Ran Lee

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Master's Thesis

Ran Lee

Department of Nuclear Engineering

Ulsan National Institute of Science and Technology

2022

Verification of STREAM3D for APR1400 Reactor

Core Benchmark

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Ran Lee

Department of Nuclear Engineering

Ulsan National Institute of Science and Technology

Verification of STREAM3D for APR1400 Reactor

Core Benchmark

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A thesis submitted to

Ulsan National Institute of Science and Technology in partial fulfillment of the

requirements for the degree of Master of Science

Ran Lee

Deokjung Lee

Verification of STREAM3D for APR1400 Reactor Core Benchmark

07.11.2022 of submission Approved by

Advisor

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Ran Lee

This certifies that the thesis of Ran Lee is approved.

07.11.2022 of submission

Advisor: Deokjung Lee

Professor: Eisung Yoon

Professor: Douglas A. Fynan

Verification of STREAM3D for APR1400 Reactor

Core Benchmark

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Abstract

The purpose of this study is to verify STREAM3D (Steady State and Transient Reactor Analysis code with Method of Characteristics) accuracy through reference results. This thesis shows the verification of STREAM3D for APR1400 reactor core benchmark. STREAM3D simulates 3D core by using the 3D MOC/DD (Three-dimensional Method of Characteristics/Diamond-difference) method.

3D MOC/DD method is developed by UNIST (Ulsan Institute of Science and Technology) CORE (Computational Reactor Physics and Experiment Laboratory) and is implemented in STREAM3D.

APR1400 (Advanced Power Reactor 1400MWe) reactor core benchmark consists of single fuel pin-cell problems, 2D fuel assembly problems, 2D core problems, 3D core problems, control rod worth problems, and 3D core depletion problem. STREAM3D results of these problems are compared to McCARD (Monte Carlo Code for Advanced Reactor Design) and MCS. Single fuel pin-cell reactivity errors for all cases are below 150 pcm. RMS (Root Mean Square) errors of pin power compared to McCARD are within 0.4%. Compared to MCS, RMS errors of pin power are below 0.7%. Reactivity errors for 2D core, and 3D core are less than 100 pcm except for CZP (Cold Zero Power, Fuel:300K, Moderator:300K, Cladding:300K) condition. RMS errors of assembly power compared to McCARD and MCS for 2D core are below 1.7%, and 3.1%. RMS errors of assembly power compared to McCARD and MCS for 3D core are below 1.5%, and 4.1% respectively. In all control rod worth problems, control rod worth differences of STREAM3D compared to McCARD and MCS indicate excellent agreement within about 3%, except when group 2 is inserted. By solving APR1400 benchmark for STREAM3D, STREAM3D is proven to be a suitable and accurate tool for PWR (Pressure Water Reactor) analysis.

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List of Figures

Figure 1. Single fuel pin-cell geometry ... 2

Figure 2. 2D fuel assembly geometry ... 3

Figure 3. APR1400 loading pattern in the cycle 1 ... 3

Figure 4. Axial position of spacer grid in APR1400 ... 4

Figure 5. Control rod geometry ... 4

Figure 6. Control rod bank ... 5

Figure 7. Pin-cell reactivity error compared to McCARD by pin-cell case ... 9

Figure 8. Pin-cell reactivity error compared to MCS by pin-cell case... 12

Figure 9. Comparison of average reactivity error by MOC ray condition ... 13

Figure 10. Comparison of average reactivity error by MOC ray condition ... 18

Figure 11. Radial power distribution and relative error for 2D core ... 26

Figure 13. Axial power distribution for 3D core ... 36

Figure 14. Control rod bank ... 38

Figure 16. Axial power distribution for 3D core ... 45

Figure 17. The result of 3D core depletion ... 48

Figure 18. The difference of boron concentration by burnup step... 48

Figure 19. STREAM 3D radial power distribution at BOC, MOC, EOC in cycle 1 ... 50

Figure 20. STREAM 3D axial power shape at BOC, MOC, EOC in cycle 1 ... 51

Figure 21. Radial power distribution and relative error for APR03V04 ... 63

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Figure 31. Radial power distribution and relative error for APR05V05 ... 73 Figure 32. Radial power distribution and relative error for APR05V06 ... 74 Figure 33. Radial power distribution and relative error for APR05V07 ... 75

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List of Tables

Table 1. Single fuel pin-cell radius ... 2

Table 2. Control rod radius ... 4

Table 3. Reactivity error compared to McCARD for pin-cell ... 7

Table 4. Reactivity error compared to MCS for pin-cell ... 10

Table 5. Case matrix of problem conditions ... 14

Table 6. UO₂ enrichment condition and number of burnable absorber rod by assembly type ... 15

Table 7. Average RMS error of pin power by assembly type... 15

Table 8. Reactivity error compared to McCARD by assembly type ... 16

Table 9. Reactivity error compared to MCS by assembly type ... 17

Table 10. Reactivity error and RMS error of assembly power compared to McCARD for 2D core... 20

Table 11. Reactivity error and RMS error of assembly power compared to MCS for 2D core ... 21

Table 14. RMS error of axial power ... 37

Table 17. Control rod worth compared to McCARD ... 41

Table 18. Control rod worth compared to MCS ... 42

Table 19. RMS error of axial power ... 46

Table 20. Depletion problem condition ... 47

Table 21. CBC of STREAM3D, MPACT, and nTRACER by burnup step ... 49

Table 22. Reactivity error and RMS error of pin power compared to McCARD for A0 assembly ... 54

Table 23. Reactivity error and RMS error of pin power compared to McCARD for B0 assembly ... 54

Table 27. Reactivity error and RMS error of pin power compared to McCARD for C0 assembly ... 56

Table 29.Reactivity error and RMS error of pin power compared to McCARD for C2 assembly ... 57

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Table 31. Reactivity error and RMS error of pin power compared to MCS for A0 assembly ... 58

Table 32. Reactivity error and RMS error of pin power compared to MCS for B0 assembly ... 59

Table 36. Reactivity error and RMS error of pin power compared to MCS for C0 assembly ... 61

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1

I. Introduction

Nowadays, a lot of research is being conducted on high-fidelity three-dimensional reactor core calculation analysis as improvement of computing capabilities. Accordingly, STREAM3D developed by UNIST CORE research team is developed based on the 3D MOC/DD [1] methodology. 3D MOC/DD method solves the disadvantages of existing methodologies and is implemented in STREAM3D.

STREAM3D accuracy are analyzed by solving APR1400 benchmark. The APR1400 is developed by the Republic of Korea in 2002. The design is based on OPR1000 (Optimum Power Reactor 1000MWe), the first standard PWR plant in Korea. APR1400 is a nuclear power plant with improved safety, economy, and convenience compared to existing nuclear power plants. Especially, safety is best all over the world [2].

