Master of Science Thesis

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WESTINGHOUSE ELECTRIC COMPANY

Nuclear fuel, nuclear services, nuclear technology, nuclear power plant design and equipment for the commercial nuclear electric power industry

GRENOBLE-INP Phelma / KTH

Double Degree in Nuclear Energy Engineering

Master of Science Thesis

Lattice physics mesh refinement study and its impact on full core nodal simulation results

Missions

Study the convergence of mesh refinement made in HELIOS modeling of fuel assembly.

Reproduce the results published by Yu Han et al., "Effect of Void Dependent Reactivity Modeling Bias on BWR Axial Power Tilt," Proc. Int. Conf. Advances in Reactor Physics to Power Nuclear Renaissance, Pittsburgh, Pennsylvania, USA, May 9-14 (2010), by studying the impact of such a mesh refinement in lattice physics on mini-

core simulation results without consideration of thermal-hydraulics feedback.

Study the impact of such a mesh refinement in lattice physics on full core simulation results based on equilibrium cycles with consideration of thermal-hydraulics feedback.

Didier Bourgin

Supervisors:

Mr. Petri Forslund Guimarães, Westinghouse Electric Sweden AB

Mr. Vasily Arzhanov, KTH Reactor Physics

Examiner:

Mr. Jan Dufek, KTH Nuclear Reactor Technology

Westinghouse Electric Sweden AB

Finnslätten, Fredholmsgatan 22, building 399

SE-721 36 Västerås, Sweden September 2^nd, 2013 to March 2^nd, 2014

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ABSTRACT

Recently, a Boiling Water Reactor (BWR) axial power tilt and reactivity bias with increased coolant void content was reported due to the application of a spatially flat source approximation in the lattice transport calculations feeding the nodal core simulator with homogenized cross section data. From this observation, a spatial and angular mesh refinement was carried out using the lattice transport code HELIOS in combination with the nodal core simulator POLCA7. The obtained two-dimensional (2D) lattice physics results demonstrate that using a sufficiently fine spatial mesh in the coolant has a major influence on the reactivity and will potentially lead to a void-dependent axial tilt in the reactivity if not properly addressed. Three-dimensional (3D) mini-core calculations enable to confirm that such an axial power tilt is induced by performing lattice physics mesh refinements. 3D full-core nodal simulations based on equilibrium cycles with consideration of thermal-hydraulics (TH) feedback indicate that a rather large shift in combination with a changed within-cycle behaviour of the hot keff is obtained by azimuthally improving the spatial mesh in the coolant of the fuel pin cells when performing lattice calculations. In this regard, such uncertainties in reactivity and power will potentially have a large impact on the design of modern challenging reactor cores in terms of fuel loading patterns and 24-month cycle operation having very high burnable absorber (BA) loading.

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ACKNOWLEDGMENTS

I would first like to thank Mrs. Ing-Marie Petersson, Mr. Juan Casal and Mr. Petri Forslund Guimarães for their warm welcome and for having accepted me within Westinghouse Electric Sweden AB.

I would like to express the deepest appreciation to my supervisor Mr. Petri Forslund Guimarães for his valuable help and his availability all along my master of science thesis project. In addition, I would like to thank Mr. Peter Olivius and Mr. Jonas Aurén for helping me and dedicating their time during my master's thesis.

I would also like to thank Mr. Pär Jonsson for his support in managing the local computing resources.

Finally, I would also like to express my gratitude to Mrs. Katarina Swiesciak, Mrs. Åsa Jonsson, Mrs. Pascale Sotto Vangeli, Mrs. Mathilde Janona, Mrs. Karolina Olofsson, Mr. Mattias Lodin, Mr. Jean-Marie Le Corre, Mr. Håkan Carlsson, Mr. Rashed Sarwar, Mr. Oscar Puebla Carcia, Mr. Manuel Auliano and all company personnel for their warmth and friendship. All of them have helped me to carry out my master’s thesis in the best possible conditions, whether in connection with the technical issues or making me feel part of the group.

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LIST OF FIGURES

Figure 1. Organization chart of the SFE. ... 11

Figure 2. Schematic of the mesh refinement study processed through several codes. ... 14

Figure 3. Azimuthal view of SVEA-96 Optima3. ... 15

Figure 4. Mini-lattice representation from Orion. ... 16

Figure 5. Material layout and spatial discretization of the high-enriched SVEA-96 Optima3 fuel segment. ... 16

Figure 6. Azimuthal and radial sectors for CC. ... 17

Figure 7. Coolant density profile (in kg/m3) displayed by POLUT. ... 20

Figure 8. Top view of the full-core in CM2. ... 21

Figure 9. Evolutions of mini-lattice kinf difference versus quality of the mesh at 1 MWd/tU. ... 22

Figure 13. Thermal and fast flux map, thermal and fast flux profile and their gradient representations for the case 9 evaluated at 20000 MWd/tU and 80% void fraction. ... 24

Figure 14. Thermal and fast flux map, thermal and fast flux profile and their gradient representations for the case 11 evaluated at 20000 MWd/tU and 80% void fraction. ... 24

Figure 15. Difference in thermal and fast flux for the case 11 relative the case 9 in the form of a map and profiles evaluated at 20000 MWd/tU and 80% void fraction. ... 25

Figure 16. Difference in thermal and fast flux for the case 11 relative the case 9 in the form of a map and profiles evaluated at 20000 MWd/tU and 0% void fraction. ... 25

Figure 17. Evolutions of full-lattice kinf difference versus quality of the mesh at 1 MWd/tU. ... 26

Figure 21. Mini-core power distributions for various mesh refinement cases with black boundaries assigned axially. ... 30

Figure 22. Differences in mini-core power distributions relative coarse mesh power distribution with black boundaries assigned axially. ... 30

Figure 23. Axial power distributions of the case 1 for four mini-core configurations. ... 31

Figure 24. keff trends of the last four cycles regarding the reference case (case 1) with keff hot and keff cold references. ... 32

Figure 25. keff trend from the 8^th cycle for each case with keff hot and keff cold references. ... 33

Figure 26. Minimum, average and maximum of the axial power profile at 0 EFPH for the various studied cases. ... 34

Figure 29. Differences in average axial power at 0 EFPH relative case 1. ... 35

Figure 32. Shutdown margin, control rod worth and core excess representation. ... 36

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LIST OF TABLES

Table 1. Spatial mesh refinement illustration for each coolant water and bypass moderator structure. ... 18

