+0.3
+0.3
+0.4
+0.2
+0.1
-0.0
+0.0
-0.1
+0.1
+0.4
+0.5
+0.4
+0.4
+0.4
+0.4
+0.7
+0.1
+0.0
-0.1
-0.1
+0.3
+0.5
+0.4
+0.2
+0.1
+0.3
+0.4
-0.0
-0.0
-0.1
-0.1
+0.4
+0.6
+0.4
+0.2
+0.1
+0.1
+0.5
+0.0
CRP
-0.1
-0.2
+0.0
-0.1
+0.2
CRP
+0.4
+0.3
+0.6
+0.4
CRP
+0.4
+0.7
+0.0
+0.2
+0.4
-0.1
-0.0
+0.1
+0.6
+0.4
+0.0
-0.1
-0.1
+0.0
+0.2
+0.5
+0.0
+0.0
+0.2
+0.2
+0.2
+0.4
+0.1
-0.1
-0.0
+0.2
+0.3
+0.6
+0.1
+0.1
+0.1
-0.0
-0.1
+0.1
+0.1
-0.4
-0.2
-0.2
+0.0
+0.2
+0.3
+0.3
+0.3
+0.1
-0.2
-0.0
-0.1
+0.2
+0.3
+0.3
+0.3
+0.2
CRP
+0.3
+0.2
+0.2
-0.0
-0.2
-0.4
+0.6
+0.1
-0.2
-0.3
-0.4
-0.3
+0.1
-0.1
-0.0
+0.2
+0.2
+0.2
+0.4
+0.2
-0.1
-0.2
-0.2
-0.1
+0.1
-0.0
+0.0
+0.1
-0.0
-0.2
-0.1
-0.1
-0.3
-0.2
-0.2
-0.1
CRP
-0.3
-0.2
-0.4
-0.5
-0.3
-0.5
-0.4
-0.2
-0.3
-0.1
CRP
-0.3
-0.3
-0.6
-0.4
-0.6
-0.4
-0.3
-0.0
-0.3
-0.2
CRP
+0.0
-0.1
-0.1
-0.1
-0.2
-0.3
+0.1
+0.1
-0.2
-0.2
+0.3
+0.3
+0.4
-0.0
+0.3
CRP
+0.4
+0.0
+0.3
-0.4
-0.4
-0.6
-0.4
-0.3
-0.4
-0.1
+0.1
+0.0
+0.1
+0.4
-0.1
-0.4
-0.4
-0.5
-0.4
-0.3
-0.4
-0.1
-0.0
-0.1
-0.1
+0.0
+0.1
-0.5
-0.7
-0.2
-0.3
-0.5
-0.2
+0.1
-0.0
+0.2
+0.1
-0.2
-0.4
-0.6
-0.2
-0.3
-0.6
-0.2
+0.1
-0.0
+0.1
-0.1
-0.2
-0.6
-0.7
Fig. 7.3-11
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "All rods out" case of the SPX core
-0.6
-0.5
-0.5
-1.3
-1.3
-0.4
-1.1
-1.3
NSHEX
+0.7
+0.7
+0.0
-0.0
-0.0
+0.1
+0.1
+0.0
MINISTRI
+0.1
-0.2
+0.5
-0.8
-1.3
-0.5
-1.5
-1.2
-0.1
-0.8
-0.5
+1.0
+0.7
+0.5
+0.2
-0.4
-0.5
-0.5
-0.3
-0.1
+0.1
+0.5
+1.0
-0.2
-0.7
-0.1
-1.3
-1.5
-0.5
-1.1
-0.8
+0.3
-0.2
+0.7
+0.3
+0.0
-0.1
-0.5
-0.7
-0.5
-0.3
-0.2
-0.1
+0.4
-0.0
CR
+0.3
-0.9
-1.1
-0.2
-0.5
CR
-1.4
-1.1
-0.7
-0.5
CR
+0.7
+1.4
-0.4
-0.2
+1.4
-0.1
+0.1
+0.7
+1.0
+1.3
-0.1
-0.3
+0.2
-0.8
-1.1
-0.3
-0.7
-0.8
+0.8
+0.2
+0.5
+1.8
+0.2
+0.0
-0.0
-0.4
-0.7
-0.4
-0.3
-0.5
+0.4
+0.3
+0.6
+1.0
+0.6
-0.2
-0.7
-0.1
-0.7
-0.8
+0.1
-0.3
+0.3
+0.2
-0.1
-0.5
-0.6
-0.5
-0.5
-0.3
-0.1
+0.4
CR
+0.9
+1.0
+0.5
+0.5
+0.5
+0.4
+1.5
+0.5
-0.1
+0.2
-0.5
-0.5
+0.2
-0.5
-0.1
+1.1
+0.7
+0.7
+1.7
+0.4
-0.1
-0.4
-0.5
-0.5
-0.4
-0.5
-0.1
+0.5
+0.6
+0.7
+0.7
+0.4
-0.2
-0.3
-0.5
-0.6
CR
+0.4
-0.6
-0.3
-0.4
-0.9
-0.9
-0.5
-0.5
-0.7
-0.6
CR
+0.5
-0.3
-0.2
+0.3
-0.6
-0.0
+0.4
+0.7
+0.2
+0.5
CRP
+1.6
+0.9
+0.7
+0.7
+0.6
+0.7
+0.9
+0.8
+0.9
+0.8
+0.8
+0.9
+1.7
+0.9
+0.5
CR
+0.5
+0.6
+0.8
-0.0
+0.9
-0.3
-0.2
+0.7
+0.3
+0.4
+1.1
+0.6
+0.7
+1.4
-0.8
-0.7
-1.0
-0.8
-0.4
-0.1
+0.2
+0.6
+0.7
+0.8
+0.8
+0.0
-0.9
+0.3
+0.9
+0.0
+0.9
-0.0
-0.1
+0.6
+0.3
+0.2
+1.0
+0.4
+0.5
-0.9
-0.7
-0.6
-0.5
-0.0
+0.2
+0.3
+0.6
+0.6
+1.0
+0.7
-1.0
Fig. 7.3-12
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "MCR half-in" case of the SPX core
㻙㻌㻣㻥㻌㻙㻌
JAEA-Data/Code 2011-018
-1.4
-1.4
-0.2
-1.7
-1.6
-0.2
-1.4
-1.1
NSHEX
+1.0
+0.8
+0.8
+0.7
+0.8
+0.9
+0.9
+1.3
MINISTRI
-1.1
-1.4
+0.5
-1.5
-1.6
+0.2
-1.6
-1.5
+0.4
-0.7
-0.3
+0.5
+0.4
+0.6
+0.4
+0.5
+0.7
+0.5
+0.5
+0.6
+1.2
+1.5
+0.4
-1.5
-1.5
+0.3
-1.6
-1.9
+0.3
-1.7
-1.3
+1.3
-0.2
-0.0
+0.1
+0.0
+0.3
+0.5
+0.4
+0.1
+0.4
+0.1
+0.4
+0.8
+1.0
+1.2
-1.1
CR
-0.2
-1.3
-1.4
+0.1
+0.1
CR
-1.3
-1.5
+0.3
-0.0
CR
-0.7
-0.4
+1.9
+0.1
+0.3
+0.4
+0.7
+0.8
-0.8
-0.8
+0.7
-0.8
-0.9
+1.0
-0.6
-0.6
+1.5
-0.7
-0.8
+1.7
+0.2
-0.3
-0.2
-0.0
-0.2
-0.3
+0.3
-0.0
+0.1
+0.5
+0.1
-0.0
+0.2
+0.3
+0.6
-0.3
-0.3
+1.0
-0.2
+0.0
+1.3
-0.1
-0.4
-0.4
-0.2
-0.2
-0.2
-0.1
+0.1
+0.2
+0.1
+0.0
CR
-0.9
-0.4
-0.4
-0.2
+1.5
-0.1
-0.1
+1.2
+0.1
-0.2
+1.3
+0.4
+0.4
+1.2
-0.5
-1.2
+1.4
-0.7
-0.5
-0.3
-0.3
-0.6
-0.2
+0.1
+0.0
+0.0
-0.3
-0.8
-0.4
-0.5
-0.1
-0.2
-0.5
-0.7
CR
+2.0
-0.4
+0.5
+0.3
-0.8
-0.8
-0.1
-0.0
-0.6
-0.3
CR
+1.6
-0.1
+0.3
+0.5
-0.4
-0.2
+0.3
+0.1
-0.2
-0.4
CRP
+1.1
-0.3
+0.2
-0.4
-0.2
-0.3
-1.2
-1.6
-0.8
-1.0
CR
-0.3
-0.2
+0.9
-0.5
-1.5
-1.0
-0.8
-0.3
+1.3
+3.4
+1.1
+0.6
+2.2
+0.6
+0.6
+1.1
-0.6
-1.1
+0.8
-1.0
-0.8
-0.7
-0.8
-0.7
-0.3
-0.2
-0.0
-0.0
-0.2
-0.5
-0.2
+0.1
+2.5
+2.5
+3.7
+0.7
+0.5
+1.4
+0.2
-0.0
+0.9
-0.8
-1.1
-0.5
-0.5
-0.4
-0.7
-0.3
-0.1
-0.2
+0.0
+0.1
-0.1
-0.1
+4.2
-0.4
Underlined means out of target (±2%).
Fig. 7.3-13
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "MCR in" case of the SPX core
-1.5
-1.3
-1.0
-1.4
-1.5
-0.9
-1.0
-0.5
NSHEX
-0.5
-0.2
-0.1
-0.1
-0.2
-0.0
+0.1
+0.5
MINISTRI
-0.9
-1.0
-0.7
-1.3
-1.5
-1.2
-1.1
-1.0
-0.3
-0.1
+0.4
-0.5
-0.6
-0.4
-0.5
-0.6
-0.5
-0.2
-0.2
+0.1
+0.4
+0.9
-0.3
-0.7
-1.0
-1.2
-1.3
-1.1
-0.8
-0.7
-0.1
+0.8
+0.7
-0.4
-0.5
-0.6
-0.7
-0.5
-0.4
-0.2
-0.2
+0.1
+0.6
+0.7
-0.3
CRP
-0.3
-1.0
-1.3
-0.5
-0.6
CRP
-1.0
-0.7
-0.3
-0.2
CRP
+1.5
+1.4
+0.3
+0.8
+1.9
+0.3
+0.5
+1.1
+2.3
+1.6
-0.1
-0.4
-0.9
-0.9
-0.8
-0.8
-0.4
+0.3
+1.0
+1.3
+1.9
+2.6
+2.7
-0.0
-0.1
-0.5
-0.2
-0.2
-0.4
-0.1
+0.4
+0.7
+0.7
+1.1
+1.4
+1.8
+0.2
-0.5
-0.7
-0.4
-0.7
-0.6
+0.2
+0.6
+1.1
+0.1
-0.2
-0.3
-0.1
-0.3
-0.3
+0.1
+0.4
+0.6
CRP
+1.9
+2.4
+3.1
+0.8
+1.3
+1.6
-0.1
-0.1
-0.5
-0.4
-0.1
-0.3
+0.0
+0.9
+1.2
+1.8
+2.0
+1.9
+2.2
+0.0
-0.1
-0.1
-0.1
-0.1
-0.2
+0.0
+0.3
+0.5
+0.8
+0.7
+0.8
+1.2
-0.1
-0.2
-0.0
-0.3
-0.3
+0.3
-0.0
+0.7
+1.7
+1.5
+1.6
-0.1
-0.2
-0.1
-0.2
-0.3
-0.1
-0.2
+0.1
+0.6
+0.5
+0.5
CRP
-0.2
-0.3
-0.3
-0.4
CRP
-0.3
-0.2
-0.3
-0.3
CR
+0.6
+1.1
+0.1
+0.4
CRP
+1.9
+0.7
+1.1
+1.2
+0.2
+0.5
-0.2
-0.2
-0.3
-0.2
+0.2
-0.1
-0.2
+0.7
+0.7
+0.6
+0.9
-0.3
-0.5
-0.4
-0.4
-0.3
-0.3
-0.3
+0.0
+0.2
-0.0
+0.1
-0.5
-0.6
+0.5
+0.4
-0.4
-0.0
-0.3
-0.2
+0.3
-0.0
+0.2
+0.3
+0.2
-0.0
-0.5
-0.3
-0.4
-0.3
-0.0
-0.0
+0.0
+0.0
-0.2
-0.1
-0.0
-0.5
Underlined means out of target (±2%).
Fig. 7.3-14
Percentage relative difference in radial power distribution by NSHEX and
MINISTRI with the standard calculation condition for "BCR in" case of the SPX core
㻙㻌㻤㻜㻌㻙㻌
JAEA-Data/Code 2011-018
0.2
Angular distretization effect [%]
All rods out
MCR half -in
S4
MCR in
BCR in
0.1
S8
S12
0.0
-0.1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
24 / N (N+2)
(Angular discretization effect)
Spatial mesh effect [%]
0.0
All rods out
MCR half-in
MCR in
BCR in
1.0cm
mesh
1.6cm mesh
-0.1
All rods out
-0.2
MCR half -in
3.1cm mesh
MCR in
BCR in
- S4 ef f ect
-0.3
0
2
4
6
8
10
12
Mesh area [cm^2]
(Distribution treatment effect)
Fig. 7.3-15
Effects of spatial mesh and angular discretization by MINISTRI for the Joyo
MK-I core
㻙㻌㻤㻝㻌㻙㻌
JAEA-Data/Code 2011-018
BF
BF
+0.1
+0.3
BF
BF
BF
+0.1
+0.1
CRP
+0.2
+0.2
-0.1
-0.1
+0.2
+0.3
Fig. 7.3-16
-0.2
-0.2
+0.0
BF
+0.1
CRP
-0.1
BF
+0.2
-0.1
-0.3
+0.0
+0.3
CRP
-0.2
-0.0
NS
BF
+0.1
+0.2
-0.1
+0.1
+0.1
-0.1
-0.2
CRP
-0.2
+0.0
-0.2
-0.2
-0.2
BF
-0.0
-0.2
-0.1
-0.2
-0.1
+0.1
-0.0
-0.1
-0.2
BF
-0.1
+0.0
-0.1
BF
+0.0
CRP
-0.2
+0.1
+0.0
+0.3
+0.0
-0.2
-0.2
-0.0
-0.1
+0.1
+0.3
+0.0
CRP
-0.0
+0.2
+0.3
+0.2
-0.0
+0.3
+0.1
+0.3
BF
+0.2
+0.3
+0.2
BF
BF
Percentage relative difference in radial power distribution by MINISTRI with
the standard calculation condition for "All rods out" case of the Joyo MK-I core
BF
BF
+0.4
+0.5
BF
BF
+0.3
BF
+0.1
+0.0
CR
+0.3
+0.4
BF
Fig. 7.3-17
+0.0
+0.4
+0.2
-0.1
-0.0
-0.1
+0.0
BF
+0.1
CRP
-0.1
+0.1
-0.2
-0.3
+0.1
+0.2
-0.3
-0.3
NS
-0.0
BF
+0.1
+0.1
-0.0
+0.3
+0.1
-0.2
CR
CRP
-0.2
+0.3
-0.2
-0.4
-0.3
BF
+0.1
-0.3
-0.4
-0.3
-0.1
+0.0
-0.1
-0.2
-0.3
BF
-0.2
-0.2
-0.2
BF
+0.0
CRP
-0.1
+0.1
+0.1
+0.3
+0.1
-0.0
-0.0
-0.1
-0.1
+0.3
+0.2
+0.0
CRP
+0.0
+0.3
+0.6
+0.1
+0.1
+0.4
+0.0
BF
+0.3
+0.3
+0.3
BF
BF
Percentage relative difference in radial power distribution by MINISTRI with
the standard calculation condition for "MCR half-in" case of the Joyo MK-I core
㻙㻌㻤㻞㻌㻙㻌
JAEA-Data/Code 2011-018
BF
BF
+0.1
+0.2
BF
BF
BF
+0.2
-0.1
-0.1
+0.1
+0.1
CRP
-0.2
-0.2
+0.1
-0.1
+0.2
+0.1
Fig. 7.3-18
+0.1
+0.2
CRP
+0.2
+0.2
-0.1
+0.0
+0.4
-0.2
-0.2
-0.1
+0.1
+0.3
-0.1
CRP
-0.1
+0.1
BF
+0.4
+0.3
+0.1
NS
+0.5
-0.1
CR
-0.2
+0.5
-0.0
-0.3
-0.1
-0.1
BF
-0.0
-0.0
-0.1
+0.1
BF
-0.0
-0.1
+0.0
BF
CRP
-0.2
-0.0
BF
-0.2
-0.1
-0.1
+0.0
BF
-0.1
+0.0
-0.2
CR
-0.1
-0.1
-0.1
-0.1
-0.2
+0.1
+0.1
-0.1
-0.1
-0.3
-0.1
+0.0
BF
+0.3
+0.3
+0.2
BF
BF
Percentage relative difference in radial power distribution by MINISTRI with
the standard calculation condition for "MCR in" case of the Joyo MK-I core
BF
BF
+0.2
-0.0
BF
BF
BF
-0.1
-0.2
-0.1
-0.0
-0.1
BF
-0.1
+0.1
-0.3
-0.3
-0.4
-0.2
-0.3
BF
-0.2
+0.2
+0.0
-0.1
+0.3