APR1400 benchmark proffers six contents: pin-cell, assembly, 2D core, 3D core, control rod worth, and 3D core depletion. The number of pin-cell problems is a total of 45. Assembly problems is made of 81 problems. 2D core, and 3D core problems is a total of 9 problems respectively. Control rod worth problems consist of 7. These problems are evaluated in accuracy by McCARD [3] reference code results and MCS [4] code results.

APR1400 benchmark problem analysis was conducted by MPACT (Michigan university’s Michigan parallel characteristics transport code) [5], KEARI (Korea Atomic Energy Research Institute) 's DeCART (Deterministic Core Analysis based on Ray Tracing) [6], and nTRACER [7].

In the case of MPACT, the reactivity errors are mostly less than 100 pcm except for CZP. All RMS errors for pin and assembly are less than 1%, and RMS errors of axial power are less than 1.65% [5].

As with MPACT, DeCART occurs the largest reactivity error for CZP. The maximum reactivity error is about 408 pcm in assembly problems. Most of the DeCART results present excellent agreement. The maximum RMS error of assembly power for 2D core and 3D core is 1.8% and 1.48% respectively. All RMS errors of axial power are within 2.25% [6].

In the case of nTRACER, reactivity errors for assembly are below 200 pcm and RMS errors of pin power are within 0.5% for all the lattices. The reactivity error is larger than 100 pcm in 2D core and 3D core at ARO state. The control rod worth gained results that agreement worth was good in all the cases [6]. In all three codes, the greatest reactivity diﬀerences occur for CZP.

Additionally, MOC condition test is conducted on ray spacing, azimuthal angle, and polar angle for single fuel pin-cell and assembly problems. These test results show the optimized MOC condition when STREAM3D is to solve the benchmark problems.

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1.1 Introduction to APR1400 Benchmark

This benchmark issue is hosted by the U.S/Korea I-NERI (International Nuclear Energy Research Initiative) program, which aims to find and improve the analytical and technical issues of APR1400 [8].

APR1400 is a new generation reactor designed by Korea Electric Power Corporation (KEPCO) and it possesses safety and economic.

Figure 1 indicates single fuel pin-cell geometry. Table 1 presents the radius of the single fuel pin- cell by each region. Fuel rod is made of UO2, Moderator, and Zirlo.

Table 1. Single fuel pin-cell radius

Figure 1. Single fuel pin-cell geometry

APR1400 assemblies are composed of 236 fuel rod, 4 guide tubes, and 1 central tube. Assembly consists of a total of nine types. Figure 2 shows the A0, and C0 assembly geometry. The assemblies are classified by various types of fuel rod. UO2 enrichment of A0 is 1.71wt%, UO2 enrichment of B0 is 3.14wt%, UO2 enrichment of C0 is 3.64wt%. 0 type assemblies have no burnable absorber rod. B1, B2, B3, C1, C2, and C3 assembly types have burnable absorber rods.

Region size[cm]

1 0.409575

2 0.41873

3 0.47498

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Figure 2. 2D fuel assembly geometry

Figure 3 is the Shin-Kori unit 3 loading pattern of the quarter symmetry in the first cycle. APR1400 core is composed of a total of 9 assemblies. APR1400 core lattice is 17 by 17. The number of FAs is 241. 3D core assembly is made of a total of nine grids.

Figure 4 indicates the grid position. Each spacer grid material consists of Zirlo. It is manufactured with a height of 4.15 cm each grid and a weight of 0.854 kg. The benchmark problem assumes that the spacer grid is smeared in the outer regions of fuel rods and tubes at the corresponding axial position [8].

Figure 3. APR1400 loading pattern in the cycle 1 [8]

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Figure 4. Axial position of spacer grid in APR1400 [8]

Figure 5 is control rod geometry. Table 2 presents the radius of the control rod in each region. Control rod materials are made of B4C, Air, Inc625, Moderator, and Zirlo. There are two types of the control rod assembly, 4-fingers and 12-fingers. These control rod assembly types consist of A, and B of shutdown rod, and 1,2,3,4, and 5 of regulating rod. Figure 6 shows the control rod bank. The control rod group insertion order is 5-4-3-2-1-B-A [8].

3D whole core depletion burnup is calculated by total 20 steps. There is no depletion McCARD reference result. Therefore, STREAM3D result compares to nTRACER and MPACT. APR1400 benchmark provides McCARD results of single fuel pin-cell, 2D fuel assembly, 2D core, 3D core, control rod worth. Problems are configured according to the fuel, cladding, moderator temperature, and boron concentration conditions difference, and are calculated at cycle 1 state.

Table 2. Control rod radius

Figure 5. Control rod geometry

Region Size[cm]

1 0.93599

2 0.94742

3 1.03632

4 1.13764

5 1.23

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5

Figure 6. Control rod bank [8]

II. Introduction to Reactor Physics Code System 2.1 STREAM3D MOC Code

STREAM3D is developed by introducing a one-step 3D neutron transport analysis method that replaces the existing two-step. The 3D neutron transport analysis code can simulate a 3D core structure by using the 3D MOC/DD method. Existing 2D/1D method shows unstable convergence behavior for a problem. In addition, float source regions in a pin-cell have the same axial leakage regardless of the fine mesh in the pin-cell and the neutron streaming angle, and thus accuracy decreases [1]. Despite 3D MOC having the advantage of stable convergence and accurate calculation results, it is not used well due to large computational requirements and long calculation time. 3D MOC/DD is developed to solve the existing method’s disadvantage by UNIST CORE and is implemented in STREAM3D. The 3D MOC/DD method is developed based on the DD scheme in the axial direction to derive the equation and this simplifies the two-step design procedure to one-step by applying a new 3D MOC/DD methodology to improve the accuracy of calculation results [1].

2.2 McCARD Monte Carlo Benchmark Reference Code

McCARD (Monte Carlo Code for Advanced Reactor Design) [3] is a Monte Carlo (MC) neutron- photon-transport simulation code designed exclusively for neutronics analyses of various nuclear reactor and fuel system [3]. The MC method can obtain accurate result because it describes accurately

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the spatial structure and cross section of the nuclear reaction is treated as a continuous energy. McCARD estimates neutronics design parameters of a nuclear reactor of a fuel system such as effective multiplication factor (𝐾_𝑒𝑓𝑓) neutron flux and current, fission power, etc. by continuous-energy cross section libraries and detailed geometrical data of the system [3]. McCARD is developed by SNU (Seoul National University) SNURPL (Seoul National University Reactor Physics Lab). McCARD calculates the accurate nuclear characteristic factor using the pointwise energy cross-section library for various reactor core structures. In particular, it is possible to consider the temperature feedback effect, so it is possible to interpret the core behavior of the reactor due to depletion [9].