Table 2. Sequence and parameterization of the angular and spatial mesh refinement for the mini-lattice and Optima3 full-lattice. ... 19

Table 3. Mini-lattice kinf differences relative the case 1 evaluated at different burnup and void conditions. ... 23

Table 4. Full-lattice kinf differences with the case 1 evaluated at different burnup and void conditions. ... 27

Table 5. Four different mini-core configurations of the case 1. ... 31

Table 6. Reactivity, nodal power and thermal margin prediction differences obtained from the last cycle (8^th). ... 37

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APPENDICES

1 Orion views of the mini-lattice spatial mesh refinement for all studied cases.

2 Illustration of the angular mesh refinement for the mini-lattice.

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ABBREVIATIONS

BWR Boiling Water Reactor

2D two-dimensional 3D three-dimensional TH Thermal-hydraulics

BA Burnable absorber

CPs Collision Probabilities

MoC Method of Characteristics

CM2 Core Master 2

mfp Mean free path

WEC Westinghouse Electric Company

WES Westinghouse Electric Sweden

SFE Sweden Fuel Engineering

PWR Pressurized Water Reactor

MG Multi-group CCCP Current Coupling Collision Probability

LWR Light Water Reactor

CD Cell Data

2G two-group

CC Current coupling

EFPH Effective full power hours

EOFP Enf of full power

APO Axial power offset

SDM Shutdown margin

LHGR Linear heat generation rate

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1. INTRODUCTION

Within the framework of my third year at the engineering school GRENOBLE-INP Phelma (Grenoble, France) and Royal Institute of Technology KTH (Stockholm, Sweden), following the double degree in energy and nuclear engineering, I have carried out my master’s thesis assignment within Westinghouse Electric Sweden AB. This project has been focused on a lattice physics mesh refinement study and its impact on full core nodal simulation results. More precisely, my master’s thesis was formulated based on the publication “Effect of Void Dependent Reactivity Modeling Bias on BWR Axial Power Tilt” [1], which states that the usual practice of flat source approximation in 2D lattice codes based on the Collision Probabilities (CPs) method or the Method of Characteristics (MoC) may cause a void dependent power tilt in BWR nodal core analyses when used to generate homogenized cross section data to the nodal core simulator. Consequently, using the transport code HELIOS in combination with the nodal core simulator POLCA7 might induce such a void dependent reactivity bias if no precautions with regard to geometrical modelling are taken to diminish the impact of the flat source approximation in the HELIOS calculations.

Therefore, a 3D full-core equilibrium cycle analysis has been performed with Core Master 2 (CM2)/POLCA7 to study such effects in particular. Angular and spatial mesh refinement has been carried out in order to attempt to counteract this potential reactivity tilt, due to the use of an angularly isotropic and spatially flat source in regions with either large spatial flux variation or strong anisotropic angular flux distribution typically encountered at high void conditions. In other words, the flux should be approximated with an appropriate resolution in situations where high void neutrons leak into parts where the thickness of the material is large in term of mean free path (mfp) such as in non-boiling water regions.

This report is organized as follows. In Section 2, an overview of Westinghouse Electric Company (WEC) is given. In Section 3 the methodology is described, i.e. short descriptions of the different codes that have been employed, sequence and parameterization in refining the spatial and angular mesh in the lattice calculations and important input parameters in the 3D mini-core and full-core nodal analyses. In Section 4, various numeral results obtained from the 2D lattice physics and 3D nodal core evaluations are provided and discussed. Finally, conclusions are provided in Section 5.

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2. WORKING ENVIRONMENT 2.1. Westinghouse Electric Company

WEC was an American manufacturing company founded by George Westinghouse on January 8th, 1886. His ventures survive him and evolve from an electric supply company (first patent filed for a "system of electrical generation") to a worldwide nuclear company. The American company was bought by the Toshiba Group on February 6th, 2006. Operated from this date by Toshiba, WEC provides fuel, services, technology, plant design and equipment for the commercial nuclear electric power industry. This company has designed almost half of the nuclear power plants in operation worldwide, and nearly sixty percent in the United States. Moreover, WEC employs about 14000 people. The four core product lines of Westinghouse are nuclear automation, nuclear fuel, nuclear power plants and nuclear services. Westinghouse nuclear automation enhances the reliability of plant control and safety systems thanks to an integrated and plant-wide approach, while Westinghouse nuclear fuel manufactures fuel-related products and components for nuclear power plants globally. Furthermore, Westinghouse nuclear power plants provides the startup and the development for new units, whereas Westinghouse nuclear services offers a full complement of nuclear services to maintain nuclear plants operating both safely and competitively. Finally, during the 20th century, Westinghouse scientists and engineers were granted more than 28000 US government patents, i.e. the third most of any company [2].

2.2. Westinghouse Electric Sweden

2.2.1. General overview

Westinghouse Electric Sweden (WES) operates in the areas of nuclear fuel, nuclear services and nuclear automation. It has more than 1000 employees and is in charge of the BWR technology. It is composed of three facilities in Västerås, i.e. fuel factory, fuel technology and central functions. Nine nuclear power plants in Sweden and two in Finland were built by this vendor, based on its own independent design. WES is today a supplier of nuclear fuel and components, plant upgrades including nuclear automation as well as nuclear services in Europe, USA and Asia [2].

2.2.2. Sweden Fuel Engineering

Sweden Fuel Engineering (SFE), situated in the fuel technology facility is composed of seven departments, as shown in the Figure 1 (BT standing for “Bränsleteknik”).

I performed my master’s thesis within the BWR methods and technology group (BTE). This group has overall responsibility for core and fuel analysis methodologies [3].

Figure 1. Organization chart of the SFE [3].

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3. METHODOLOGY 3.1. Codes

3.1.1. HELIOS

HELIOS is a multi-group (MG), 2D transport code based on the current coupling collision probability (CCCP) method. HELIOS solves the integral neutron transport equation using the CCCP method. It is mainly used for lattice burnup calculations using a 45 or 190 energy group nuclear data library providing full geometrical flexibility in order to model complex Light Water Reactor (LWR) fuel lattice designs. The HELIOS code package is composed of four codes. First, there is the AURORA code, which is a pre-processing code used for the system geometry treatment and the assignment of the various compositions to the different regions of the modelled system. This code also prepares all input data to be used by the calculation module of HELIOS. Another code in the HELIOS package is the ZENITH code which processes the output of HELIOS. All these codes share one data base which is accessed and maintained by HERMES subroutines. Finally there is the ORION code, which is a graphical user interface used to verify the geometrical, material and temperature overlays used in the HELIOS calculations. It draws the lattice geometry layout as a post script file. Except for the nuclear data library, two input files are necessary to perform computations with HELIOS: the AURORA and ZENITH inputs [4]. The version 1.8.1 of HELIOS has been used in the 2D lattice physics analysis.

