investigation on debris related fuel failures in bwr ...732472/fulltext01.pdf · the master thesis...

Investigation on debris related fuel failures in BWRsupported by CFD simulations

Rafa l Baranowski

Supervisors:

Henryk Anglart

Britta Helmersson

Master of Science ThesisDivision of Nuclear Reactor Technology

Royal Institute of TechnologyStockholm, Sweden, June 2014

White

TRITA-FYS 2014:39ISSN 0280-316XISRN KTH/FYS/–14:39—SE

Copyright Rafa l Baranowski, 2014

Printed by Universitetsservice US-AB, Stockholm 2014

Abstract

The master thesis summaries an investigation on debris related fuel failures in BWR whichwas done in conjunction between Westinghouse Electric Sweden and KTH. The final resultsextend the Westinghouse’s current knowledge of debris preferential locations for depositionby radial and axial distribution within a spacer grid. It appears that the positions of aspacer cell closest to the frame has lower proportion of fuel failures compared to more innerregions, an exception from this is found for the spacer design featuring a mixing vane.There are indications that most of the debris caught either in the frame structure or by aspacer spring is not able to fail the fuel. The horizontal edges of the spacer are suspectedto be the dominant cause of debris catching that results in a fuel failure.

It is concluded, based on the number of the fuel failures, that the lower part of a spaceris more susceptible to through-wall debris fretting and accounts for about 2/3rd of totalnumber of primary failures It was observed that the introduction of mixing vanes in thespacers affected the 2/3rd distribution by increasing the number of frets at the upper halfof the spacer. CFD simulation of a flow sub-channel with mixing vane shows increasedflow velocity and particle concentration for the upper part of the spacer in regions regardedpotentially dangerous for debris capture and fuel rod failure. This supports the increase ofleakers at the upper edge of the spacer compared to the lower edge for spacers with mixingvane. In addition, it implicates a higher frequency of fuel failures for spacers with mixingvanes compared to spacers without mixing vanes.

i

Acknowledgments

I would like to offer my special thanks to Professor Henryk Anglart for giving me this greatopportunity, for the useful comments and guidance throughout this master thesis. I amdeeply grateful to Britta Helmersson for valuable suggestions, encouragement to do more,and for providing an excellent atmosphere making this work enjoyable and so much easier.I would like to thank Roman Thiele for all advices about computational simulations andfor help in resolving any software issue I have encountered in that matter.

I am particularly grateful to Pawe l Kobus for his willingness and patient while reading andcorrecting the statistical analysis, for his suggestions and valuable comments.

I wish to express my love and gratitude to my girlfriend, Karolina, whose patience andsupport helped me to overcome many crisis situations through the duration of these studies.

iii

Contents

I Analysis of Fuel Failure Data 1

1 Introduction 3

1.1 Fuel failure mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Primary fuel failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Fretting due to debris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Secondary degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 Mitigation of debris fretting failure . . . . . . . . . . . . . . . . . . . . . . 5

2 Data Interpretation and Processing 7

2.1 Data source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Data interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Results of Fuel Failures Distribution within a Spacer 11

3.1 Axial distribution of fuel failures . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Introduction of the DF filter and mixing vanes . . . . . . . . . . . . . . . . 12

3.3 Radial distribution of fuel failures . . . . . . . . . . . . . . . . . . . . . . . 14

3.3.1 Locations of failed rods in an assembly . . . . . . . . . . . . . . . . 14

3.3.2 Locations of failed rods in DMV . . . . . . . . . . . . . . . . . . . . 15

3.3.3 Radial location comparisons between different spacer designs . . . . 15

3.3.4 Detailed radial location of fuel failures . . . . . . . . . . . . . . . . 17

3.4 Types of fretting mark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Data Processing from Debris Search in Plant K 21

4.1 Axial distribution of debris within a spacer . . . . . . . . . . . . . . . . . . 21

4.2 Compilation of debris observations excluding debris in the frame . . . . . . 22

4.3 Conclusion on data from the plant K . . . . . . . . . . . . . . . . . . . . . 23

v

vi CONTENTS

5 Conclusions on Part I 25

II CFD simulation of the mixing vane effect 27

6 Introduction 29

7 Theoretical Background 31

7.1 Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

7.2 Reynolds-Averaged Navier-Stokes equations . . . . . . . . . . . . . . . . . 32

7.3 Boussinesq eddy-viscosity approximation . . . . . . . . . . . . . . . . . . . 33

7.4 Turbulence energy equation . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7.5 Standard k − ε turbulence model . . . . . . . . . . . . . . . . . . . . . . . 34

7.6 Realizable k − ε turbulence model . . . . . . . . . . . . . . . . . . . . . . 34

7.7 Wall-bounded flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

7.8 Wall functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

8 Lagrangian Particle Tracking 39

8.1 Stokes number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

8.2 Phase coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

8.3 Forces acting on a particle . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

8.4 Drag coefficient for non-spherical particles . . . . . . . . . . . . . . . . . . 42

8.5 Particle-wall interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

9 CFD in OpenFOAM 43

9.1 Case structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

9.2 Solvers and numerics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

10 Methodology 47

10.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

10.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

10.3 Initial and boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . 51

10.3.1 Inlet boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 51

10.3.2 Setup of boundary conditions . . . . . . . . . . . . . . . . . . . . . 52

10.4 Fluid properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

10.5 Particle properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

CONTENTS vii

11 Results 59

11.1 Fluid phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

11.2 Particle tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

12 Conclusions on Part II 65

viii CONTENTS

List of Figures

1.1 Primary fuel failure causes in BWR (B. Helmersson, November 2009). . . . 4

2.1 Examples of varying debris size and shape as well as possible lodge positions. 8

2.2 Schematic view of a fuel cell used for the purpose of data collection. . . . . 8

2.3 Example of the identification procedure for debris location within a fuel cell. 9

3.1 Compilation of fretting marks provided by the investigation for spacer de-signs: B, C, D and DMV. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Comparison of the fuel failures proportions with regard to contribution fromthe mixing vanes and the DF filter. . . . . . . . . . . . . . . . . . . . . . . 13

3.3 Radial locations of failed rods. . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4 Location of the failed rods in DMV. . . . . . . . . . . . . . . . . . . . . . . 15

3.5 Orientation of fretting marks within a spacer grid. Includes: B, C and D. . 18

3.6 Examples of the wiper type of fretting marks. . . . . . . . . . . . . . . . . 18

3.7 Examples of the horizontal type of fretting marks. . . . . . . . . . . . . . . 19

4.1 Debris distribution from the inspected fuel assemblies. . . . . . . . . . . . 22

9.1 Overview of OpenFOAM structure (OpenFOAM, 2013). . . . . . . . . . . 43

10.1 Fuel cells of the D spacer (left) and the DMV spacer (right). . . . . . . . . 48

10.2 Front view of the final model (left) and its isometric view (right). . . . . . 48

10.3 Background mesh. Green color denotes the symmetry planes, blue denotesthe inlet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

10.4 The background mesh and the STL geometry. . . . . . . . . . . . . . . . . 50

10.5 Representation of the geometry in the final mesh. . . . . . . . . . . . . . . 51

10.6 Streamwise component of the velocity along the channel axis. . . . . . . . 52

10.7 The outlet velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

ix

x LIST OF FIGURES

10.8 An example of the flow velocity along the fuel assembly in a peripheral, anaverage power, and a high power assembly (K. Ryttersson, et al., 2007). . . 54

10.9 Particle velocity along the channel axis measured from the inlet to the spacerregion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