2.3 MCS Monte Carlo Code

MCS [4] is Monte Carlo neutron/photon transport code, it is developed by UNIST CORE to perform the PWR analysis. The MC method is to solve transport equations that can calculate reliable solutions by continuous-energy nuclear data and explicit geometry modeling [4]. Serpent [10] that is MC code is faster than the other MC code but, it is not suitable whole core simulation [4]. MC21[11] and RMC [12]

are suitable whole core simulation but not open to public. MCS was developed by supplementing the previously stated disadvantages, its accuracy was verified by solving many benchmarks [4].

III.Verification of STREAM3D for APR1400 Reactor Core Benchmark 3.1 Single Fuel Pin-cell

Single fuel pin-cell problems deal with a total of 45 problems. As shown in Table 3, there are 45 pin- cell problems with five UO2 enrichment (1.71 wt%, 2.00 wt%, 2.64 wt%, 3.14 wt%, 3.64 wt%). Table 3 presents reactivity error compared to McCARD. The maximum reactivity error is about 142 pcm from APR01V01. Figure 7 presents the reactivity error compared to McCARD by pin-cell case. In the case of the CZP condition, the error is the lowest at 2000 ppm of boron concentration. In the case of HZP and HFP conditions, the error is somewhat lower when boron is 0 ppm. Table 4 summarizes the reactivity error compared to MCS of pin-cell problems. The maximum reactivity error occurs at APR01V01 and is about 105 pcm. Figure 8 compares the reactivity of MCS and STREAM3D by pin - cell case. In the case of the CZP, the error is lowest at 1000 ppm of boron concentration. In the case of HZP and HFP conditions, the error is lower when boron is 2000 ppm. Overall, the maximum reactivity error occurs at APR01V01 and is below about 150 pcm. In addition, in the case of CZP, reactivity error between boron concentrations is most significant. Results of the STREAM3D compared to the results of McCARD, and MCS appear good agreement.

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Table 3. Reactivity error compared to McCARD for pin-cell

Pin-cell

UO

2

enrich ment [wt%]

Temperature

condition [K] k-inf Reacti

vity error

[pcm]

Fuel Clad. Mod. McCARD std. STREAM 3D

APR01V

01 1.71 300 300 300 1.24098 5 1.2388 -142

APR01V

02 2.00 300 300 300 1.29037 5 1.28875 -97

APR01V

03 2.64 300 300 300 1.36867 5 1.36701 -89

APR01V

04 3.14 300 300 300 1.41131 5 1.40967 -82

APR01V

05 3.64 300 300 300 1.44397 5 1.44258 -67

APR01V

06 1.71 600 600 600 1.18617 5 1.18472 -103

APR01V

07 2.00 600 600 600 1.22952 5 1.22806 -97

APR01V

08 2.64 600 600 600 1.29754 5 1.29631 -73

APR01V

09 3.14 600 600 600 1.33472 6 1.33341 -74

APR01V

10 3.64 600 600 600 1.36301 6 1.36183 -64

APR01V

11 1.71 900 600 600 1.17598 5 1.17429 -122

APR01V

12 2.00 900 600 600 1.21894 5 1.21733 -109

APR01V

13 2.64 900 600 600 1.28678 6 1.28513 -100

APR01V

14 3.14 900 600 600 1.32364 6 1.32201 -93

APR01V

15 3.64 900 600 600 1.35176 6 1.35029 -81

APR01V

16 1.71 300 300 300 1.02175 5 1.02065 -105

APR01V

17 2.00 300 300 300 1.07997 6 1.07902 -82

APR01V

18 2.64 300 300 300 1.17721 6 1.17630 -66

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8 APR01V

19 3.14 300 300 300 1.23313 6 1.23217 -63

APR01V

20 3.64 300 300 300 1.27731 6 1.27628 -63

APR01V

21 1.71 600 600 600 1.03939 6 1.03815 -115

APR01V

22 2.00 600 600 600 1.09077 6 1.08962 -97

APR01V

23 2.64 600 600 600 1.17499 6 1.17386 -82

APR01V

24 3.14 600 600 600 1.22257 6 1.2214 -78

APR01V

25 3.64 600 600 600 1.25989 6 1.25872 -74

APR01V

26 1.71 900 600 600 1.03040 5 1.02904 -128

APR01V

27 2.00 900 600 600 1.08156 6 1.08013 -122

APR01V

28 2.64 900 600 600 1.16517 6 1.16379 -102

APR01V

29 3.14 900 600 600 1.21243 6 1.21104 -95

APR01V

30 3.64 900 600 600 1.24949 7 1.24815 -86

APR01V

31 1.71 300 300 300 0.87299 6 0.87233 -87

APR01V

32 2.00 300 300 300 0.93297 5 0.93243 -62

APR01V

33 2.64 300 300 300 1.03677 6 1.03624 -49

APR01V

34 3.14 300 300 300 1.09875 7 1.09805 -58

APR01V

35 3.64 300 300 300 1.14891 7 1.14808 -63

APR01V

36 1.71 600 600 600 0.92836 6 0.92738 -114

APR01V

37 2.00 600 600 600 0.98320 6 0.9824 -83

APR01V

38 2.64 600 600 600 1.07615 6 1.07517 -85

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9 APR01V

39 3.14 600 600 600 1.13003 6 1.1291 -73

APR01V

40 3.64 600 600 600 1.17331 6 1.17225 -77

APR01V

41 1.71 900 600 600 0.92027 6 0.9193 -115

APR01V

42 2.00 900 600 600 0.97499 6 0.97391 -114

APR01V

43 2.64 900 600 600 1.06706 6 1.06603 -91

APR01V

44 3.14 900 600 600 1.12081 6 1.11961 -96

APR01V

45 3.64 900 600 600 1.16362 6 1.16251 -82

*Boron Concentration: APR01V01~15: 0ppm / APR01V16~30: 1000ppm / APR01V31~45: 2000ppm

Figure 7. Pin-cell reactivity error compared to McCARD by pin-cell case

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Table 4. Reactivity error compared to MCS for pin-cell

Pin-cell

UO

2

enrich ment [wt%]

Temperature

condition [K] k-inf Reacti

vity error [pcm]