3.1.2. LATTGEN

LATTGEN is the driver to a set of subprograms that runs the lattice code HELIOS to obtain nodal cross section data for a 2D slice of an assembly, and then transforms the output of HELIOS to a so-called ASCII lattic.txt file. This lattic.txt file has a format that CoreLink (explained in 3.1.3) can read, in order to generate a so-called Cell Data (CD) file provided to the core simulator POLCA7. Cross sections, fluxes, pin powers and isotopic number densities notably are first computed by HELIOS along the burnup path and for each depletion (historical void) case.

Then, the branch cases, which consist of perturbation calculations where one or several parameters are changed, such as void, fuel temperature, boron content, control rod presence and spacer grid, are performed after the depletion cases have finished successfully. The branches are carried out via restart calculations from depletion data. All results are written and gathered in the lattic.txt file [5].

3.1.3. CoreLink

CoreLink is a data handling and post-processing code, which prepares nodal cross section data (in terms of CD tables) for the POLCA7 nodal core simulator from data files generated by a lattice physics code such as HELIOS or PHOENIX4. CoreLink generates tables for a wide variety of data types, such as macroscopic and microscopic cross sections, discontinuity factors, pin power and pin burnup form factor maps, detector constants, kinetics data and control rod history data. The general representation for CD given in ASCII format consists of 3D tables,

T E ( , ,  

_his

)

, with entries for burnup, instantaneous coolant density and coolant density history [6]. The CoreLink version 6.2.0 has been employed in this study.

3.1.4. TABBE

TABBE is a menu-driven service program for binary CD files. Although it has a lot of different functions, it has been used in this project for reading the ASCII tables generated by CoreLink and then storing them in a binary CD file [7]. TABBE version 4.16.0 has been utilized in the 3D mini-core nodal analysis.

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13 / 42 3.1.5. POLCA7

POLCA7 is a two-group (2G) 3D code for simulating neutronics and TH behaviour of a BWR reactor core at steady state conditions. It solves the coupled neutron diffusion and thermal-hydraulics problem and provides high spatial resolution through the application of a pin power reconstruction method. POLCA7 is the main working tool for in-core fuel management activities as well as for core on-line monitoring [8]. The input processor of POLCA7, POLIN, allows to both process and structure input data such that it can be efficiently used by POLCA7, but also performs verifications on paramount input parameters. The input file of POLCA7 is named a so-called source file.

Other important files used by POLCA7 include the distribution file, the CD file, the summary file and the print file.

The summary file contains one record of results from each POLCA7 case, the CD file stores cell data tables generated by the lattice code (HELIOS here) and the print file lists results, while distribution file describes the state of various core entities as a function of space and time. The distribution file can be created by POLDIS. Finally, POLUT is the output processor of POLCA7 that enables the users to print calculation results [9], [10]. The version 4.16.0 of POLCA7, POLIN and POLUT has been utilized in the 3D mini-core nodal analysis.

3.1.6. Core Master 2

CM2 is a complete computational environment dedicated to reactor calculations with core monitoring functionality also available. Its main features include the 3D core simulator POLCA7, graphical user interfaces and an integrated database with full capabilities for steady state core analyses as well as support for reactor dynamics analyses. Contrary to conventional calculation systems in which the user has to manage number of codes, input and output structures, assignments are performed directly from the graphical environment. CM2, linked to POLCA7, supports all the tasks typically performed during in-core fuel management, such as reload design, fuel rod tracking, core operation analysis, cold critical calculations and shutdown margin analysis [11]. The versions 3.7.6 and 4.12.4 of CM2 and POLCA7, respectively have been used in 3D full-core equilibrium cycle studies.

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3.2. Schematic presentation

The different steps carried out and the various connections between the previously described codes are shown in Figure 2.

Figure 2. Schematic of the mesh refinement study processed through several codes.

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3.3. Problem description

3.3.1. 2D lattice physics analysis

The objective of the 2D lattice physics analysis part is first to establish a reference mesh solution and then to evaluate different mesh refinement orders using HELIOS. This study was performed both on a mini-lattice and on a full-lattice configuration. The latter corresponds to a SVEA-96 Optima3 10x10 lattice design for Forsmark 3. Both voided and non-voided conditions were considered in the calculations.

3.3.1.1. Geometry and fuel material composition

3.3.1.1.1. Mini‐lattice

Calculations considering the coarse mesh representation (in this study referred as the standard mesh representation) and the various mesh refinement steps were first carried out on a mini-lattice. The same scale between the mini-lattice and the full-lattice structures has been retained. The full-lattice geometrical design SVEA-96 Optima3 is shown in Figure 3. The mini-lattice corresponds to a subchannel’s row of five fuel pin cells enriched at 4.50 w/o (weight percentage) containing no BA. An Orion view of the 2D reference mesh mini-lattice, defined by the mesh of the structures, subsequently named case 1, is given in Figure 4. Specular reflection is applied at the boundaries of the mini-lattice.

Assembly wall

15.475 cm Central canal Box

Dimple

Boiling water

Outside perimeters Perimeter of outer channel Perimeter of

subchannel

Water wing

Non-boiling water outside channel

Outer gap

Figure 3. Azimuthal view of SVEA-96 Optima3 [12].

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3.3.1.1.2. Full‐lattice

The evaluation of the coarse mesh and various mesh refinement configurations was then performed based on a modern SVEA-96 Optima3 full-lattice design. The nuclear design of this fuel type contains BA with an axial variation targeting a core with an as even as possible power distribution. The nuclear design has also efficiently handled the challenging thermal margins and stability restrains imposed by the core operation. Consequently the fuel bundle has been divided into five axial segments, each required for 2D evaluation. In this 2D analysis the third fuel segment was selected for numerical evaluation. In Figure 5 the radial layout of the middle high-enriched axial segment (fuel- segment 3) of the considered fuel bundle is shown including the spatial mesh adopted in the baseline transport calculations.

.