10.10Flow channel with particle collector marked in blue. The near rods regionis marked in red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

11.1 Streamwise velocity (left) and turbulent kinetic energy (right) recorded dur-ing the spacer DMV simulation in the channel center at the upper edge. . . 60

11.2 Velocity at the upper edge of the D spacer. . . . . . . . . . . . . . . . . . . 61

11.3 Velocity at the upper edge of the DMV spacer. . . . . . . . . . . . . . . . . 62

11.4 Velocity plotted over the horizontal line for D. . . . . . . . . . . . . . . . . 62

11.5 Velocity plotted over the horizontal line for spacer DMV. . . . . . . . . . . 63

11.6 Particle dispersion at the point of the injection. . . . . . . . . . . . . . . . 63

11.7 Particle dispersion for the spacer D at the upper edge. . . . . . . . . . . . 64

11.8 Particle dispersion for the spacer DMV at the upper edge. . . . . . . . . . 64

.1 Mesh refinement seen from the inlet side. . . . . . . . . . . . . . . . . . . . 69

.2 Mesh refinement seen in the spacer region. . . . . . . . . . . . . . . . . . . 70

.3 Mesh refinement around the mixing vane. The lines going through the meshcells are due to wrong interpretation of the tetrahedral cells, cut with aplane, by the visualization software and have no representation in the mesh. 70

.4 Stream lines from the DMV simulation seen from upstream. . . . . . . . . 71

.5 Stream lines from the DMV simulation seen from downstream. . . . . . . . 71

.6 Particles path lines (tracks) around the mixing vane, seen from downstream. 72

.7 Particles path lines (tracks) around the mixing vane, seen from upstream. 72

List of Tables

2.1 Number of fuel failures for each spacer design available for the investigation. 7

3.1 Comparison of fuel failures location between axial regions of the spacers. . 11

3.2 Increased fraction of fuel failures observed in the upper part for the spacerDMV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.3 Radial distribution of failed fuels for each fuel design. . . . . . . . . . . . . 16

3.4 Expected values for the total number of failures. . . . . . . . . . . . . . . . 16

3.5 Types of fretting marks and their numbers for each fuel type. . . . . . . . . 19

4.1 Distribution of observed debris compared to the fuel failures. . . . . . . . . 23

7.1 Closure coefficients of the Launder-Sharma k − ε model . . . . . . . . . . . 34

7.2 Closure coefficients of the realizable k − ε model . . . . . . . . . . . . . . . 35

9.1 Discretization schemes for the fluid simulation. . . . . . . . . . . . . . . . 45

9.2 Solver schemes for the fluid simulation. . . . . . . . . . . . . . . . . . . . . 45

10.1 Basic dimensions and parameters of the models. . . . . . . . . . . . . . . . 49

10.2 Fraction of each fuel cell type in the final mesh. . . . . . . . . . . . . . . . 50

10.3 Mesh quality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

10.4 Setup of boundary conditions at the inlet and the outlet. . . . . . . . . . . 52

10.5 Setup of boundary conditions at the geometry. . . . . . . . . . . . . . . . 53

10.6 Mixture properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

10.7 Fluid properties for a high burnup assembly. . . . . . . . . . . . . . . . . . 55

10.8 Particle properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

11.1 Final residuals for the fluid simulation of spacer DMV and D. . . . . . . . 60

11.2 Particle distribution at the upper and lower edge of the spacers D and DMV. 61

xi

xii LIST OF TABLES

Nomenclature

Dimensionless Symbols

Re Reynolds numberRep Particle Reynolds numberSt Stokes numberStm Modified Stokes numberu+ Velocity at the near wall regiony+ Wall distance

Greek Symbols

α Void fractionδij Kronecker deltaε Dissipation per unit massεijk Permutation tensorκ Krmn constant; wave numberµ Dynamic viscosity; Meanν Kinematic viscosityνt Turbulent eddy viscosityρ Mass densityρf Fluid mass densityρp Particle mass densityρm Mixture mass densityτf Characteristic flow timeτij Specific Reynolds stress tensorτp Particle relaxation timeτp0 Particle relaxation time in Stokes flowτw Wall shear stressφ Particle sphericityωi Fluctuating vorticity in tensor notationΩij Rotation tensorΩij Mean-rotation tensor

xiii

xiv LIST OF TABLES

Roman letters

B Additive constant in the law of the wallCD Drag coefficientdp Particle diameterdr Rod diameterDh Hydraulic diameterE Expected frequencyFi Force vectorg GravityG Mass fluxk Specific turbulent kinetic energylh Channel entrance lengthmp Particle massO Observed frequencyp Instantaneous static pressurepl Lattice pitchs Surface area of a spheresij Instantaneous strain-rate tensorS Shear rate; Particle surface areaSp Slip ratioSij Mean strain-rate tensort Timetij Instantaneous viscous stress tensorT Characteristic time scaleu Instantaneous velocityu Instantaneous velocity in vector notationui Instantaneous velocity in tensor notationu′i Fluctuating velocity in tensor notation

u′i Temporal average of fluctuating velocity

up Particle instantaneous velocity in vector notationuτ Friction velocityU Mean velocityUi Mean velocity in tensor notationUi Temporal average of mean velocity

vN,imp Impact velocity normal to the collision wallxa Steam actual qualityxi Position vector in tensor notation

Abbreviations

BTP Bottom Tie PlateBWR Boiling Water ReactorCFD Computational Fluid DynamicsCP Contact PointDF Debris FilterGAMG Geometric Algebraic Multi GridKTH Kungliga Tekniska HogskolanLHR Linear Heat RateMV Mixing VanePBiCG Preconditioned Bi Conjugate GradientPCI Pellet Clad InteractionRANS Reynolds Averaged Navier StokesRPV Reactor Pressure VesselSIMPLE Semi Implicit Linked Equations

xv

xvi LIST OF TABLES

Part I

Analysis of Fuel Failure Data

1

Chapter 1

Introduction

It is essential that the fuel cladding, which is a key barrier to containing fission products, isrobust and stays intact. Fuel failures contribute to increased plant background radiation,which impacts plan outage and increases workers’ exposure. At any time the fuel perfor-mance should be sufficient to limit radiological release. Fuel failures have a large financialimpact on a power plant. Electricity production is reduced when the plant is forced to stopand remove the failed fuel assembly.

Debris related fuel failure is the remaining most frequent mode of the fuel failure in theWestinghouse BWR fuels accounting for 93% of occurrences in the recent years, 1993-2008(B. Helmersson, November 2009). Debris filters, innovative spacer designs and a goodunderstanding of the failure mechanism are hence of paramount importance.

Debris fretting occurs when there is a mechanical interaction between debris and cladding.The coolant flow will induce debris vibration, which will fret the cladding and lead to thefuel failure. Debris in the primary system is known to be generated by various types ofmaintenance and repair works. Wires from steel brushes, metal turnings, threads are exam-ples of such debris. It can also be generated on occasion when filters or pumps break down(K. Rytterson et al., 2007). A debris-fretting hole is usually used to deduce debris frettingas a primary failure cause. The confined structure of a spacer is a preferential location fordebris catching but also imposes difficulties for visual detection of debris primary failure.

The purpose of this part of the work is to investigate if any preferred positions for debriscatching and through-wall fretting within a spacer grid exist by quantifying where axiallyand radially debris most likely locates. The work provides analyses of five spacer designs,in chronological order: A, B, C, D and DMV. Due to the confidentiality the true nameswere replaced. The work is based on reported fuel failures that occurred in the past 20years of Westinghouse’s experience as well as a debris search performed in K nuclear powerplant in 2010. The position of debris within spacer grid is judged based on the location offretting marks for primary failure. All the fretting marks analysed in this work have led tothe fuel failure, thus, hereafter the term ‘fretting mark’ is used is a sense of a fretting thatcaused a fuel failure.