Fuel Clad. Mod. MCS std. STREAM 3D

APR01V

01 1.71 300 300 300 1.24042 6 1.23880 -105

APR01V

02 2.00 300 300 300 1.28960 6 1.28875 -51

APR01V

03 2.64 300 300 300 1.36778 7 1.36701 -41

APR01V

04 3.14 300 300 300 1.41050 7 1.40967 -42

APR01V

05 3.64 300 300 300 1.44322 7 1.44258 -31

APR01V

06 1.71 600 600 600 1.18564 6 1.18472 -65

APR01V

07 2.00 600 600 600 1.22894 7 1.22806 -58

APR01V

08 2.64 600 600 600 1.29715 7 1.29631 -50

APR01V

09 3.14 600 600 600 1.33409 7 1.33341 -38

APR01V

10 3.64 600 600 600 1.36236 8 1.36183 -29

APR01V

11 1.71 900 600 600 1.17549 7 1.17429 -87

APR01V

12 2.00 900 600 600 1.21838 7 1.21733 -71

APR01V

13 2.64 900 600 600 1.28604 8 1.28513 -55

APR01V

14 3.14 900 600 600 1.32297 7 1.32201 -55

APR01V

15 3.64 900 600 600 1.35133 8 1.35029 -57

APR01V

16 1.71 300 300 300 1.02071 6 1.02065 -6

APR01V

17 2.00 300 300 300 1.07895 6 1.07902 6

APR01V

18 2.64 300 300 300 1.17604 7 1.1763 19

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11 APR01V

19 3.14 300 300 300 1.23199 7 1.23217 12

APR01V

20 3.64 300 300 300 1.27606 8 1.27628 14

APR01V

21 1.71 600 600 600 1.03875 6 1.03815 -56

APR01V

22 2.00 600 600 600 1.09007 7 1.08962 -38

APR01V

23 2.64 600 600 600 1.17440 7 1.17386 -39

APR01V

24 3.14 600 600 600 1.22197 7 1.2214 -38

APR01V

25 3.64 600 600 600 1.25915 8 1.25872 -27

APR01V

26 1.71 900 600 600 1.02984 6 1.02904 -75

APR01V

27 2.00 900 600 600 1.08083 6 1.08013 -60

APR01V

28 2.64 900 600 600 1.16449 7 1.16379 -52

APR01V

29 3.14 900 600 600 1.21176 7 1.21104 -49

APR01V

30 3.64 900 600 600 1.24886 8 1.24815 -46

APR01V

31 1.71 300 300 300 0.87187 6 0.87233 60

APR01V

32 2.00 300 300 300 0.93189 6 0.93243 62

APR01V

33 2.64 300 300 300 1.03558 7 1.03624 62

APR01V

34 3.14 300 300 300 1.09732 7 1.09805 61

APR01V

35 3.64 300 300 300 1.14749 7 1.14808 45

APR01V

36 1.71 600 600 600 0.92787 6 0.92738 -57

APR01V

37 2.00 600 600 600 0.98262 6 0.9824 -23

APR01V

38 2.64 600 600 600 1.07540 7 1.07517 -20

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12 APR01V

39 3.14 600 600 600 1.12936 7 1.1291 -20

APR01V

40 3.64 600 600 600 1.17248 7 1.17225 -17

APR01V

41 1.71 900 600 600 0.91988 6 0.9193 -69

APR01V

42 2.00 900 600 600 0.97435 6 0.97391 -46

APR01V

43 2.64 900 600 600 1.06635 7 1.06603 -28

APR01V

44 3.14 900 600 600 1.12003 7 1.11961 -33

APR01V

45 3.64 900 600 600 1.16286 7 1.16251 -26

*Boron Concentration: APR01V01~15: 0ppm / APR01V16~30: 1000ppm / APR01V31~45: 2000ppm

Figure 8. Pin-cell reactivity error compared to MCS by pin-cell case

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3.1.1 Pin-cell MOC Condition

Figure 9 compares the average reactivity error of pin-cell problems by MOC ray condition. MOC f1 f2 f3 means that f1 is ray spacing, f2 is the number of azimuthal angles and f3 is the number of polar angles. In the case of the polar angle, the sensitivity test does not proceed because the pin-cell problems address two-dimensional. The default value of the MOC ray condition is 0.05 48 6. The sensitivity test is conducted by modifying the default value of the MOC ray condition. The narrower the ray spacing, reactivity error is lower. when ray spacing is changed from 0.05 to 0.03 cm in MOC 0.05 48 6, the average reactivity error decrease from about 233 pcm to 140 pcm. In addition, when the number of azimuthal angles is set to 96, the average reactivity error is lower from 140 pcm to 89 pcm. As a result of testing all three conditions, the average error is the lowest at 89 pcm when the MOC option is 0.03 96 6. Therefore, assembly problems to be calculated are conducted into MOC 0.03 96 6. In the case of the whole core, it is performed as the default value by consideration of simulation time.

Figure 9. Comparison of average reactivity error by MOC ray condition

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3.2 2D Fuel Assembly

In the 2D fuel assembly case, there are 9 types of assemblies in the benchmark. The total problems are configured the number of a total 81 problems and condition of the problem is according to Table 5 for each assembly type. Table 6 summarizes the UO2 enrichment condition and the number of burnable absorber rods by assembly type. Each assembly difference is UO2 enrichment and the number of burnable absorber rods. For example, A0 assembly consists of 1.71wt% fuel rods, but C1 assembly consists of 3.64wt%, 3.14wt% for fuel rods, and 12 burnable absorbers. Table 7 indicates the average RMS error of pin power. The maximum average RMS error of pin power compared to McCARD occurs at C1 assembly and is about 0.18%. Compared to MCS, the maximum average RMS error of pin power is about 0.34% from C2 assembly. Average RMS errors of pin power appear good agreement by under 1%. Table 8 presents reactivity error compared to McCARD. The maximum reactivity error is about 204 pcm from APR02B2V04. Table 9 provides reactivity error compared to MCS. The maximum reactivity error occurs at APR02B3V02 and is about 156 pcm. Overall, all STREAM3D results by assembly case compared to McCARD and MCS show excellent accuracy.

In Section 3.1.1 above, as a result of the MOC condition test, MOC 0.03 96 6 is the most accurate.

Therefore, assembly is calculated by the option of MOC 0.03 96 6. Figure 10 compares the difference in average reactivity error between the default value and MOC 0.03 96 by assembly type, it has shown that the blue bar (MOC 0.03 96 6) has a lower error than the orange bar (MOC 0.05 48 6). The greatest difference is about 30 pcm from the A0 assembly, and average difference is about 15 pcm.

Table 5. Case matrixof problem conditions

Temperature condition [K] Boron concentration

[ppm]

Fuel Clad. Mod.