+0.2
-0.0
NS
BF
+0.3
+0.2
-0.1
+0.4
+0.3
+0.0
-0.0
-0.0
CR
-0.0
+0.4
+0.1
CRP
+0.1
+0.1
-0.2
CR
+0.2
+0.1
+0.2
+0.1
BF
+0.2
-0.0
+0.1
-0.3
BF
+0.0
CR
-0.1
+0.0
BF
-0.1
-0.2
+0.1
-0.3
+0.1
Fig. 7.3-19
-0.1
+0.1
-0.2
-0.1
-0.1
CRP
+0.3
+0.2
-0.1
CR
-0.2
-0.2
-0.1
+0.2
-0.2
-0.1
-0.3
+0.1
BF
+0.2
+0.5
+0.5
BF
BF
Percentage relative difference in radial power distribution by MINISTRI with
the standard calculation condition for "BCR in" case of the Joyo MK-I core
㻙㻌㻤㻟㻌㻙㻌
JAEA-Data/Code 2011-018
0.1
Angular distretization effect [%]
All rods out
Central MCR in
Of f -center MCR in
1 BCR in
S4
S8
S12
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
24 / N / (N+2)
(Angular discretization effect)
0.0
Spatial mesh effect [%]
1.9cm mesh
4.7cm mesh
All rods out
Central MCR in
Of f -center MCR in
1 BCR in
- S4 ef f ect
-0.1
0
5
10
15
20
25
Mesh area [cm^2]
(Distribution treatment effect)
Fig. 7.3-20
Effects of spatial mesh and angular discretization by MINIHEX and
MINISTRI for the BFS-62-3A core
㻙㻌㻤㻠㻌㻙㻌
JAEA-Data/Code 2011-018
0.5
All rods out
Relative difference [%k]
0.4
Rods half -in
0.3
Rods in
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
0.20
0.22
0.24
0.26
0.28
0.30
minimum
(For ȣ minimum of 0.2 through 0.3)
0.20
All rods out
Relative difference [%k]
0.15
Rods half -in
0.10
Rods in
0.05
0.00
-0.05
-0.10
-0.15
-0.20
0.23
0.24
0.25
0.26
0.27
minimum
(For ȣ minimum of around 0.25)
Fig. 7.4-1
Dependence of relative difference of eigenvalue to the reference on the angular
quadrature set of S4 for the KNK-II core
㻙㻌㻤㻡㻌㻙㻌
JAEA-Data/Code 2011-018
8. ௒ᚋࡢㄢ㢟
NSHEXࠊMINIHEXࠊMINISTRI ࡢ 3 ࡘࡢ㍺㏦ィ⟬ࢥ࣮ࢻ࡟ඹ㏻ࡋ࡚ࠊ࠸ࡎࢀࡶ㐺ษ࡞ຍ
㏿ἲࡢᑟධ➼࡟ࡼࡿ཰᮰ᛶࡢᨵၿࡀㄢ㢟࡜ࡋ࡚ᣲࡆࡽࢀࡿࠋࡲࡓࠊᚋ⥆ࡢᦤືィ⟬࡜ࡢ᥋⥆ࡶ
ㄢ㢟࡜ࡋ࡚ᣲࡆࡽࢀࡿࠋ
ࡲࡎࠊࣀ࣮ࢻἲ࡟ᇶ࡙ࡃ NSHEX ࡟ࡘ࠸࡚㏙࡭ࡿࠋNSHEX ⏝ࡢຍ㏿ἲ࡜ࡋ࡚ࡣࠊ⌧≧࡛ࡣ
ෆഃ཯᚟࡟࠾ࡅࡿࣀ࣮ࢻ༢఩ࣜࣂࣛࣥࢫἲࡀྲྀࡾධࢀࡽࢀ࡚࠸ࡿࡀ 27)ࠊ཰᮰ᛶࡢᨵၿࡣᚓࡽࢀ
ࡿࡶࡢࡢィ⟬᫬㛫ࡢ▷⦰ࡣᚲࡎࡋࡶᅗࡽࢀࡿࢃࡅ࡛ࡣ࡞࠸ࠋᚑࡗ࡚ࠊࣜࣂࣛࣥࢫἲࡢຠ⋡໬ࡀ
᭱ඃඛࡉࢀࡿ࡜⪃࠼ࡽࢀࡿࠋ୍⯡ࡢ᭷㝈ᕪศἲ࡟࠾࠸࡚㠀ᖖ࡟ຠᯝⓗ࡞ຍ㏿ᛶ⬟ࢆ᭷ࡍࡿᣑᩓ
ྜᡂἲ࡟ࡘ࠸࡚ࡣࠊࣀ࣮ࢻἲィ⟬ࢥ࣮ࢻ࡟ᑐࡍࡿຠᯝࡢ᭷↓ࡣ୙࡛᫂࠶ࡿࡀࠊ᳨ウࡢ౯್ࡣ࠶
ࡿ࡜⪃࠼ࡽࢀࡿࠋࡲࡓࠊᦤືィ⟬࡛ࡣࣀ࣮ࢻෆࡢṇつཬࡧ㝶కࡢ୰ᛶᏊ᮰ศᕸࢆ⢭ᗘࡼࡃ෌ᵓ
⠏ࡍࡿᚲせࡀ࠶ࡿࡀࠊභゅయ⣔⏝ࡢ㍺㏦ࣀ࣮ࢻἲ࡟ᑐࡋ࡚㐺ษ࡞෌ᵓ⠏ἲࡣぢฟࡏ࡚࠸࡞࠸ࠋ
ࡼࡗ࡚ࠊᦤືィ⟬࡜ࡢ᥋⥆⤖ྜ࡟ࡋ࡚ࡶࠊ㐺ษ࡞ᡭἲࢆぢฟࡍᚲせࡀ࠶ࡾࠊ኱ࡁ࡞◊✲㛤Ⓨㄢ
㢟ࡀṧࡉࢀ࡚࠸ࡿ࡜ゝ࠼ࡿࠋ
ḟ࡟ࠊ᭷㝈ᕪศἲ࡟ᇶ࡙ࡃ MINIHEX ࡜ MINISTRI ࡟㛵ࡋ࡚♧ࡍࠋ⌧≧࡛ࡣࠊ୧ࢥ࣮ࢻ࡟
ࢳ࢙ࣅࢩ࢙ࣇຍ㏿ἲࡀᑟධࡉࢀ࡚࠾ࡾࠊእഃ཯᚟࡬ࡢ㐺⏝࡟ࡼࡾࠊィ⟬᫬㛫ࡀ࡯ࡰ༙ศ࡟▷⦰
ࡉࢀࡿࡇ࡜ࡀศ࠿ࡗ࡚࠸ࡿ
5)ࠋ᭦࡞ࡿィ⟬᫬㛫ࡢ▷⦰ࡢࡓࡵ࡟ࡣࠊ᭷㝈ᕪศἲࢥ࣮ࢻ࡟࠾ࡅࡿ
ᐇ⦼࠿ࡽࠊᣑᩓྜᡂἲࡀ㠀ᖖ࡟᭷ຠ࡛࠶ࡿ࡜⪃࠼ࡽࢀࠊᑟධࡢ౯್ࡣ኱࠸࡟࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋ
MINISTRI ࡛ࡣࠊゅᗘ࣓ࢵࢩࣗࡸ✵㛫࣓ࢵࢩࣗࢆヲ⣽࡟ྲྀࡗࡓሙྜ࡟ࡋࡤࡋࡤィ⟬ࡀ཰᮰ࡋ࡞
࠸ሙྜࡀぢࡽࢀࡓࡇ࡜࠿ࡽࡶࠊຠᯝⓗ࡞ຍ㏿ἲࡢᑟධࡣษᮃࡉࢀࡿࠋࡲࡓࠊᦤືィ⟬࡜ࡢ᥋⥆
࡟ࡘ࠸࡚ࡶࠊMINIHEX ࡟ࡘ࠸࡚ࡣ᪤࡟ᩚഛ῭ࡳ࡛࠶ࡾ 5)ࠊMINISTRI ࡟ᑐᛂࡉࡏࡿࡇ࡜ࡣẚ
㍑ⓗᐜ࡛᫆࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋ
㻙㻌㻤㻢㻌㻙㻌
JAEA-Data/Code 2011-018
9. ⤖ㄽ
ᐇᶵ㧗㏿⅔⅔ᚰࡸࣟࢩ࢔ࡢ BFS ⮫⏺ᐇ㦂య⣔ࡢ୰ᛶᏊ㍺㏦ィ⟬ࢆ㧗⢭ᗘ࡛⾜࠺ࡇ࡜ࡀྍ⬟
࡞Ỵᐃㄽⓗᡭἲ࡟ᇶ࡙ࡃ 3 ḟඖභゅయ⣔⏝㍺㏦ィ⟬ࢥ࣮ࢻࠊࡍ࡞ࢃࡕࠊࣀ࣮ࢻἲ࡟ᇶ࡙ࡃ
NSHEX ࢥ࣮ࢻࠊභゅ࣓ࢵࢩࣗ᭷㝈ᕪศἲ࡟ᇶ࡙ࡃ MINIHEX ࢥ࣮ࢻࠊ୕ゅ࣓ࢵࢩࣗ᭷㝈ᕪศ
ἲ࡟ᇶ࡙ࡃ MINISTRI ࢥ࣮ࢻࢆࡑࢀࡒࢀᩚഛࡋࡓࠋ
NSHEX ࡟ࡘ࠸࡚ࡣࠊ㐺ྜᛶྥୖࡢࡓࡵࡢࣀ࣮ࢻෆከ㡯ᘧᒎ㛤ḟᩘࡢᣑᙇ࡜཰᮰ᛶᨵၿࡢࡓ
ࡵࡢึᮇ᭷㝈ᕪศィ⟬ࡢᑟධࢆ⾜ࡗࡓࠋࡲࡓࠊMINIHEX ࡟ࡘ࠸࡚ࡣࠊ㈇ࡢ୰ᛶᏊ᮰Ⓨ⏕᫬ࡢ
ฎ⌮ࡢぢ┤ࡋࢆ⾜ࡗࡓࠋ᭦࡟ࠊMINIHEX ࢆᇶᮏ࡜ࡋ࡚ MINISTRI ࢆ᪂ࡓ࡟సᡂࡋࡓࠋ
Ỵᐃㄽⓗᡭἲィ⟬࡜ྠࡌ᩿㠃✚ࢆ⏝࠸ࡓࣔࣥࢸ࢝ࣝࣟἲ࡟ࡼࡿィ⟬⤖ᯝࢆཧ↷ゎ࡜ࡋ࡚ࠊᩚ
ഛᚋࡢ NSHEXࠊMINIHEXࠊMINISTRI ࡢ᳨ドཬࡧ㐺⏝ᛶホ౯ࢆ⾜ࡗࡓࠋ┠ᶆ⢭ᗘ࡜ࡋ࡚ࠊ
ᅛ᭷್㸦ᐇຠቑಸ⋡㸧࡟ࡘ࠸࡚ࡣ 0.1%ࢆࠊ㞟ྜయẖฟຊศᕸ࡟ࡘ࠸࡚ࡣ 2%ࢆᬻᐃࡋࡓࠋ
᳨ドࡣ NSHEX ࡜ MINISTRI ࢆᑐ㇟࡜ࡋࠊ୰ᛶᏊ᮰ࡢゅᗘ࡜✵㛫ศᕸ࡟㛵ࡍࡿྲྀࡾᢅ࠸ࢆ
༑ศ࡟ヲ⣽࡟ࡋࡓ᮲௳࡛ࠊ୧ࢥ࣮ࢻࢆᐇᶵ㧗㏿⅔⅔ᚰ࡟㐺⏝ࡍࡿࡇ࡜࡟ࡼࡾ⾜ࡗࡓࠋࡑࡢ⤖ᯝࠊ
NSHEX ࡟ࡼࡿ⤖ᯝࡣࠊ࠸ࡎࢀࡢ⅔ᚰయ⣔ࡢᅛ᭷್ཬࡧ㞟ྜయẖฟຊศᕸ࡟ࡘ࠸࡚ࡶ┠ᶆ⢭ᗘ
ࢆ‶㊊ࡍࡿࡇ࡜ࡀศ࠿ࡗࡓࠋࡑࢀ࡟ᑐࡋࠊMINISTRI ࡟㛵ࡋ࡚ࡣࠊ┠ᶆ⢭ᗘࢆ‶㊊ࡍࡿ࡜᥎ᐃ
ࡉࢀࡿ᮲௳࡛ࡣィ⟬ࡀ཰᮰ࡋ࡞࠸ሙྜࡀከࡃぢࡽࢀࡿࡇ࡜ࡀศ࠿ࡗࡓࠋ
ࡲࡓࠊゅᗘศⅬ࡜✵㛫࣓ࢵࢩࣗ࠶ࡿ࠸ࡣከ㡯ᘧᒎ㛤ࢆヲ⣽࡟ࡍࡿຠᯝࡣ஫࠸࡟ᡴᾘࡋྜ࠺࡜
ࡢ≉ᛶࢆ⏕࠿ࡋ࡚ࠊNSHEXࠊMINIHEXࠊMINISTRI ࢆᑐ㇟࡟ᐇᶵ㧗㏿⅔⅔ᚰཬࡧ BFS ⮫⏺
ᐇ㦂య⣔࡟㐺⏝ࡍࡿࡇ࡜࡟ࡼࡾ㐺⏝ᛶホ౯ࢆ⾜ࡗࡓࠋࡑࡢ⤖ᯝࠊゅᗘศⅬ S4 ࡢ᮲௳ୗ࡛ࠊ
NSHEX ࡟ࡘ࠸࡚ࡣ 2 ḟከ㡯ᘧᒎ㛤ࡀࠊMINIHEX ࡜ MINISTRI ࡟ࡘ࠸࡚ࡣࠊᑠᆺ⅔ᚰ࡛ࡣ
2.5cm ࣓ࢵࢩࣗࡀࠊ୰ᆺཬࡧ኱ᆺ⅔ᚰ࡛ࡣ 5.0cm ࣓ࢵࢩࣗ࡜ࡋࡓ᮲௳ࡀ┠ᶆ⢭ᗘࡢ‶㊊࡜ィ⟬
᫬㛫▷⦰ࡢほⅬ࠿ࡽ᭱㐺࡛࠶ࡿࡇ࡜ࡀศ࠿ࡗࡓࠋ࡞࠾ࠊ௒ᅇࡢຍ㏿ἲ㠀㐺⏝᮲௳࡛ࡢᐇᶵ㧗㏿
⅔⅔ᚰ࡬ࡢ㐺⏝࡟࠾ࡅࡿィ⟬᫬㛫ࡢẚ㍑࡛ࡣࠊNSHEX ࡢ᪉ࡀ MINISTRI ࡼࡾࡶඃࢀ࡚࠸ࡿࡇ
࡜ࡀศ࠿ࡗࡓࠋ
௒ᚋࡣࠊྛィ⟬ࢥ࣮ࢻ࡟ඹ㏻ࡋ࡚ᣑᩓྜᡂἲ➼ࡢຍ㏿ἲࡢ㐺⏝࡟ࡼࡾࠊィ⟬᫬㛫ࡢ▷⦰ࡸ཰
᮰ᛶࡢᨵၿࡀᚲせ࡛࠶ࡿࡇ࡜ࡀศ࠿ࡗࡓࠋࡲࡓࠊᦤືィ⟬࡬ࡢ᥋⥆࡟㛵ࡋ࡚ࠊࣀ࣮ࢻἲࢥ࣮ࢻ
࡛࠶ࡿ NSHEX ࡟ࡘ࠸࡚ࡣ኱ࡁ࡞◊✲㛤Ⓨㄢ㢟ࡀṧࡉࢀ࡚࠸ࡿࡀࠊ᭷㝈ᕪศἲࢥ࣮ࢻ࡛࠶ࡿ
MINISTRI ࡟ࡘ࠸࡚ࡣࠊMINIHEX ࡜ྠᵝ࡟ẚ㍑ⓗᐜ᫆࡟ᶵ⬟ᩚഛࡀྍ⬟࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋ
ࡇࡢࡼ࠺࡟ࠊࡑࢀࡒࢀࡢィ⟬ࢥ࣮ࢻࡢ௒ᚋࡢᐇ⏝ᛶࢆ㧗ࡵࡿࡓࡵࡢㄢ㢟ࢆᩚ⌮ࡋࡓࠋ
㻙㻌㻤㻣㻌㻙㻌
JAEA-Data/Code 2011-018
ཧ⪃ᩥ⊩
1) Ikeda, H. and Takeda, T., A New Nodal SN Transport Method for Three-dimensional
Hexagonal Geometry, J. Nucl. Sci. Technol., Vol. 31, No. 6, 1994, pp. 497-509.
2) Sugino, K. and Takeda, T., An Improvement of the Transverse Leakage Treatment for
Nodal SN Transport Calculation Method in Hexagonal-Z Geometry, J. Nucl. Sci. Technol.,
Vol. 33, No. 8, 1996, pp. 620-627.
3) Yamato, A. and Aratani, K., The Present Status of International Cooperation Pertaining
to Russia Surplus Weapons Plutonium Disposition, ➨ 2 ᅇ JNC ཎᏊຊᖹ࿴฼⏝ᅜ㝿ࣇ࢛
࣮࣒ࣛ㈨ᩱ㞟, JNC TN1450 2000-001, 2000, pp. 104-107.
4) ᮡ㔝 ࿴㍤, ᶓᒣ ㈼἞, ௚, ᰾タィᇶᮏࢹ࣮ࢱ࣮࣋ࢫࡢᩚഛ(VII) 㸫JUPITER ᐇ㦂ゎᯒࡢ
㧗ᗘ໬㸫, PNC TN9410 97-098, 1997.
5) ⯪᭥ ῟, ゅ⏣ ᘯ࿴, BN ཬࡧ BFS ⅔ᚰゎᯒࢩࢫࢸ࣒ࡢᩚഛ (II) 㸫3 ḟඖ Hex-Z య⣔⏝㍺
㏦᰾≉ᛶゎᯒࢥ࣮ࢻࡢᩚഛ㸫, JNC TJ9410 2002-001, 2002.
6) Hazama, T., Shono, A., et al., Verification of a Nuclear Analysis System for Fast Reactors
using BFS-62 Critical Experiment, J. Nucl. Sci. Technol., Vol. 41, No. 12, 2004, pp.
1145-1154.
7) ⯪᭥ ῟, ゅ⏣ ᘯ࿴, BN ཬࡧ BFS ⅔ᚰゎᯒࢩࢫࢸ࣒ࡢᩚഛ," JNC TJ9400 2001-008, 2001.
8㸧Wagner, M. R., Three-Dimensional Nodal Diffusion and Transport Theory Methods for
Hexagonal-z Geometry, Nucl. Sci. Eng., Vol. 103, 1989, pp. 377-391.
9) Sugino, K. and Takeda, T., A New Method of Treating Radial Leakage in Nodal SN
Transport Calculation for Hexagonal Geometry, Proc. Int. Conf. on the Physics of
Reactors PHYSOR 96, Mito, Japan, Sept. 16-20, 1996, A153-A162.
10) Sugino, K. and Kugo, T., Effect of Polynomial Expansion Order of Intranode Flux
Treatment in Nodal SN Transport Calculation Code NSHEX for Large-size Fast Power
Reactor Core Analysis, J. Nucl. Sci. Technol., Vol. 48, No. 3, 2011, p. 421-428.
11) ụ⏣ ୍୕, Ⳣ ኴ㑻, ௚, 3 ḟඖ୕ゅ࣓ࢵࢩࣗ Sn ᰾ィ⟬ࢥ࣮ࢻࡢ㛤Ⓨ, ᪥ᮏཎᏊຊᏛ఍
ࠕ1994 ᖺ⛅ࡢ኱఍ࠖண✏㞟, 1994, G57.
12) ⏣ῡ ኈ㑻, ụ⏣ ୍୕, ௚, 3 ḟඖ୕ゅ࣓ࢵࢩࣗ Sn ᰾ィ⟬ࢥ࣮ࢻࡢ㛤Ⓨ(II), ᪥ᮏཎᏊຊᏛ
఍ࠕ1995 ᖺ⛅ࡢ኱఍ࠖண✏㞟, 1995, A45.
13) Ⳣ ኴ㑻, ụ⏣ ୍୕, ௚, 㧗㏿⅔⅔ᚰ≉ᛶィ⟬ࡢ☜⋡ㄽⓗᡭἲཬࡧỴᐃㄽⓗᡭἲ࡜ࡢẚ㍑,
᪥ᮏཎᏊຊᏛ఍ࠕ2000 ᖺ᫓ࡢᖺ఍ࠖண✏㞟, 2000, O26.
14) Takeda, T. and Ikeda, H., Three-dimensional Neutron Transport Benchmarks,
NEACRP-L-330, 1991.
15) Nakashima, F., Kaise, Y., et al., Core Performance and Characteristics of the Prototype
Fast Breeder Reactor MONJU, Proc. Inter. Conf. on Fast Reactors and Related Fuel
Cycles (FR’91), 1991, Vol.1, pp.8.2-1 - 9, Kyoto, Japan.
16) 㧗ୗ ᾈᩥ, ᵽཱྀ ┿ྐ, ௚, ᰾タィᡭἲሗ࿌᭩, JNC TN8410 2000-011, 2000.
㻙㻌㻤㻤㻌㻙㻌
JAEA-Data/Code 2011-018
17) Gourdon, J. and Mesnage B., An Overview of Superphenix Commissioning Tests, Nucl.
Sci. Eng., 106, 1990, pp.1-10.
18) Hunter, S. N., Super-Phenix Benchmark Used for Comparison of PNC and CEA
Calculation Methods, and of JENDL-3.2 and CARNAVAL IV Nuclear Data, PNC TN9410
98-015, 1998.
19) Palmiotti, G., Salvatores, M., et al., A Global Approach to the Physics Validation of
Simulation Codes for Future Nuclear Systems, Proc. Inter. Conf. on Reactor Physics,
Nuclear Power: A Sustainable Resource, Interlaken, Switzerland, Sept. 14-19, 2008.
20) ᑠᕝ 㝯, ᑠᯘ Ⓩ, ௚, ࢼࢺ࣒ࣜ࢘෭༷⅔ࡢ⅔ᚰ࣭⇞ᩱタィ᳨ウ㸦MOX ⇞ᩱ⅔ᚰ㸧㸫2006
ᖺᗘሗ࿌㸫, JAEA-Research 2007-084, 2007.
21) ⩚ᵝ ᖹ, ༓ⴥ ㇦, ௚, 㧗㏿⅔⏝⤫ྜ⅔ᐃᩘ ADJ2000R ࡢసᡂ, JNC TN9400 2002-064,
2002.
22) Nagaya, Y., Okumura, K., et al., MVP/GMVP II: General Purpose Monte Carlo Codes
for Neutron and Photon Transport Calculations based on Continuous Energy and
Multigroup Methods, JAERI 1348, 2005.
23) Lathrop, K. D. and Carlson, B. G., Discrete Ordinates Angular Quadrature of the
Neutron Transport Equation, Rep. LA-3186, 1065, Los Alamos National Laboratory, Los
Alamos, N.M. .
24) Lathrop, K. D. and Brinkley, F. W., Theory and Use of the General-Geometry
TWOTRAN Program, Rep. LA-4432, 1970, Los Alamos National Laboratory, Los Alamos,
N.M. .
25) NEA Nuclear Science Committee, Japan's Experimental Fast Reactor Joyo MK-I Core:
Sodium-Cooled Uranium-Plutonium Mixed Oxide Fueled Fast Core Surrounded by UO2
Blanket,
International
Handbook
of
Evaluated
Reactor
Physics
Benchmark
Experiments NEA/NSC/DOC(2006)01.
26) NEA Nuclear Science Committee, BFS-62-3A Experiment: Fast Reactor Core with U
and U-Pu Fuel of 17% Enrichment and Partial Stainless Steel Reflector, International
Handbook
of
Evaluated
Reactor
Physics
Benchmark
Experiments
NEA/NSC/DOC(2006)01.
27) ᮡ㔝 ࿴㍤, 3 ḟඖ HexZ య⣔⏝ࣀ࣮ࢻἲ㍺㏦ィ⟬ࢥ࣮ࢻ NSHEX ࡢᐇ⏝ᛶྥୖࡢࡓࡵࡢᨵ
Ⰻ, PNC TN9410 98-064, 1998.