3

4 CHAPTER 1. INTRODUCTION

1.1 Fuel failure mechanism

Fuel reliability is fundamental to a safe and economical operation of nuclear plants. Failurefree fuel has always been of paramount importance for nuclear utilities and fuel vendors.The knowledge of the root cause of every fuel leaker is invaluable in the development workfor a high reliable fuel with failure free performance.

1.2 Primary fuel failure

Industry-wide, several causes of the primary fuel failure in BWR have been addressed,schematically depicted in Figure 1.1.

Manufacturing defects resulting from a primary hydriding, organic contamination andresidual moisture in the fuel pellets. These defects can be effectively diminished by limitsof hydrogen content in the fuel and well established manufacturing processes.

Pellet-clad interaction occurs as a consequence of a rapid power increase, usually by themovement of a neighboring control rod. The standard BWR cladding material, Zircaloy-2, is relatively susceptible to PCI. Low-alloyed zirconium used in the liner materials onthe cladding inner surface is much less sensitive and widely used now by many vendors(B. Helmersson et al., 2009). In modern Westinghouse’s fuel this type of failure have beenreduced to zero by introducing a liner cladding, in 10x10 fuel design, and effective operatingguidelines (B. Helmersson, November 2009).

Corrosion is a mechanism of primary fuel failure related to water chemistry and its ag-gressive interaction with cladding under abnormal conditions. Cladding material, plantadjustments and coolant chemistry surveillance are examples of means for dealing withthis issue.

Dryout occurs when a liquid film, cooling the rod surface, is replaced by a thin vapor filmwith very low thermal conductivity which results in overheating of the fuel cladding. Anextensive experience and conservative approach in Critical Power Ratio calculations resultin minute number of dryout induced fuel failures (B. Helmersson, November 2009).

Debris fretting, in most of the BWR nuclear power plants, is the remaining most frequentmode of the fuel failure (K. Rytterson et al., 2007). It is the main primary failure causeof Westinghouse BWR and many efforts have been focused on debris related failures theirmechanism and remedies.

Figure 1.1: Primary fuel failure causes in BWR (B. Helmersson, November 2009).

1.3. FRETTING DUE TO DEBRIS 5

1.3 Fretting due to debris

The entrapment of metallic debris in fuel assemblies, which can lead to rapid fretting andpenetration of the cladding wall is a common mechanism of the debris induced fuel failure.Debris in the primary system can be generated by various types of maintenance and repairworks.

The current statistical analysis of debris fretting failures in Westinghouse BWR 10X10 fuelshows that (K. Rytterson et al., 2007):

The frequency of occurrence of the penetrating debris fretting increases with theelevation of the fuel rod. Thus, it indicates dependency for fretting failure on increasedflow velocity.

The debris particle vibrates under influence of the coolant flow and causes fretting erosionof the cladding. The increased flow velocity with axial position and with increasing powerpromotes higher frequency and more rapid erosion of the oxide layer and the cladding.

The majority of the debris fretting failures occurs during the first half of the fuelsnormal operating life.

The younger fuels have less wear resistant oxide coating than older fuels which forms onthe cladding surface as a result of corrosion during irradiation and is much harder than thebase alloy.

1.4 Secondary degradation

The primary failure is commonly a small hole or crack in the cladding material throughwhich water can enter the fuel rod and then vaporize. When the steam penetrates thefailed rod it undergoes radiolysis forming hydrogen. The steam also oxidizes the fuel andcladding material, which contributes to the hydrogen production (P. Rudling, T. Ingemans-son, 2004). If the partial pressure of the hydrogen is sufficiently high a rapid uptake by thecladding will follow leading to high local concentration of hydride. Zirconium hydrides arevery brittle and the cladding zone that is completely transformed into zirconium hydridemay easily fracture. If the fuel develops an open secondary failure in form of open cracksin the cladding, a path for fuel dissolution and uranium washout exists. The developmentof the secondary failure depends on many parameters in the fuel as well as in the reac-tor power history. Cladding material, burnup, local power and power transients or thesize and position of the primary failure are examples of such parameters (P. Rudling, T.Ingemansson, 2004).

The secondary failure occurs at a distance from the primary failures and its severity in-creases with rod average Linear Heat Rate. The breaks tend to occur at positions wherethe LHR is high (K. Rytterson et al., 2007).

1.5 Mitigation of debris fretting failure

The mitigation of debris fretting failure can be implemented at many different stages in-cluding a defense in depth strategy. It starts from eliminating sources of debris from which,


work activities in systems connected to the feedwater system are the dominant one. Changein workers’ awareness and appropriate trainings and education are common practices amongnuclear power plants but it is also recognized that this is the most difficult thing and takesthe longest time.

Once the debris reaches the primary loop it must be kept outside of the fuel assembly.Debris filters and debris traps are means which, to some extent, can protect the fuel fromreaching by the debris. An example is an advanced debris filter, DF (the true name isreplaced), developed by Westinghouse and aimed at catching long and thin debris. Studieshave shown that this type of debris constitutes the largest fretting risk. Trapping efficiencytests demonstrate that DF reduces the risk of harmful debris entering the fuel assemblyby one to two orders of magnitude (B. Helmersson, November 2009, K. Rytterson et al.,2007).

The next step to minimize the risk of the fuel failure is to reduce the potential places wheredebris can be caught and fret through the cladding. This can be done by a spacer design.The idea is to ensure that all debris that passes a filter are too small to be caught in thespacer grid and pose a risk on the fuel integrity.

Removal of existing debris in RPV and primary loop is the last preventing measure, how-ever, feasible only during a maintenance shutdown. Debris that are loosely lodged in a fuelassembly falls out during the core shuffle. The intent is to remove the debris that derivesfrom the previous shutdown and operation. Vacuuming the sludge from the bottom of theRPV is thus the mean to remove some residual debris.

Chapter 2

Data Interpretation and Processing

2.1 Data source

In total, up to year 2013, there have been 133 fuel failures for the Westinghouse 10x10 fueltypes as listed in Table 2.1. Spacer A is used in the analysis only to some extent due toinsufficiently information provided by the reports. The necessary information was collectedfrom different available sources (e.g. inspection videos, archived reports, fuel failure database), which sometimes made it difficult to clearly identify the point of debris capture.Moreover, some of the failures are not relevant to the objectives of this work where thelocations of their primary failures are either far above or far below the spacer grid e.g. justabove the bottom tie plate.

In total, 103 instances of a fuel failure constitute the basis for detailed analyses.

Fuel type Number offuel failures

Not included inthe detailed

analyses

Source

A 20 20 Not investigated indetails

B 41 3 VHS, CDs, ArchiveC 36 6 DVDs, ArchiveD 9 1 Data base

DMV 27 0 Data baseTotal 133 30

Table 2.1: Number of fuel failures for each spacer design available for the investigation.

2.2 Data interpretation

Due to the various size and shape of expected debris, especially for fuels not equipped witha debris filter, the precise identification of location for debris that caused fuel failure islimited. Figure 2.1 shows examples of variation in debris size and ways it can be caught.Thus, it was decided to divide a fuel cell into four vertical regions and three horizontal to

7

8 CHAPTER 2. DATA INTERPRETATION AND PROCESSING

which every fretting mark will be assigned with accordance to available information. Aschematic view of the fuel cell used for the purpose of data collection is presented in Figure2.2.