1.3 cm

Internal bypass

Active coolant

Fuel pin

BA pin External bypass

Internal bypass

Active coolant

Fuel pin

Figure 4. Mini-lattice representation from Orion.

External bypass

Figure 5. Material layout and spatial discretization of the high-enriched SVEA-96 Optima3 fuel segment.

This reference spatial mesh constitutes the baseline for the mesh refinement.

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17 / 42 3.3.1.2. Mesh refinement and collision probabilities

3.3.1.2.1. Angular mesh refinement and collision probabilities

As mentioned previously, HELIOS solves the integral neutron transport equation using the CCCP method.

More precisely, the 2D lattice is divided into many space elements (constituting of one or more merged structures), which are further divided into flat flux and source regions. All these space elements are coupled by interface currents with the CPs method applied within each of them (first-flight collision probabilities). The currents that couple the space elements together are spatially constant over the interface segments with the half sphere of incoming directions on each of these segments then angularly discretized into sectors k. Inside each sector, the currents are assumed to be constant in the azimuthal angle and to vary with the cosine of the polar angle. The integer k specifies the angular discretization (or coupling order). If k=0, there is no current coupling (CC) and the CPs extend across the interface of the relevant two structures on either side of the interface segment thereby fusioned into one space element. The k=0 coupling order enables to improve the modeling, but increases prohibitively run times. The different values taken by k are shown in Figure 6 where the negative k-values correspond to the same number of azimuthal and polar subdivisions. The k value (with k≠0) corresponds to the angular mesh refinement [4].

3.3.1.2.2. Spatial mesh refinement

Defined by the “mesh index n”, two orders of spatial mesh refinement were applied to different structures/pin- cells of the lattice coupled together and constituting the internal bypass, external bypass and subchannel coolant (set of fuel/BA pin pellets with cladding surrounded by active coolant). The spatial mesh refinement of the BA pin pellets has been disregarded since it was sufficiently fine from the start. The coarse mesh representation is defined by n=1, while the first and second order of mesh refinement correspond to n=2 and n=4, respectively. Furthermore, an additional ring in the active coolant region and BA-free fuel pellet radial rings as well as azimuthal sectors have been taken into account in the mesh refinement sequence. Globally, the first mesh refinement order corresponds to the division of a quadrilateral (structure) and triangle (structure) into two equal surface area parts, whereas the second order consists of the split of a quadrilateral (structure) into two new equal surface area parts, while the triangle (structure) is split in three equal surface area parts from its initial geometry defined by the first order. This spatial mesh refinement corresponds therefore to the division of one structure into several regions. All structures of the 2D reference mesh are depicted in Figures 4 and 5, while the refined mesh with additional new regions created within each coolant water and bypass moderator structure is displayed in Table 1.

Figure 6. Azimuthal and radial sectors for CC [4].

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18 / 42 Table 1. Spatial mesh refinement illustration for each coolant water and bypass moderator structure.

3.3.1.3. Description of the different mesh refinement cases

The same mesh refinement sequence and parameterization have globally been retained between the mini- lattice and full-lattice representations. They are displayed in Table 2 with the total number of regions included for each case. Orion views of the mini-lattice spatial mesh refinement for all cases studied are displayed in Appendix 1. In addition, an illustration of the angular mesh refinement for two mini-lattice cases is shown in Appendix 2.

Parts of the lattice

Spatial mesh refinement

Structure/pin-cell refinement

Fuel pin pellet refinement Radial and azimuthal divisions

Active coolant refinement

n=1 n=2 n=4 Refined Additional ring

Internal bypass

External bypass

Active coolant region

&

Fuel pin pellet (except

BA)

Mini- lattice

Full- lattice

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Table 2. Sequence and parameterization of the angular and spatial mesh refinement for the mini-lattice and Optima3 full-lattice. * Fuel pin pellet (except BA) Azimuthal sectors Full-lattice 0 0 0 0 0 0 0 8 8 8 8 8

Mini-lattice 0 0 0 0 0 0 0 8 8 8 8 8

Radial rings Full-lattice 2 2 2 2 2 2 2 3 3 3 3 3

Mini-lattice 2 2 2 2 2 2 2 6 6 6 6 6

Active coolant Additional ring No No No No No No No No Yes Yes Yes Yes

n 1 1 2 1 1 2 4 4 4 4 4 4

k +4 -4 0 -4 -4 -4 -4 -4 -4 -4 -4 0

External bypass n 1 1 4 4 4 4 4 4 4 4 4 4

k +4 -4 0 -4 -4 -4 -4 -4 -4 0 0 0

Internal bypass n 1 1 1 1 4 4 4 4 4 4 4 4

k +4 -4 0 -4 -4 -4 -4 -4 -4 -4 0 0

Total number of regions Full-lattice† 2302 2302 N/A‡ 2764 3230 3606 4358 6118 6758 6758 6758 N/A

Mini-lattice 41 41 70 47 55 75 115 310 350 350 350 350

Case # 1 2 3 4 5 6 7 8 9 10 11 12 * Cells marked with gray in Table 2 indicate a parameterization change against the previous case. † The total number of regions corresponds to that of fuel segment 3. ‡ As will be indicated in Section 4.1.1.2., cases 3 and 12 were not evaluated in full-lattice geometry.

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20 / 42 3.3.1.4. Convergence criteria

Regarding the convergence criteria set in Aurora input files, the specific values used for the inner iterations (currents) enabling to solve the flux in a given group with a given source, and outer iterations (eigenvalue) allowing to find the correct group sources depending on the flux in other groups, were equal to 1.0E-05 and 1.0E-06, respectively.

The corresponding values used for the full-lattice geometry were equal to 2.5E-05 and 5.0E-06. Moreover, for both lattices, the maximum distance between two successive chords and minimum allowed width of the macrobands were set to 0.01 cm and 0.001 cm, respectively.

3.3.2. 3D mini‐core nodal analysis

The purpose of the 3D mini-core nodal analysis is to confirm the observations made in Ref. [1], i.e. applying different spatial and angular mesh refinements in 2D lattice physics generating nodal cross section data to the nodal core simulator will induce an axial power tilt.