㻙㻌㻤㻥㻌㻙㻌
JAEA-Data/Code 2011-018
௜㘓 1 NSHEX ࡢᐇ⾜᪉ἲཬࡧධຊ࣐ࢽࣗ࢔ࣝ㸦᪥ᮏㄒ∧㸧
NSHEX ࡢᐇ⾜᪉ἲ
㸯.NSHEX ࡢධฟຊࣇ࢓࢖ࣝ␒ྕ
# 1㸸ࣜࢫࢱ࣮ࢺࣇ࢓࢖ࣝ
㸦READ㸧
# 2㸸ࣜࢫࢱ࣮ࢺࣇ࢓࢖ࣝ
㸦WRITE㸧
# 6㸸ィ⟬ࡢ⤒㐣⾲♧
㸦WRITE㸧
# 8㸸࢖ࣥࣉࢵࢺ
㸦READ㸧
# 9㸸࢔࢘ࢺࣉࢵࢺ
㸦WRITE㸧
#12㸸ࣀ࣮ࢻෆ୰ᛶᏊ᮰࡜ࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰ࡢࢲࣥࣉ
㸦WRITE㸧
#20㸸ᛂ⟅⾜ิࡢ୰㛫ࣇ࢓࢖ࣝ㸦IOP7=1 ࡢ᫬ᚲせ㸧
㸦READ & WRITE㸧
#21㹼20+NGMX
㸸ゅᗘ୰ᛶᏊ᮰ࡢ୰㛫ࣇ࢓࢖ࣝ㸦IOP6=1 ࡢ᫬ᚲせ㸧*
㸦READ & WRITE㸧
#21, 22㸸ゅᗘ୰ᛶᏊ᮰ࡢ୰㛫ࣇ࢓࢖ࣝ㸦IOP6=2 ࡢ᫬ᚲせ㸧*
㸦READ & WRITE㸧
*: IOP6=1 ࡢሙྜࡣ࢚ࢿࣝࢠ࣮⩌ẖ࡟୍ࡘࡢグ᠈⿦⨨㸦୰㛫ࣇ࢓࢖ࣝ㸧ࡀ๭ࡾᙜ࡚ࡽࢀࠊ
IOP6=2 ࡢሙྜࡣእഃ཯᚟ẖ࡟ 21 ␒࡜ 22 ␒ࣇ࢓࢖ࣝࡢㄞࡳ㎸ࡳ࣭᭩ࡁ㎸ࡳࡀධࢀ᭰ࢃࡿࠋ
IOP6=1 ࡢ᪉ࡀ୰㛫ࣇ࢓࢖ࣝᐜ㔞ࡣᑡ࡞࠸ࡀࠊࡼࡾከࡃࡢグ᠈⿦⨨ࢆせࡍࡿࠋ
㸰.Variable Dimension ࡢྲྀࡾᢅ࠸
NSHEX ࡛ࡣࠊィ⟬ᶵᐜ㔞⠇⣙ࡢほⅬ࠿ࡽ඲㓄ิࢹ࣮ࢱࡣ Variable Dimension(௨ୗࠊVD)
࡟ࡼࡾྲྀࡾᢅࢃࢀ࡚࠸ࡿࠋVD ࡢ኱ࡁࡉࡣ࣓࢖࣮ࣥࣝࢳࣥ㸦main000.f㸧ࡢࣃ࣓࣮ࣛࢱᩥ࡛ࠊ
PARAMETER (LIMIT=######, LIMIT2=####)
࡟ࡼࡾࠊᣦᐃࡉࢀ࡚࠸ࡿࠋLIMIT ࡀ඲ᐇᩘ㓄ิࡢ኱ࡁࡉࢆࠊLIMIT2 ࡀ඲ᩚᩘ㓄ิࡢ኱ࡁࡉࢆ
ࡑࢀࡒࢀ♧ࡋ࡚࠸ࡿࠋࡑࡋ࡚ࠊࢥ࣮ࢻࢆᐇ⾜ࡍࡿ࡜ࢱ࢖ࢺࣝࡢ┤ᚋ࡟ᚲせ࡞ VD ࡢ኱ࡁࡉࡀ⾲
♧ࡉࢀࡿࡀࠊࡑࢀࡽࡢ኱ࡁࡉࡀ LIMIT ࡲࡓࡣ LIMIT2 ࢆୖᅇࡿ࡜ᐇ⾜ࡀ୰᩿ࡉࢀࡿࠋࡑࡢ㝿ࠊ
ࢯ࣮ࢫ୰ࡢୖグࡢࣃ࣓࣮ࣛࢱᩥࢆ┤᥋⦅㞟ࡋ࡚タᐃࡋ┤ࡍᚲせࡀ࠶ࡿࠋࡓࡔࡋࠊ࠶ࡲࡾ኱ࡁ࡞
ᩘᏐࢆ୚࠼ࡿ࡜ࠊィ⟬ᶵࡢチᐜ᭱኱࣓࣮ࣔࣜࢆ㉺࠼ࡿ࠾ࡑࢀࡀ࠶ࡿࡢ࡛ࠊὀពࡀᚲせࠋ
㻙㻌㻥㻜㻌㻙㻌
JAEA-Data/Code 2011-018
NSHEX ࡢධຊ࣐ࢽࣗ࢔ࣝ
㸦3 ศࡢ 1 ⅔ᚰ∧: Ver.10A.1ࠊ඲⅔ᚰ∧: Ver.10B.1㸧
3 ศࡢ 1 ⅔ᚰ∧㸦ᅇ㌿ᑐ⛠ቃ⏺᮲௳㸧࡜඲⅔ᚰ∧ࡀಶู࡟ᩚഛࡉࢀ࡚࠸ࡿࠋධຊࡣቃ⏺᮲௳
࡜࣐ࢵࣉࡢᣦᐃࡀ␗࡞ࡿࡢ࡛ὀពࡉࢀࡓ࠸ࠋ
㸺JOINT ࢆ⏝࠸ࡿሙྜࡢࡳ Card 0 ࡀᚲせ㸼
Card 0-1: NSHEX (A5)
NSHEX: ไᚚᩥᏐ㸦ࡑࡢࡲࡲ"NSHEX"࡜ධຊ㸧
Card 0-2: INCORE,SLAROM (A6, 4X, A6)
INCORE: ௦⾲ⓗ࡞᩿㠃✚ PDS ࣇ࢓࢖࣓ࣝࣥࣂ࣮ྡࢆᣦᐃ
㸦PDS ࣇ࢓࢖ࣝࡢ FORMAT ᣦᐃ㸧
SLAROM: ᩿㠃✚సᡂࢥ࣮ࢻྡ㸦ࡑࡢࡲࡲ"SLAROM"࡜ධຊ㸧
Card 0-3: ITOT (I5)
ITOT: Ȋt ࡢ࢜ࣉࢩࣙࣥ
1, 2࣭࣭Ȋt=Ȋtransport
0࣭࣭࣭Ȋt=Ȋtotal
-1࣭࣭࣭Ȋt=1/3Dav
-2࣭࣭࣭Ȋt=1/3Dԋ
-3࣭࣭࣭Ȋt=1/3Dҋ
-4࣭࣭࣭Ȋt=2/3(Dҋ+Dԋ)
-5࣭࣭࣭Ȋt=1/(2Dҋ+Dԋ)
-6࣭࣭࣭Ȋt=1/(Dҋ+2Dԋ)
ͤ⮬⩌ᩓ஘᩿㠃✚ࡣࢥ࣮ࢻୖ࡛ḟᘧ࡟ࡼࡾ෌ᐃ⩏ࡉࢀࡿࠋ
6 s,g o g
6 t ,g 6 a,g ¦6
g cz g
s,g o gc
Card 1: ISTART, IRET, CONFCT (2I12, F12.5)
ISTART: ィ⟬࢜ࣉࢩࣙࣥ
0࣭࣭࣭࣭ࣜࢫࢱ࣮ࢺ㸦ࣇ࢓࢖ࣝ#1 ࡀᚲせ㸧
1࣭࣭࣭࣭᪂つィ⟬
IRET: ཰᮰ุᐃ᮲௳ࢆ⦆࿴ࡋ࡚෌ィ⟬ࡍࡿ᭱኱ᅇᩘ
CONFCT: ཰᮰ุᐃ᮲௳⦆࿴ಀᩘ㸦1.0 ௨ୗࢆᣦᐃࡋࡓሙྜ࡟ࡣ⮬ືⓗ࡟ 2.0
࡟タᐃࡉࢀࡿࠋ㸧
Card 2: NLAY, NGMX, MAPMX, NSN (4I12)
NLAY: ᚄ᪉ྥࣀ࣮ࢻᩘ㸦⅔ᚰᒙᩘ㸧
NGMX: ࢚ࢿࣝࢠ࣮⩌ᩘ
MAPMX: 㡿ᇦ㸦࣐ࢸࣜ࢔ࣝ㸧ᩘ
NSN: SN ḟᩘ㸦2㹼16 ࡢഅᩘ㸧
Card 3: IDUMP, IBR, NODR (3I12)
IDUMP: ࣀ࣮ࢻෆ୰ᛶᏊ᮰࡜ࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰ࢆࢲࣥࣉࡍࡿࠋ᭩
ᘧࡣࢧࣈ࣮ࣝࢳࣥ SDUMP ࢆཧ↷ࡢࡇ࡜ࠋ
0࣭࣭࣭࣭YES㸦ࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰ࡢࡳ㸧
1࣭࣭࣭࣭NO
2࣭࣭࣭࣭YES㸦ࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰࡜ࣀ࣮ࢻෆ୰ᛶᏊ᮰㧗ḟ࣮࣓ࣔ
ࣥࢺ㸧
3࣭࣭࣭࣭YES㸦ࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰࡜ࣀ࣮ࢻෆ୰ᛶᏊ᮰㧗ḟ࣮࣓ࣔ
ࣥࢺ࡜ࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰㸧
IBR: ᚄ᪉ྥቃ⏺᮲௳
0࣭࣭࣭࣭࿘ᮇⓗ᮲௳㸦1/3 ⅔ᚰ∧ࡢࡳ㸧
㻙㻌㻥㻝㻌㻙㻌
JAEA-Data/Code 2011-018
1࣭࣭࣭࣭཯ᑕ᮲௳㸦1/3 ⅔ᚰ∧ࡢࡳ㸧
2࣭࣭࣭࣭┿✵᮲௳
NODR: ࣀ࣮ࢻෆ୰ᛶᏊ᮰ࡢᒎ㛤ḟᩘ㸦᭱኱ 6ࠊ㏻ᖖ 2㸧
Card 4: KMX, KCM, IBT, IBB (4I12)
KMX: ㍈᪉ྥ඲ࣀ࣮ࢻᩘ
KCM: ㍈᪉ྥ㡿ᇦᩘ
IBT/IBB: ㍈᪉ྥୖ㒊/ୗ㒊ቃ⏺᮲௳
0࣭࣭࣭࣭┿✵᮲௳
1࣭࣭࣭࣭཯ᑕ᮲௳
Card 5: IOP1, IOP2, IOP2D (3I12)
IOP1: ୰ᛶᏊ᮰㧗ḟ࣮࣓ࣔࣥࢺ㠀ィ⟬࣮ࣔࢻ⛣⾜࢜ࣉࢩࣙࣥ㸦㏻ᖖ 3㹼5㸧
0࣭࣭࣭࣭0 ḟ࣮࣓ࣔࣥࢺ㸦ࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰㸧ࡢእഃ཯᚟࡟࠾ࡅ
ࡿ཯᚟ㄗᕪࡀ CONCR2 ௨ୗ࡟࡞ࡗࡓࡽࠊ㧗ḟ࣮࣓ࣔࣥࢺ
ࡢィ⟬ࢆᡴࡕษࡿࠋ
Ӎ1࣭࣭࣭0 ḟ࣮࣓ࣔࣥࢺࡢእഃ཯᚟࡟࠾ࡅࡿ཯᚟ㄗᕪࡀ CONCR2
௨ୗ࡟࡞ࡗࡓࡽࠊእഃ཯᚟ IOP1 ᅇẖ࡟㧗ḟ࣮࣓ࣔࣥࢺࡢ
ィ⟬ࢆ⾜࠺ࠋ
IOP2: ᶓ᪉ྥࡶࢀ㧗ḟ࣮࣓ࣔࣥࢺࡢィ⟬࢜ࣉࢩࣙࣥ㸦㏻ᖖ 0㸧
0࣭࣭࣭࣭඲ෆഃ཯᚟๓࡟ 1 ᅇィ⟬
1࣭࣭࣭࣭඲ෆഃ཯᚟ᚋ࡟ 1 ᅇィ⟬
IOP2D: ᚄ᪉ྥࢫ࢘࢕࣮ࣉ᫬㍈᪉ྥࡶࢀ㧗ḟ࣮࣓ࣔࣥࢺィ⟬᪉ἲ
㸦㏻ᖖ 0㸧
0࣭࣭࣭࣭୰ᛶᏊ᮰ෆᤄἲ
1࣭࣭࣭࣭2 ḟᶓ᪉ྥࡶࢀ㏆ఝ㸦QLA㸧
Card 6: IOP3, IOP4, IOP5, IOP6, IOP7 (5I12)
IOP3: ຍ㏿ἲࡢ㐺⏝㸦㏻ᖖ 0㸧
㸼0࣭࣭࣭YES㸦ࣜࣂࣛࣥࢫຍ㏿ἲࢆෆഃ཯᚟ IOP3 ᅇẖ࡟㐺⏝㸧
0࣭࣭࣭࣭NO
IOP4: እഃ཯᚟ࡢ཰᮰ุᐃ࡟⏝࠸ࡿ≀⌮㔞ࡢᣦᐃ㸦㏻ᖖ-1㸧
-1࣭࣭࣭࣭ࣀ࣮ࢻᖹᆒ᰾ศ⿣୰ᛶᏊ※
0࣭࣭࣭࣭ࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰
1࣭࣭࣭࣭ࣀ࣮ࢻᖹᆒཬࡧࣀ࣮ࢻቃ⏺᰾ศ⿣୰ᛶᏊ※
2࣭࣭࣭࣭ᣦᐃ㡿ᇦࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰㸦Card 12 ࡛㡿ᇦࢆᣦᐃ㸧
IOP5: ィ⟬࣮ࣔࢻࡢᣦᐃ
0࣭࣭࣭࣭୰ᛶᏊ᮰ィ⟬
1࣭࣭࣭࣭㝶క୰ᛶᏊ᮰ィ⟬
2࣭࣭࣭࣭㝶క୰ᛶᏊ᮰ィ⟬㸦ᅛ᭷್ᅛᐃ㸧
IOP6: ゅᗘ୰ᛶᏊ᮰ࡢ୰㛫ࣇ࢓࢖ࣝ౑⏝ࡢᣦᐃ
0࣭࣭࣭࣭୙౑⏝
1࣭࣭࣭࣭౑⏝㸦࢚ࢿࣝࢠ࣮⩌ẖ࡟ 1 グ᠈⿦⨨๭ᙜ㸧
2࣭࣭࣭࣭౑⏝㸦እഃ཯᚟㝸ᅇẖ࡟ 1 グ᠈⿦⨨๭ᙜ㸧
IOP7: ᛂ⟅⾜ิࡢ୰㛫ࣇ࢓࢖ࣝ౑⏝ࡢᣦᐃ
0࣭࣭࣭࣭୙౑⏝
1࣭࣭࣭࣭౑⏝
ͤヲ⣽ࡣᐇ⾜᪉ἲࡢ㡯ཧ↷
Card 7: CONCR, CONCR2, CONCRI, CONCRE, FACT (4E12.5, F12.5)
CONCR: እഃ཯᚟୰ᛶᏊ᮰ࡲࡓࡣ᰾ศ⿣୰ᛶᏊ※཰᮰᮲௳㸦㏻ᖖ 5.0E-4㸧
CONCR2: ୰ᛶᏊ᮰㧗ḟ࣮࣓ࣔࣥࢺィ⟬᮲௳㸦㏻ᖖ 2CONCRࠊIOP1 ཧ↷㸧
CONCRI: ෆഃ཯᚟୰ᛶᏊ᮰཰᮰᮲௳㸦㏻ᖖ CONCR ࡜ྠࡌ㸧
CONCRE: ᅛ᭷್㸦ᐇຠቑಸ⋡㸧཰᮰᮲௳㸦㏻ᖖ 1.0E-5㸧
FACT: つ᱁໬ᐃᩘ
>0࣭࣭࣭ȤȊfȭࡢ✵㛫࣭࢚ࢿࣝࢠ࣮ྜィ್࡟ࡼࡾつ᱁໬
㻙㻌㻥㻞㻌㻙㻌
JAEA-Data/Code 2011-018
<0࣭࣭࣭Ȋfȭࡢ✵㛫࣭࢚ࢿࣝࢠ࣮ྜィ್࡟ࡼࡾつ᱁໬
Card 8: ITINMX, ITOUTMX, TIMOUT, EIGEN, ACUT, CONIFD (2I12, 3F12.5, E12.5)
ITINMX: ᭱኱ෆഃ཯᚟ᅇᩘ
ITOUTMX: ᭱኱እഃ཯᚟ᅇᩘ
TIMOUT: ィ⟬ไ㝈᫬㛫 [ศ]
EIGEN: ᅛ᭷್㸦ᐇຠቑಸ⋡㸧ึᮇ್㸦㏻ᖖ 1.0㸧
ACUT: ᚄ᪉ྥࢫ࢘࢕࣮ࣉ᫬ࡢ㍈᪉ྥࡶࢀィ⟬᮲௳
㸦㏻ᖖ 0.0ࠊIOP2D=0 ࡢሙྜࡢࡳ㸧
CONIFD: ึᮇ᭷㝈ᕪศィ⟬཰᮰ุᐃ᮲௳㸦㏻ᖖ 2.0E-2㸧
Card 9: (IHK(KC), KC=1, KCM) (25I3)
IHK(KC): ㍈᪉ྥ㡿ᇦ KC ࡢ㍈᪉ྥࣀ࣮ࢻᩘ㸦ୗ㒊࠿ࡽୖ㒊࡬ࡢ㡰㸧
Card 10: (ZC(KC), KC=1, KCM+1) (6E12.5)
ZC(KC): ㍈᪉ྥ㡿ᇦቃ⏺ࡢᗙᶆ [cm]㸦ୗ㒊࠿ࡽୖ㒊࡬ࡢ㡰㸧
㸦㍈᪉ྥ㡿ᇦ KC ࡣ ZC(KC)ӌZӌZC(KC+1)࡟Ꮡᅾࡍࡿࡇ࡜࡟࡞ࡿ㸧
Card 11: HP (E12.5)
HP: ᚄ᪉ྥࣀ࣮ࢻࣆࢵࢳ [cm]
Card 12: (IMJ(MP), MP=1, MAPMX) (25I3) 㸦IOP4=2 ࡢሙྜࡢࡳධຊ㸧
IMJ(MP): 㡿ᇦ MP ࡢ཰᮰ุᐃࣇࣛࢢ
0ุ࣭࣭࣭࣭ᐃᑐ㇟
1ุ࣭࣭࣭࣭ᐃ㠀ᑐ㇟
Card 13: MAP(N, KC) (Free Format)
MAP(N, KC): 㡿ᇦ㸦࣐ࢸࣜ࢔ࣝࠊ࣐ࢵࣉ㸧␒ྕ
㍈᪉ྥ㡿ᇦ㸦PLANE㸧ẖ࡟ୗ㒊࠿ࡽୖ㒊࡬ࡢ㡰࡟୚࠼ࠊࡑࢀࢆ KCM
ᅇ⧞ࡾ㏉ࡍࠋFig. A.1-1㹼5 ཧ↷ࠋJOINT ࢆ⏝࠸ࡿሙྜࡣ 80 ิ௨ෆ
࡛ධຊࡍࡿᚲせࡀ࠶ࡿࠋ
㸺JOINT ࢆ⏝࠸࡞࠸ሙྜ㸼
Card 14: XABS(NG, NR), XFIS(NG, NR), XSGF(NG, NR), XTRA(NG, NR),
(XSCT(NG, NN, NR), NN=1, NGMX) (6E12.5)
XABS(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ྾཰᩿㠃✚Ȋa
XFIS(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ⏕ᡂ᩿㠃✚ȤȊf
XSGF(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ᰾ศ⿣᩿㠃✚Ȋf
XTRA(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ඲᩿㠃✚Ȋt
XSCT(NG, NN, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NGЍNN ࡢᩓ஘᩿㠃✚
Ȋs(ngЍnn)
㸦ࡇࢀࢆ NGMX ᅇ⧞ࡾ㏉ࡋࠊ᭦࡟ MAPMX ᅇ⧞ࡾ㏉ࡍࠋ㸧
㸺JOINT ࢆ⏝࠸ࡿሙྜ㸼
Card 14-1: XS@ (A4)
XS@: ไᚚᩥᏐ㸦ࡑࡢࡲࡲ"XS@ "࡜ධຊ㸧
Card 14-2: MEMBER1, SLAROM (A6, 4X, A6)
MEMBER1: ᩿㠃✚ PDS ࣇ࢓࢖ࣝࡢ࣓ࣥࣂ࣮ྡ
SLAROM: ᩿㠃✚సᡂࢥ࣮ࢻྡ㸦ࡑࡢࡲࡲ"SLAROM"࡜ධຊ㸧
㸦Card14-2 ࢆ MAPMX ᅇ⧞ࡾ㏉ࡍࠋ㸧
ͤ⮬⩌ᩓ஘᩿㠃✚ࡣࢥ࣮ࢻୖ࡛ḟᘧ࡟ࡼࡾ෌ᐃ⩏ࡉࢀࡿࠋ
6 s,g o g
6 t ,g 6 a,g ¦6
g cz g
s,g o gc
㻙㻌㻥㻟㻌㻙㻌
JAEA-Data/Code 2011-018
㸺JOINT ࢆ⏝࠸࡞࠸ሙྜ㸼
Card 15: (CHI(NG), NG=1, NGMX) (6E12.5)
CHI(NG): ᰾ศ⿣ࢫ࣌ࢡࢺࣝ㸦࢚ࢿࣝࢠ࣮⩌ NG ࡬ࡢ᰾ศ⿣࡟ࡼࡿ୰ᛶᏊᨺ
ฟ๭ྜࠋࢥ࣮ࢻෆ࡛ྜィࡀ 1.0 ࡟࡞ࡿࡼ࠺࡟つ᱁໬ࡉࢀࡿࠋ㸧
㸺JOINT ࢆ⏝࠸ࡿሙྜ㸼
Card 15: MEMBER2, SLAROM (A6, 4X, A6)
MEMBER2: ィ⟬࡟⏝࠸ࡿ᰾ศ⿣ࢫ࣌ࢡࢺࣝࢆྵࡴ᩿㠃✚ PDS ࣇ࢓࢖ࣝࡢ
࣓ࣥࣂ࣮ྡ㸦᰾ศ⿣ࢫ࣌ࢡࢺࣝࡣ 1 ✀㢮ࡢࡳᣦᐃྍ⬟㸧
SLAROM: ᩿㠃✚సᡂࢥ࣮ࢻྡ㸦ࡑࡢࡲࡲ"SLAROM"࡜ධຊ㸧
㻙㻌㻥㻠㻌㻙㻌
JAEA-Data/Code 2011-018
Fig. A.1-1
3 ศࡢ 1 ⅔ᚰ∧ NSHEX ࡟࠾ࡅࡿᅇ㌿ᑐ⛠⅔ᚰ㡿ᇦࡢྲྀࡾ᪉
Fig. A.1-2
Fig. A.1-3
3 ศࡢ 1 ⅔ᚰ∧ NSHEX ࡢࣀ࣮ࢻ␒ྕ
3 ศࡢ 1 ⅔ᚰ∧ NSHEX ࡢࣀ࣮ࢻ␒ྕ࡜࣐ࢵࣉධຊ࡜ࡢᑐᛂ
㻙㻌㻥㻡㻌㻙㻌
JAEA-Data/Code 2011-018
Fig. A.1-5
Fig. A.1-㸲
඲⅔ᚰ∧ NSHEX ࡢࣀ࣮ࢻ␒ྕ
඲⅔ᚰ∧ NSHEX ࡢࣀ࣮ࢻ␒ྕ࡜࣐ࢵࣉධຊ࡜ࡢᑐᛂ
㻙㻌㻥㻢㻌㻙㻌
JAEA-Data/Code 2011-018
௜㘓 2 NSHEX ࡢᐇ⾜᪉ἲཬࡧධຊ࣐ࢽࣗ࢔ࣝ㸦ⱥㄒ∧㸧
HOW TO USE NSHEX
1. INTERFACE UNIT ID
# 1: Restart file
(READ)
# 2: Restart file
(WRITE)
# 6: Monitor output
(WRITE)
# 8: Input
(READ)
# 9: Standard output
(WRITE)
#12: Dump of intra-node flux and node-boundary flux
(WRITE)
#20: Work file of the response matrices (Required when IOP7=1) (READ & WRITE)
#21 through 20+NGMX
: Work file of the angular flux (Required when IOP6=1)*
(READ & WRITE)
#21 and 22
: Work file of the angular flux (Required when IOP6=2)*
(READ & WRITE)
*: When IOP6=1, the interface units or work files are occupied every energy group. When
IOP6=2, the interface units 21 and 22 are occupied one after the other every outer iteration.