Figure 2.1: Examples of varying debris size and shape as well as possible lodge positions.

The octagonal fuel cell is similar for all analyzed spacers with respect to location andnumber of fix contact points and springs. This allows a consistency in fuel failures mappingand analyses. All fuel failures were processed in similar manner. Marks made either by thefix contact points or by the spring contact points served as an indication of debris lodgeposition and region within a fuel cell. If the location corresponds to any of the four regionswithin the lower part of the spacer it is placed at the lower edge of the schematic view andsimilarly for the upper edge. Figure 2.3 shows two examples of the identification procedure.

Figure 2.2: Schematic view of a fuel cell used for the purpose of data collection.

2.2. DATA INTERPRETATION 9

Figure 2.3: Example of the identification procedure for debris location within a fuel cell.

10 CHAPTER 2. DATA INTERPRETATION AND PROCESSING

Chapter 3

Results of Fuel Failures Distributionwithin a Spacer

3.1 Axial distribution of fuel failures

Higher numbers of fuel failures in the lower part of spacer are observed for each spacerregardless the design or total number of instances. The lower part of a spacer clearlydominates the axial distribution with 67% of the total number of failures, while 31% isobserved for the upper part and 2% for the spring region, Table 3.1. It must be stressedthat one of the fretting marks assigned to the spring region is identified with low confidence(weak evidence) thus possibly decreasing the fraction of the failures attributed to the springregion to a single one. Very low number of failures observed for the spring region triggeredadditional analysis devoted to it and the results are presented in chapter 4.

B C D DMV Sum

Upperedge

1026%

930%

225%

1141%

3231%

Springs 13%

13%

00%

00%

22%

Loweredge

2771%

2067%

675%

1659%

6967%

Total 38 30 8 27 103

Table 3.1: Comparison of fuel failures location between axial regions of the spacers.

Figure 3.1 shows the schematic of a fuel cell with all investigated fretting marks mappedtogether. Each fretting mark is denoted by a number corresponding to its position inthe data base for 10x10 fuel. Characteristic fretting marks are denoted by additionalunderlying or an asterisk and they are discussed in section 3.4. The failures are coloredwith the following rule.

N - high certainty of fretting mark location, N - low certainty of fretting mark location

N- horizontal type of fretting mark, N* - wiper type of fretting mark

11

12CHAPTER 3. RESULTS OF FUEL FAILURES DISTRIBUTIONWITHIN A SPACER

Figure 3.1: Compilation of fretting marks provided by the investigation for spacer designs:B, C, D and DMV.

3.2 Introduction of the DF filter and mixing vanes

DMV was the first design of Westinghouse’s fuels where mixing vanes were introducedinside a spacer grid. Enhanced flow mixing and increased thermal margin to dryout isprominent features of this fuel. Each flow channel is equipped with one vane deflecting andswirling the coolant stream around the four neighboring rods. The equal number of theright-hand steered vanes and the left-hand steered vanes are designed to provide balancedmomentum exerted on the spacer grid.

The difference in design of DMV and previous fuel types is not only mixing vanes. The DFfilter is another innovation introduced and applied in large scale to the new design. TheDF filter lowers the size range of the debris passing through the bundle. For 27 fuel failuresrecorded for DMV only 6 of them lacked the DF filter. Thus the comparison between thisdesign and previous ones with respect to fuel failures is not straightforward; two factorsmay contribute to any new unusual observation.

Table 3.2 compares the observed number of the fuel failures for DMV and the number offuel failures recorded for the three previous spacer designs, the spacer A is not includedin this analysis. A significant increase is observed for the upper edge. Figure 3.2 shows asignificant change in the fuel failure proportions between the upper and the lower edge forDMV.

In order to analyze the influence of the mixing vanes and the DF filter, the comparison ismade in two ways. The two left bars compare the fuel failures regarding contribution fromthe mixing vanes, here the fuel failures with MV corresponds to all failures for DMV andthe fuel failures without MV to the failures recorded for the older designs. The two right

3.2. INTRODUCTION OF THE DF FILTER AND MIXING VANES 13

bars are made for fuels with the DF filter and without DF, respectively. In both casesthe increase in the proportion of the fuel failures between the upper edge and the loweredge is observed. However, none of the comparisons presented in Figure 3.1 exclusivelydepict influence of only one factor; the fuel failures with DF also include fuel failureswith the mixing vanes and some of the fuel failures with MV lack DF. Although, thereis slightly higher change for the case with the mixing vanes it is still too subtle for anyclear statement. Ideally, in order to rule out one of the factors, one need to compare fuelfailures that happened, for instance, for fuels not equipped with DF filter but featuredmixing vanes. From the analysed data base there are only 6 instances of DMV that fulfillthis criterion (with MV and without DF) and the proportion is 50%. Obviously, a fairjudgment cannot be made based on such small number. There is an apparent change butdue to mentioned factors a sole possible cause cannot be stated.

B C D Sum DMV

Upper edge 1026%

930%

225%

2128%

1141%

Springs 13%

13%

0 23%

0

Lower edge 2771%

2067%

675%

5370%

1659%

Total 38 30 8 76 27

Table 3.2: Increased fraction of fuel failures observed in the upper part for the spacer DMV.

Figure 3.2: Comparison of the fuel failures proportions with regard to contribution fromthe mixing vanes and the DF filter.

The disturbed flow between lower and upper part of the spacer caused by mixing vanes is


one of the suggested causes for the increased fraction of fuel failures observed in the upperpart of the spacer.

The influence of the mixing vane on the proportional increase for the upper edge through-wall fretting is subjected to further analysis by means of CFD simulation. Part II of thiswork is solely devoted to this issue.

3.3 Radial distribution of fuel failures

The fuel failure distribution in radial direction is presented in two ways. Firstly, generaldistribution according to the failed rod location in an assembly. Secondly, location of eachfretting mark with respect to its orientation inside a fuel cell is shown.

3.3.1 Locations of failed rods in an assembly

Figure 3.3 presents radial locations of failed rods for five spacer designs i.e. A, B, C, D andDMV. An apparent difference in failures per location is observed between an inner region(mark in red) and peripheral (mark in blue), with higher proportion of failures occurringin the inner region. There are 60 peripheral positions and 36 interior positions which areused to normalize the number of failures in each position.

Figure 3.3: Radial locations of failed rods.

It is clear that the fuel failures are not distributed uniformly in radial direction. Twopossible explanations could be considered. First one is the difference in the flow velocitiesbetween those regions, which may result in different vibrations of debris and probabilitiesfor causing fuel failure. A flat surface, like the channel wall next to the peripheral positions,lowers the flow velocity. A lower flow velocity leads to a lower probability for debris tobe able to fret through the cladding. The frame structure may be another factor that canaffect debris distribution in that region. In section 4 the latter is investigated further.

3.3. RADIAL DISTRIBUTION OF FUEL FAILURES 15

3.3.2 Locations of failed rods in DMV

The locations of the failed rods for DMV are presented in Figure 3.4. The total number offuel failures for this spacer recorded in the database is 27. The sub-bundle B is where mostof the failed rods were located. Moreover, high asymmetry within that bundle is observedwith failures concentrating around the 1/3 part length rod. This corner is circled in Figure3.4.

Figure 3.4: Location of the failed rods in DMV.

All the 7 failed rods in the closest vicinity of the 1/3 part length rod have the primaryfailure above the shorter rod. This unusual concentration of fuel failures raises a suspicionthat the free space above the part length rod may somehow promote debris concentrationin that region and thus higher number of fuel failures. However, from the symmetry of theassembly the other corners should exhibit similar accumulation of through-wall fretting butthey do not. Due to the relatively low number of fuel failures for this spacer the observedhigh asymmetry may result from a pure randomness.