The 3D mini-core was modeled as a clustering of four SVEA-96 Optima3 fuel assemblies (i.e. two fuel assembly layers in north-south direction and west-east direction). The four fuel assemblies were identical with regard to material composition and geometrical layout of fuel pins and the fuel box. In this analysis, all control rods including handle were fully withdrawn and any spacer grids were disregarded. A predefined axial coolant density profile was imposed over the core (i.e. no TH feedback). Radially, reflective boundary conditions were assigned at the periphery of the core, whereas black (i.e. vacuum) boundary conditions were applied in the axial direction. The spatial and angular mesh refinement carried out on fuel segment 3 in the 2D analysis was expanded to the four other fuel segments constituting the full SVEA-96 Optima3 fuel bundle design.

The parameters considered as input in the POLDIS distribution file were the fuel and moderator temperatures, the Xenon Xe-135 and Iodine I-135 concentrations at equilibrium and the axial coolant density profile. The moderator and fuel temperatures were taken from the fuel segment 3 CoreLink output file to obtain their base values of 289°C and 427°C, respectively, and were assigned to each of the 25 nodes (axially). Moreover, typical equilibrium values of magnitude 1.0E15 cm^-3 and 1.0E16 cm^-3 were employed for the Xe-135 and I-135 number densities. Finally, the coolant density profile adopted in this analysis, varying axially from 735.00 kg/m³ in the bottom to 177.64 kg/m³ on the top at saturated pressure of 73 bar, is displayed in Figure 7.

Figure 7. Coolant density profile (in kg/m3) displayed by POLUT.

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21 / 42 3.3.3. 3D full‐core equilibrium cycle nodal analysis

The objective of the 3D full-core equilibrium cycle nodal analysis is to quantify the effect of the spatial and angular mesh refinements in lattice physics (from sets of nodal cross section data) on full-core reactivity, power distribution and thermal margin predictions. Note that this analysis includes TH feedback.

A reactor core of ASEA-Atom design containing 700 fuel assemblies (SW01) and being operated at 3775 MWth was chosen for numerical work in this study. A loading pattern based on kinf-ranking using 148 feed assemblies was utilized at each cycle refuelling. The geometrical layout of core constitutes of 30 fuel assembly layers in the north-south direction as well as in the west-east direction as illustrated in Figure 8.

Control Rod (CR82 type)

Detector (WEST type)

Fuel assembly (SW01 type)

4.62795 m

Figure 8. Top view of the full-core in CM2.

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4. NUMERICAL RESULTS 4.1. 2D lattice physics analysis

4.1.1. Results

4.1.1.1. Mini‐lattice

In Figure 9 through Figure 12, the evolution of mini-lattice kinf versus mesh discretization is shown in terms of the difference relative the reference coarse mesh value (case 1) at the four burnup points 1 MWd/tU, 20000 MWd/tU, 40000 MWd/tU and 60000 MWd/tU and the two different void fractions 0% and 80%. In addition, kinf difference values obtained by comparison with case 1 are summarized in Table 3. Finally, thermal and fast flux maps as well as thermal and fast flux and their gradients along the mini-lattice line crossing the middle of the left half of the mini- lattice has been depicted in Figure 13 through Figure 16 for cases 9 and 11.

Figure 9. Evolutions of mini-lattice kinf difference versus quality of the mesh at 1 MWd/tU.

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Table 3. Mini-lattice kinf differences relative the case 1 evaluated at different burnup and void conditions.

Bu (MWd/tU) Case

#

1 20000 40000 60000

Void fraction (%) 0 80 0 80 0 80 0 80

Ref. value 1 1.39070 1.22870 1.17650 1.03290 1.00790 0.93118 0.86383 0.86559

Difference in kinf relative case 1 (pcm)

2 39 80 39 82 19 63 -14 41

3 105 241 94 259 -3 199 -124 127

4 25 45 25 45 5 27 -28 7

5 57 93 62 97 39 70 0 38

6 -242 -184 -263 -177 -180 -139 -29 -103

7 -260 -184 -280 -178 -196 -140 -40 -104

8 -227 -168 -261 -190 -195 -160 -56 -129

9 -235 -168 -268 -189 -201 -160 -60 -128

10 -205 24 -226 43 -156 56 -15 61

11 -199 62 -219 81 -150 88 -12 85

12 104 256 80 247 -21 181 -153 108

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24 / 42 Figure 13. Thermal and fast flux map, thermal and fast flux profile and their gradient representations for the case 9

evaluated at 20000 MWd/tU and 80% void fraction.

Figure 14. Thermal and fast flux map, thermal and fast flux profile and their gradient representations for the case 11 evaluated at 20000 MWd/tU and 80% void fraction.

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25 / 42 Figure 15. Difference in thermal and fast flux for the case 11 relative the case 9 in the form of a map and profiles

evaluated at 20000 MWd/tU and 80% void fraction.

Figure 16. Difference in thermal and fast flux for the case 11 relative the case 9 in the form of a map and profiles evaluated at 20000 MWd/tU and 0% void fraction.

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26 / 42 4.1.1.2. Full‐lattice

In Figure 17 through Figure 20, the evolution of full-lattice kinf versus mesh discretization is shown in terms of the difference relative the reference coarse mesh value (case 1) at the four burnup points 1 MWd/tU, 20000 MWd/tU, 40000 MWd/tU and 60000 MWd/tU and the two different void fractions 0% and 80%. Furthermore, kinf differences obtained by comparison with case 1, are provided in Table 4.

It should be noted that some cases in full-lattice configuration were not evaluated (cases 3 and 12) because of the too high computational burden when using the current 32-bits HELIOS. For these cases, 3D mini-core and full- core evaluations have therefore not been performed.

Figure 17. Evolutions of full-lattice kinf difference versus quality of the mesh at 1 MWd/tU.

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Table 4. Full-lattice kinf differences with the case 1 evaluated at different burnup and void conditions.

Bu (MWd/tU)

Case #

1 20000 40000 60000

Void fraction

(%) 0 80 0 80 0 80 0 80

Ref. value 1 1.02940 0.98297 1.14750 1.11040 0.92184 0.95435 0.74061 0.83425

Difference in kinf relative case 1 (pcm)

2 21 37 45 89 11 50 -23 -2

4 -50 -55 -14 19 -30 -4 -48 -39

5 -107 -145 -64 -47 -65 -54 -58 -63

6 282 543 -437 -339 -182 -204 54 -44

7 239 540 -485 -345 -215 -211 35 -53

8 278 568 -501 -355 -238 -225 13 -69

9 267 590 -513 -356 -246 -226 7 -70

10 274 633 -507 -288 -235 -174 21 -39

11 286 661 -498 -258 -229 -154 24 -30

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28 / 42 4.1.2. Discussions

From the set of mini-lattice and full-lattice results introduced in the previous part 4.1.1, an analysis of the impact of the changes in mesh parameterization on kinf predictions is conducted in this section.