In the case when IOP6=1, less file volume but more interface units are required.
2. TREATMENT OF THE VARIABLE DIMENSION
For a computation memory economy most of dimensions are allocated by single variable
dimension, and the sizes of the variable dimensions are specified by the following
statement in the main routine (main000.f):.
PARAMETER (LIMIT=######, LIMIT2=####)
The value LIMIT specifies the size of the real-type (R) variable dimension and the value
LIMIT2 that of the integer-type (I) one. They must be greater than required sizes,
otherwise calculation stops. You can check required sizes of the variable dimensions in the
monitor output (Unit # 6).
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JAEA-Data/Code 2011-018
NSHEX INPUT MANUAL
(Ver.10A.1 for one third core and Ver.10B.1 for whole core)
There are 2 subversions of NSHEX, which are 1/3 core and whole code subversions.
Inputs for boundary condition and map specification are different.
<Card 0 is necessary only when JOINT is used.>
Card 0-1: NSHEX (A5)
NSHEX: Control character (Just specify "NSHEX")
Card 0-2: INCORE,SLAROM (A6, 4X, A6)
INCORE: Representative member name of the PDS file
(For the specification of the PDS file format)
SLAROM: Code name for the cross sections (Specify "SLAROM")
Card 0-3: ITOT (I5)
ITOT: Option for the total cross sections
1, 2
=Transport cross sections
0
=Total cross sections
-1
=1/3Dav (Averaged diffusion coefficients)
-2
=1/3D(Benoist's perpendicular)
-3
=1/3D(Benoist's parallel)
-4
=2/3(D(B's perpendicular)+D(B's parallel))
-5
=1/(D(B's perpendicular)+2D(B's parallel))
-6
=1/(2D(B's perpendicular)+D(B's parallel))
REMARK: Within-group scattering cross sections are redefined by following equation:
6 s,g o g
6 t ,g 6 a,g ¦6
g cz g
s,g o gc
Card 1: ISTART, IRET, CONFCT (2I12, F12.5)
ISTART: Calculation option
0
Restart calculation (File #1 is required.)
1
New calculation
IRET: Maximum retrial counts
CONFCT: Relaxation factor of convergence criterions (Automatically set
2.0 if specified less or equal to 1.0)
Card 2: NLAY, NGMX, MAPMX, NSN (4I12)
NLAY: Number of the radial nodes (Number of layers)
NGMX: Number of energy groups
MAPMX: Number of regions (materials)
NSN: SN order (2 through 16 and even number)
Card 3: IDUMP, IBR, NODR (3I12)
IDUMP: Dump option for the intra-node flux and node-boundary flux to
file #12 (Format is referred to the subroutine "SDUMP")
0
YES (Node-average flux only)
1
NO
2
YES (Node-average flux and intra-node high order flux
moment)
3
YES (Node-average flux, intra-node high order flux
moment and node-boundary flux)
IBR: Boundary condition in the radial direction
0
Periodic (1/3 core version only)
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JAEA-Data/Code 2011-018
1
Reflective (1/3 core version only)
2
Vacuum
NODR: Expansion order of the intra-node flux (Maximum: 6, Normal: 2)
Card 4: KMX, KCM, IBT, IBB (4I12)
KMX: Total number of axial nodes (planes)
KCM: Number of axial regions
IBT/IBB: Boundary condition in the axial direction (Top / Bottom)
0
Vacuum
1
Reflective
Card 5: IOP1, IOP2, IOP2D (3I12)
IOP1: Calculation option for the high order flux moments (Normally 3
through 5)
0
Calculation stopped when maximum iteration error of
node average (0th order) flux becomes less than
CONCR2.
>0
Calculation performed every IOP1 times of outer
iteration after maximum iteration error of node average
(0th order) flux becomes less than CONCR2.
IOP2: Calculation option for the high order transverse leakage moments
(Normally 0)
0
Once before all inner iterations
1
Once after all inner iterations
IOP2D: Calculation method for the high order axial leakage moments in
the radial sweep (Normally 0)
0
Scalar flux interpolation method
1
Quadratic leakage approximation (QLA)
Card 6: IOP3, IOP4, IOP5, IOP6, IOP7 (5I12)
IOP3: Application of the acceleration methods (Normally 0)
>0
YES (Rebalance applied in inner iterations every IOP3
times)
0
NO
IOP4: Parameters for the convergence judgment in outer iteration
(Normally -1)
-1
Fission source (Node average)
0
Flux (Node average)
1
Fission source (Node average and node boundaries)
2
Flux (Node average) in the specified regions by Card 12
IOP5: Calculation mode
0
Real
1
Adjoint
2
Adjoint with fixed eigenvalue
IOP6: Option for the work files of the angular flux
0
Not used
1
Used (1 unit per every energy group)
2
Used (1 unit per every other outer iteration)
IOP7: Option for the work file of the response matrices
0
Not used
1
Used
See "HOW TO USE NSHEX"
Card 7: CONCR, CONCR2, CONCRI, CONCRE, FACT (4E12.5, F12.5)
CONCR: Convergence criterion on flux in outer iteration (Normally
1.0E-4)
CONCR2: Calculation condition on the high order flux moments
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JAEA-Data/Code 2011-018
(Normally 2CONCR, See the description on IOP1)
CONCRI: Convergence criterion on flux in inner iteration
(Normally same as CONCR)
CONCRE: Convergence criterion on eigenvalue (Normally 1.0E-5)
FACT: Normalization factor
>0
By neutron production
<0࣭࣭࣭By fission source
Card 8: ITINMX, ITOUTMX, TIMOUT, EIGEN, ACUT, ITOUTFD (2I12, 3F12.5, E12.5)
ITINMX: Maximum number of inner iteration
ITOUTMX: Maximum number of outer iteration
TIMOUT: CPU time limit [minute]
EIGEN: Initial Eigenvalue (Normally 1.0)
ACUT: Axial leakage calculation condition in radial sweep
(Normally 0.0,
only if IOP2D=0)
CONIFD: Convergence criterion on the initial finite difference calculation
(Normally 2.0E-2)
Card 9: (IHK(KC), KC=1, KCM) (25I3)
IHK(KC): Number of axial nodes (planes) in axial region KC
(From bottom to top)
Card 10: (ZC(KC), KC=1, KCM+1) (6E12.5)
ZC(KC): Coordinates of the radial region boundaries [cm]
(From bottom to top) (Axial region KC exists in the extent of
ZC(KC) through ZC(KC+1))
Card 11: HP (E12.5)
HP: Radial node across flat length [cm]
Card 12: (IMJ(MP), MP=1, MAPMX) (25I3) (Required only when IOP4=2)
IMJ(MP): Convergence judgment flag of region MP
0
Considered
1
Ignored
Card 13: MAP(N, KC) (Free Format)
MAP(N, KC): Region (material) numbers (Region map)
Specify them for every axial plane and repeat KCM times from
bottom to top. See Fig. A.2.1-1 through 5. When JOINT is used,
this card should be specified within 80 columns.
<When JOINT is not used>
Card 14: XABS(NG, NR), XFIS(NG, NR), XSGF(NG, NR), XTRA(NG, NR),
(XSCT(NG, NN, NR), NN=1, NGMX) (6E12.5)
XABS(NG, NR): Absorption cross sections of energy group NG in region
NR
XFIS(NG, NR): Production cross sections of energy group NG in region NR
XSGF(NG, NR): Fission cross sections of energy group NG in region NR
XTRA(NG, NR): Total cross sections of energy group NG in region NR
XSCT(NG, NN, NR): Scattering cross sections from energy group NG to
NN in region NR