300 300 300 0

600 600 600 0

900 600 600 0

300 300 300 1000

600 600 600 1000

900 600 600 1000

300 300 300 2000

600 600 600 2000

900 600 600 2000

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Table 6. 𝐔𝐎_𝟐 enrichment condition and number of burnable absorber rod by assembly type

Assembly type

𝐔𝐎_𝟐

Enrichment

Number of burnable absorber

rod

A0 1.71wt% 0

B0 3.14wt% 0

B1 3.14/2.64wt% 12

B2 3.14/2.64wt% 12

B3 3.14/2.64wt% 16

C0 3.64/3.14wt% 0

C1 3.64/3.14wt% 12

C2 3.64/3.14wt% 16

C3 3.64/3.14wt% 16

Table 7. Average RMS error of pin power by assembly type

Assembly type

Average RMS error of pin power [%]

STREAM3D compared to

McCARD

STREAM3D compared to

MCS

A0 0.09 0.15

B0 0.10 0.16

B1 0.17 0.33

B2 0.17 0.32

B3 0.17 0.33

C0 0.12 0.18

C1 0.18 0.33

C2 0.17 0.34

C3 0.16 0.33

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Table 8. Reactivity error compared to McCARD by assembly type

A0 B0 B1

Case

Reactivity error [pcm]

Case

APR02A0V01 -137 APR02B0V01 -93 APR02B1V01 -138

APR02A0V02 -123 APR02B0V02 -94 APR02B1V02 91

B2 B3 C0

Case

APR02B2V01 -149 APR02B3V01 -150 APR02C0V00 -87

APR02B2V02 5 APR02B3V02 181 APR02C0V01 -94

C1 C2 C3

Case

APR02C1V01 -126 APR02C2V01 -135 APR02C3V01 -134

APR02C1V02 70 APR02C2V02 152 APR02C3V02 160

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Table 9. Reactivity error compared to MCS by assembly type

A0 B0 B1

Case

APR02A0V07 -31 APR02B0V07 29 APR02B1V07 -25

B2 B3 C0

Case

APR02B2V02 -5 APR02B3V02 156 APR02C0V01 -62

APR02B2V04 -128 APR02B3V04 -94 APR02C0V03 6

APR02B2V07 -45 APR02B3V07 -56 APR02C0V06 29

C1 C2 C3

Case

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Figure 10. Comparison of average reactivity error by MOC ray condition

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3.3 2D Core and 3D Core in BOC State

3.3.1 2D Core

2D whole core is performed according to Table 5. Table 10 provides reactivity error and RMS error of assembly power compared to McCARD. The maximum reactivity error is about 204 pcm and occurs at APR03V07. The reactivity error is below 100 pcm except for CZP. In the case of RMS error of assembly power, the maximum RMS error is about 1.74 % from APR03V01. In all cases, RMS error is below 1.8%. Table 11 summarizes reactivity error and RMS error of assembly power compared to MCS.

The maximum reactivity error is 114 pcm from APR03V01. As with compared to McCARD results, a large reactivity error occurs for CZP. The maximum RMS error is 3.09 % from APR03V09. Overall, STREAM3D results show that k-values are lower than McCARD and MCS. Also, STREAM3D results present good agreement with McCARD and MCS. Figure 11 schematizes the 2D core radial power distribution for STREAM3D and relative error compared to McCARD and MCS. Figure 11 consist of APR03V01, APR03V02, APR03V03, APR03V06, and APR03V09. Compared to McCARD results, there is a consistent tendency with a high error at the edge and a low error at the center but compared to MCS results, there is no consistent tendency.

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Table 10. Reactivity error and RMS error of assembly power compared to McCARD for 2D core

2D CORE

McCARD STREAM 3D RMS

error of assembly

power [%]

k-inf std. k-inf

APR03V01 1.22244 6 1.22037 -139 1.74

APR03V02 1.14686 6 1.14651 -27 1.08

APR03V03 1.13804 6 1.13742 -48 1.25

APR03V04 1.03657 6 1.03515 -132 0.98

APR03V05 1.02289 6 1.02238 -49 1.10

APR03V06 1.01469 7 1.01437 -31 1.28

APR03V07 0.91033 7 0.90864 -204 0.60

APR03V08 0.92979 7 0.92937 -49 1.12

APR03V09 0.92284 6 0.92221 -74 1.05

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Table 11. Reactivity error and RMS error of assembly power compared to MCS for 2D core

2D CORE

MCS STREAM 3D RMS

power [%]

k-inf std. k-inf

APR03V01 1.22207 5 1.22037 -114 2.19

APR03V02 1.14675 5 1.14651 -18 1.11

APR03V03 1.13788 5 1.13742 -36 1.25

APR03V04 1.03573 4 1.03515 -54 2.04

APR03V05 1.02267 5 1.02238 -28 1.28

APR03V06 1.01492 4 1.01437 -53 0.66

APR03V07 0.90931 4 0.90864 -81 2.47

APR03V08 0.92969 4 0.92937 -37 0.67

APR03V09 0.92265 4 0.92221 -52 3.09

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Figure 11. Radial power distribution and relative error for 2D core

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3.3.2 3D Core

This section deals with the 3D whole core results of STREAM3D compared to McCARD and MCS.

The 3D core problem is configured according to Table 5. Table 12 summarizes reactivity error and RMS error of assembly power compared to McCARD. The reactivity error is below about 100 pcm except for CZP. The maximum RMS error is about 1.46% from APR04V01. Table 13 indicates reactivity error and RMS error of assembly power compared to MCS. The reactivity error is below 60 pcm, which appears excellent agreement. As with the other problems, maximum reactivity error occurs for CZP but the error is a relatively low numerical value. The maximum RMS error of assembly power is about 4.10%

from APR04V07. Overall, the maximum reactivity error occurs for CZP.

Figure 12 schematizes the 3D core radial power distribution for STREAM3D and relative error compared to McCARD and MCS. Figure 12 consists of APR04V01, APR04V02, APR04V03, APR04V06, and APR04V09. As with 2D core, compared to McCARD results, there is a consistent tendency with a high error at the edge and a low error at the center but compared to MCS results, there is no consistent tendency. At the same temperature condition, the power of the center decrease as boron concentration is higher. Figure 13 presents the axial power distribution and it appears that all three codes have a similar axial power shape. Table 14 summarizes the RMS error of axial power. The maximum RMS error compared to McCARD is 3.86% from APR04V04. Compared to MCS, the maximum RMS error of axial power is about 2.47% from APR04V07. Consistently, the largest errors occur for CZP.

This suggests that the largest error caused by CZP may be caused by an incorrect hydrogen scattering matrix or there may be a spatial discretization error in which there are too few rings in the mesh for the moderator [5].

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3D CORE

power [%]

k-inf std. k-inf

APR04V01 1.21738 4 1.21547 -129 1.46

APR04V02 1.13941 4 1.13931 -8 1.07

APR04V03 1.13055 4 1.13025 -23 1.22

APR04V04 1.03385 4 1.03241 -135 1.15

APR04V05 1.01743 4 1.01706 -36 0.97

APR04V06 1.00964 4 1.00922 -41 1.39

APR04V07 0.90877 4 0.90755 -148 0.92

APR04V08 0.92584 4 0.92551 -39 0.52

APR04V09 0.91877 4 0.91833 -52 1.22

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3D CORE

power [%]

k-inf std. k-inf

APR04V01 1.21635 4 1.21547 -60 1.45

APR04V02 1.13921 4 1.13931 8 1.88

APR04V03 1.13033 4 1.13025 -6 1.42

APR04V04 1.03259 4 1.03241 -17 1.62

APR04V05 1.01714 4 1.01706 -8 0.41

APR04V06 1.00938 4 1.00922 -16 1.16

APR04V07 0.90767 4 0.90755 -15 4.10

APR04V08 0.92547 4 0.92551 5 0.82

APR04V09 0.91844 4 0.91833 -13 1.44

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Figure 13. Axial power distribution for 3D core

