1. Korea Atomic Energy Research Institute
‘2015 원자력안전해석 심포지엄, ‘ , 대천
3차원 중성자수송해석 기반 핵설계 체계
CHO Jin-young
Korea Atomic Energy Research Institute

2. Conventional Nuclear Design Code System
ENDF
Multi-group Library
Few-group Library
Transport Cal.
Diffusion Cal.
Φ(x,y,z), k
Lattice Code
Editing Program
3-D Nodal Code
Library Generation

3. New Nuclear Design System

4. Introduction Procedure of Nuclear Design System
Highly Depend on the Capability of Lattice Code
The Conventional System uses 2-D Lattice Code with Ideal Boundary Condition
Recently Sugimura Proposed Hybrid core calculation system using CASMO-4 2-D whole core transport capability, which reflects realistic radial interface effects.
N. SUGIMURA et al., “Development of Hybrid Core Calculation System using Two-Dimensional Full-Core Heterogeneous Transport Calculation and Three-Dimensional Advanced Nodal Calculation,” J. of Nuc. Sci. and Tech., 43, No. 7, p (2006).
KAERI Proposed DeCART/CHORUS/MASTER Code System using DeCART 3-D Whole Core Calculation
Jin Young Cho, Jae Seung Song, and Kyung Hoon Lee, “Three Dimensional Nuclear Analysis System DeCART/CHORUS/MASTER,” ANS 2013 Annual Meeting, June 16-20, 2013
Jin Young Cho, “3-D Whole-Core Transport based Nuclear Analysis System, DeCART/CHORUS/MASTER,” 2013 KNS 추계 원자로물리 및 계산과학 연구현홍 워크숍, 10.23, 2013

5. Introduction DeCART/CHORUS/MASTER
Uses the 3-D whole core transport calculation capability of the DeCART code.
Though 3-D whole core transport calculation is possible, all the design calculation of more than ten thousand for safety related data generation can not be performed by the DeCART code.
DeCART has a role to produce the nodewise equivalent constants for MASTER nodal code by 3-D transport calculation.
CHORUS: Editing Program to generate MASTER Library
MASTER: 3-D Nodal Code
Reduce the design uncertainties to the DeCART Uncertainty Level
Applied to YGN3 Cycle 1 BOC and EOC, and Hexagonal Benchmark problems

6. DeCART Code Adaptation of KARMA Library Format
Sub-Pin Level Planar MOC Transport Calculation
Cell or Assembly based Modular Ray Tracing
Resonance Treatment based on Subgroup or RIT Method for Whole Core
Depletion Calculation based on Krylov Subspace Method
Up to P3 Anisotropic Calculation
Double Heterogeneity Treatment by Sanchez Method
Pin Based Axial SP3 Transport Calculation with Subplane Scheme
CMFD Acceleration for Irregular Mesh
Gamma Diffusion Calculation
MPI and OpenMP based Parallel Computation
Transient Calculation (need more verification)
Thermal Feedback (Simplified T-H or Coupling with CORONA or KARMA)
Reload Core Calculation
Lattice Code Capability: B1 Criticality Calculation, HGC File Generation

7. CHORUS Cross section HOmogenization and Re-Union System
Program to Provide a Few Group Constant Library for the Coarse Mesh Core Calculation from the Data Generated by the DeCART Code
Cross Section Functionalization
Calculation Order for CHORUS
Order
Description
PPM Tf
Tm,Dm Xe
Restart (HFP, Eq. Xe)
CBC
Reference
Feedback
Eq. 1
Base
Constant
Freeze 2
PPM Variation
ppm1 3
Tf Variation
-100 ˚C 4
Dm Variation 1
Constant1 5
Dm Variation 2
Constant2

8. MASTERv4.0 Code References for SENM and TPEN
New Writing Version of MASTER
Maintains Most of all Capabilities of MASTER Original
Module Based Derived Type Variables
Nodal Method: SENM for Rectangular Core and TPEN method for Hexagonal Core
Depletion Based on Krylov Subspace Method
CMFD Acceleration
Treatment of Mixed Types of Fuel Assembly, ex) 16x16 and 12x12
References for SENM and TPEN
J.I.Yoon and H.G.Joo, “Two-Level Coarse Mesh Finite Difference Formulation with Multigroup Source Expansion Nodal Kernel,” J. of Nuc. Sic. And Tech., 45, No (2008)
J. Y. Cho et al., “Hexagonal CMFD Formulation Employing Triangle-Based Polynomial Expansion Nodal Kernel,” M&C 2001, Salt Lake City, Utah, USA