3.3.3 Radial location comparisons between different spacer de-signs

Another distinguishing feature of DMV is observed for proportions of failures between theinner region and the periphery of a fuel bundle which is summarized in Table 3.3. For fueldesigns prior to DMV, the inner region was dominant, with one exception for B where thefractions are close to equality. In the case of DMV more failures per location is recordedfor the periphery.

The significance of the observed differences is tested with Pearson’s chi-squaredtest

The objective is to test if the distribution between the inner region and the periphery isdependent on the spacer type. In other words, how likely is that the observed differencesare due to pure chance and can be explained by randomness.

In this case we consider two categorical variables, region of a spacer and type of a spacer,and the total number of failures as the frequency of events (the count). The null and thealternative hypotheses are stated as follows.


Inner Region Periphery

Totalnumber of

failures

Failuresper

location

Totalnumber of

failures

Failuresper

locationA 13 0,36 7 0,12B 15 0,42 26 0,43C 19 0,53 17 0,28D 5 0,14 4 0,07

DMV 7 0,19 20 0,33

Table 3.3: Radial distribution of failed fuels for each fuel design.

H0 : The location of failure is independent of spacer type.

H1 : The location of failure is dependent on spacer type.

The value of the test-statistic is calculated according to Eq. (3.1)

χ2 =r∑i=1

c∑j=1

(Oi,j − Ei,j)2

Ei,j(3.1)

Where

Oi,j is an observed frequency (number of failures for each region and spacer type)

Ei,j is an expected frequency, asserted by the null hypothesis

r and c denote number of rows and columns in Table 3.3, respectively.

The calculation of the expected frequency is carried out using Eq. (3.2) and the obtainedvalues are presented in Table 3.4.

Ei,j =

(∑cj=1Oi,j

)(∑r

i=1Oi,j)

N(3.2)

N is the total number of observations

Inner Region Periphery

A 8.9 11.1B 18.2 22.8C 16.0 20.0Da 4.0 5.0

DMV 12.0 15.0

Table 3.4: Expected values for the total number of failures.

The resulting value of the chi-squared test is 9.66. For this case there are 4 degree offreedom and the corresponding probability of the resulting value or higher under the null

3.4. TYPES OF FRETTING MARK 17

hypothesis is 0.0465, thus the null hypothesis must be rejected on the significance level of0.05. The probability of the observed differences being an effect of pure chance is 4.65%meaning that the proportion of fuel failures between inner and peripheral region dependson the spacer type.

The next test is performed for all spacer designs except DMV. The goal is to check whetherthe resulting significance in the fuel failures distribution is introduced by DMV or it is alsopresent for the designs prior to DMV. For this case the chi-squared test gives value of 4.94and the number of degree of freedom reduces to 3. Hence, the probability of the observeddifferences is 17.6% and the null hypothesis cannot be rejected at any typical significancelevel.

Based on the above it is concluded that the observed increase in the fuel failures in theperiphery for DMV is significant and cannot be explained by coincidence.

It should be stressed that with chi-squared test the frequency of the fuel failures was tested,i.e. the number of failures for a given region divided by the total number of failures for thegiven spacer, not the number of failures recorded for each spacer type. In latter case, thedifference between spacer designs is obvious and results simply from the time and numberof fuel assemblies that have been in service for particular spacer design.

3.3.4 Detailed radial location of fuel failures

The identification procedure of fretting marks utilizing four regions of a fuel cell allowsmore detailed summary of fuel failures occurrence in a radial direction. It is not adaptedto the cases where sufficient information about the fretting mark was not obtained, section2.1. Those identified with low confidence, as mentioned in section 2.1, are marked with bluenumbers and placed in the center of the fuel cell. The results are mapped on a schematicview of a sub-bundle B and presented in Figure 3.5.

The results do not include failures for DMV due to inconsistency between the spacer designs.The locations of the fix contact points and the spring contact points do not correspondbetween the previous designs and DMV design. The older spacers have the fix contactpoints (C) and springs (S) in the same positions, with only one exception for the fuel cellF1 in the spacer D. No fuel rods have failed in that position for the spacer D.

In order to compile all four sub-bundles on a single one each of the sub-bundles was rotatedaround the central point of the assembly by an adequate angle.

Observation on failed fuel rods and their distribution within an assembly concluded thatthe likelihood for a rod to fail in the periphery is lower than in the inner region. Further,based on the detailed distribution in Figure 3.5, the likelihood for a rod located in theperiphery to be fretted from the frame side is lower than for the same rod to be frettedfrom the inner side. One of the factors that can contribute to this, as mentioned in section3.3.1, is the spacer frame which may serve as a protective barrier from debris to reach andfail a rod. This is discussed more in section 4.

3.4 Types of fretting mark

The investigation reveals a relative increase in number of fretting marks that differ in manyaspects from the most common horizontal. A characteristic feature of the new type is a


Figure 3.5: Orientation of fretting marks within a spacer grid. Includes: B, C and D.

circular mark accompanied with perpendicular crack or fret, henceforth called “wiper”.Figure 3.6 gives examples of this type of fret. The true mechanism is not easy for identi-fication. For instance, the right picture in Figure 3.6 shows a fretting mark located closeto the mark made by the fix contact point, which could suggest that the contact point ispreferable location for this mark to occur. However, it is observed in the left picture thatthe fix contact point is not the essential requirement for this to happen.

Figure 3.6: Examples of the wiper type of fretting marks.

A relative increase in number of the wiper type of fretting marks is observed for the DMVdesign, this is shown in Table 3.5.

3.4. TYPES OF FRETTING MARK 19

Figure 3.7: Examples of the horizontal type of fretting marks.

B C D DMV Sum

Horizontal 47% 42% 63% 48% 47%Wipers 13% 3% 13% 22% 13%Other 39% 55% 25% 30% 40%

Table 3.5: Types of fretting marks and their numbers for each fuel type.

The horizontal fretting marks account for about 47% of total observed frets, Figure 3.7.A successor of DMV spacer, developed by Westinghouse, features means to eliminate fuelfailures resulting from the mechanism behind the horizontal fretting marks. By this, andregarding the fraction of the horizontal type of fretting marks, a substantial improvementin the fuel performance can be achieved.

Chapter 4

Data Processing from Debris Searchin Plant K

The debris search performed in K power plant on 356 fuel assemblies with spacer B providesvast number of information regarding debris preferential locations and distribution fordebris that has not led to through-wall fretting. Each sub-assembly was inspected along itsentire length and from all four sides. Visually detected debris was noted in the inspectionrecord.

The geometry of the fuel imposes limitations for an inspection of this kind on sub-bundlelevel compared to fuel rod inspection as was done on the leaking fuel in section 3. Roughly,half of a fuel cell is visible and available for the inspection, where remaining part is shadowedby the rod, while the two springs of each cell are viewable. Nevertheless, it is assumed thatthe inspection is equally precise and efficient regarding the upper or the lower edge of aspacer and hence do not impair obtained proportions for debris accumulation between thoseedges.

Reasonable assumptions for types of debris potentially dangerous to the fuel must be es-tablished a priori. Debris considered harmful to the fuel and relevant to the objectives ofthis work consists of all kind of metals, like wires or threads. Debris considered not harmfuland thus not included in the statistics is: oxide flake, crud flake, debris flake.

Processing of the data revealed a large number of debris caught by sharp edges of the frame.For this reason, two different methods of interpretation were devised. One that takes intoaccount debris in the frame and one that excludes them.