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Table 14. RMS error of axial power

3D CORE

RMS error [%]

McCARD MCS

APR04V01 2.01 1.09

APR04V02 2.23 1.39

APR04V03 1.96 1.60

APR04V04 3.86 1.97

APR04V05 1.85 1.53

APR04V06 1.46 1.72

APR04V07 2.09 2.47

APR04V08 1.41 1.79

APR04V09 1.40 1.49

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3.4 Control Rod Worth

APR1400 core is controlled by a total of 7 types control rod bank. Figure 14 indicates the 7 types of control rod banks. The seven control rods consist of 4-fingers (bank A, B, 1, 2) and 12-fingers (bank 2, 3, 4, 5). Additionally, 1, 2, 3, 4, and 5 are regulating banks. B, A are shutdown bank. The control rod group insertion order is 5-4-3-2-1-B-A [8]. All condition of problems is that fuel is 600K, the moderator is 600K, cladding is 600K, and boron concentration is 0 ppm.

Table 15 appears the reactivity error and RMS error of assembly power compared to McCARD for 3D core. Table 16 proffers the reactivity error and RMS error of assembly power compared to MCS for 3D core. In both cases, the reactivity error is greatest when all control rod banks are inserted, and RMS error of assembly power is largest when groups 5, 4, 3, 2, 1, and B are inserted. Table 17 contains the accumulated worth and group worth compared to McCARD for STREAM3D. The greatest error appears when group 2 is inserted. As shown in Table 17, the largest group worth is about 5.81%. Table 18 provides the control rod worth compared to MCS. The largest group worth is about 6.77%. In all control rod cases, control rod worth differences compared to McCARD and MCS indicate excellent agreement within about 3%, except when group 2 is inserted. Figure 15 presents 3D core radial power distribution for STREAM3D and reactivity error compared to McCARD and MCS. Figure 16 compares the axial power distribution of STREAM3D, McCARD, and MCS, and it shows that the three codes appear a similar shape. Table 19 summarizes the RMS error of axial power. The largest RMS error of axial power compared to McCARD is about 2.24%. Compared to MCS, the maximum RMS error of axial power is about 1.96%. When all control rod banks are inserted, RMS error of axial power tends to be the greatest.

Figure 14. Control rod bank [8]

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3D CORE Bank

Inserted

power [%]

k-inf std.

[pcm] k-inf

APR04V02 ARO 1.13941 4 1.13931 -8 1.07

APR05V01 5 1.13463 4 1.13462 -1 1.32

APR05V02 5-4 1.13044 4 1.13052 6 0.85

APR05V03 5-4-3 1.11786 4 1.11803 14 0.73

APR05V04 5-4-3-2 1.10487 4 1.10429 -48 1.01

APR05V05 5-4-3-2-1 1.08072 4 1.08052 -17 0.92

APR05V06 5-4-3-2-1-B 1.03458 4 1.03459 1 3.40

APR05V07 5-4-3-2-1-B-A 0.96248 5 0.96408 172 2.69

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3D CORE Bank

Inserted

power [%]

k-inf std.

[pcm] k-inf

APR04V02 ARO 1.13921 4 1.13931 8 1.88

APR05V01 5 1.13438 4 1.13462 19 0.55

APR05V02 5-4 1.13025 4 1.13052 21 0.64

APR05V03 5-4-3 1.11762 4 1.11803 33 0.84

APR05V04 5-4-3-2 1.10475 4 1.10429 -38 0.85

APR05V05 5-4-3-2-1 1.08071 4 1.08052 -16 1.09

APR05V06 5-4-3-2-1-B 1.03440 4 1.03459 18 2.49

APR05V07 5-4-3-2-1-B-A 0.96248 5 0.96408 172 2.18

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Table 17. Control rod worth compared to McCARD

Bank Inserted

McCARD STREAM3D

Accum.

Diff [%]

Group Diff [%]

Accum.

worth [pcm]

Group worth [pcm]

Accum.

worth [pcm]

ARO - - - -

5 369.74 369.74 362.81 362.81 -1.87 -1.87

5-4 696.41 326.67 682.45 319.64 -2.01 -2.15 5-4-3 1691.92 995.51 1670.61 988.17 -1.26 -0.74 5-4-3-2 2743.67 1051.75 2783.50 1112.88 1.45 5.81 5-4-3-2-1 4766.18 2022.52 4775.61 1992.11 0.20 -1.50 5-4-3-2-1-B 8892.86 4126.68 8884.22 4108.61 -0.10 -0.44 5-4-3-2-1-B-A 16133.54 7240.68 15953.41 7069.19 -1.12 -2.37

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Table 18. Control rod worth compared to MCS

Bank Inserted

MCS STREAM3D

Accum.

Diff [%]

Group Diff [%]

Accum.

worth [pcm]

Accum.

worth [pcm]

ARO - - - -

5 373.75 373.75 362.81 362.81 -2.93 -2.93

5-4 695.87 322.12 682.45 319.64 -1.93 -0.77

5-4-3 1695.72 999.85 1670.61 988.17 -1.48 -1.17

5-4-3-2 2738.09 1042.37 2783.50 1112.88 1.66 6.77 5-4-3-2-1 4751.63 2013.54 4775.61 1992.11 0.50 -1.06 5-4-3-2-1-B 8894.27 4142.64 8884.22 4108.61 -0.11 -0.82 5-4-3-2-1-B-A 16118.13 7223.86 15953.41 7069.19 -1.02 -2.14

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Figure 16. Axial power distribution for 3D core

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Table 19. RMS error of axial power

3D CORE

RMS error [%]

McCARD MCS

APR05V01 1.64 1.55

APR05V02 1.93 1.69

APR05V03 1.38 1.51

APR05V04 1.47 1.69

APR05V05 1.57 1.46

APR05V06 1.77 1.49

APR05V07 2.24 1.96

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47 3.5 3D Core Depletion with Hot Full Power Condition.

This section describes a 3D core depletion problem. 3D whole core depletion problem is calculated by HFP condition. Operating conditions for thermal-hydraulic feedback calculation are given in Table 20 [8]. There is no McCARD reference result. Therefore, in this thesis, STREAM3D compares to nTRACER and MPACT. Figure 17 presents the CBC (Critical Boron Concentration) search for each burnup step. STREAM3D reaches 17 MWD/kgU. The first burnup step is calculated without xenon.

Table 21 summarizes numerical changes in boron concentration at each step. The largest difference between the three codes occurs at 8 MWD/kgU. There are many reasons for this difference at 8 MWD/kgU, one thing is that the timing of gad burning out different from code to code. In addition, there are reasons for options or library version and so on. Figure 18 indicates the difference in boron concentration at each burnup step. The maximum difference compared to MPACT is about 46.62 ppm.