9. Procedure of New Nuclear Design System
Depletion
DeCART
BOC
MOC
EOC
Variation
DeCART
PPM, Temperature Variation Calculations
XS Edit
Few Group MASTER XS for each Burnup
Core Analysis
MASTER
3-Dimenstional Nodal Diffusion Analyses

10. Equivalent Constants for MASTER Code
Equivalent Group Constant: Homogenized Group Constants and Surface Flux Discontinuity Factor(SDF)
Homogenized Group Constant can be Calculated by the DeCART Solution
SDF requires Homogeneous Surface Flux
which is not a DeCART Solution
Implementation of One-Node SENM and TPEN Kernel to DeCART

11. Equivalent Constants for MASTER Code
Given Condition for One-Node SENM
Node Average Flux and Eigenvalue
Homogeneous Group Constants
Surface Flux and Net Currents
Transverse Leakage
Given Conditions for TPEN
Transverse Leakage for Axial NEM
Node m
Node m-1
Node m+1
Eigenvalue

12. Homogeneous SENM Solver in DeCART
Procedure
Assume Homogeneous Surface Flux by Heterogeneous Ones, and Set Moments to Zero
Solve One-Node SENM Equation: Update Surface Flux and Moments
Convergence Check by Surface Flux and go to Step 2) if not Converged
Solve 1) ~ 3) for all Nodes

13. Overview of the TPEN Method
TPEN: Triangle-Based Polynomial Expansion Nodal Method
Two Transverse-Integrated Equations
2D Radial Equation and 1D Axial Equation within Hex-Octahedron
Coupled through Transverse-Leakages
Radial Equation Solved by HOPEN Employing Triangular Nodes (6/Hexagon)
Axial Solution by NEM (1 per Hex-Octahedron)
Axial Transverse-Leakage Shape
Axial Transverse Leakage by Interpolating 7 Hexagon Average Axial Leakages
Corner Point Flux Evaluation
13 Term Polynomial (6 Surface Fluxes, 6 Corner Fluxes, 1 Average Flux)
Corner Leakage Balance  Linear System for Corners (Gauss-Seidel)
HOPEN
NEM

14. Homogeneous TPEN Solver in DeCART
Procedure for Radial Calculation
Assume Homogeneous Surface Flux and Corner Flux by Heterogeneous Ones, and the Triangular Flux by Hexagonal Average Flux, and Set Moments to Zero
Approximate CDF by Neighboring SDFs
Solve CPB Equation: Update Corner Flux
Solve One-Node TPEN Equation: Update Surface Flux, Triangular Flux and Moments
Convergence Check by Surface Flux and go to Step 2) if not Converged
Procedure for Axial Calculation
Assume Homogeneous Surface Flux by Heterogeneous Ones, and Set Moments to Zero
Solve One-Node NEM Equation: Update Surface Flux and Moments
Convergence Check by Surface Flux and go to Step 2) if not Converged
Solve 1) ~ 3) for all Nodess

15. SDF Treatment in MASTER
Features of MASTER
Stores Heterogeneous Partial Currents at Node Surfaces
Solves One-Node Problem using Homogenous Incoming Partial Current
Applies ADF to Generate the Boundary Incoming Partial Currents for Homogeneous Node
Two Surface Conditions for Homogeneous and Heterogeneous Partial Currents
Surface Flux Discontinuity Condition
Net Current Continuity Condition
Incoming Homogeneous Partial Current
Outgoing Partial Current for Heterogeneous Node

16. Examination for Rectangular Core
YGN3 (Yong Gwang Unit 3) Cycle 1 BOC and EOC
2-D Fixed Temperature Problem
3-D HFP Problem at BOC
3-D HFP Problem at EOC
DeCART Calculation Model
1/8 Symmetric Core
Explicit Shroud Modeling
Barrel is Replaced by Coolant
Explicit Axial Position Model for Spacer Grid
Assemblywise Enthalpy Calculation and Pin-wise Fuel Temperature Calculation using C-E Correlation

17. Examination
DeCART 2D Radial Model

18. 2-D Fixed Temperature Problem
0.8962
0.8960
-0.02
1.1051
1.1048
-0.03
1.2791
1.2788
0.9002
0.9000
1.2311
1.2310
-0.01
1.0566
1.0567
0.01
1.1785
1.1788
0.03
0.9549
0.9554
0.05
1.3384
1.3380
0.9160
0.9158
1.3341
1.3339
0.8741
0.00
1.2112
1.2113
1.1369
1.1372
0.8111
0.8115
1.2363
1.2360
0.8467
0.8466
1.1887
1.1886
0.8449
1.0857
1.0859
0.02
0.5427
0.5429
0.04
1.1652
1.1651
0.8272
1.2137
0.9737
0.9738 k
1.1278
1.1277
1.0461
0.5484
DeCART
MASTER
Diff.(%)
0.0005
0.6501