(Repeat NGMX times, and repeat MAPMX times)
<When JOINT is used>
Card 14-1: XS@ (A4)
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JAEA-Data/Code 2011-018
XS@: Control character (Just specify "XS@ ")
Card 14-2: MEMBER1, SLAROM (A6, 4X, A6)
MEMBER1: Member name of the PDS file
SLAROM: Code name for the cross sections (Specify "SLAROM")
(Repeat Card14-2 MAPMX times)
REMARK: Within-group scattering cross sections are redefined by following equation:
6 s,g o g
6 t ,g 6 a,g ¦6
g cz g
s,g o gc
<When JOINT is not used>
Card 15: (CHI(NG), NG=1, NGMX) (6E12.5)
CHI(NG): Fission spectrum (Releasing fraction to energy group NG.
Normalized so as to set sum of them equal to 1.0.)
<When JOINT is used>
Card 15: MEMBER2, SLAROM (A6, 4X, A6)
MEMBER2: Member name of the PDS file including the one
representative fission spectrum
SLAROM: Code name for the cross sections (Specify "SLAROM")
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JAEA-Data/Code 2011-018
Fig. A.2-1
Fig. A.2-2
Node addressing of the NSHEX 1/3 core version (NLAY=8)
Fig. A.2-3
Configuration of the 1/3 rotational core
Relationship between the node addressing and the map input format of the
NSHEX 1/3 core version (NLAY=8)
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JAEA-Data/Code 2011-018
Fig. A.2-4
Node addressing of the NSHEX whole core version (NLAY=4)
Fig. A.2-5
Relationship between the node addressing and the map input format of the
NSHEX whole core version (NLAY=4)
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JAEA-Data/Code 2011-018
௜㘓 3 MINIHEX ࡢᐇ⾜᪉ἲཬࡧධຊ࣐ࢽࣗ࢔ࣝ
MINIHEX ࡢᐇ⾜᪉ἲ
1. ᴫせ
MINIHEX ࡣࠊBFS-2 ⮫⏺ᐇ㦂⿦⨨ࢆ⏝࠸࡚⾜ࢃࢀࡿ⮫⏺ᐇ㦂ゎᯒࢆ᝿ᐃࡋ࡚సᡂࡉࢀࡓ
Hex-Z య⣔⏝᭷㝈ᕪศ SN ㍺㏦ィ⟬ࢥ࣮ࢻ࡛࠶ࡿࠋ
BFS-2 ⮫⏺ᐇ㦂⿦⨨ࡣ㛫㝸 5.1cm ࡢṇභゅ᱁Ꮚ࡛ᵓᡂࡉࢀ࡚࠾ࡾࠊ᭷㝈ᕪศ㍺㏦⌮ㄽࢆ㐺⏝
ࡋ࡚ࡶࠊᚄ᪉ྥࡢ✵㛫࣓ࢵࢩࣗㄗᕪࡀ༑ศ࡟పῶྍ⬟࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࡓࡵࠊᙜࢥ࣮ࢻࡢస
ᡂ࡟⮳ࡗࡓࠋ
ྲྀࡾᢅ࠸ྍ⬟࡞య⣔ࡣࠊ඲⅔ᚰయ⣔ࡢࡳ࡛࠶ࡾࠊቃ⏺᮲௳ࡣ඲࡚┿✵᮲௳࡜࡞ࡿࠋ
2. ᐇ⾜᪉ἲ
2-1. MINIHEX ࢥ࣮ࢻࡢධฟຊࣇ࢓࢖ࣝ␒ྕ
㸡㸯㸸ࣜࢫࢱ࣮ࢺࣇ࢓࢖ࣝ
㸦READ㸧
㸡㸰㸸ࣜࢫࢱ࣮ࢺࣇ࢓࢖ࣝ
㸦WRITE㸧
㸡㸴㸸ィ⟬ࡢ⤒㐣⾲♧
㸦WRITE㸧
㸡㸵㸸㡿ᇦᖹᆒ୰ᛶᏊ᮰
㸦WRITE㸧
㸡㸶㸸࢖ࣥࣉࢵࢺ
㸦READ㸧
㸡㸷㸸࢔࢘ࢺࣉࢵࢺ
㸦WRITE㸧
㸡㸱㸯㸸཰᮰≧ἣ㸦୰ᛶᏊ᮰ࠊᅛ᭷್㸧ࡢฟຊ
㸦WRITE㸧
2-2. Variable Dimension ࡢྲྀࡾᢅ࠸
MINIHEX ࡛ࡣࠊィ⟬ᶵᐜ㔞⠇⣙ࡢほⅬ࠿ࡽ඲㓄ิࢹ࣮ࢱࡣ Variable Dimension(௨ୗࠊVD)
࡟ࡼࡾྲྀࡾᢅࢃࢀ࡚࠸ࡿࠋVD ࡢ኱ࡁࡉࡣ࣓࢖࣮ࣥࣝࢳࣥ㸦main000.f㸧ࡢࣃ࣓࣮ࣛࢱᩥ࡛ࠊ
PARAMETER (LIMIT=######, LIMIT2=####)
࡟ࡼࡾࠊᣦᐃࡉࢀ࡚࠸ࡿࠋLIMIT ࡀ඲ᐇᩘ㓄ิࡢ኱ࡁࡉࢆࠊLIMIT2 ࡀ඲ᩚᩘ㓄ิࡢ኱ࡁࡉࢆ
ࡑࢀࡒࢀ♧ࡋ࡚࠸ࡿࠋࡑࡋ࡚ࠊࢥ࣮ࢻࢆᐇ⾜ࡍࡿ࡜ࢱ࢖ࢺࣝࡢ┤ᚋ࡟ᚲせ࡞ VD ࡢ኱ࡁࡉࡀ⾲
♧ࡉࢀࡿࡀࠊࡑࢀࡽࡢ኱ࡁࡉࡀ LIMIT ࡲࡓࡣ LIMIT2 ࢆୖᅇࡿ࡜ᐇ⾜ࡀ୰᩿ࡉࢀࡿࠋࡑࡢ㝿ࠊ
ࢯ࣮ࢫ୰ࡢୖグࡢࣃ࣓࣮ࣛࢱᩥࢆ┤᥋⦅㞟ࡋ࡚タᐃࡋ┤ࡍᚲせࡀ࠶ࡿࠋࡓࡔࡋࠊ࠶ࡲࡾ኱ࡁ࡞
ᩘᏐࢆ୚࠼ࡿ࡜ࠊィ⟬ᶵࡢチᐜ᭱኱࣓࣮ࣔࣜࢆ㉺࠼ࡿ࠾ࡑࢀࡀ࠶ࡿࡢ࡛ࠊὀពࡀᚲせࠋ
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JAEA-Data/Code 2011-018
MINIHEX ධຊ࣐ࢽࣗ࢔ࣝ
㸦Ver.2.1㸧
඲⅔ᚰ∧ࡢࡳࡀᩚഛࡉࢀ࡚࠸ࡿࠋ
㸺JOINT ࢆ⏝࠸ࡿሙྜࡢࡳ Card 0 ࡣᚲせ㸼
Card 0-1: NSHEX (A5)
NSHEX: ไᚚᩥᏐ㸦ࡑࡢࡲࡲ"NSHEX"࡜ධຊ㸧
Card 0-2: INCORE,SLAROM (A6, 4X, A6)
INCORE: ௦⾲ⓗ࡞᩿㠃✚ PDS ࣇ࢓࢖࣓ࣝࣥࣂ࣮ྡࢆᣦᐃ
㸦PDS ࣇ࢓࢖ࣝࡢ FORMAT ᣦᐃ㸧
SLAROM: ᩿㠃✚సᡂࢥ࣮ࢻྡ㸦ࡑࡢࡲࡲ"SLAROM"࡜ධຊ㸧
Card 0-3: ITOT (I5)
ITOT: Ȋt ࡢ࢜ࣉࢩࣙࣥ
1, 2࣭࣭Ȋt=Ȋtransport
0࣭࣭࣭Ȋt=Ȋtotal
-1࣭࣭࣭Ȋt=1/3Dav
-2࣭࣭࣭Ȋt=1/3Dԋ
-3࣭࣭࣭Ȋt=1/3Dҋ
-4࣭࣭࣭Ȋt=2/3(Dҋ+Dԋ)
-5࣭࣭࣭Ȋt=1/(2Dҋ+Dԋ)
-6࣭࣭࣭Ȋt=1/(Dҋ+2Dԋ)
ͤJOINT 㛵ಀࡢධຊࡣ NSHEX ࡜ඹ㏻࡞ࡢ࡛ࠊࢥ࣮ࢻྡࡣ NSHEX ࡛Ⰻ࠸ࠋ
ͤ⮬⩌ᩓ஘᩿㠃✚ࡣࢥ࣮ࢻୖ࡛ḟᘧ࡟ࡼࡾ෌ᐃ⩏ࡉࢀࡿࠋ
6 s,g o g
6 t ,g 6 a,g ¦6
g cz g
s,g o gc
Card 1: ISTART (I12)
ISTART:
ィ⟬࢜ࣉࢩࣙࣥ
0࣭࣭࣭࣭ࣜࢫࢱ࣮ࢺ㸦ࣇ࢓࢖ࣝ#1 ࡀᚲせ㸧
1࣭࣭࣭࣭᪂つィ⟬
Card 2: NLAY, NGMX, MAPMX, NSN (4I12)
NLAY: ᚄ᪉ྥ࣓ࢵࢩࣗᩘ㸦⅔ᚰᒙᩘ㸧
NGMX: ࢚ࢿࣝࢠ࣮⩌ᩘ
MAPMX: 㡿ᇦ㸦࣐ࢸࣜ࢔ࣝ㸧ᩘ
NSN: Sn ḟᩘ㸦2㹼16 ࡢഅᩘ㸧
Card 3: IDUMP, IBR, NODR (3I12)
IDUMP: ࢲ࣑࣮
IBR: ࢲ࣑࣮
NODR: ࢲ࣑࣮
Card 4: KMX, KCM, IBT, IBB (4I12)
KMX: ㍈᪉ྥ඲࣓ࢵࢩࣗᩘ
KCM: ㍈᪉ྥ㡿ᇦ㸦⢒࣓ࢵࢩࣗ㸧ᩘ
IBT/IBB: ࢲ࣑࣮/ࢲ࣑࣮
Card 5: IOP1, IOP2, NODRL (3I12)
IOP1: ὶฟ୰ᛶᏊ᮰ࡀ㈇࡜࡞ࡗࡓሙྜࡢฎ⌮㸦㏻ᖖ 1㸧
<0࣭࣭࣭࣭ฎ⌮ࢆ⾜ࢃ࡞࠸ࠋ
=0࣭࣭࣭࣭㈇࡜࡞ࡗࡓὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡍࡿࠋ
=1࣭࣭࣭࣭㈇࡜࡞ࡗࡓὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋ࡚ᖹᆒ୰ᛶᏊ
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JAEA-Data/Code 2011-018
᮰ࢆ෌ィ⟬ࡍࡿࠋ
>1࣭࣭࣭࣭㈇࡜࡞ࡗࡓὶฟ୰ᛶᏊ᮰ࢆࢮࣟ࡟ࢭࢵࢺࡋ࡚ᖹᆒ୰ᛶᏊ
᮰ࢆ෌ィ⟬ࡋࠊ᭦࡟ࠊ㈇࡜࡞ࡗ࡚࠸࡞࠿ࡗࡓὶฟ୰ᛶᏊ᮰
ࢆ෌ィ⟬ࡍࡿࠋ
IOP2: ࢲ࣑࣮
NODRL: ࢲ࣑࣮
Card 6: IOP3, IOP4, IOP5, IOP6, Integer*6 (4I12, 6I3)
IOP3: እഃ཯᚟࡟࠾ࡅࡿຍ㏿ἲ㸦୰ᛶᏊ᮰እᤄἲ㸧ࡢ㐺⏝ࡢ᭷↓
0࣭࣭࣭࣭࡞ࡋ
1࣭࣭࣭࣭࠶ࡾ
IOP4: እഃ཯᚟ࡢ཰᮰ุᐃ࡟⏝࠸ࡿ≀⌮㔞ࡢᣦᐃ
0࣭࣭࣭࣭୰ᛶᏊ᮰
1࣭࣭࣭࣭᰾ศ⿣୰ᛶᏊ※
2࣭࣭࣭࣭ᣦᐃ㡿ᇦ୰ᛶᏊ᮰㸦Card 12 ࡛㡿ᇦࢆᣦᐃ㸧
IOP5: ィ⟬࣮ࣔࢻࡢᣦᐃ
0࣭࣭࣭࣭୰ᛶᏊ᮰ィ⟬
1࣭࣭࣭࣭㝶క୰ᛶᏊ᮰ィ⟬
2࣭࣭࣭࣭㝶క୰ᛶᏊ᮰ィ⟬㸦ᅛ᭷್ᅛᐃ㸧
IOP6: ࢲ࣑࣮
NSTA_OUTACC: እᤄࢆ㛤ጞࡍࡿእഃ཯᚟ᅇᩘ
MXODR_OUTACC: እᤄᑐ㇟࣮࣓ࣔࣥࢺḟᩘ
INOFF_OUTACC: 㧗ḟ࣮࣓ࣔࣥࢺ࡬ࡢእᤄ㐺⏝ࡢ೵Ṇ࢜ࣉࢩࣙࣥ
ྛ⩌ࡢ๓ᅇࡢෆഃ཯᚟ᅇᩘࡀ INOFF_OUTACC ௨ୗࡢሙྜࠊࡑࡢ⩌
࡬ࡢእᤄ㐺⏝ࢆ೵Ṇࡍࡿࠋ
IOP_RECAL_FISSEIGEN: እᤄᚋࡢ୰ᛶᏊ※ཬࡧᅛ᭷್෌ィ⟬࢜ࣉࢩࣙࣥ
0࣭࣭࣭࣭࡞ࡋ
1࣭࣭࣭࣭࠶ࡾ
IOP_CHEB1:࣭࣭࣭࣭1 ࡟タᐃ
IOP_CHEB2:࣭࣭࣭࣭1 ࡟タᐃ
Card 7: CONCR, CONCR2, CONCRI, CONCRE, FACT (4E12.5, F12.5)
CONCR: እഃ཯᚟୰ᛶᏊ᮰཰᮰᮲௳㸦㏻ᖖ 1.0E-4㸧
CONCR2: ࢲ࣑࣮
CONCRI: ෆഃ཯᚟୰ᛶᏊ᮰཰᮰᮲௳㸦㏻ᖖ CONCR ࡜ྠࡌ㸧
CONCRE: ᅛ᭷್㸦ᐇຠቑಸ⋡㸧཰᮰᮲௳㸦㏻ᖖ 1.0E-5㸧
FACT: つ᱁໬ᐃᩘ
>0࣭࣭࣭ȤȊfȭࡢ✵㛫࣭࢚ࢿࣝࢠ࣮ྜィ್࡟ࡼࡾつ᱁໬
<0࣭࣭࣭Ȋfȭࡢ✵㛫࣭࢚ࢿࣝࢠ࣮ྜィ್࡟ࡼࡾつ᱁໬
Card 8: ITINMX, ITOUTMX, TIMOUT, EIGEN (2I12, 2F12.5)
ITINMX: ᭱኱ෆഃ཯᚟ᅇᩘ
ITOUTMX: ᭱኱እഃ཯᚟ᅇᩘ
TIMOUT: ィ⟬ไ㝈᫬㛫 [ศ]
EIGEN: ᅛ᭷್㸦ᐇຠቑಸ⋡㸧ึᮇ್㸦㏻ᖖ 1.0㸧
Card 9: (IHK(KC), KC=1, KCM) (25I3)
IHK(KC): ㍈᪉ྥ㡿ᇦ KC ࡢ㍈᪉ྥ࣓ࢵࢩࣗᩘ㸦ୗ㒊࠿ࡽୖ㒊࡬ࡢ㡰㸧
Card 10: (ZC(KC), KC=1, KCM+1) (6E12.5)
ZC(KC): ㍈᪉ྥ㡿ᇦቃ⏺ࡢᗙᶆ [cm] 㸦ୗ㒊࠿ࡽୖ㒊࡬ࡢ㡰㸧
㸦㍈᪉ྥ㡿ᇦ KC ࡣ ZC(KC)ӌZӌZC(KC+1)࡟Ꮡᅾࡍࡿࡇ࡜࡟࡞ࡿ㸧
Card 11: HP (E12.5)
HP: ᚄ᪉ྥ࣓ࢵࢩࣗ㛫㝸 [cm]
㻙㻌㻝㻜㻢㻌㻙㻌
JAEA-Data/Code 2011-018
Card 12 (IMJ(MP), MP=1, MAPMX) (25I3) 㸦IOP4=2 ࡢሙྜࡢࡳධຊ㸧
IMJ(MP): 㡿ᇦ MP ࡢ཰᮰ุᐃࣇࣛࢢ
0ุ࣭࣭࣭࣭ᐃᑐ㇟
1ุ࣭࣭࣭࣭ᐃ㠀ᑐ㇟
Card 13: MAP(N, KC) (Free Format)
MAP(N, KC): 㡿ᇦ㸦࣐ࢸࣜ࢔ࣝࠊ࣐ࢵࣉ㸧␒ྕࠋ
㍈᪉ྥ㡿ᇦ㸦PLANE㸧ẖ࡟ୗ㒊࠿ࡽୖ㒊࡬ࡢ㡰࡟୚࠼ࠊࡑࢀࢆ KCM
ᅇ⧞ࡾ㏉ࡍࠋFig. A.3-1ࠊ2 ཧ↷ࠋMAPMX ࡼࡾࡶ኱ࡁ࠸್ࢆ୚࠼ࡓ
ሙྜ࡟ࡣࠊࡑࡢ㡿ᇦࡣ Black absorber ࡜ㄆ㆑ࡉࢀࡿࠋJOINT ࢆ⏝
࠸ࡿሙྜࡣ 80 ิ௨ෆ࡛ධຊࡍࡿᚲせࡀ࠶ࡿࠋ
㸺JOINT ࢆ⏝࠸࡞࠸ሙྜ㸼
Card 14: XABS(NG, NR), XFIS(NG, NR), XSGF(NG, NR), XTRA(NG, NR),
(XSCT(NG, NN, NR), NN=1, NGMX) (6E12.5)
XABS(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ྾཰᩿㠃✚Ȋa
XFIS(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ⏕ᡂ᩿㠃✚ȤȊf
XSGF(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ᰾ศ⿣᩿㠃✚Ȋf
XTRA(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ඲᩿㠃✚Ȋt
XSCT(NG, NN, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NGЍNN ࡢᩓ஘᩿㠃✚
Ȋs(ngЍnn)
㸦ࡇࢀࢆ NGMX ᅇ⧞ࡾ㏉ࡋࠊ᭦࡟ MAPMX ᅇ⧞ࡾ㏉ࡍࠋ㸧
㸺JOINT ࢆ⏝࠸ࡿሙྜ㸼
Card 14-1: XS@ (A4)
XS@: ไᚚᩥᏐ㸦ࡑࡢࡲࡲ"XS@ "࡜ධຊ㸧
Card 14-2: MEMBER1, SLAROM (A6, 4X, A6)
MEMBER1: ᩿㠃✚ PDS ࣇ࢓࢖ࣝࡢ࣓ࣥࣂ࣮ྡ
SLAROM: ᩿㠃✚సᡂࢥ࣮ࢻྡ㸦ࡑࡢࡲࡲ"SLAROM"࡜ධຊ㸧
㸦Card14-2 ࢆ MAPMX ᅇ⧞ࡾ㏉ࡍࠋ㸧
ͤ⮬⩌ᩓ஘᩿㠃✚ࡣࢥ࣮ࢻෆ࡛ḟᘧ࡟ࡼࡾ෌ᐃ⩏ࡉࢀࡿࠋ
6 s,g o g
6 t ,g 6 a,g ¦6
g cz g
s,g o gc
㸺JOINT ࢆ⏝࠸࡞࠸ሙྜ㸼
Card 15: (CHI(NG), NG=1, NGMX) (6E12.5)
CHI(NG): ᰾ศ⿣ࢫ࣌ࢡࢺࣝ㸦࢚ࢿࣝࢠ࣮⩌ NG ࡬ࡢ᰾ศ⿣࡟ࡼࡿ୰ᛶᏊᨺ
ฟ๭ྜࠋࢥ࣮ࢻෆ࡛ྜィࡀ 1.0 ࡟࡞ࡿࡼ࠺࡟つ᱁໬ࡉࢀࡿࠋ㸧
㸺JOINT ࢆ⏝࠸ࡿሙྜ㸼
Card 15: MEMBER2, SLAROM (A6, 4X, A6)
MEMBER2: ィ⟬࡟⏝࠸ࡿ᰾ศ⿣ࢫ࣌ࢡࢺࣝࢆྵࡴ᩿㠃✚ PDS ࣇ࢓࢖ࣝࡢ
࣓ࣥࣂ࣮ྡ㸦᰾ศ⿣ࢫ࣌ࢡࢺࣝࡣ 1 ✀㢮ࡢࡳᣦᐃྍ⬟㸧
SLAROM: ᩿㠃✚సᡂࢥ࣮ࢻྡ㸦ࡑࡢࡲࡲ"SLAROM"࡜ධຊ㸧
㻙㻌㻝㻜㻣㻌㻙㻌
JAEA-Data/Code 2011-018
Fig. A.3-1
Fig. A.3-2
MINIHEX ࡢ࣓ࢵࢩࣗ␒ྕ
MINIHEX ࡢ࣓ࢵࢩࣗ␒ྕ࡜࣐ࢵࣉධຊ࡜ࡢᑐᛂ
㻙㻌㻝㻜㻤㻌㻙㻌
JAEA-Data/Code 2011-018
௜㘓 4 MINISTRI ࡢᐇ⾜᪉ἲཬࡧධຊ࣐ࢽࣗ࢔ࣝ
MINISTRI ࡢᐇ⾜᪉ἲ
1. ᴫせ
MINISTRI ࡣࠊNSHEX ࢥ࣮ࢻࡢ⿵᏶ⓗᙺ๭ࢆ┠ⓗ࡜ࡋ࡚ࠊ୍⯡ࡢᐇᶵ㧗㏿⅔ゎᯒࢆ᝿ᐃࡋ
࡚సᡂࡉࢀࡓ Tri-Z య⣔⏝᭷㝈ᕪศ SN ㍺㏦ィ⟬ࢥ࣮ࢻ࡛࠶ࡿࠋ
ྲྀࡾᢅ࠸ྍ⬟࡞య⣔ࡣࠊ඲⅔ᚰయ⣔ࡢࡳ࡛࠶ࡾࠊቃ⏺᮲௳ࡣ඲࡚┿✵᮲௳࡜࡞ࡿࠋ
2. ᐇ⾜᪉ἲ
2-1. MINISTRI ࢥ࣮ࢻࡢධฟຊࣇ࢓࢖ࣝ␒ྕ
㸡㸯㸸ࣜࢫࢱ࣮ࢺࣇ࢓࢖ࣝ
㸦READ㸧
㸡㸰㸸ࣜࢫࢱ࣮ࢺࣇ࢓࢖ࣝ
㸦WRITE㸧
㸡㸴㸸ィ⟬ࡢ⤒㐣⾲♧
㸦WRITE㸧
㸡㸵㸸㡿ᇦᖹᆒ୰ᛶᏊ᮰
㸦WRITE㸧
㸡㸶㸸࢖ࣥࣉࢵࢺ
㸦READ㸧
㸡㸷㸸࢔࢘ࢺࣉࢵࢺ