4.1.2.1. Effects of the spatial mesh refinement

For the full-lattice configuration, spatial mesh refinement performed in bypass non-boiling water regions, i.e.

cases 4 and 5 in Figures 17-20, has a somewhat larger effect (up to 128 pcm) in comparison to that of the mini-lattice (see in Figures 9-12). This is believed to be caused by the larger volume of non-boiling water in the full-lattice geometry compared to the mini-lattice.

The largest effect of spatial mesh refinement comes from the azimuthal division of the active coolant area in four additional sectors, as seen by comparing case 6 with 5. A rather large impact, up to 325 pcm and 688 pcm, for mini-lattice and full-lattice configurations, respectively, can be noticed from Tables 3 and 4. These observations are in contrast with the results provided in Ref. [13] in which azimuthal discretization had a minor influence (less than 18 pcm) in a directionally symmetric single pin cell system. One should therefore be very careful regarding the extrapolation of the results from simplistic systems to more complex and realistic configurations presenting a higher degree of anisotropy and flux spatial variation. Note also how the shift in kinf changes sign with burnup due to the presence of BA in the full-lattice geometry (Only BA-free pins were modelled in the mini-lattice geometry).

A deviation in kinf going from +299 pcm at 1 MWd/tU to -93 pcm at 60000 MWd/tU (i.e. compare cases 6 and 5 in Table 4) can also be recognized between voided and non-voided conditions. Consequently, not only will such a void-dependent kinf shift potentially induce an axial power tilt at a certain point of time in the cycle, it will also change its significance during the cycle.

Radial and azimuthal divisions of the fuel pin pellet has small impact on mini-lattice and full-lattice kinf, i.e.

about 18 pcm and 17 pcm (average over the burnup range at 80% void fraction), respectively, as seen from Figures 9- 12 for case 8. Furthermore, as seen for cases 7 and 9, an even smaller effect can be noticed when adding coolant regions radially. This is in agreement with the observations made in Ref. [13] where adding more well-placed radial rings in BA-free fuel and increasing the number of coolant rings (up to the fourth) will not affect kinf more than 15 pcm. In other words, a well-placed ring in the fuel pellet seems to cover almost all of the self-shielding effects.

4.1.2.2. Effects of the angular mesh refinement: current coupling

As seen from case 2 results in Tables 3 and 4, improving the angular representation using CC has a limited impact on kinf below 100 pcm for both mini-lattice and full-lattice configurations. The voided condition seems to be somewhat more sensitive to such angular mesh refinements. This might be explained by the fact that lack of collisions in high void fraction regions reinforces the anisotropic movement of neutrons and therefore the consequences of the use of an angular isotropic source.

4.1.2.3. Effects of the best estimate physics modeling option: collision probabilities

For the mini-lattice geometry, the impact of a fine spatial mesh refinement in the bypass water combined with the CPs applied on larger sub-domains of the moderator is truly significant at high void with a reactivity worth around 213-270 pcm by comparing cases 11 and 9 in Figures 9-12. At high void fraction, the mfp of neutrons increases, which enhances the leakage into the surrounding moderator regions and increases the importance of slowing down neutrons. At the burnup point 20000 MWd/tU, the migration area of the homogenized mini-lattice in case 11 goes from 56.6 cm² at 0% void fraction to 149 cm² at 80% void fraction. Moreover, from Figures 13-16, it can be noticed that gradients in the thermal and fast flux are respectively 1.6 and 2.2 times higher at voided condition than at non- voided in the active coolant region close to the external bypass, comparing cases 11 and 9. Furthermore, magnitudes of the thermal and fast flux gradient in bypass regions are globally two times higher at voided condition than at non-

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29 / 42 voided condition. Using a fine spatial mesh in the inner and outer bypass with CPs inside has a lower effect at non- voided condition since the moderation capacity of the active coolant is comparable to that in surrounding moderator regions, thereby reducing the leakage into moderator water regions and consequently its importance.

For the full-lattice configuration, a non-expected much smaller change in k_inf, i.e. 170 pcm less (average over the burnup range at 80% void fraction), can be observed by comparing cases 11 and 9 from Tables 3 and 4 between the full-lattice and mini-lattice geometries. This might be explained by the prevailing larger gradient flux in the longitudinal direction of the mini-lattice (due to the presence of non-boiling water regions at the bottom and top parts combined with the use of specular reflection at its periphery) thereby amplifying the effect of the best estimate physics modelling option in the surrounding moderator regions.

A final observation, mini-lattice kinf values from cases 3 and 12 differ only by 8.5 pcm (average over the burnup range at 80% void), leading to the conclusion that, with such a system-wise direction-preferential flux gradient prevailing, the applied spatial mesh refinement in case 3 might be sufficient for getting first indications of how mesh refinement affects the reactivity.

4.1.3. Conclusions

This 2D lattice physics analysis, first performed on a mini-lattice system and then on a realistic modern full- lattice configuration, shows that spatial mesh refinement in the active coolant area is of importance and might introduce an axial reactivity bias. Moreover, applying CPs in internal and external bypass water regions of a full BWR fuel lattice segment seems to have no major impact on kinf and thus might be not advantageous compared to the much cheaper CC methodology. However, many more and different types of fuel lattice designs need to be analyzed in order to confirm this observation on a broader base.

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4.2. 3D mini‐core nodal analysis

4.2.1. Results

Axial power distributions and their differences relative the reference coarse mesh power distribution (case 1) for the mini-core configuration 1 (see Table 5) with black boundary conditions applied in the axial direction are depicted in Figures 21 and 22. Furthermore, axial power profiles of the case 1 for four different mini-core configurations and conditions (described in Table 5) are displayed in Figure 23.

Figure 21. Mini-core power distributions for various mesh refinement cases with black boundaries assigned axially.

Figure 22. Differences in mini-core power distributions relative coarse mesh power distribution with black boundaries assigned axially.

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31 / 42 Table 5. Four different mini-core configurations of the case 1.