4.1 Axial distribution of debris within a spacer

The random collection of reported debris allowed plotting its distribution while increasingthe number of analysed data. The proportions of debris locations converged to constantvalues already for 80% of the inspected assemblies which ensures that the number of anal-ysed instances is sufficient to draw firm conclusions. The final distribution is presented bythe left bar in Figure 4.1.

It is clear that the fraction of the debris lodged on a spring does not correspond to theobserved fretting marks and primary failures for that region, as discussed in section 3.1. By

21

22 CHAPTER 4. DATA PROCESSING FROM DEBRIS SEARCH IN PLANT K

taking into account that the spring is more easily viewed than the edges the percentage forspring should be at least halved giving 10%. But still, the fraction of the debris caught bythe springs is much higher than the observed fraction of fuel failures for this region whichis 2%.

There may be many factors coming into play e.g. flow characteristic, spring flexibilityetc. One of the distinctive features of the spring region is lack of the horizontal edgessurrounding it. This may suggest that the contact points have had a secondary importancefor debris captured in a way that results in a fuel failure and the main contributor tothrough-wall debris fretting has been horizontal sharp edges.

The most concrete conclusion that can be drawn at this point is that debris lodged in thespring either is not able to fret the nearby rod or cannot stay at that position long enoughto fail the rod.

4.2 Compilation of debris observations excluding de-

bris in the frame

It can be postulated that most of the debris being caught in the frame is too small toreach the cladding. The reason for this is that most of the potential places at the framein which debris can be caught are farther away from the rod than the potential places fordebris capture at any fuel cell inside the spacer. The debris does hence not pose a riskwhen captured in this area. Any debris that was found on the upper part of the frame isthus regarded as disabled to cause fuel failure and is not included in the statistics. Theright bar in Figure 4.1 shows the final results which substantially differ from the resultsthat include debris in the frame.

Figure 4.1: Debris distribution from the inspected fuel assemblies.

An interesting outcome is observed when comparing the fuel failures distribution to the

4.3. CONCLUSION ON DATA FROM THE PLANT K 23

distribution of debris with and without debris in the frame. Table 4.1 shows percentages offuel failures for two parts of a spacer, spring failures are not included, and percentages ofdebris found in the corresponding parts, also debris found in springs are not included. Theresults without debris in the frame exactly correspond to the fuel failures of spacer B andare very close to the sum of the failures for three spacer designs: B, C and D. This supportsthat the debris in the plant has been of a size that has not been able to fret through thecladding when caught on the spacer frame.

It must be stressed that the proportions of fuel failures for spacer B are calculated for boththe inner and peripheral regions of the sub-bundle. It can be argued that these two regionsmay have had different proportions of fuel failures between the upper and lower edge.Their compilation can hence not serve as a proof that the debris lodged in the frame hasbeen harmless to the fuel since the proportions should be compared only for the peripheralregions. However, there are only 15 fuel failures recorded in that region for spacer B andstatistic may not be representative. For information, the upper edge for the peripheralregion had 27% of the fretting marks, whereas the lower edge had 73% which is in goodagreement with the assumption that debris caught in the frame has been harmless to thefuel cladding.

The reason for these observations of debris caught in the frame being harmless could be dueto different conditions. The lower flow velocity in that region may promote the vibrationof the debris less compared to the inner region. Moreover, debris that is wedged in theframe in a way that it is bent by the flow may break and defragment fairly quickly due tofatigue and thus no longer be able to reach the fuel cladding and cause a fuel failure.

Fuel failures Debris search

Spacer BSum of threespacer designs

Including debris inthe frame

Excluding debris inthe frame

Upperedge

27% 28% 38% 27%

Loweredge

73% 72% 62% 73%

Table 4.1: Distribution of observed debris compared to the fuel failures.

4.3 Conclusion on data from the plant K

The fraction of the debris caught by the springs is much higher than the observed fractionof fuel failures for this region. The horizontal edges of the spacer in the upper and lowerpart can hence be suspected to be the dominant cause of debris catching that frets throughthe cladding. There are indications that most of the debris caught in the frame is not ableto fail the fuel, which could be that the frame structure works as a catcher of debris andkeeps it far from the cladding. This could perhaps also explain the lower proportion ofthrough-wall fretting marks in the peripheral parts of the spacer.

24 CHAPTER 4. DATA PROCESSING FROM DEBRIS SEARCH IN PLANT K

Chapter 5

Conclusions on Part I

Based on the reported fuel failures and the debris search performed in K power plant it isconcluded that:

The lower part of a spacer is more susceptible to catching debris and through-walldebris fretting than the upper part and accounts for about 2/3rd of total number ofprimary failures.

From the observations on failed fuel rods and their distribution within an assembly,the proportions for a rod to fail in the periphery have been lower than in the innerregion. The DMV spacer design does however not show this propensity. Further,based on the detailed distribution, the proportion for a rod located in the peripheryto be fretted from the frame side is lower than for the same rod to be fretted fromthe inner side for both the older designs as well as for the DMV design.

The fraction of the debris caught by the springs is much higher than the observedfraction of fuel failures for this region. The horizontal edges of the spacer in theupper and lower part are hence suspected to be the dominant cause of harmful debriscatching.

There are indications that most of the debris caught in the frame is not able to failthe fuel.

The disturbed flow between lower and upper part of the spacer caused by mixingvanes is one of the suggested causes for the increased fraction of fuel failure observedin the upper part of the spacer. The influence of the mixing vane on the proportionalincrease for the upper edge through-wall fretting is subjected for further analysis bymeans of CFD simulation.

25

26 CHAPTER 5. CONCLUSIONS ON PART I

Part II

CFD simulation of the mixing vaneeffect

27

Chapter 6

Introduction

The disturbed flow between lower and upper part of the spacer caused by mixing vanes isone of the suggested causes for the increased fraction of fuel failure observed in the upperpart of the spacer. In this part the mixing vane effect is investigated by CFD simulation.The computational simulation is limited to a single flow channel without heat sources. Twospacer designs, D and DMV, are modelled. The fluid is approximated by a steam-watermixture at the core near outlet conditions. Debris are modelled as non-spherical particlesof one size. The simulation is divided into two steps. First, the flow of the fluid phaseis resolved using steady-state simpleFoam solver for incompressible, turbulent flow. Then,particles tracks are computed using icoUncoupledKinematicParcelFoam solver.

The confined region between fuel rods and the spacer grid is a potential place for debriscapture. The relative change of particles passing that region is measured and comparedbetween two spacer designs.

29

Chapter 7

Theoretical Background

7.1 Navier-Stokes equations

For an incompressible flow with constant property the conservation of mass (continuity)and momentum equations are

∂ui∂xi

= 0 (7.1)

ρ∂ui∂t

+ ρuj∂ui∂xj

= − ∂p

∂xi+∂tij∂xj

+ ρgi (7.2)

Where tij is the viscous stress tensor, which for a Newtonian fluid is proportional to therates of deformation and is defined by

tij = 2µsij (7.3)

Where µ is the molecular viscosity and sij is the strain-rate tensor

sij =1

2

(∂ui∂xj

+∂uj∂xi

)(7.4)

Combining the above equations yields the Navier-Stokes equations, which in conservationform are as follows

∂ui∂xi

= 0 (7.5)

ρ∂ui∂t

+∂ui∂xj

(ujui) = − ∂p

∂xi+

∂

∂xj(2µsij) + ρgi (7.6)

The obtained system of equations governs the time-dependent three-dimensional fluid flowof an incompressible Newtonian fluid without heat sources. With four unknowns, threevelocity components and pressure, and four equations this system is mathematically closedand can be solved providing suitable initial and boundary conditions.