㸦WRITE㸧
㸡㸱㸯㸸཰᮰≧ἣ㸦୰ᛶᏊ᮰ࠊᅛ᭷್㸧ࡢฟຊ
㸦WRITE㸧
2-2. Variable Dimension ࡢྲྀࡾᢅ࠸
MINISTRI ࡛ࡣࠊィ⟬ᶵᐜ㔞⠇⣙ࡢほⅬ࠿ࡽ඲㓄ิࢹ࣮ࢱࡣ Variable Dimension(௨ୗࠊVD)
࡟ࡼࡾྲྀࡾᢅࢃࢀ࡚࠸ࡿࠋVD ࡢ኱ࡁࡉࡣ࣓࢖࣮ࣥࣝࢳࣥࡢࣃ࣓࣮ࣛࢱᩥ࡛ࠊ
PARAMETER (LIMIT=######, LIMIT2=####)
࡟ࡼࡾࠊᣦᐃࡉࢀ࡚࠸ࡿࠋLIMIT ࡀ඲ᐇᩘ㓄ิࡢ኱ࡁࡉࢆࠊLIMIT2 ࡀ඲ᩚᩘ㓄ิࡢ኱ࡁࡉࢆ
ࡑࢀࡒࢀ♧ࡋ࡚࠸ࡿࠋࡑࡋ࡚ࠊࢥ࣮ࢻࢆᐇ⾜ࡍࡿ࡜ࢱ࢖ࢺࣝࡢ┤ᚋ࡟ᚲせ࡞ VD ࡢ኱ࡁࡉࡀ⾲
♧ࡉࢀࡿࡀࠊࡑࢀࡽࡢ኱ࡁࡉࡀ LIMIT ࡲࡓࡣ LIMIT2 ࢆୖᅇࡿ࡜ᐇ⾜ࡀ୰᩿ࡉࢀࡿࠋࡑࡢ㝿ࠊ
ࢯ࣮ࢫ୰ࡢୖグࡢࣃ࣓࣮ࣛࢱᩥࢆ┤᥋⦅㞟ࡋ࡚タᐃࡋ┤ࡍᚲせࡀ࠶ࡿࠋࡓࡔࡋࠊ࠶ࡲࡾ኱ࡁ࡞
ᩘᏐࢆ୚࠼ࡿ࡜ࠊィ⟬ᶵࡢチᐜ᭱኱࣓࣮ࣔࣜࢆ㉺࠼ࡿ࠾ࡑࢀࡀ࠶ࡿࡢ࡛ࠊὀពࡀᚲせࠋ
㻙㻌㻝㻜㻥㻌㻙㻌
JAEA-Data/Code 2011-018
MINISTRI ධຊ࣐ࢽࣗ࢔ࣝ
㸦Ver.1.1㸧
඲⅔ᚰ∧ࡢࡳࡀᩚഛࡉࢀ࡚࠸ࡿࠋ
㸺JOINT ࢆ⏝࠸ࡿሙྜࡢࡳ Card 0 ࡣᚲせ㸼
Card 0-1: NSHEX (A5)
NSHEX: ไᚚᩥᏐ㸦ࡑࡢࡲࡲ"NSHEX"࡜ධຊ㸧
Card 0-2: INCORE,SLAROM (A6, 4X, A6)
INCORE: ௦⾲ⓗ࡞᩿㠃✚ PDS ࣇ࢓࢖࣓ࣝࣥࣂ࣮ྡࢆᣦᐃ
㸦PDS ࣇ࢓࢖ࣝࡢ FORMAT ᣦᐃ㸧
SLAROM: ᩿㠃✚సᡂࢥ࣮ࢻྡ㸦ࡑࡢࡲࡲ"SLAROM"࡜ධຊ㸧
Card 0-3: ITOT (I5)
ITOT: Ȋt ࡢ࢜ࣉࢩࣙࣥ
1, 2࣭࣭Ȋt=Ȋtransport
0࣭࣭࣭Ȋt=Ȋtotal
-1࣭࣭࣭Ȋt=1/3Dav
-2࣭࣭࣭Ȋt=1/3Dԋ
-3࣭࣭࣭Ȋt=1/3Dҋ
-4࣭࣭࣭Ȋt=2/3(Dҋ+Dԋ)
-5࣭࣭࣭Ȋt=1/(2Dҋ+Dԋ)
-6࣭࣭࣭Ȋt=1/(Dҋ+2Dԋ)
ͤJOINT 㛵ಀࡢධຊࡣ NSHEX ࡜ඹ㏻࡞ࡢ࡛ࠊࢥ࣮ࢻྡࡣ NSHEX ࡛Ⰻ࠸ࠋ
ͤ⮬⩌ᩓ஘᩿㠃✚ࡣࢥ࣮ࢻୖ࡛ḟᘧ࡟ࡼࡾ෌ᐃ⩏ࡉࢀࡿࠋ
6 s,g o g
6 t ,g 6 a,g ¦6
g cz g
s,g o gc
Card 1: ISTART (I12)
ISTART:
ィ⟬࢜ࣉࢩࣙࣥ
0࣭࣭࣭࣭ࣜࢫࢱ࣮ࢺ㸦ࣇ࢓࢖ࣝ#1 ࡀᚲせ㸧
1࣭࣭࣭࣭᪂つィ⟬
Card 2: NLAY, NGMX, MAPMX, NSN (4I12)
NLAY: ᚄ᪉ྥ࣓ࢵࢩࣗᩘ㸦⅔ᚰᒙᩘ㸧
NGMX: ࢚ࢿࣝࢠ࣮⩌ᩘ
MAPMX: 㡿ᇦ㸦࣐ࢸࣜ࢔ࣝ㸧ᩘ
NSN: Sn ḟᩘ㸦2㹼16 ࡢഅᩘ㸧
Card 3: IDUMP, IBR, NTMX (3I12)
IDUMP: ࢲ࣑࣮
IBR: ࢲ࣑࣮
NTMX: 㞟ྜయෆᚄ᪉ྥ࣓ࢵࢩࣗᩘ㸦6ࠊ24ࠊ54ࠊ96 ࡢ࠸ࡎࢀ࠿㸧
Card 4: KMX, KCM, IBT, IBB (4I12)
KMX: ㍈᪉ྥ඲࣓ࢵࢩࣗᩘ
KCM: ㍈᪉ྥ㡿ᇦ㸦⢒࣓ࢵࢩࣗ㸧ᩘ
IBT/IBB: ࢲ࣑࣮/ࢲ࣑࣮
Card 5: IOP1, IOP2, NODRL (3I12)
IOP1: ὶฟ୰ᛶᏊ᮰࡜㡬Ⅼ୰ᛶᏊ᮰ࡀ㈇࡜࡞ࡗࡓሙྜࡢฎ⌮㸦㏻ᖖ 2㸧
<0࣭࣭࣭࣭ฎ⌮ࢆ⾜ࢃ࡞࠸ࠋ
=0࣭࣭࣭࣭㈇࡜࡞ࡗࡓὶฟ୰ᛶᏊ᮰࠶ࡿ࠸ࡣ㡬Ⅼ୰ᛶᏊ᮰ࢆࢮࣟ࡟
ࢭࢵࢺࡍࡿࠋ
㻙㻌㻝㻝㻜㻌㻙㻌
JAEA-Data/Code 2011-018
=1࣭࣭࣭࣭㈇࡜࡞ࡗࡓὶฟ୰ᛶᏊ᮰࠶ࡿ࠸ࡣ㡬Ⅼ୰ᛶᏊ᮰ࢆࢮࣟ࡟
ࢭࢵࢺࡋ࡚ᖹᆒ୰ᛶᏊ᮰ࢆ෌ィ⟬ࡍࡿࠋ
=2࣭࣭࣭࣭㈇࡜࡞ࡗࡓὶฟ୰ᛶᏊ᮰࠶ࡿ࠸ࡣ㡬Ⅼ୰ᛶᏊ᮰ࢆࢮࣟ࡟
ࢭࢵࢺࡋ࡚ᖹᆒ୰ᛶᏊ᮰ࢆ෌ィ⟬ࡋࠊ᭦࡟ࠊ㈇࡜࡞ࡗ࡚࠸
࡞࠿ࡗࡓὶฟ୰ᛶᏊ᮰࡜㈇࡜࡞ࡗࡓ୰ᛶᏊὶฟ㠃཯ᑐഃࡢ
㡬Ⅼ୰ᛶᏊ᮰ࢆ෌ィ⟬ࡍࡿࠋ
=5࣭࣭࣭࣭Step ㏆ఝࢆ㐺⏝ࡍࡿ㸦࣓ࢵࢩࣗᖹᆒ୰ᛶᏊ᮰ࢆࢭࢵࢺ㸧ࠋ
IOP2: ෆഃ཯᚟࡟࠾ࡅࡿຍ㏿ἲࡢ㐺⏝ࡢ᭷↓㸦㏻ᖖ 0㸧
0࣭࣭࣭࣭࡞ࡋ
1࣭࣭࣭࣭࠶ࡾ㸦୰ᛶᏊ᮰እᤄἲ㸧
2࣭࣭࣭࣭࠶ࡾ㸦⢒࣓ࢵࢩࣗࣜࣂࣛࣥࢫἲ㸧
NODRL: ࢲ࣑࣮
Card 6: IOP3, IOP4, IOP5, IOP6, Integer*6 (4I12, 6I3)
IOP3: እഃ཯᚟࡟࠾ࡅࡿຍ㏿ἲࡢ㐺⏝ࡢ᭷↓㸦㏻ᖖ 1㸧
0࣭࣭࣭࣭࡞ࡋ
1࣭࣭࣭࣭࠶ࡾ㸦୰ᛶᏊ᮰እᤄἲ㸧ͤIOP2 ࢆ 2 ௨እ࡟タᐃ
2࣭࣭࣭࣭࠶ࡾ㸦⢒࣓ࢵࢩࣗࣜࣂࣛࣥࢫἲ㸧ͤIOP2 ࢆ 1 ௨እ࡟タᐃ
IOP4: እഃ཯᚟ࡢ཰᮰ุᐃ࡟⏝࠸ࡿ≀⌮㔞ࡢᣦᐃ
-1࣭࣭࣭࣭㞟ྜయᖹᆒ᰾ศ⿣୰ᛶᏊ※
0࣭࣭࣭࣭୰ᛶᏊ᮰
1࣭࣭࣭࣭᰾ศ⿣୰ᛶᏊ※
2࣭࣭࣭࣭ᣦᐃ㡿ᇦ୰ᛶᏊ᮰㸦Card 12 ࡛㡿ᇦࢆᣦᐃ㸧
IOP5: ィ⟬࣮ࣔࢻࡢᣦᐃ
0࣭࣭࣭࣭୰ᛶᏊ᮰ィ⟬
1࣭࣭࣭࣭㝶క୰ᛶᏊ᮰ィ⟬
2࣭࣭࣭࣭㝶క୰ᛶᏊ᮰ィ⟬㸦ᅛ᭷್ᅛᐃ㸧
IOP6: ࢲ࣑࣮
NSTA_OUTACC: እᤄࢆ㛤ጞࡍࡿእഃ཯᚟ᅇᩘ
MXODR_OUTACC: እᤄᑐ㇟࣮࣓ࣔࣥࢺḟᩘ
INOFF_OUTACC: 㧗ḟ࣮࣓ࣔࣥࢺ࡬ࡢእᤄ㐺⏝ࡢ೵Ṇ࢜ࣉࢩࣙࣥ
ྛ⩌ࡢ๓ᅇࡢෆഃ཯᚟ᅇᩘࡀ INOFF_OUTACC ௨ୗࡢሙྜࠊࡑࡢ⩌
࡬ࡢእᤄ㐺⏝ࢆ೵Ṇࡍࡿࠋ
IOP_RECAL_FISSEIGEN: እᤄᚋࡢ୰ᛶᏊ※ཬࡧᅛ᭷್෌ィ⟬࢜ࣉࢩࣙࣥ
0࣭࣭࣭࣭࡞ࡋ
1࣭࣭࣭࣭࠶ࡾ
IOP_CHEB1:࣭࣭࣭࣭1 ࡟タᐃ
IOP_CHEB2:࣭࣭࣭࣭1 ࡟タᐃ
Card 7: CONCR, CONCR2, CONCRI, CONCRE, FACT (4E12.5, F12.5)
CONCR: እഃ཯᚟୰ᛶᏊ᮰཰᮰᮲௳㸦㏻ᖖ 1.0E-4㸧
CONCR2: ࢲ࣑࣮
CONCRI: ෆഃ཯᚟୰ᛶᏊ᮰཰᮰᮲௳㸦㏻ᖖ CONCR ࡜ྠࡌ㸧
CONCRE: ᅛ᭷್㸦ᐇຠቑಸ⋡㸧཰᮰᮲௳㸦㏻ᖖ 1.0E-5㸧
FACT: つ᱁໬ᐃᩘ
>0࣭࣭࣭ȤȊfȭࡢ✵㛫࣭࢚ࢿࣝࢠ࣮ྜィ್࡟ࡼࡾつ᱁໬
<0࣭࣭࣭Ȋfȭࡢ✵㛫࣭࢚ࢿࣝࢠ࣮ྜィ್࡟ࡼࡾつ᱁໬
Card 8: ITINMX, ITOUTMX, TIMOUT, EIGEN (2I12, 2F12.5)
ITINMX: ᭱኱ෆഃ཯᚟ᅇᩘ
ITOUTMX: ᭱኱እഃ཯᚟ᅇᩘ
TIMOUT: ィ⟬ไ㝈᫬㛫 [ศ]
EIGEN: ᅛ᭷್㸦ᐇຠቑಸ⋡㸧ึᮇ್㸦㏻ᖖ 1.0㸧
Card 9: (IHK(KC), KC=1, KCM) (25I3)
IHK(KC): ㍈᪉ྥ㡿ᇦ KC ࡢ㍈᪉ྥ࣓ࢵࢩࣗᩘ㸦ୗ㒊࠿ࡽୖ㒊࡬ࡢ㡰㸧
㻙㻌㻝㻝㻝㻌㻙㻌
JAEA-Data/Code 2011-018
Card 10: (ZC(KC), KC=1, KCM+1) (6E12.5)
ZC(KC): ㍈᪉ྥ㡿ᇦቃ⏺ࡢᗙᶆ [cm]㸦ୗ㒊࠿ࡽୖ㒊࡬ࡢ㡰㸧
㸦㍈᪉ྥ㡿ᇦ KC ࡣ ZC(KC)ӌZӌZC(KC+1)࡟Ꮡᅾࡍࡿࡇ࡜࡟࡞ࡿ㸧
Card 11: HP (E12.5)
HP: ᚄ᪉ྥ࣓ࢵࢩࣗ㛫㝸㸦㞟ྜయ㓄ิࣆࢵࢳ㸧 [cm]
Card 12 (IMJ(MP), MP=1, MAPMX) (25I3) 㸦IOP4=2 ࡢሙྜࡢࡳධຊ㸧
IMJ(MP): 㡿ᇦ MP ࡢ཰᮰ุᐃࣇࣛࢢ
0ุ࣭࣭࣭࣭ᐃᑐ㇟
1ุ࣭࣭࣭࣭ᐃ㠀ᑐ㇟
Card 13: MAP(N, KC) (Free Format)
MAP(N, KC): 㡿ᇦ㸦࣐ࢸࣜ࢔ࣝࠊ࣐ࢵࣉ㸧␒ྕࠋ
㍈᪉ྥ㡿ᇦ㸦PLANE㸧ẖ࡟ୗ㒊࠿ࡽୖ㒊࡬ࡢ㡰࡟୚࠼ࠊࡑࢀࢆ KCM
ᅇ⧞ࡾ㏉ࡍࠋFig. A.4-1ࠊ2 ཧ↷ࠋMAPMX ࡼࡾࡶ኱ࡁ࠸್ࢆ୚࠼ࡓ
ሙྜ࡟ࡣࠊࡑࡢ㡿ᇦࡣ Black absorber ࡜ㄆ㆑ࡉࢀࡿࠋJOINT ࢆ⏝
࠸ࡿሙྜࡣ 80 ิ௨ෆ࡛ධຊࡍࡿᚲせࡀ࠶ࡿࠋ
㸺JOINT ࢆ⏝࠸࡞࠸ሙྜ㸼
Card 14: XABS(NG, NR), XFIS(NG, NR), XSGF(NG, NR), XTRA(NG, NR),
(XSCT(NG, NN, NR), NN=1, NGMX) (6E12.5)
XABS(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ྾཰᩿㠃✚Ȋa
XFIS(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ⏕ᡂ᩿㠃✚ȤȊf
XSGF(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ᰾ศ⿣᩿㠃✚Ȋf
XTRA(NG, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NG ࡢ඲᩿㠃✚Ȋt
XSCT(NG, NN, NR): 㡿ᇦ NRࠊ࢚ࢿࣝࢠ࣮⩌ NGЍNN ࡢᩓ஘᩿㠃✚
Ȋs(ngЍnn)
㸦ࡇࢀࢆ NGMX ᅇ⧞ࡾ㏉ࡋࠊ᭦࡟ MAPMX ᅇ⧞ࡾ㏉ࡍࠋ㸧
㸺JOINT ࢆ⏝࠸ࡿሙྜ㸼
Card 14-1: XS@ (A4)
XS@: ไᚚᩥᏐ㸦ࡑࡢࡲࡲ"XS@ "࡜ධຊ㸧
Card 14-2: MEMBER1, SLAROM (A6, 4X, A6)
MEMBER1: ᩿㠃✚ PDS ࣇ࢓࢖ࣝࡢ࣓ࣥࣂ࣮ྡ
SLAROM: ᩿㠃✚సᡂࢥ࣮ࢻྡ㸦ࡑࡢࡲࡲ"SLAROM"࡜ධຊ㸧
㸦Card14-2 ࢆ MAPMX ᅇ⧞ࡾ㏉ࡍࠋ㸧
ͤ⮬⩌ᩓ஘᩿㠃✚ࡣࢥ࣮ࢻෆ࡛ḟᘧ࡟ࡼࡾ෌ᐃ⩏ࡉࢀࡿࠋ
6 s,g o g
6 t ,g 6 a,g ¦6
g cz g
s,g o gc
㸺JOINT ࢆ⏝࠸࡞࠸ሙྜ㸼
Card 15: (CHI(NG), NG=1, NGMX) (6E12.5)
CHI(NG): ᰾ศ⿣ࢫ࣌ࢡࢺࣝ㸦࢚ࢿࣝࢠ࣮⩌ NG ࡬ࡢ᰾ศ⿣࡟ࡼࡿ୰ᛶᏊᨺ
ฟ๭ྜࠋࢥ࣮ࢻෆ࡛ྜィࡀ 1.0 ࡟࡞ࡿࡼ࠺࡟つ᱁໬ࡉࢀࡿࠋ㸧
㸺JOINT ࢆ⏝࠸ࡿሙྜ㸼
Card 15: MEMBER2, SLAROM (A6, 4X, A6)
MEMBER2: ィ⟬࡟⏝࠸ࡿ᰾ศ⿣ࢫ࣌ࢡࢺࣝࢆྵࡴ᩿㠃✚ PDS ࣇ࢓࢖ࣝࡢ
࣓ࣥࣂ࣮ྡ㸦᰾ศ⿣ࢫ࣌ࢡࢺࣝࡣ 1 ✀㢮ࡢࡳᣦᐃྍ⬟㸧
SLAROM: ᩿㠃✚సᡂࢥ࣮ࢻྡ㸦ࡑࡢࡲࡲ"SLAROM"࡜ධຊ㸧
㻙㻌㻝㻝㻞㻌㻙㻌
JAEA-Data/Code 2011-018
Fig. A.4-1
Fig. A.4-2
MINISTRI ࡢ࣓ࢵࢩࣗ␒ྕ
MINISTRI ࡢ࣓ࢵࢩࣗ␒ྕ࡜࣐ࢵࣉධຊ࡜ࡢᑐᛂ
㻙㻌㻝㻝㻟㻌㻙㻌
JAEA-Data/Code 2011-018
௜㘓 5 NSHEX ࡟࠾ࡅࡿᚄ᪉ྥࡶࢀྲྀࡾᢅ࠸ᡭἲࡢ㑅ᐃ
┤஺ᗙᶆ⣔ࡢࣀ࣮ࢻἲ୍࡛⯡࡟᥇⏝ࡉࢀ࡚࠸ࡿᶓ᪉ྥࡶࢀ 2 ḟከ㡯ᘧ㏆ఝ㸦ᙜヱࣀ࣮ࢻ࡜୧
㞄᥋ࡢィ 3 ࡘࡢᖹᆒᶓ᪉ྥࡶࢀ࠿ࡽᙜヱࣀ࣮ࢻࡢࡶࢀࢆ 2 ḟᘧ࡛⾲ࡍ᪉ἲ㸧ࡣࠊභゅᗙᶆయ⣔
⏝ࣀ࣮ࢻἲ࡛ࡣᶓ᪉ྥࡶࢀࡀࣀ࣮ࢻቃ⏺࡜ࣀ࣮ࢻ୰ᚰ㸦x=0㸧࡛୙㐃⥆࡟࡞ࡿࡓࡵ࡟㐺⏝୙ྍ
⬟࡛࠶ࡿࠋࡑࡢࡓࡵ࡟ࠊNSHEX ࡛ࡣᶓ᪉ྥࡶࢀࡢᐃ⩏࡟❧ࡕᡠࡾࠊᶓ᪉ྥࡶࢀࡢィ⟬࡟ᚲせ
࡞ࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰ࡢศᕸࢆࣀ࣮ࢻ㡬Ⅼࡢ୰ᛶᏊ᮰ࢆ⏝࠸࡚⾲ࡍࡇ࡜࡜ࡋ࡚࠸ࡿࠋ
௒ࠊFig. A.5-1 ୰ࡢࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰\ u ࡢ x ᪉ྥ౫Ꮡᛶ࡟ࡘ࠸࡚⪃࠼ࡿࠋ\ u xc ࢆ 2 ḟ
ከ㡯ᘧ࡛ᒎ㛤ࡍࡿ࡜ࠊḟᘧࡀᚓࡽࢀࡿࠋ
\ u xc 2
¦\
i 0
u ,i
g i xc .
(A.5-1)
ࡇࡇ࡛ࠊࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰࣮࣓ࣔࣥࢺ\ u ,i ࡣࠊFig. A.5-1 ࡟♧ࡍᙜヱࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶ
Ꮚ᮰\ u ࡜୧➃ࡢࣀ࣮ࢻ㡬Ⅼ୰ᛶᏊ᮰\ A ཬࡧ\ B ࢆ⏝࠸࡚ḟᘧ࡛⾲グ࡛ࡁࡿࠋ
\ u , 0 \ u °
®\ u ,1 2\ A \ B °\
12\ A \ B 2\ u .
¯ u ,2
(A.5-2)
ࡲࡓࠊᒎ㛤㛵ᩘ⣔ g i x ࡣḟࡢ㏻ࡾᐃ⩏ࡉࢀࡿࠋ

° g 0 x 1
°°
1
® g1 x x 4
°
° g 2 x x 2 1 x 1
°
2
24 .
¯
(A.5-3)
ࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰ࡣ㏻ᖖࡢࣀ࣮ࢻἲࣂࣛࣥࢫᘧ࠿ࡽᚓࡽࢀࡿࡀࠊࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰ࡢ⟬
ฟ࡟ࡣࠊఱࡽ࠿ࡢ㏆ఝࡀᚲせ࡛࠶ࡿࠋ⪃࠼ࡽࢀࡿࡢࡣࠊࣀ࣮ࢻ㡬Ⅼ࿘㎶ࡢࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰
ࡸࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰࠿ࡽࠊᒁᡤⓗ࡞㛵ᩘ⣔ࢆ௬ᐃࡋ࡚ෆᤄࡍࡿࡇ࡜࡛࠶ࡿࠋ௨ୗࠊ௒ᅇ᳨ウ
ᑐ㇟࡜ࡋࡓᡭἲ࡜ᡭἲ㛫ࡢゎᯒ⤖ᯝࡢẚ㍑ࢆ♧ࡋࠊ᭱㐺࡞ᚄ᪉ྥྲྀࡾᢅ࠸ᡭἲࢆᑟฟࡍࡿࡇ࡜
࡜ࡍࡿࠋ
(1) ᡭἲ A
ᑐ㇟࡜ࡍࡿࣀ࣮ࢻ㡬Ⅼ௜㏆ࡢᒁᡤⓗ࡞୰ᛶᏊ᮰ࡀ 2 ḟඖࡢ 1 ḟᘧ࡛⾲ࡍࡇ࡜ࡀྍ⬟࡛࠶ࡿ࡜
௬ᐃࡋࠊࣀ࣮ࢻ㡬Ⅼࡢ࿘㎶ࡢࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶᏊ᮰࠿ࡽ᥎ᐃࡍࡿ᪉ἲ࡛࠶ࡿࠋࡲࡎࠊḟࡢ 2
㻙㻌㻝㻝㻠㻌㻙㻌
JAEA-Data/Code 2011-018
ḟඖ 1 ḟᘧࢆ⪃࠼ࡿࠋ
\~ x, y \~00 \~10 x \~01 y .
(A.5-4)
ࣀ࣮ࢻ㡬Ⅼ୰ᛶᏊ᮰\ A ࢆྲྀࡾୖࡆࡿ࡜ࠊࡑࡢ࿘㎶ࡢࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶᏊ᮰\ u ࠊ\ x ࠊཬ
ࡧ\ v ࡣᘧ(A.5-4)ࢆ⏝࠸࡚ḟࡢࡼ࠺࡟⾲ࡉࢀࡿࠋ
§1 1 4
¨
¨1 1 2
¨¨
©1 3 4
§\ u ·
¸
¨
¨\ x ¸
¨\ ¸
© v ¹
3
0
3
4 ·§\~00 ·
¸¨
¸
¸¨\~10 ¸
.
¸
4 ¸¹¨©\~01 ¸¹
(A.5-5)
ᘧ(A.6-5)ࢆゎࡁࠊࣀ࣮ࢻ㡬Ⅼ A ࡢᗙᶆ x
1 2, y
1 2 3 ࢆ௦ධࡍࡿ࡜ࠊࣀ࣮ࢻ㡬Ⅼ୰ᛶᏊ
᮰\ A ࡀᚓࡽࢀࡿࠋࣀ࣮ࢻ㡬Ⅼ୰ᛶᏊ᮰\ B ࡟ࡘ࠸࡚ࡶྠᵝ࡟ࠊࡑࡢ࿘㎶ࡢࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶ
Ꮚ᮰\ u ࠊ \ x ࠊཬࡧ\ v ࡟ࡘ࠸࡚ᘧ(A.6-4)ࢆ⏝࠸࡚⾲グࡋࠊᚓࡽࢀࡓ⾲グᘧࢆゎ࠸࡚ࣀ࣮ࢻ
㡬Ⅼ B ࡢᗙᶆ x
0, y 1
3 ࢆ௦ධࡍࡿ࡜ࠊࣀ࣮ࢻ㡬Ⅼ୰ᛶᏊ᮰\ B ࡀᚓࡽࢀࡿࠋ⤖ᒁࠊᡭἲ
A ࢆ⏝࠸ࡓሙྜࡢࣀ࣮ࢻ㡬Ⅼ୰ᛶᏊ᮰ࡣḟᘧ࡛⾲ࡉࢀࡿࠋ

°\ A
®
°\ B
¯
\ u \ x \ v
3
\ u \ x \ v .
(A.5-6)
3
(2) ᡭἲ B
ᑐ㇟࡜ࡍࡿࣀ࣮ࢻቃ⏺௜㏆ࡢᒁᡤⓗ࡞୰ᛶᏊ᮰ࡀ 2 ḟඖࡢ 2 ḟᘧ࡛⾲ࡍࡇ࡜ࡀྍ⬟࡛࠶ࡿ࡜
௬ᐃࡋࠊࣀ࣮ࢻቃ⏺࿘㎶ࡢࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶᏊ᮰࡜ࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰࠿ࡽ᥎ᐃࡍࡿ᪉ἲ࡛
࠶ࡿࠋࡲࡎࠊḟࡢ 2 ḟඖ 2 ḟᘧࢆ⪃࠼ࡿࠋ
\~ x, y \~00 \~10 x \~ 20 x 2 \~01 y \~02 y 2 \~11 xy .