Compared to nTRACER, the maximum difference is about 71.58 ppm large numerical value relatively.

STREAM3D result is closer to MPACT result than nTRACER result.

Table 20. Depletion problem condition

Parameter Value

Pressure 15.51315MPa

Core thermal power 3983 MWt

Coolant lnlet temperature 563.75K

Coolant outlet temperature 597.05K

Coolant mass flow rate 75.6 x

10⁶kg/hr

Control rod state All rod out

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Figure 17. The result of 3D core depletion

Figure 18. The difference of boron concentration by burnup step

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Table 21. CBC of STREAM3D, MPACT, and nTRACER by burnup step

Burnup

[MWD/kgU]

STREAM3D CBC [ppm]

MPACT CBC [ppm]

nTRACER CBC [ppm]

Difference from MPACT

Difference from nTRACER

0 1096.36 1083.5 1085.05 -12.86 -11.31

0.05 832.28 804.13 804.85 -28.15 -27.43

0.5 767.42 753.12 745.33 -14.30 -22.09

1 769.28 758.04 760.32 -11.24 -8.96

2 755.59 755.54 759.79 -0.05 4.20

3 727.48 735.58 748.58 8.10 21.10

4 696.92 710.47 727.85 13.55 30.93

5 665.36 686.32 707.17 20.96 41.81

6 637.17 666.70 690.03 29.53 52.86

7 614.34 654.05 680.34 39.71 66.00

8 598.17 644.79 669.75 46.62 71.58

9 585.00 622.80 639.88 37.80 54.88

10 562.13 579.05 586.93 16.92 24.80

11 516.20 519.56 519.66 3.36 3.46

12 452.57 451.16 444.04 -1.41 -8.53

13 377.85 377.69 362.94 -0.16 -14.91

14 299.27 301.01 281.73 1.74 -17.54

15 216.64 221.85 192.45 5.21 -24.19

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16 134.41 140.83 105.68 6.42 -28.73

17 47.59 58.76 15.43 11.17 -32.16

18 0 0 0 0 0

Figure 19 shows the radial power distribution at BOC (Beginning of Cycle), MOC (Middle of Cycle), and EOC (End of Cycle). There is no conspicuous power change by cycle. But axial power distribution can observe change. Figure 20 presents the STREAM3D axial power shape at BOC, MOC, and EOC.

At the BOC, the highest power is located in the middle of the core. Therefore, the fuel burnup in middle region is higher than the other regions. This phenomenon led to the result of relatively lower power in that region. For this reason, the axial power shape is flatter in the middle region than in another cycle at the end of the cycle [13]. For another reason, the accumulation of fission products can affect this phenomenon [14].

Figure 19. STREAM 3D radial power distribution at BOC, MOC, EOC in cycle 1

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Figure 20. STREAM 3D axial power shape at BOC, MOC, EOC in cycle 1

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IV. Conclusion

In this thesis, many problems given in the APR1400 benchmark are calculated by neutron transport code, STREAM3D. The STREAM3D results are compared to the McCARD reference code results and MCS code results. McCARD was developed by SNU, MCS was developed by UNIST and both codes are simulated by the Monte Carlo methodology. The accuracy of each problem is evaluated by the reactivity error of each problem and power distribution.

STREAM3D compared to McCARD presents that reactivity errors for pin-cell are below 150 pcm, reactivity errors for assembly are within about 200 pcm. The maximum RMS error of pin power is about 0.4%. Reactivity errors for 2D core, and 3D core are less than 100 pcm except for CZP. RMS errors of assembly power compared to McCARD for 2D core are below 1.7%. RMS errors of assembly power for 3D core are below 1.5%. RMS errors of axial power are within about 2% except when APR04V04 is about 3.84%.

Compared to MCS, results appear that reactivity errors for pin-cell are within about 105 pcm, and reactivity errors for assembly are below 160 pcm. RMS errors of pin power are within 0.7%. Reactivity errors for 2D core, and 3D core are consistently less than 100 pcm except for CZP. The maximum RMS error of assembly power for 2D core is 3.1%. RMS errors of assembly power for 3D core are below 4.1%. In case of axial power, RMS errors are within about 2.5%. Control rod worth differences compared to McCARD and MCS indicate excellent agreement within about 3%, except when group 2 is inserted. Meanwhile, depletion problem results have no a Monte Carlo code result. The result of STREAM3D depletion is closer than the results of MPACT and the largest difference appears at 8 MWD/kgU. In all results, the largest reactivity errors occur for CZP. Nevertheless, STREAM3D results indicate excellent agreement with the results of McCARD, and MCS.

MOC sensitivity test is conducted into pin-cell and assembly problems. In the case of the pin-cell MOC test, the MOC condition test is performed in a total of 3 cases. Results have demonstrated the MOC 0.03 96 6 (ray spacing, azimuthal angle, polar angle) is an optimized MOC condition. Therefore, the lowest reactivity errors could be obtained when the MOC condition is 0.03 96 6, but 2D core, and 3D core problems are conducted on MOC 0.05 48 6 (default value in STREAM3D) considering the simulation time.

Previous research was conducted by DeCART, nTRACER, and MPACT. As with STREAM3D, the results of DeCART, MPACT, and nTRACER show the largest reactivity error at CZP. For the development of a more accurate simulation code, more research should be conducted into CZP temperature conditions.

Lastly, In the future, studies of STREAM3D are expected to be performed by utilizing various reactor design codes, coupling them with thermal-hydraulic, and nuclear fuel codes. STREAM3D

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demonstrates a good agreement by comparing the result of McCARD, and MCS. Therefore, STREAM3D is proven to be able to accurately analyze the APR1400 reactor core.

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Appendix

Table 22. Reactivity error and RMS error of pin power compared to McCARD for A0 assembly

A0 assembly

Reactivity Error [pcm]

RMS error of pin power

[%]

k-inf std.[pcm] k-inf

APR02A0V01 1.23419 5 1.23211 -137 0.19

APR02A0V02 1.20266 5 1.20088 -123 0.07

APR02A0V03 1.19363 5 1.19126 -167 0.05

APR02A0V04 0.98255 6 0.98098 -163 0.14

APR02A0V05 1.02908 5 1.02752 -148 0.05

APR02A0V06 1.02117 6 1.01936 -174 0.05

APR02A0V07 0.82269 6 0.82151 -175 0.12

APR02A0V08 0.90365 6 0.90227 -169 0.06

APR02A0V09 0.89668 6 0.89512 -194 0.05

Table 23. Reactivity error and RMS error of pin power compared to McCARD for B0 assembly

B0 assembly

[%]