31

32 CHAPTER 7. THEORETICAL BACKGROUND

However, numerical solution of Navier-Stokes equations is computationally expensive re-quiring a very fine grid and time resolution. Here, another approach is taken.

7.2 Reynolds-Averaged Navier-Stokes equations

Before presenting the averaged form of the Navier-Stokes equations suitable for the purposeof this work a few comments about general concepts of averaging are given. There are threeforms mostly used in turbulence-model research namely: the time average, the spatialaverage and the ensemble average. For stationary turbulence i.e. a turbulent flow that, onthe average, does not vary with time, which is of our interest, the time averaging is themost appropriate (D. Wilcox, 2006). This concept is utilized in the decomposition of theinstantaneous velocity ui (x, t) into the sum of a mean Ui(x) and a fluctuating part u

′i(x, t).

ui (x, t) = Ui(x) + u′

i(x, t) (7.7)

Where the quantity Ui(x) is the time-averaged, or mean, velocity defined by

Ui(x) = lim1

T

ˆui (x, t) dt (7.8)

Noteworthy are properties of such decomposition

The time average of the mean velocity is again the same time-averaged value U i(x) =Ui(x)

The time average of the fluctuating part of the velocity is zero u′i(x, t) = 0

Further from the above, follows that the average of product of two properties equals productof their means and the mean of the product of their fluctuations, for instance, for twoproperties φ and ψ we have the following

φψ = ΦΨ + φ′ψ′ (7.9)

This fact has profound implications on the averaging procedure of the Navier-Stokes equa-tions. Time averaging of Eq. (7.5) and Eq. (7.6) yields the Reynolds-averaged Navier-Stokes equation (RANS) presented below

∂Ui∂xi

= 0 (7.10)

ρ∂Ui∂t

+ ρUj∂Ui∂xj

= −∂P∂xi

+∂

∂xj

(2µSij − ρu

′iu′j

)+ ρgi (7.11)

Where the averaging of the no-linear convection term yields the quantity −ρu′ju′i known as

the Reynolds-stress tensor or the specific Reynolds stress tensor given by

τij = −u′iu′j (7.12)

7.3. BOUSSINESQ EDDY-VISCOSITY APPROXIMATION 33

The τij is a symmetric tensor, and thus it introduces six independent unknowns togetherwith the three velocity components and pressure, we have ten unknowns but still fourequations and as a result of Reynolds averaging our system is not closed anymore. Hereturbulence modelling begins.

7.3 Boussinesq eddy-viscosity approximation

Boussinesq approximation, or assumption, postulates that the momentum transfer causedby turbulent eddies can be modelled with an eddy viscosity. This is in analogy with themomentum transfer by molecular motion in a gas and molecular viscosity. The assumptionstates that the Reynolds stresses are proportional to the local mean flow strain rate Sij,which for incompressible flow can be written in the following form

τij = 2νTSij −2

3kδij (7.13)

This assumption is the foundation most turbulence models use in practical computations.The last term in Equation (7.13) was added so that the normal stresses would sum to thespecific turbulence kinetic energy, which is explained in the next section.

7.4 Turbulence energy equation

The turbulence kinetic energy was introduced by Prandtl (1945) as a characteristic scale forturbulent velocity thus obviating the need for assuming it from the mixing length theory.The turbulence kinetic energy by definition is

k =1

2u′iu′i (7.14)

And is proportional to the trace (sum of diagonals) of the Reynolds stress tensor

τii = −u′iu′i = −2k (7.15)

Now the task is to determine k. This is done by applying the transport equation and theterm-by-term modelling, which eventually, after a fairly complicated developing processproduces the turbulence kinetic energy equation that is used in virtually all turbulenceenergy equation models (D. Wilcox, 2006).

∂k

∂t+ Uj

∂k

∂xj= τij

∂Ui∂xj− ε+

∂

∂xj

[(ν +

νTσk

)∂k

∂xj

](7.16)

Where σk is a closure coefficient. The quantity ε is the dissipation per unit mass definedby Eq. (7.17) and is the last term that need to be determined to complete the closure ofthe kinetic energy equation.

ε = ν∂u′i

∂xk

∂u′i

∂xk(7.17)


7.5 Standard k − ε turbulence model

To close the k equation we need to determine ε and this is again proceeded with thetransport equation and the term-by-term modelling approach. However, in this case theresult of introducing closures for the unknown terms is that the modelled equation isdrastically simplified and might be derived in very different ways hence giving rise todifferent concepts of two equations turbulence models. The most widely used two equationmodel is the standard k − ε model with the following equation for the dissipation rate (D.Wilcox, 2006).

∂ε

∂t+ Uj

∂ε

∂xj= Cε1

ε

kτij∂Ui∂xj− Cε2

ε2

k+

∂

∂xj

[(ν +

νTσε

)∂ε

∂xj

](7.18)

Together with the kinematic energy equation Eq. (7.16) and the kinematic eddy viscositydefined by Eq. (7.19) the model is complete, i.e., can be used to predict properties of agiven turbulent flow with no prior knowledge of turbulence structure (D. Wilcox, 2006).

νT = Cµk2

ε(7.19)

The model closure coefficients are presented in Table 7.1

Cε1 Cε2 Cµ σk σε

1.44 1.92 0.09 1.0 1.3

Table 7.1: Closure coefficients of the Launder-Sharma k − ε model

Although, the standard k − ε turbulence model is the most widely used and validatedit fails to accurately predict flows with streamline curvature and high swirling flows (B.Andersson, et al., 2011. ANSYS, 2012).

7.6 Realizable k − ε turbulence model

One of the weaknesses of the standard k-e model lies with the modeled equation for thedissipation rate (ANSYS, 2012). The realizable k − ε model provides a new model forthe dissipation rate equation and a new realizable eddy viscosity formulation. The neweddy viscosity formulation ensures realizability and contains the effect of mean rotation onturbulence stresses. The term “realizable” refers to the certain mathematical constrainsrelated to the Reynolds stresses that the model satisfies. The dissipation equation is derivedfrom the exact equation for the transport of the mean-square vorticity fluctuation (T.-H.Shih, et al., 1994). The k equation Eq. (7.16) is the same as that in the standard k − εmodel, except for the model constant.

The new equation for the dissipation rate for an incompressible flow without heat sourcesis (T.-H. Shih, et al., 1994).

∂ε

∂t+ Uj

∂ε

∂xj= C1Sε− C2

ε2

k +√νε

+∂

∂xj

[(ν +

νTσε

)∂ε

∂xj

](7.20)

where

7.7. WALL-BOUNDED FLOWS 35

C1 = max[0.43, η

η+5

], η = S k

ε, S =

√2SijSij

The Cµ constant in the eddy viscosity equation Eq. (1.21) is no longer constant and iscomputed from

Cµ =1

A0 + AskU∗

ε

(7.21)

where

U∗ =

√SijSij + ΩijΩij (7.22)

and

Ωij = Ωij − 2εijkωk, Ωij = Ωij − εijkωk

The model closure coefficients are presented in Table 7.2

σk σε C2

1.0 1.2 1.9

Table 7.2: Closure coefficients of the realizable k − ε model

The model was tested in various benchmark flows including: rotating homogeneous shearflows, channel and boundary layer flows with and without pressure gradients, backwardfacing step flows, flows with strong streamline curvature. For all these cases, the perfor-mance of the model has been found to be substantially better than that of the standardk − ε model (ANSYS, 2012. T.-H. Shih, et al., 1994).

From the above, this model is chosen for the fluid simulations in this work.