(A.5-7)
ࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰\ u x ࢆᑐ㇟࡜ࡋࡓሙྜࠊ᥎ᐃ࡟⏝࠸ࡿࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶᏊ᮰࡜ࡋ࡚
ࡣࠊ\ u ࠊ\ x ࠊ\ v ࠊ\ x ࠊཬࡧ\ v ࡟㝈ᐃࡍࡿࡇ࡜ࡀ㐺ษ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋࡋ࠿ࡋ࡞ࡀ
ࡽࠊᘧ(A.5-7)࠿ࡽ᫂ࡽ࠿࡞ࡼ࠺࡟ࠊᮍ▱ᩘࡣ 6 ಶ࠶ࡿࡢ࡛ࠊ᥎ᐃ࡟⏝࠸ࡿࣃ࣓࣮ࣛࢱࡣ 6 ಶ௨
ୖᚲせ࡛࠶ࡿࠋࡍ࡞ࢃࡕࠊ5 ಶࡢࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶᏊ᮰࠿ࡽࡔࡅ࡛ࡣ᥎ᐃࡀ୙༑ศ࡛࠶ࡾࠊ
ࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰ࡶ⏝࠸ࡿᚲせࡀ࠶ࡿࠋࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰ࡢೃ⿵࡜ࡋ࡚ࡣࠊᑐ㇟ࡢࣀ࣮ࢻ
㻙㻌㻝㻝㻡㻌㻙㻌
JAEA-Data/Code 2011-018
ቃ⏺ࢆᣳࡴࣀ࣮ࢻࡢᖹᆒ୰ᛶᏊ᮰ \ D ཬࡧ \ E ࡜ᑐ㇟ࡢࣀ࣮ࢻቃ⏺ࡢ୧➃㒊࡟఩⨨ࡍࡿࣀ࣮ࢻ
ࡢᖹᆒ୰ᛶᏊ᮰\ J ཬࡧ\ G ࡀᣲࡆࡽࢀࡿࠋᡭἲ B ࡛ࡣࠊࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰\ D ࡜\ E ࢆ⏝࠸ࡿ
ࡇ࡜࡜ࡍࡿࠋ
ࡉ࡚ࠊᘧ(A.5-7)ࢆ⏝࠸ࡿ࡜ࠊࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶᏊ᮰\ u ࠊ\ x ࠊ\ v ࠊ\ x ࠊ\ v ࠊཬࡧࠊ
ࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰\ D ࠊ\ E ࡣ௨ୗࡢ㏻ࡾ⾲グࡉࢀࡿࠋ
§\ u ·
¨
¸
¨\ v ¸
¨\ ¸
¨ x ¸
¨\ x ¸
¨\ ¸
¨ v ¸
¨\D ¸
¨¨
¸
\ E ¸¹
©
§1 1 4
1 12
¨
¨1 1 4 1 12
¨
14
¨1 1 2
¨1
0
0
¨
¨1 3 4 7 12
¨1
0
5 72
¨¨
©1 1 2 23 72
3 18 · ~
¸§\ 00 ·
3 18 ¸¨ ~ ¸
¸¨\ 10 ¸
0 ¸¨ ~ ¸
\ 20
3 2 79
0 ¸¨ ~ ¸ .
¸¨\ 01 ¸
3 4 7 36 7 3 36 ¸¨ ~ ¸
\ 02
0
5 72
0 ¸¨¨ ~ ¸¸
¸©\ 11 ¹
3 2 59 72
3 4 ¸¹
3 4
3 4
0
7 36
7 36
1 36
(A.5-8)
(A.5-8)ᘧࡣᮍ▱ᩘ 6 ಶ࡟ᑐࡋ࡚᪤▱ᩘ㸦ᘧࡢᩘ㸧ࡣ 7 ಶ࡛࠶ࡿࡢ࡛ࠊ᭱ᑠ஧஌ἲࢆ⏝࠸࡚ࠊ
ᮍ▱ᩘࢆồࡵࡿࡇ࡜࡜࡞ࡿࠋ7 ಶࡢ᪤▱ᩘ࡟ࡘ࠸࡚ྠࡌ㔜ࡳ௜ࡅ࡛᭱ᑠ஧஌ࢆྲྀࡗࡓሙྜ࡜ࠊ
ࣀ࣮ࢻቃ⏺୰ᛶᏊ᮰ࢆᅛᐃࡋ࡚ṧࡾ 6 ಶࡢࣃ࣓࣮ࣛࢱࢆྠࡌ㔜ࡳ௜ࡅ࡛᭱ᑠ஧஌ࢆྲྀࡗࡓሙྜ
ࢆྲྀࡾᢅࡗࡓࡀࠊ୧⪅ࡢ⤖ᯝࡣྠࡌ࡛࠶ࡗࡓࠋᚓࡽࢀࡓᘧ࡟ࠊࣀ࣮ࢻ㡬Ⅼ A ཬࡧ B ࡢᗙᶆࢆ௦
ධࡍࡿࡇ࡜࡟ࡼࡾࠊ⤖ᒁࠊᡭἲ B ࢆ⏝࠸ࡓሙྜࡢࣀ࣮ࢻ㡬Ⅼ୰ᛶᏊ᮰ࡣḟࡢ㏻ࡾᚓࡽࢀࡿࠋ

°°\ A
®
°\ B
°
¯
95\ u 33\ x \ v 10\ v \ x 6\ D \ E 129
.
95\ u 33\ v \ x 10\ x \ v 6\ D \ E (A.5-9)
129
(3) ᡭἲ C
ᡭἲ B ࡜ྠࡌࡃࠊᑐ㇟࡜ࡍࡿࣀ࣮ࢻቃ⏺௜㏆ࡢᒁᡤⓗ࡞୰ᛶᏊ᮰ࡀ 2 ḟඖࡢ 2 ḟᘧ࡛⾲ࡍࡇ
࡜ࡀྍ⬟࡛࠶ࡿ࡜௬ᐃࡋࠊࣀ࣮ࢻቃ⏺࿘㎶ࡢࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶᏊ᮰࡜ࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰࠿
ࡽ᥎ᐃࡍࡿ᪉ἲ࡛࠶ࡿࠋᡭἲ B ࡜ࡢ┦㐪ࡣࠊࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰\ D ࡜\ E ࡢ௦ࢃࡾ࡟ࣀ࣮ࢻᖹ
ᆒ୰ᛶᏊ᮰\ J ࡜\ G ࢆ⏝࠸ࡿⅬ࡛࠶ࡿࠋ
ᘧ(A.6-7)ࢆ⏝࠸ࡿ࡜ࠊࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶᏊ᮰ \ u ࠊ \ x ࠊ \ v ࠊ \ x ࠊ \ v ࠊཬࡧࠊࣀ࣮
ࢻᖹᆒ୰ᛶᏊ᮰\ J ࠊ\ G ࡣ௨ୗࡢ㏻ࡾ⾲グࡉࢀࡿࠋ
㻙㻌㻝㻝㻢㻌㻙㻌
JAEA-Data/Code 2011-018
§\ u ·
¨
¸
¨\ v ¸
¨\ ¸
¨ x ¸
¨\ x ¸
¨\ ¸
¨ v ¸
¨\J ¸
¨
¸
\G ¹
©
§1 1 4
1 12
¨
¨1 1 4 1 12
¨
14
¨1 1 2
¨1
0
0
¨
7 12
¨1 3 4
¨1
1
77 72
¨¨
©1 1 2 23 72
3 18 · ~
¸§\ 00 ·
3 18 ¸¨ ~ ¸
¸¨\ 10 ¸
0 ¸¨ ~ ¸
\ 20
3 2 79
0 ¸¨ ~ ¸ .
¸¨\ 01 ¸
3 4 7 36 7 3 36 ¸¨ ~ ¸
\ 02
0
5 72
0 ¸¨¨ ~ ¸¸
¸©\ 11 ¹
3 2 59 72 3 4 ¸¹
3 4
3 4
0
7 36
7 36
1 36
(A.5-10)
ᡭἲ B ࡢᑟฟ࡛♧ࡋࡓ㏻ࡾࡢᡭ㡰࡟ࡼࡾࠊᡭἲ C ࢆ⏝࠸ࡓሙྜࡢࣀ࣮ࢻ㡬Ⅼ୰ᛶᏊ᮰ࡣḟࡢ
㏻ࡾᚓࡽࢀࡿࠋ
417\ u 16\ x \ v 31\ v \ x 65\ J 29\ G

°° \ A
423
.
®
417\ u 16\ vv \ x 31\ x \ v 65\ G 29\ J
°\ B
°
423
¯
(A.5-11)
(4) ᡭἲ D
ᡭἲ BࠊC ࡜ྠࡌࡃࠊᑐ㇟࡜ࡍࡿᒁᡤⓗ࡞ࣀ࣮ࢻቃ⏺௜㏆ࡢ୰ᛶᏊ᮰ࡀ 2 ḟඖࡢ 2 ḟᘧ࡛⾲
ࡍࡇ࡜ࡀྍ⬟࡛࠶ࡿ࡜௬ᐃࡋࠊࣀ࣮ࢻቃ⏺࿘㎶ࡢࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶᏊ᮰࡜ࣀ࣮ࢻᖹᆒ୰ᛶᏊ
᮰࠿ࡽ᥎ᐃࡍࡿ᪉ἲ࡛࠶ࡿࠋᡭἲ D ࡛ࡣࠊೃ⿵࡜࡞ࡿࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰ࢆ඲࡚⏝࠸ࡿࠋ
ᘧ(A.6-7)ࢆ⏝࠸ࡿ࡜ࠊࣀ࣮ࢻቃ⏺ᖹᆒ୰ᛶᏊ᮰ \ u ࠊ \ x ࠊ \ v ࠊ \ x ࠊ \ v ࠊཬࡧࠊࣀ࣮
ࢻᖹᆒ୰ᛶᏊ᮰\ D ࠊ\ E ࠊ\ J ࠊ\ G ࡣ௨ୗࡢ㏻ࡾ⾲グࡉࢀࡿࠋ
§\ u ·
¨
¸
¨\ v ¸
¨\ ¸
¨ x ¸
¨\ x ¸
¨\ ¸
¨ v ¸
¨\D ¸
¨
¸
¨\ E ¸
¨\J ¸
¨¨
¸
\ G ¸¹
©
§1 1 4
1 12
¨
¨1 1 4 1 12
¨
14
¨1 1 2
¨1
0
0
¨
7 12
¨1 3 4
¨1
0
5 72
¨
¨1 1 2 23 72
¨1
1
77 72
¨
¨1 1 2 23 72
©
3 4
3 4
0
3 2
3 4
0
3 2
0
3 2
3 18 ·
¸
3 18 ¸ ~
¸§\ 00 ·
1 36
0 ¸¨ ~ ¸
¨\ 10 ¸
79
0 ¸¨ ~ ¸
¸ \ 20
7 36 7 3 36 ¸¨ ~ ¸
¨\ 01 ¸
5 72
0 ¸¨ ~ ¸
¸ \ 02
59 72
3 4 ¸¨¨ ~ ¸¸
©\ 11 ¹
5 72
0 ¸
¸
59 72 3 4 ¸¹
.
7 36
7 36
(A.5-12)
9 ಶ඲࡚ࡢ᪤▱ᩘ࡟ᑐࡋ࡚ྠࡌ㔜ࡳ௜ࡅ࡛᭱ᑠ஧஌ࢆྲྀࡿࡇ࡜࡟ࡼࡾࠊ6 ࡘࡢᮍ▱ᩘࢆᚓ࡚ࠊ
ࣀ࣮ࢻ㡬Ⅼ A ཬࡧ B ࡢᗙᶆࢆ௦ධࡍࡿࡇ࡜࡟ࡼࡾࠊᡭἲ D ࢆ⏝࠸ࡓሙྜࡢࣀ࣮ࢻ㡬Ⅼ୰ᛶᏊ
᮰ࡣḟࡢ㏻ࡾᚓࡽࢀࡿࠋ
㻙㻌㻝㻝㻣㻌㻙㻌
JAEA-Data/Code 2011-018
\ A ^115071\ u 73184 \ x \ v 43615 \ v \ x °
15763\ J 43375\ G 27468 \ D \ E ` 266121
°
.
®\
^
115071\ u 73184 \ v \ x 43615 \ x \ v B
°
°¯
15763\ G 43375\ J 27468 \ D \ E ` 266121
(A.5-13)
(5) ᡭἲࡢ㑅ᐃ
ࡇࡇ࡛ࡣࠊィ⟬⢭ᗘ࡜ィ⟬᫬㛫ࡢほⅬ࠿ࡽࠊ᭱㐺࡞ᚄ᪉ྥࡶࢀࡢྲྀࡾᢅ࠸ᡭἲࢆ㑅ᐃࡍࡿࠋ
ᚄ᪉ྥࡶࢀࡢྲྀࡾᢅ࠸ᡭἲ࡜ࡋ࡚ࡣࠊཧ⪃ࢣ࣮ࢫ࡜ࡋ࡚ࣀ࣮ࢻࡢṇࡢ᪉ྥ࡜㈇ࡢ᪉ྥࡑࢀࡒࢀ
୍࡛ᐃ࡜ࡋࡓሙྜ㸦Constant㸧ࠊ1 ḟከ㡯ᘧᒎ㛤࡜ࡋࡓሙྜࠊ2 ḟከ㡯ᘧᒎ㛤࡜ࡋࡓሙྜࢆ᳨ウ
ᑐ㇟࡜ࡋࡓࠋ1 ḟከ㡯ᘧᒎ㛤ࡢሙྜࡣࠊᒁᡤⓗ࡞୰ᛶᏊ᮰࡟㛵ࡋ࡚ 1 ḟ㏆ఝࢆ௬ᐃࡋࡓᡭἲ A
ࢆ㐺⏝ࡋࡓࠋ2 ḟከ㡯ᘧᒎ㛤ࡢሙྜࡣࠊᒁᡤⓗ࡞୰ᛶᏊ᮰࡟㛵ࡋ࡚ 2 ḟ㏆ఝࢆ௬ᐃࡋࡓᡭἲ Bࠊ
CࠊD ࡢ௚࡟ 1 ḟ㏆ఝࢆ௬ᐃࡋࡓᡭἲ A ࡶ㐺⏝ࡋࡓࠋ᳨ドయ⣔ࡣࠊKNK-II ⅔ᚰࠊࠕࡶࢇࡌࡹࠖ
⅔ᚰࠊSPX ⅔ᚰࡢྛไᚚᲬᤄධ≧ែ࡜ࡋࡓࠋNSHEX ࡢィ⟬᮲௳ࡣ Table 5.1-7 ࡟♧ࡍ㏻ࡾ࡛
࠶ࡿࡀࠊࣀ࣮ࢻෆ୰ᛶᏊ᮰ᒎ㛤ḟᩘࡣ 4 ࡜ࡋࡓࠋཧ↷ゎࡣ GMVP ࡟ࡼࡾᚓࡽࢀࡓ⤖ᯝ࡜ࡋࡓࠋ
᳨ウ⤖ᯝࢆ Table A.5-1㹼A.5-3 ࡟♧ࡍࠋ
ࡲࡎࠊTable A.5-1 ࡟♧ࡍ KNK-II ⅔ᚰࡢ⤖ᯝ࡟ࡘ࠸࡚ࠋᚄ᪉ྥࡶࢀࢆ୍ᐃ࡜ࡋࡓሙྜ࡟ࡣࠊ
ཧ↷ゎ࡟ᑐࡋ 0.1㸣௨ୖࡢ㐣኱ホ౯ࡀぢࡽࢀࠊไᚚᲬᤄධ๭ྜࡢቑຍ࡜ඹ࡟ࡑࡢᗘྜ࠸ࡀ኱ࡁ
ࡃぢࡽࢀࡿࡇ࡜ࡀศ࠿ࡿࠋࡑࢀ࡟ᑐࡋࠊᚄ᪉ྥࡶࢀࢆ 1 ḟࡲࡓࡣ 2 ḟࡢከ㡯ᘧᒎ㛤࡟ࡼࡾྲྀࡾ
ᢅࡗࡓሙྜ࡟ࡣࠊ኱ᖜ࡞ᨵၿࡢぢࡽࢀࡿࡇ࡜ࡀศ࠿ࡿࠋࡑࡢ୰࡛ࡶ 2 ḟከ㡯ᘧᒎ㛤ࡢᡭἲ A ࡜
ᡭἲ D ࡛ࡣཧ↷ゎ࡟ᑐࡋ࡚"Rods in"ࡢࢣ࣮ࢫ࡛ 0.1㸣๓ᚋࡢ㐣ᑠホ౯ࡀぢࡽࢀ࡚࠾ࡾࠊࡸࡸຎ
ࡿ⤖ᯝࢆ♧ࡋ࡚࠸ࡿࠋィ⟬᫬㛫࡟㛵ࡋ࡚ࡣࠊィ⟬⢭ᗘ࡛ຎࡿᚄ᪉ྥࡶࢀࢆ୍ᐃ࡟ࡋࡓሙྜࢆ㝖
ࡃ࡜ࠊ⮬᫂࡞ࡼ࠺࡟ 1 ḟከ㡯ᘧᒎ㛤ࡀ᭱ࡶ▷࠸ࡇ࡜ࡀศ࠿ࡿࠋ
ḟ࡟ࠊTable A.5-2 ࡟♧ࡍࠕࡶࢇࡌࡹࠖ⅔ᚰࡢ⤖ᯝ࡟ࡘ࠸࡚ࠋᚄ᪉ྥࡶࢀࢆ୍ᐃ࡜ࡋࡓሙྜࡣࠊ
KNK-II ⅔ᚰ࡯࡝࡛ࡣ࡞࠸ࡀࠊ"MCR in"ࡲࡓࡣ"BCR in"ࡢࢣ࣮ࢫ࡛ 0.1%࡟ࡲ࡛ཬࡪ㐣኱ホ౯
ࡀぢࡽࢀࡿࠋᚄ᪉ྥࡶࢀࢆከ㡯ᘧᒎ㛤࡛ྲྀࡾᢅࡗࡓሙྜ࡟ࡣࠊ୍ᐃ࡜ࡋࡓሙྜ࡟ᑐࡋᨵၿࡀぢ
ࡽࢀࡿࡀࠊᡭἲ㛫࡛࡯࡜ࢇ࡝ඃຎࡀぢࡽࢀ࡞࠸ࠋ࡞࠾ࠊィ⟬᫬㛫ࡢほⅬ࠿ࡽࡣ 1 ḟከ㡯ᘧᒎ㛤
࡛ᡭἲ A ࢆ᥇⏝ࡋࡓሙྜࡀ᭱ࡶඃࢀ࡚࠸ࡿࠋ
᭱ᚋ࡟ࠊTable A.5-3 ࡟♧ࡍ SPX ⅔ᚰࡢ⤖ᯝ࡟㛵ࡋ࡚ࠋᚄ᪉ྥࡶࢀࢆ୍ᐃ࡜ࡋࡓሙྜࡣࠊ
KNK-II ⅔ᚰࡸࠕࡶࢇࡌࡹࠖ⅔ᚰࡢሙྜ࡜ྠᵝ࡟ไᚚᲬࡀᤄධࡉࢀ࡚࠸ࡿ"MCR half-in"ࡸ"MCR
in"ࡢࢣ࣮ࢫ࡛ཧ↷ゎ࡟ᑐࡋ࡚኱ࡁ࡞㐣኱ホ౯ࡀぢࡽࢀ࡚࠸ࡿࠋᚄ᪉ྥࡶࢀࢆከ㡯ᘧᒎ㛤࡛ྲྀࡾ
ᢅࡗࡓሙྜ࡟ࡣࠊ≉࡟"MCR in"ࡢࢣ࣮ࢫ࡟࠾ࡅࡿ㐣ᑠホ౯ࡢᗘྜ࠸࠿ࡽࠊ1 ḟከ㡯ᘧᒎ㛤ࡢᡭ
ἲ A ࡜ 2 ḟከ㡯ᘧᒎ㛤ࡢᡭἲ C ࡀඃࢀ࡚࠾ࡾࠊィ⟬᫬㛫ࡢほⅬ࠿ࡽࡣ 1 ḟከ㡯ᘧᒎ㛤ࡢ᪉ࡀ
᭷฼࡛࠶ࡿࠋ
௨ୖࡢ᳨ウ⤖ᯝࡼࡾࠊィ⟬⢭ᗘࡢほⅬ࠿ࡽࡣࠊ1 ḟከ㡯ᘧᒎ㛤㸦ᡭἲ A㸧࡜ 2 ḟከ㡯ᘧᒎ㛤
ࡢᡭἲ C ࡀ᭱ࡶඃࢀ࡚࠸ࡿࡀࠊィ⟬᫬㛫ࡢほⅬࡶ⪃៖࡟ධࢀࡿ࡜ࠊ᭱㐺࡞ᚄ᪉ྥࡶࢀࡢྲྀࡾᢅ
࠸ᡭἲ࡜ࡋ࡚ 1 ḟከ㡯ᘧᒎ㛤ࡀ㑅ᐃࡉࢀࡿࠋ
1 ḟከ㡯ᘧᒎ㛤࡟ᑐࡋ࡚ィ⟬⢭ᗘ㠃࡛ 2 ḟከ㡯ᘧᒎ㛤࡟฼Ⅼࡀぢฟࡏ࡞࠿ࡗࡓ⌮⏤࡜ࡋ࡚ࡣࠊ
㻙㻌㻝㻝㻤㻌㻙㻌
JAEA-Data/Code 2011-018
2 ḟከ㡯ᘧᒎ㛤࡟࠾ࡅࡿࣃ࣓࣮ࣛࢱ࡜ࡋ࡚⏝࠸ࡓࣀ࣮ࢻᖹᆒ୰ᛶᏊ᮰ࡣࠊࡑࡢࣀ࣮ࢻࡀẚ㍑ⓗ
ᗈ⠊ᅖ࡟ࢃࡓࡗ࡚࠸ࡿࡢ࡛ࠊࣀ࣮ࢻቃ⏺㒊ࡢᒁᡤⓗ࡞୰ᛶᏊ᮰ศᕸࢆ᥎ᐃࡍࡿࡓࡵࡢ⢭ᗘྥୖ
࡟ࡣࡘ࡞ࡀࡽ࡞࠸ࡇ࡜ࡀᣲࡆࡽࢀࡿࠋ
㻙㻌㻝㻝㻥㻌㻙㻌
JAEA-Data/Code 2011-018
y
ȯx-
ȯț
ȯș
ȯB
ȯv+
ȯu+
ȯȘ
ȯ
ȯu+[
vȯA
ȯx+
ȯȚ
y=0
x=0
Fig. A.5-1
x=x’
x
Node parameters for calculating the node vertex fluxes
㻙㻌㻝㻞㻜㻌㻙㻌
JAEA-Data/Code 2011-018
Table A.5-1
Comparison in eigenvalue among treatments of the radial leakage for the
KNK-II core
Radial leakage
Rods half-in
Rods in
+0.123*2
+0.149*2
+0.216*2
7
[A]
+0.047
+0.037
+0.022
8
[A]
+0.044
-0.016
-0.125
9
[B]
+0.046
+0.015
-0.038
9
[C]
+0.050
+0.029
-0.003
9
[D]
+0.047
-0.006
-0.097
9
1.09527
0.98349
0.87966
±0.024*3
±0.026*3
±0.026*3
treatment [Method]
Constant
First*1
Second*1
Average time
All rods out
GMVP (Ref.)