19. Assembly Power Error at 3-D HFP BOC
0.8568
0.8582
0.16
1.0493
1.0506
0.12
1.2152
1.2165
0.11
0.8755
0.8761
0.07
1.1983
1.1986
0.03
1.0497
1.0491
-0.06
1.1873
1.1861
-0.10
0.991
0.00
1.2628
1.2642
0.8837
0.8845
0.09
1.2802
1.2812
0.08
0.8646
0.8647
0.01
1.2007
1.2001
-0.05
1.1513
1.15
-0.11
0.8501
1.1875
1.1886
0.8338
0.8342
0.05
1.1717
1.1719
0.02
0.857
0.8565
1.1112
1.1104
-0.07
0.5765
0.5768
1.1475
1.1479
0.8364
0.8361
-0.04
1.2276
1.2266
-0.08
1.0093
1.009
-0.03 k
1.1429
1.1421
1.0811
1.0803
0.5847
0.5848
DeCART
MASTER
% Diff.
-0.010
0.6895
0.6898
0.04

20. Assembly Power Error at 3-D HFP EOC
0.9438
1.0849
1.1325
0.9556
1.1341
1.0958
1.1323
0.8525
0.9404
1.0815
1.1298
0.9532
1.1327
1.0953
1.1336
0.8562
-0.36
-0.31
-0.24
-0.25
-0.12
-0.05
0.11
0.43
1.1335
0.9547
1.2517
0.9536
1.1275
1.1077
0.7658
1.1305
0.9519
1.2499
0.9520
1.1272
1.1085
0.7687
-0.26
-0.29
-0.14
-0.17
-0.03
0.07
0.38
1.1962
0.9615
1.1894
0.9309
1.0693
0.5705
1.1941
0.9594
1.1886
0.9303
1.0705
0.5733
-0.18
-0.22
-0.07
-0.06
0.49
1.1964
0.9549
1.1884
0.9163
1.1953
0.9540
1.1892
0.9191
-0.09
0.31
1.1684
1.0845
0.5894
1.1688
1.0860
0.5921 k
0.03
0.14
0.46
DeCART
0.6997
MASTER
0.7028
% Diff.
0.044
0.44

21. Axial Power Distribution at 3-D HFP

22. YGN-3 Control Rod ConfigurationP B R1 R3 R2 A
Control Rod XS Treatment

23. Rod Impact on XS – Conventional
Absorption XS %Diff. (ARI)
-0.86
-1.04
-1.75
-1.08
-1.22
-1.96
-0.37
0.04
-0.03
-0.81
-0.41
-0.09
-0.38
-0.08
-1.17
-1.23
-2.74
-0.01
0.00
-2.18
-1.70
-1.79
-0.52
-0.63
-0.27
-0.26
-1.54
2.02
-0.94
0.28
-1.13
-1.82
-0.36
-0.21
-0.07
-1.21
-1.63
1.84
-1.31
0.26
Fast
-2.70
Thermal
-0.54

24. Bank Worth Comparison - Conventional
DeCART
ΔΣ by Procedure
Worth (pcm)
Diff(%)
MASTER
Δρ (PCM)
ARO
0.3 R5
1.1
431
430
-0.20
R54
2.1
942
940
-0.19
R543
5.0
1504
1499
-0.31
R5432
9.5
2019
2010
-0.46
R54321
30.8
3721
3690
-0.82
ARI
862.2
17537
16675
-4.92

25. Pseudo Control Rod XS XS Functionalization
and are Functionalized for the All assemblies
Introduce Bank Insertion Indicator
12 Finger R1 for
Shutdown Bank (SB) for
If Bank Insertion Indicator for 12 Finger R1 is Detected, Pseudo Control Rod XS is Added for Unrodded Nodes.
If Bank Insertion Indicator of SB is Detected, Pseudo Control Rod XS is Added to Unrodded and R Bank Inserted Nodes.