Configuration

# Mini-core composition Coolant density profile

1 All fuel segments (from 1 to 5) Realistic (Figure 8)

2 All fuel segments (from 1 to 5) Fixed (set at 456.32 kg.m^-3, i.e. 40% void fraction) 3 Only one fuel segment (3^rd one) Realistic (Figure 8)

4 Only one fuel segment (3^rd one) Fixed (set at 456.32 kg.m^-3, i.e. 40% void fraction)

4.2.2. Discussions

A non-conventional axial power distribution was obtained due to the imposed realistic void profile (Figure 7) and the extreme nuclear design employed for the fuel bundle, as shown in Figure 21. The first fuel segment, filling the fuel bundle from 0 cm to 15 cm, contained indeed no BA but a relatively high enrichment to be a blanket zone whereas the next three segments above contained relatively high BA loading. However, as seen in Figure 23, for the configuration 4 an expected axial cosine distribution was obtained over the radially infinite mini-core when it was only filled by one fuel-segment type (fuel-segment 3 here) and when a constant void profile was imposed over this mini-core.

As can be recognized from Figure 22, spatial mesh refinement performed by adding more regions azimuthally in the active coolant area (case 6) has a large impact on the axial power. A rather strong power tilt, i.e. from -3.55% in the bottom part to +1.83% in the top part of the mini-core, was obtained. An even larger power tilt can be observed after then applying CPs within the internal bypass and external bypass water regions (case 11) with a power difference varying axially from -4.59% to 2.45%.

4.2.3. Conclusions

The above observations seem to be in agreement with those made in Ref. [1], i.e. applying different angular and spatial discretizations in lattice physics using a flat source approximation generating nodal cross section data to the nodal core simulator may potentially lead to an axial power tilt.

Figure 23. Axial power distributions of the case 1 for four mini-core configurations.

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4.3. 3D full‐core equilibrium cycle nodal analysis

4.3.1. Results

4.3.1.1. keff trend

4.3.1.1.1. Equilibrium cycle condition

An equilibrium fuel cycle was investigated for each mesh refinement case based on the keff trend available in CM2. Convergence that occurs in equilibrium condition may diverge due to the introduction of a perturbation via the mesh refinement and has normally to be remediated via notably a new fuel design. In this regard, a quantitative criterion needs to be given for confirming the equilibrium state: if the absolute value of keff difference between two consecutive cycles is less than 15 pcm at 9600 EFPH (Effective full power hours), then the system has reached the equilibrium state. Oscillations in this point, 9600 EFPH, are checked because it corresponds to the correct cycle length given by end of full power (EOFP). Small oscillations in the beginning and middle of the cycles can be handled by adjusting the control rod pattern during each cycle. According to this criterion, all investigated mesh refinement cases reached equilibrium. However, some cases did not meet the preset keff target. Figure 24 shows equilibrium fuel cycles for the reference mesh case (case 1).

Figure 24. keff trends of the last four cycles regarding the reference case (case 1) with keff hot and keff cold references.

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33 / 42 4.3.1.1.2. keff comparisons

The equilibrium cycle keff behaviour as function of the cycle burnup in units of EFPH for each mesh refinement case is illustrated by Figure 25.

Figure 25. keff trend from the 8^th cycle for each case with keff hot and keff cold references.

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34 / 42 4.3.1.2. Axial power distributions

The node minimum, average (over the core) and maximum axial power profiles at three different exposures 0 EFPH, 4500 EFPH and 9600 EFPH, as well as the node average axial power differences relative case 1 for the various mesh qualities (evaluated at the 8^th cycle) are displayed in Figure 26 to Figure 31.

Figure 26. Minimum, average and maximum of the axial power profile at 0 EFPH for the various studied cases.

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Figure 29. Differences in average axial power at 0 EFPH relative case 1.

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36 / 42 4.3.1.3. Core axial power offset

During core operation, the core axial power offset (APO ) measures the axial power tilting in the core, i.e.

the relative difference between power in the upper part and lower part half of the core [14].

The overall APO is defined as [14]:

APO ¹

∙ ∆ ∆

where is the relative node power density at axial elevation k (k=1,…, KMAX) in assembly a (a=1,…, AMAX),

∆ the height of node k and H the total height of an assembly.

If the APO is larger than one, the axial power shape of the core is top peaked, while if the APO is smaller than one, the core is bottom peaked. The axial power shape has a strong influence on reactor stability. Bottom- peaked power shapes are most unstable because they tend to increase the axially averaged void fraction. Equilibrium cycle APO predictions are provided in Table 6.

4.3.1.4. Shutdown margin

The shutdown margin (SDM) is the instantaneous amount of reactivity by which a reactor would be subcritical from its present condition assuming all control rods are fully inserted, except for the single rod with the highest integral worth (total reactivity worth of the control rod at that particular degree of withdrawal), which is assumed to be fully withdrawn. Shutdown margin is required to be valid at any time, even when the reactor is critical. Enough negative reactivity capable of being inserted by the control rods to ensure complete shutdown at all times during the core lifetime is paramount [15].

Mathematically, the shutdown margin for a given control rod “i” is defined as the relative difference between the critical of the reactor core (noted ) and the that is obtained if all control rods are fully inserted except the one that is investigated (noted ), which is fully withdrawn [16]:

∀ ∈ 1, … , , ∙ 100 .

The relationship between total control rod worth, core excess and shutdown margin is also illustrated by Figure 32.

In this analysis, the design criterium of 1.6% for the SDM has been imposed. Equilibrium cycle SDM predictions keeping the kref fixed are presented in Table 6.

Figure 32. Shutdown margin, control rod worth and core excess representation.

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37 / 42 4.3.1.5. Linear heat generation rate

The linear heat generation rate (LHGR) corresponds to the heat generated by a unit length of a fuel rod in the axial direction. The LHGR quantity is related to fuel temperature and to fission gas release and pressure build up. For instance, the LHGR is monitored to prevent cladding cracking that eventually could lead to cladding failure if a certain power level is exceeded, caused by the difference in the thermal expansion rate between the fuel pellet and cladding material. The LHGR depends both on the type of fuel and exposure. Equilibrium cycle LHGR values are summarized in Table 6.

4.3.1.6. Summary results

Table 6 provides differences in important equilibrium cycle nuclear design parameters for different mesh representations relative the reference coarse mesh values (case 1).

Table 6. Reactivity, nodal power and thermal margin prediction differences obtained from the last cycle (8^th).

Cases

#

keff diff.

(pcm)

Node max. power diff.

(%)

APOcore diff.

(%)

Min. SDM diff.