APR02B0V01 1.41388 5 1.41203 -93 0.21

APR02B0V02 1.36053 5 1.3588 -94 0.06

APR02B0V03 1.35029 6 1.34841 -103 0.06

APR02B0V04 1.20097 6 1.19947 -104 0.17

APR02B0V05 1.22370 6 1.22207 -109 0.07

APR02B0V06 1.21468 6 1.21275 -131 0.08

APR02B0V07 1.05016 6 1.04874 -129 0.16

APR02B0V08 1.11505 6 1.11357 -119 0.07

APR02B0V09 1.10678 6 1.10512 -136 0.06

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B1 assembly

[%]

APR02B1V01 1.22686 6 1.22478 -138 0.34

APR02B1V02 1.14201 6 1.1432 91 0.12

APR02B1V03 1.13328 7 1.13414 67 0.11

APR02B1V04 1.05294 6 1.05137 -142 0.29

APR02B1V05 1.04049 7 1.04106 53 0.12

APR02B1V06 1.03245 6 1.03289 41 0.10

APR02B1V07 0.92809 7 0.92667 -165 0.28

APR02B1V08 0.95801 6 0.95835 37 0.10

APR02B1V09 0.95072 6 0.95092 22 0.10

B2 assembly

[%]

APR02B2V01 1.21635 6 1.21415 -149 0.33

APR02B2V02 1.13136 6 1.13143 5 0.11

APR02B2V03 1.12265 7 1.12355 71 0.11

APR02B2V04 1.04071 7 1.03851 -204 0.29

APR02B2V05 1.02888 6 1.0294 49 0.10

APR02B2V06 1.02095 6 1.0213 34 0.09

APR02B2V07 0.91529 6 0.91394 -161 0.27

APR02B2V08 0.94584 6 0.94616 36 0.10

APR02B2V09 0.93857 6 0.9388 26 0.11

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B3 assembly

[%]

APR02B3V01 1.17476 6 1.17269 -150 0.35

APR02B3V02 1.08259 7 1.08471 181 0.10

APR02B3V03 1.07417 7 1.07604 162 0.10

APR02B3V04 1.01213 7 1.00969 -239 0.30

APR02B3V05 0.99066 7 0.99199 135 0.10

APR02B3V06 0.98306 6 0.98417 115 0.11

APR02B3V07 0.89455 6 0.8934 -144 0.28

APR02B3V08 0.91549 6 0.9164 108 0.09

APR02B3V09 0.90850 6 0.90927 93 0.08

Table 27. Reactivity error and RMS error of pin power compared to McCARD for C0 assembly

C0 assembly

[%]

APR02C0V00 1.44026 5 1.43845 -87 0.26

APR02C0V01 1.38404 6 1.38225 -94 0.07

APR02C0V02 1.37366 6 1.37175 -101 0.07

APR02C0V03 1.23616 6 1.23474 -93 0.02

APR02C0V04 1.25472 6 1.25301 -109 0.07

APR02C0V05 1.24543 6 1.24353 -123 0.07

APR02C0V06 1.08915 7 1.08791 -105 0.17

APR02C0V07 1.15067 7 1.14897 -129 0.07

APR02C0V08 1.14211 7 1.14034 -136 0.08

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Table 28. Reactivity error and RMS error of pin power compared to McCARD for C1 assembly

C1 assembly

[%]

APR02C1V01 1.27188 6 1.26985 -126 0.34

APR02C1V02 1.18695 7 1.18794 70 0.11

APR02C1V03 1.17790 6 1.17866 55 0.11

APR02C1V04 1.10469 6 1.10315 -126 0.30

APR02C1V05 1.08996 7 1.09118 103 0.13

APR02C1V06 1.08172 7 1.08203 26 0.10

APR02C1V07 0.98209 7 0.98078 -136 0.27

APR02C1V08 1.01005 6 1.01028 23 0.11

APR02C1V09 1.00242 6 1.00257 15 0.13

Table 29.Reactivity error and RMS error of pin power compared to McCARD for C2 assembly

C2 assembly

[%]

APR02C2V01 1.22195 6 1.21994 -135 0.36

APR02C2V02 1.13040 7 1.13235 152 0.08

APR02C2V03 1.12173 7 1.12345 136 0.11

APR02C2V04 1.06450 7 1.06310 -124 0.31

APR02C2V05 1.04174 7 1.04302 118 0.09

APR02C2V06 1.03370 7 1.03492 114 0.08

APR02C2V07 0.94879 7 0.94754 -139 0.29

APR02C2V08 0.96832 6 0.96914 87 0.10

APR02C2V09 0.96111 7 0.96172 66 0.09

Ran Lee

Master's Thesis

Ran Lee

Department of Nuclear Engineering

Ulsan National Institute of Science and Technology

2022

Verification of STREAM3D for APR1400 Reactor

Core Benchmark

Ran Lee

Department of Nuclear Engineering

Ulsan National Institute of Science and Technology

Verification of STREAM3D for APR1400 Reactor

Core Benchmark

A thesis submitted to

Ulsan National Institute of Science and Technology in partial fulfillment of the

requirements for the degree of Master of Science

Ran Lee

Deokjung Lee

Verification of STREAM3D for APR1400 Reactor Core Benchmark

07.11.2022 of submission Approved by

Advisor

Ran Lee

This certifies that the thesis of Ran Lee is approved.

07.11.2022 of submission

Advisor: Deokjung Lee

Professor: Eisung Yoon

Professor: Douglas A. Fynan

Verification of STREAM3D for APR1400 Reactor

Core Benchmark

Abstract

Contents

List of Figures

List of Tables

I. Introduction

1.1 Introduction to APR1400 Benchmark

II. Introduction to Reactor Physics Code System 2.1 STREAM3D MOC Code

2.2 McCARD Monte Carlo Benchmark Reference Code

2.3 MCS Monte Carlo Code

III.Verification of STREAM3D for APR1400 Reactor Core Benchmark 3.1 Single Fuel Pin-cell

Pin-cell

UO

enrich ment [wt%]

Temperature

condition [K] k-inf Reacti

vity error

[pcm]

Fuel Clad. Mod. McCARD std. STREAM 3D

Pin-cell

UO

enrich ment [wt%]

Temperature

condition [K] k-inf Reacti

vity error [pcm]

Fuel Clad. Mod. MCS std. STREAM 3D

3.1.1 Pin-cell MOC Condition

3.2 2D Fuel Assembly

Temperature condition [K] Boron concentration

[ppm]

Fuel Clad. Mod.

300 300 300 0

600 600 600 0

900 600 600 0

300 300 300 1000

600 600 600 1000

900 600 600 1000

300 300 300 2000

600 600 600 2000

900 600 600 2000

Assembly type

Enrichment

Number of burnable absorber

rod

A0 1.71wt% 0

B0 3.14wt% 0

B1 3.14/2.64wt% 12

B2 3.14/2.64wt% 12

B3 3.14/2.64wt% 16

C0 3.64/3.14wt% 0

C1 3.64/3.14wt% 12

C2 3.64/3.14wt% 16