26. Power Distribution Comparison w/ Pseudo XS
R54321-in Case
0.197
0.347
0.954
0.920
0.960
0.986
0.702
0.589
0.346
0.953
0.919
0.704
0.591
-0.2
-0.1
0.0
0.1
0.2
0.4
0.487
0.676
1.508
1.022
1.294
0.916
0.416
0.486
0.675
1.023
1.295
0.918
0.419
0.6
1.331
1.137
1.618
1.035
0.825
0.414
0.826
1.643
1.132
1.611
1.195
1.644
1.612
1.194
1.084
1.281
0.741
1.085
1.282
0.740
Worth (pcm)
DeCART
3721
0.559
MASTER
3720
0.562
%Diff.
-0.02

27. Power Distribution Comparison w/ Pseudo XS
ARI Case
0.234
0.345
0.620
0.335
0.577
0.869
1.823
2.694
0.233
0.344
0.618
0.334
0.578
0.873
1.835
2.714
-0.5
-0.4
-0.3
-0.1
0.2
0.4
0.7
0.422
0.336
0.511
0.414
0.973
1.904
1.665
0.421
0.510
0.415
0.977
1.915
1.683
-0.2
0.1
0.6
1.1
0.649
0.354
0.637
0.687
1.518
1.355
0.647
0.353
0.688
1.524
1.361
0.0
0.544
1.222
1.603
1.221
1.605
1.101
1.614
1.248
1.100
1.610
1.239
Worth (pcm)
-0.6
DeCART
17537
1.014
MASTER
17531
1.016
%Diff.
-0.03

28. Bank Worth Comparison w/ Pseudo XS
DeCART
ΔΣ by Procedure
Worth (pcm)
Diff(%)
DeCART2D
/MASTER
MASTER
Δρ (PCM)
ARO
0.3 R5
1.1
431
430
-0.20
461
7.00
R54
2.1
942
940
-0.19
1007
6.94
R543
5.0
1504
1499
-0.31
1579
5.01
R5432
9.5
2019
2010
-0.46
2090
3.52
R54321
1.0
3721
3720
-0.02
3886
4.44
ARI
6.0
17537
17531
-0.03

29. Examination for Hexagonal Core
Use Assembly Configuration and XSEC of C5G7 Hexagonal Variation Problem 1
11.9 cm 5 6 4 5 6 3 2 7
Uranium FA (UA-1)
MOX FA (MA)
Reflector (RA)
UA-2: UA-1 with Control Rod Inserted

30. Examination of Equivalent Group Constants
4 Problems
MA RA
UA-1
UA RA
RA RA RA
UA-1 RA
7 Asy Problem(7AP)
19 Asy Problem(19AP)
MA MA RA
UA UA-1
UA UA RA
MA MA MA
UA UA RA
UA UA RA
RA MA RA
RA RA RA
MA MA
UA RA
UA UA-2
MA MA RA
UA RA
RA RA RA
37 Asy Problem(37AP)
61 Asy Problem(61AP)

31. CDF Treatment As MASTER
CDF Treatment in MASTER
Does Not Support CDF Explicitly
Assume CDF by Neighbor SDF’s:
Solves CPB Equation for All the Corner Point Flux
Merit
Require Neither Corner Leakage and Heterogeneous Corner Flux

32. CDF Treatment As MASTER
Problem
DeCART, k
MASTER, pcm
7AP
+26
19AP +4
37AP +1
61AP +0
1.543
1.542
1.106
0.713
0.00
19AP
0.426
0.02
1.701
0.733
0.03
DeCART2D
MASTER
Error(%)
37AP
61AP

33. Conclusion
The Nodewise Equivalent Group Constants are Generated using DeCART 3-D Whole Core Transport Calculation
ADF is Generated using SENM Formulation for Rectangular Core and TPEN for Hexagonal Core, which are the Same Solution Method of MASTER
The Equivalence Theory is Applied to YGN3 Cycle 1 Core Problems and Hexagonal Benchmark Problems.
The Generated Equivalent Group Constants Reproduced the Near DeCART Solution for Unrodded Cases of YGN3 and Hexagonal Benchmark problems.
For Rodded Case, the Pseudo Control Rod XS and Bank Insertion Indicator were introduced and worked well Reducing the ARI Bank Worth Error of 4.92% to 0.03%.
3D Transport Calculation Based DeCART/CHORUS/MASTER Works well.

34. On-going and Future Work
For Rectangular Problem
Application to SMART Core
Application to Reload Core
For Hexagonal Problem
Extension to 3-D
Development of DeCART3D/CHORUS/MASTER System for Hexagonal Core
Pin Power Reconstruction
Assembly-wise HFF(Heterogeneous Form Function) Generation
Pin Power Distribution Comparison