(%)

Max. LHGR diff.

(kW/m) 0

EFPH

4500 EFPH

9600 EFPH

0 EFPH

4500 EFPH

9600 EFPH

0 EFPH

4500 EFPH

9600 EFPH

0 EFPH

4500 EFPH

9600 EFPH

0 EFPH

4500 EFPH

9600 EFPH

Ref.

value ^0.99550^0.994480.99411 2.369 2.209 1.893 -17.9 -15.8 13.0 1.74 2.33 2.47 44.7 38.1 34.1

2 ⁴⁵ ^{37 32 0.5}^-0.9 ^0.3 ^0.1 ^0.0 0.1 -0.11 0.00 0.06 0.0 0.1 0.4

4 -12 -10 -15 0.5 0.5 0.1 -0.3 -0.2 0.2 -0.02 -0.03 0.06 -0.1 0.2 0.0

5 -47 -36 -51 0.3 -0.6 -0.3 -0.3 -0.2 0.1 0.04 0.00 0.09 -0.1 0.1 0.4

6 -78 -274 -317 -1.9 -3.2 -0.8 -0.1 0.7 -1.0 0.18 0.38 0.50 0.0 0.0 0.6

7 -98 -294 -342 -1.3 -3.2 -0.7 -0.1 0.7 -1.0 0.35 0.55 0.67 0.1 0.0 0.7

8 -105 -305 -351 -0.7 -3.2 -0.6 -0.3 0.6 -0.9 0.36 0.55 0.69 0.3 0.0 0.7

9 -121 -329 -376 -0.2 -3.3 -0.7 -0.3 0.6 -1.0 0.41 0.61 0.76 -0.1 0.0 0.7

10 -94 -303 -359 -0.9 -3.4 -0.7 -0.3 0.7 -1.0 0.44 0.62 0.78 -0.2 0.0 0.7

11 -78 -291 -350 -0.9 -3.5 -0.6 -0.2 0.8 -1.0 0.45 0.67 0.83 -0.3 0.0 0.7

4.3.2. Discussions

In Figure 25, the equilibrium cycle hot keff behaviour for the considered mesh refinement cases seems to be in agreement with the 2D full-lattice kinf trend presented in Figures 17-20. Small level shifts in keff are obtained by improving either the angular discretization (case 2) or the spatial mesh refinement in the internal and external bypass water regions (cases 4 and 5). However, a rather large hot keff level shift around -350 pcm as well as a changed within- cycle reactivity behaviour was obtained by an improved spatial mesh in the coolant water region (i.e. case 6) and/or using the best estimate method represented by case 11. It should be noted that such large level shifts might be handled by only adjusting the loading pattern and the related control rod sequence in the framework of equilibrium cycle analyses. Furthermore, these reactivity shifts, likely to occur in real core operation evaluations, are undesired as they introduce an uncertainty in the batch size of fresh fuel bundles loaded into the core (i.e. neutron economy).

From Figures 26-31 and Table 6, it is seen that improving the spatial meshing in the active coolant region and in the fuel pellet combined with the CPs inside the surrounding moderator regions (case 11) has the largest impact on the predicted power profiles, i.e. up to –3.5% in maximum node power. Largest deviations in thermal margin predictions are also observed for case 11 with a burnup dependence of the APOcore (indicating an axial power swing during the cycle) going from -1.0% to +0.8% and a non-wished SDM-change of 0.83%, where the latter is above the design margin commonly adopted. On the other hand, lattice physics mesh refinement seems to affect little less the LHGR, but still significant.

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38 / 42 4.3.3. Conclusions

Consequently, one conclusion is that nuclear design parameters seem to be quite sensitive to mesh refinement.

Appropriate measures have to be taken in order to assure that all margins are met. Important consequences due to these uncertainties in predicting the cycle keff behaviour and especially the core axial power distribution could occur on the design of the initial cores, but also during the 24-month reactor cores operation.

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5. CONCLUSIONS

Recently, a BWR void-dependent axial power tilt and relating reactivity bias was observed due to the use of a spatially flat source approximation in 2D lattice codes based on the CPs method or the MoC providing homogenized cross section data to the nodal core simulator. For transport codes based on CCCP method, the only viable approach is to employ an adapted mesh in lattice calculations in order to cope with this void-dependent reactivity bias. In this work, the code package HELIOS/POLCA7 was used to address the effect of spatial and angular mesh refinement as well as using CPs over larger sub-domains of the moderator on 3D mini-core and full-core nodal simulation results.

From the 2D lattice physics analysis, it has been seen that improving azimuthally the spatial mesh in the active coolant area is of most importance and might lead to an axial power tilt if not correctly addressed. The 3D mini-core analysis, without consideration of TH feedback but employing an imposed axial void profile over the core, enabled to confirm that such an axial power tilt is induced by improving the angular and spatial discretization as well as applying the CPs method in more extensively non-boiling moderator regions.

A 3D full-scale realistic 12-month BWR equilibrium cycle analysis showed that a rather large change in the keff behaviour is expected when active coolant mesh is azimuthally improved. In addition, large shift in power distribution was also observed where the axial power tilt varies also during the cycle. Overall, rather large uncertainties in important nuclear design parameters were recognized which may have significant consequences on the design of challenging initial cores in terms of complex fuel loading patterns and 24-month cycle core operation having very high BA loading.

Master of Science Thesis

WESTINGHOUSE ELECTRIC COMPANY

Nuclear fuel, nuclear services, nuclear technology, nuclear power plant design and equipment for the commercial nuclear electric power industry

GRENOBLE-INP Phelma / KTH

Double Degree in Nuclear Energy Engineering

Master of Science Thesis

Lattice physics mesh refinement study and its impact on full core nodal simulation results

Missions

Didier Bourgin

ABSTRACT

ACKNOWLEDGMENTS

CONTENTS

LIST OF FIGURES

LIST OF TABLES

APPENDICES

ABBREVIATIONS

1. INTRODUCTION

2. WORKING ENVIRONMENT 2.1. Westinghouse Electric Company

2.2. Westinghouse Electric Sweden

3. METHODOLOGY 3.1. Codes

T E ( , ,  

)

3.2. Schematic presentation

3.3. Problem description

4. NUMERICAL RESULTS 4.1. 2D lattice physics analysis

4.2. 3D mini‐core nodal analysis

4.3. 3D full‐core equilibrium cycle nodal analysis

5. CONCLUSIONS