[min]
287
*1: Polynomial expansion order of the radial leakage
*2: Relative difference to the reference [%]
*3: Statitical uncertainty (1) [%]
Table A.5-2
Comparison in eigenvalue among treatments of the radial leakage for the
Monju core
Radial leakage
treatment [Method]
Second*1
MCR
half-in
MCR in
BCR in
Average
time [min]
+0.035*2
+0.035*2
+0.099*2
+0.099*2
314
[A]
+0.016
-0.004
+0.031
+0.028
389
[A]
+0.017
-0.016
+0.004
+0.001
429
[B]
+0.016
-0.009
+0.020
+0.017
438
[C]
+0.019
-0.003
+0.032
+0.027
414
[D]
+0.017
-0.010
+0.016
+0.012
428
1.03861
0.98551
0.93493
0.95665
±0.010*3
±0.010*3
±0.010*3
±0.010*3
Constant
First*1
All rods out
GMVP (Ref.)
*1: Polynomial expansion order of the radial leakage
*2: Relative difference to the reference [%]
*3: Statitical uncertainty (1) [%]
㻙㻌㻝㻞㻝㻌㻙㻌
307
JAEA-Data/Code 2011-018
Table A.5-3
Comparison in eigenvalue among treatments of the radial leakage for the
SPX core
Radial leakage
treatment [Method]
Second*1
MCR
half-in
MCR in
BCR in
Average
time [min]
+0.014*2
+0.076*2
+0.077*2
+0.031*2
676
[A]
-0.005
+0.011
-0.050
-0.001
820
[A]
-0.007
-0.008
-0.099
-0.006
899
[B]
-0.006
+0.005
-0.069
-0.003
875
[C]
-0.004
+0.014
-0.047
+0.001
928
[D]
-0.005
+0.004
-0.071
-0.002
882
1.02256
0.97474
0.93021
1.01278
±0.005*3
±0.006*3
±0.006*3
±0.005*3
Constant
First*1
All rods out
GMVP (Ref.)
*1: Polynomial expansion order of the radial leakage
*2: Relative difference to the reference [%]
*3: Statitical uncertainty (1) [%]
㻙㻌㻝㻞㻞㻌㻙㻌
269
JAEA-Data/Code 2011-018
௜㘓 6 ゅᗘศⅬࢭࢵࢺࡢᩚ⌮
᏶඲ᑐ⛠᮲௳࡛ࡢゅᗘศⅬࢭࢵࢺࢆᩚ⌮ࡋࡓࠋᩚ⌮ࡋࡓゅᗘศⅬࢭࢵࢺࢆ Table A.6-1 ࡟♧
ࡍࠋࡇࡇ࡛♧ࡍゅᗘศⅬࢭࢵࢺࡣࠊTWOTRAN ࢥ࣮ࢻࡢࢹࣇ࢛ࣝࢺ࡛୚࠼ࡽࢀ࡚࠸ࡿࡶࡢ
㸦"Reference"㸧24)ࠊഅᩘ࣮࣓ࣔࣥࢺಖᏑ᮲௳࡟ࡼࡾᚓࡽࢀࡿࡶࡢ㸦"Even moment condition"
ࡲ ࡓ ࡣ "Even condition"㸧 23) ࠊ ࣞ ࣋ ࣝ ẖ ࣔ ࣮࣓ ࣥ ࢺ ಖ Ꮡ᮲ ௳ ࡟ ࡼ ࡾᚓ ࡽ ࢀ ࡿ ࡶࡢ 㸦 "Level
moment condition"ࡲࡓࡣ"Level condition"㸧23)࡛࠶ࡿࠋ⾲୰ࡢ࢖ࣥࢹࢵࢡࢫ㸦"Index"㸧ࡢᐃ
⩏ࡣࠊX ㍈᪉ྥవᘻȣ࡜ゅᗘศⅬ㔜ࡳ w ࡜࡛␗࡞ࡗ࡚࠾ࡾࠊFig. A.6-1 ࡟♧ࡍ㏻ࡾ࡛࠶ࡿࠋ⾲
࠿ࡽศ࠿ࡿࡼ࠺࡟ࠊ"Reference"ࡢศⅬࢭࢵࢺࡣ"Level moment condition"࡜㠀ᖖ࡟㢮ఝࡋ࡚࠸
ࡿࡇ࡜ࡀศ࠿ࡿࠋ
࡞࠾ࠊ3 ḟඖ┤஺ᗙᶆయ⣔࡟࠾ࡅࡿ࢜ࢡࢱࣥࢺᩘࡣ 8 ࡛࠶ࡿࡀࠊ3 ḟඖභゅయ⣔࡛ࡣ࢜ࢡࢱ
ࣥࢺᩘࡣ 12 ࡜࡞ࡿࠋᚑࡗ࡚ࠊࡑࢀ࡟ᛂࡌ࡚ゅᗘศⅬࢭࢵࢺࢆභゅయ⣔⏝࡟ኚ᥮ࡍࡿᚲせࡀ࠶
ࡿࡀࠊࡑࡢኚ᥮ࡣྛࢥ࣮ࢻෆ࡛⾜ࢃࢀࡿࠋ
㻙㻌㻝㻞㻟㻌㻙㻌
JAEA-Data/Code 2011-018
w
w
6
1
2
5
1
1
4
(S2 )
3
3
3
2
2
1
1
1
1
2
1
2
4
5
4
2
5
5
3
1
3
3
4
3
2
2
1
(S12 )
(S4 )
7
3
6
1
2
2
1
1
1
5
2
2
2
3
4
1
4
3
(S6 )
3
2
4
1
1
3
2
2
2
1
1
2
1
2
5
3
2
1
2
1
2
2
3
5
4
4
3
2
2
2
4
3
3
3
4
4
1
1
5
3
2
2
1
2
1
2
5
6
7
6
5
3
6
8
8
6
3
2
7
8
7
4
4
4
6
6
4
3
5
3
(S16 )
(S10 )
Fig. A.6-1
6
3
1
7
2
4
6
4
8
1
1
3
6
4
2
2
2
6
7
3
6
4
3
(S14 )
(S8 )
5
6
2
3
5
6
2
2
Definition of indices for the angular quadrature sets
㻙㻌㻝㻞㻠㻌㻙㻌
2
2
1
JAEA-Data/Code 2011-018
Table A.6-1
Comparison of angular quadrature sets for the discrete ordinates method
Reference
Angular
quadrature set
S2
S4
S6
S8
S10
S12
S14
,QGH[
Even moment condition
Level moment condition
w
w
w
1
0.57735027
1.00000000
0.57735027
1.00000000
0.57735027
1.00000000
1
0.30163878
0.33333333
0.35002117
0.33333333
0.29879685
0.33333333
2
0.90444905
-
0.86889030
-
0.90633376
-
1
0.23009194
0.16944656
0.26663540
0.17612613
0.22702927
0.17005970
2
0.68813432
0.16388677
0.68150773
0.15720720
0.68864276
0.16327363
3
0.94557676
-
0.92618094
-
0.94705619
-
1
0.19232747
0.11678847
0.21821789
0.12098765
0.19033876
0.11716461
2
0.57735027
0.09325523
0.57735027
0.09074074
0.57735027
0.09317489
3
0.79352178
0.09010320
0.78679579
0.09259259
0.79400115
0.08945683
4
0.96229948
-
0.95118973
-
0.96308998
-
1
0.16962228
0.08984204
0.18932133
0.08930315
0.16712436
0.08941160
2
0.50714192
0.06728871
0.50888176
0.07252915
0.50693455
0.06731572
3
0.69686020
0.05578007
0.69431889
0.04504377
0.69716191
0.05575763
4
0.84500612
0.05313381
0.83975996
0.05392811
0.84562806
0.05353267
5
0.97080202
-
0.96349098
-
0.97166810
-
1
0.15395746
0.07332178
0.16721265
0.07076259
0.15074906
0.07228677
2
0.45769112
0.05266740
0.45954763
0.05588110
0.45726372
0.05279200
3
0.62869660
0.04161495
0.62801910
0.03733767
0.62885208
0.04139769
4
0.76225828
0.03895667
0.76002101
0.05028190
0.76277112
0.03974576
5
0.87568027
0.03249018
0.87227054
0.02585129
0.87646141
0.03292142
6
0.97600932
-
0.97163772
-
0.97701046
-
1
0.14238965
0.06217163
0.15198586
0.05799704
0.13840299
0.06065293
2
0.42048076
0.04332570
0.42215698
0.04890080
0.41981467
0.04354652
3
0.57735027
0.03321761
0.57735027
0.02354750
0.57735027
0.03283231
4
0.69990185
0.03183706
0.69889209
0.03790526
0.70030158
0.03155849
5
0.80398498
0.03048632
0.80222626
0.03659115
0.80468086
0.03152217
6
0.89605866
0.02454512
0.89369110
0.02734734
0.89699512
0.02509682
7
0.97951538
0.01998445
0.97662715
0.00374577
0.98065755
0.01994529
1
0.13344572
0.05415425
0.13895688
0.04898724
0.12866550
0.05222585
2
0.39119433
0.03679653
0.39228926
0.04132960
0.39027815
0.03713534
3
0.53689687
0.02777273
0.53709656
0.02123263
0.53673015
0.02721805
4
0.65075610
0.02580284
0.65042645
0.02562065
0.65103109
0.02544962
5
0.74746822
0.02494275
0.74675057
0.03604859
0.74806665
0.02613194
6
0.83302700
0.01962325
0.83199656
0.01445893
0.83388604
0.02023875
7
0.91058181
0.01879762
0.90928550
0.03449579
0.91166230
0.01950839
8
0.98203079
0.01544801
0.98050088
0.00851811
0.98330584
0.01538363
S16
㻙㻌㻝㻞㻡㻌㻙㻌
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国際単位系（SI）
表１．SI 基本単位
SI 基本単位
基本量
名称
記号
長
さメートル m
質
量キログラム kg
時
間
秒
s
電
流アンペア A
熱力学温度ケルビン K
物質量モ
ル mol
光
度カンデラ cd
面
体
速
加
波
密
面
表２．基本単位を用いて表されるSI組立単位の例
SI 基本単位
組立量
名称
記号
積平方メートル
m2
積立法メートル
m3
さ，速度メートル毎秒
m/s
速
度メートル毎秒毎秒
m/s2
数毎メートル
m-1
度，質量密度キログラム毎立方メートル
kg/m3
積
密
度キログラム毎平方メートル
kg/m2
比
体
電
流
密
磁界の強
(a)
量濃度
，濃
質
量
濃
輝
屈
折
率
比透磁率
積立方メートル毎キログラム
度アンペア毎平方メートル
さアンペア毎メートル
度モル毎立方メートル
度キログラム毎立法メートル
度カンデラ毎平方メートル
(b)
（数字の）　１
(b)
（数字の）　１
乗数　24
10
1021
1018
1015
1012
109
106
103
3
m /kg
A/m2
A/m
mol/m3
kg/m3
cd/m2
1
1
102
101
ゼ
タ
エクサ
Ｚ
Ｅ
10-2
ペ
テ
タ
ラ
Ｐ
Ｔ
ギ
メ
ガ
ガ
Ｇ
Ｍ
マイクロ
ノ
10-9 ナ
コ
10-12 ピ
10-15 フェムト
キ
ロ
ヘクト
デ
カ
ｋ
ｈ
da
d
°
’
日
度
分
10-3
10-6
記号
センチ
ミ
リ
ト
10-18 ア
10-21 ゼプト
10-24 ヨクト
d
c
m
µ
n
p
f
a
z
y
1 d=24 h=86 400 s
1°=(π/180) rad
1’=(1/60)°=(π/10800) rad
”
1”=(1/60)’=(π/648000) rad
ha 1ha=1hm2=104m2
L，l 1L=11=1dm3=103cm3=10-3m3
t
1t=103 kg
秒
ヘクタール
リットル
SI基本単位による
表し方
m/m
2/ 2
m m
s-1
m kg s-2
m-1 kg s-2
m2 kg s-2
m2 kg s-3
sA
m2 kg s-3 A-1
m-2 kg-1 s4 A2
m2 kg s-3 A-2
m-2 kg-1 s3 A2
m2 kg s-2 A-1
kg s-2 A-1
m2 kg s-2 A-2
K
cd
m-2 cd
s-1
トン
表７．SIに属さないが、SIと併用される単位で、SI単位で
表される数値が実験的に得られるもの
名称
記号
SI 単位で表される数値
電子ボルト
ダルトン
統一原子質量単位
eV
Da
u
天
ua
文
単
位
1eV=1.602 176 53(14)×10-19J
1Da=1.660 538 86(28)×10-27kg
1u=1 Da
1ua=1.495 978 706 91(6)×1011m
表８．SIに属さないが、SIと併用されるその他の単位
名称
記号
SI 単位で表される数値
バ
ー
ル bar １bar=0.1MPa=100kPa=105Pa
水銀柱ミリメートル mmHg 1mmHg=133.322Pa
m2 s-2
m2 s-2
s-1 mol
(a)SI接頭語は固有の名称と記号を持つ組立単位と組み合わせても使用できる。しかし接頭語を付した単位はもはや
コヒーレントではない。
(b)ラジアンとステラジアンは数字の１に対する単位の特別な名称で、量についての情報をつたえるために使われる。
実際には、使用する時には記号rad及びsrが用いられるが、習慣として組立単位としての記号である数字の１は明
示されない。
(c)測光学ではステラジアンという名称と記号srを単位の表し方の中に、そのまま維持している。
(d)ヘルツは周期現象についてのみ、ベクレルは放射性核種の統計的過程についてのみ使用される。
(e)セルシウス度はケルビンの特別な名称で、セルシウス温度を表すために使用される。セルシウス度とケルビンの
単位の大きさは同一である。したがって、温度差や温度間隔を表す数値はどちらの単位で表しても同じである。
(f)放射性核種の放射能（activity referred to a radionuclide）は、しばしば誤った用語で”radioactivity”と記される。
(g)単位シーベルト（PV,2002,70,205）についてはCIPM勧告2（CI-2002）を参照。
表４．単位の中に固有の名称と記号を含むSI組立単位の例
SI 組立単位
組立量
SI 基本単位による
名称
記号
表し方
-1
粘
度パスカル秒
Pa s
m kg s-1
力のモーメントニュートンメートル
Nm
m2 kg s-2
表
面
張
力ニュートン毎メートル
N/m
kg s-2
角
速
度ラジアン毎秒
rad/s
m m-1 s-1=s-1
角
加
速
度ラジアン毎秒毎秒
rad/s2
m m-1 s-2=s-2
熱流密度 , 放射照度ワット毎平方メートル
W/m2
kg s-3
熱容量 , エントロピージュール毎ケルビン
J/K
m2 kg s-2 K-1
比熱容量，比エントロピージュール毎キログラム毎ケルビン J/(kg K)
m2 s-2 K-1
比エネル
ギージュール毎キログラム
J/kg
m2 s-2
熱
伝
導
率ワット毎メートル毎ケルビン W/(m K) m kg s-3 K-1
体積エネルギージュール毎立方メートル J/m3
m-1 kg s-2
電
界
の
強
さボルト毎メートル
V/m
m kg s-3 A-1
電
荷
密
度クーロン毎立方メートル C/m3
m-3 sA
表
面
電
荷クーロン毎平方メートル C/m2
m-2 sA
電束密度，電気変位クーロン毎平方メートル C/m2
m-2 sA
誘
電
率ファラド毎メートル
F/m
m-3 kg-1 s4 A2
透
磁
率ヘンリー毎メートル
H/m
m kg s-2 A-2
モルエネルギージュール毎モル
J/mol
m2 kg s-2 mol-1
モルエントロピー, モル熱容量ジュール毎モル毎ケルビン J/(mol K) m2 kg s-2 K-1 mol-1
照射線量（Ｘ線及び γ 線）クーロン毎キログラム
C/kg
kg-1 sA
吸
収
線
量
率グレイ毎秒
Gy/s
m2 s-3
放
射
強
度ワット毎ステラジアン
W/sr
m4 m-2 kg s-3=m2 kg s-3
放
射
輝
度ワット毎平方メートル毎ステラジアン W/(m2 sr) m2 m-2 kg s-3=kg s-3
酵素活性
濃度カタール毎立方メートル kat/m3
m-3 s-1 mol
表５．SI 接頭語
記号乗数　接頭語
Ｙ
シ
10-1 デ
表６．SIに属さないが、SIと併用される単位
名称
記号
SI 単位による値
分
min 1 min=60s
時
h 1h =60 min=3600 s
（a）量濃度（amount concentration）は臨床化学の分野では物質濃度
（substance concentration）ともよばれる。
（b）これらは無次元量あるいは次元１をもつ量であるが、そのこと
を表す単位記号である数字の１は通常は表記しない。
表３．固有の名称と記号で表されるSI組立単位
SI 組立単位
組立量
他のSI単位による
名称
記号
表し方
（ｂ）
平
面
角ラジアン(ｂ)
rad
1
（ｂ）
(ｂ)
(c)
立
体
角ステラジアン
sr
1
周
波
数ヘルツ（ｄ）
Hz
力
ニュートン
N
圧
力
応
力パスカル
,
Pa
N/m2
エネルギー , 仕事 , 熱量ジュール
J
Nm
仕事率，工率，放射束ワット
W
J/s
電
荷
電
気
量クーロン
,
C
電位差（電圧） , 起電力ボルト
V
W/A
静
電
容
量ファラド
F
C/V
電
気
抵
抗オーム
Ω
V/A
コンダクタンスジーメンス
S
A/V
磁
束ウエーバ
Wb
Vs
磁
束
密
度テスラ
T
Wb/m2
インダクタンスヘンリー
H
Wb/A
セルシウス温度セルシウス度(ｅ)
℃
光
束ルーメン
lm
cd sr(c)
照
度ルクス
lx
lm/m2
Bq
放射性核種の放射能（ｆ）ベクレル（ｄ）
吸収線量, 比エネルギー分与,
グレイ
Gy
J/kg
カーマ
線量当量, 周辺線量当量, 方向
Sv
J/kg
シーベルト（ｇ）
性線量当量, 個人線量当量
酸
素
活
性カタール
kat
接頭語
ヨ
タ
オングストローム
海
里
バ
ー
ン
Å
Ｍ
１Å=0.1nm=100pm=10-10m
１M=1852m
b
ノ
ネ
ベ
ト
パ
ル
kn
Np
Ｂ
１b=100fm2=(10-12cm)2=10-28m2
１kn=(1852/3600)m/s
ル
dB
ッ
ー
デ
ジ
ベ
SI単位との数値的な関係は、
対数量の定義に依存。
表９．固有の名称をもつCGS組立単位
名称
記号
SI 単位で表される数値
ル
グ erg 1 erg=10-7 J
エ
ダ
ポ
イ
ア
ス
ス
トーク
チ
ル
フ
ガ
ォ
ン dyn 1 dyn=10-5N
ズ P 1 P=1 dyn s cm-2=0.1Pa s
ス St 1 St =1cm2 s-1=10-4m2 s-1
ブ sb 1 sb =1cd cm-2=104cd m-2
ト ph 1 ph=1cd sr cm-2 104lx
ル Gal 1 Gal =1cm s-2=10-2ms-2
マクスウｪル
ガ
ウ
ス
エルステッド（ｃ）
Mx
G
Oe
1 Mx = 1G cm2=10-8Wb
1 G =1Mx cm-2 =10-4T
1 Oe　(103/4π)A m-1
（c）３元系のCGS単位系とSIでは直接比較できないため、等号「　」
は対応関係を示すものである。
キ
レ
ラ
名称
ュ
リ
ン
レ
ガ
ト
表10．SIに属さないその他の単位の例
記号
SI 単位で表される数値
ー Ci 1 Ci=3.7×1010Bq
ゲ
ン
ン R
ド rad
ム rem
マ γ
準
大
気
1 rad=1cGy=10-2Gy
1 rem=1 cSv=10-2Sv
1γ=1 nT=10-9T
1フェルミ=1 fm=10-15m
フ
ェ
ル
ミ
メートル系カラット
ト
標
1 R = 2.58×10-4C/kg
1メートル系カラット = 200 mg = 2×10-4kg
ル Torr 1 Torr = (101 325/760) Pa
圧 atm 1 atm = 101 325 Pa
カ
ロ
リ
ー
cal
ミ
ク
ロ
ン
µ
1cal=4.1858J（｢15℃｣カロリー），4.1868J
（｢IT｣カロリー）4.184J（｢熱化学｣カロリー）
1 µ =1µm=10-6m
（第8版，2006年改訂）
この印刷物は再生紙を使用しています