7.7 Wall-bounded flows

In wall-bounded flows the boundary layer is a region where the velocity increases rapidlyfrom zero at the wall to the free-stream velocity. In turbulent flows the boundary layer ischaracterized by unsteady swirling and mixing giving higher mass, momentum and heattransfer rates but also higher shear stresses.

The inner region of the turbulent boundary layer is commonly divided into three sub-layers.The innermost, the viscous sub-layer, is a region where the viscous stress in dominant andthe Reynolds stresses vanish. The buffer layer, where the viscous and turbulent stressesare equally important. And the fully turbulent layer, where viscous effects are negligible(B. Andersson, et al., 2011). It is common to use scaled variable u+and y+ to express thephysical extent of these sub-layers

u+ =U

uτ(7.23)


y+ = yuτν

(7.24)

Where the characteristic velocity scale or the friction velocity uτ is give by

uτ =

√τwρ

(7.25)

And the wall shear stress

τw = µ∂U

∂y|y=0 (7.26)

Based on experimental investigations and the scalable variables these layers can be classifiedas follows (B. Andersson, et al., 2011).

Viscous sub-layer 0 < y+ < 5

Buffer sub-layer 5 < y+ < 30

Fully turbulent sub-layer 30 < y+ < 300

In most high Reynolds number flows a wall function approach is utilized. This approachsubstantially saves computational resources, because the viscosity-affected near-wall regiondoes not need to be resolved. The wall function approach is discussed in the next section.

7.8 Wall functions

The basic idea of the wall functions is to apply boundary conditions not directly at the wallbut some distance away. The wall function approach obviates the need of a very fine meshin the near-wall region. For turbulence models that are not valid in the viscosity affectedregion the wall function approach is an alternative solution.

Integration of Eq. (7.26) with respect to y gives the relation between the mean streamwisevelocity and the distance from the wall for the viscous sub-layer, which in the dimensionlessform is

u+ = y+ (7.27)

In the fully turbulent layer, where the turbulent stresses are dominant and the total stresstensor reduces to τij = −ρuiuj, integration over y gives the formula known as a law of thewall

u+ =1

κln(y+) +B (7.28)

where κ is the von Karman’s constant κ ≈ 0.41 and B is a dimensionless integrationconstant, which for smooth surfaces equals 5.0 (D. Wilcox, 2006).

From the above, in the viscous sub-layer the velocity varies linearly with y+, whereas inthe buffer sub-layer it approaches the log law.

7.8. WALL FUNCTIONS 37

Wall functions bridge the gap between the wall and the log region where the first centroidis located. However, maintaining a prescribed value of y+ in wall-adjacent cells throughoutthe domain is challenging, especially for simulation with complex geometry. In such casescalable wall functions are convenient choice. They operate in two modes, based on the y+

value switching between the low- and high-Reynolds number turbulent flow at a prescribedvalue of y+

Chapter 8

Lagrangian Particle Tracking

8.1 Stokes number

The Stokes number is an important parameter in fluid-particle flows. It defines the degreeto which particle motion is tied to fluid motion, in other words, it relates the response timeof a particle to changes in flow velocity. The Stokes number is defined as the ratio of thecharacteristic time of a particle (particle relaxation time) to the characteristic time of theflow (C. Crowe, et al., 1998).

St =τpτf

(8.1)

For a spherical particle in Stokes flow (flow with Rep << 1 ) the particle relaxation timeis calculated using Eq. (8.2)

τp0 =ρpd

2p

18µ(8.2)

The particle Reynolds number is defined as

Rep =ρfdp | u− up |

µ(8.3)

The correction for higher particle Reynolds number flows takes the form of Eq. (8.4)

τp =τp0

ϕ(Rep)(8.4)

ϕ(Rep) =

1 + 0.15Re0.687p

0.11Rep6

at Rep ≤ 1000

at Rep > 1000

39

40 CHAPTER 8. LAGRANGIAN PARTICLE TRACKING

And the characteristic time of the flow through a channel may be define as

τf =Dh

u(8.5)

If St << 1, the response time of the particle is much less than the characteristic time ofthe flow field, the particle and fluid velocities will be nearly equal. If St >> 1 the particlevelocity will be little affected by the changes in the flow field and the particle flow will bedominated by particle-wall interactions (C. Crowe, et al., 1998).

8.2 Phase coupling

There are three different techniques to couple particle and fluid phase motion:

one-way coupling: the fluid phase influences particle motion but the opposite is ne-glected,

two-way coupling: particle motion and fluid phase dynamics influence each other,

four-way coupling: particle-particle collisions are taken into account.

The complexity of the interaction increases with the degree of coupling.

Since debris passage through a spacer grid is relatively rare the four-way coupling is notconsidered straightaway. Moreover, the two-way coupling is expected only for a dense flow,where the particle loading is greater than 0.2 (C. Crowe, et al., 1998), where the loadingis defined as a ratio of mass flux of the dispersed phase to the mass flux of the continuousphase. The mass flux of a single debris is negligible when comparing to the mass flux of thecoolant. Thus, the only coupling technique suitable for the objective of this work in theone-way coupling. This technique is adopted for all particle tracking simulations conductedin this study.

8.3 Forces acting on a particle

Basically there are two ways of modeling the movement of a particle or a group of particlesinside a fluid. The Eulerian-Eulerian model, where particles are treated as a continuousphase and the particle characteristics are calculated at fixed point within the flow fieldwith conservation equations. This model is convenient for large particle concentrations.For flows where the particles are relatively sparse in the flow field the Eulerian-Lagrangianapproach is usually applied. The fluid phase is solved with continuum equations, while forthe particulate phase the Newton’s equations of motion are solved. Once the forces actingon the particle are determined the particles trajectories are obtained from the principalequation.

mpdupdt

=∑

Fi (8.6)

S. Elghobashi (1994) considered the following force acting on a particle as it moves alongits trajectory:

8.3. FORCES ACTING ON A PARTICLE 41

forces due to viscous and pressure drag

fluid pressure gradient and viscous stresses

inertia of virtual mass

viscous drag due to unsteady relative acceleration (Basset history force)

buoyancy

Saffman’s lift force due to shear in the carrier flow

The force vector is a matter of complex choice, it depends on involved phenomena anddesired level of details that are wished to be resolved.

In this work the following forces are considered: the viscous drag force, the gravity and thebuoyancy force. The choice is mainly dictated by the Stokes number, calculated in the nextsection, which in our case is much higher than unity. For high Stokes number the particletrajectories are in lesser extent affected by the flow, thus only the largest forces are takeninto account (S. Elghobashi, 1994).

From that the force balance on a particle is written

F = FD + Fg + FB (8.7)

The drag force exerted on a spherical particle is calculated as

FD = mp18µfρpd2p

CDRep24

(uf − up) (8.8)

Where the drag coefficient CD is obtained from the following equation

CD =

24Rep

if Rep < 124Rep

(1 + 0.15Re0.687p

)if 1 ≤ Rep ≤ 1000

0.44 if Rep > 1000

(8.9)

The gravity force and the buoyancy force can be combined together giving

Fg + FB = mpg

(1 +

ρfρp

)(8.10)

The above drag coefficient was extensively validated for spherical particles. However, forthe purpose of this work a formula that can describe drag coefficient for non-spericalparticles is sought.

42 CHAPTER 8. LAGRANGIAN PARTICLE TRACKING

8.4 Drag coefficient for non-spherical particles

Haider and Levenspiel (1988) developed a correlation for non-spherical particles, wherethey used concept of particle sphericity φ to account for particle shape.

φ =s

S(8.11)

Where s is the surface of sphere having the same volume as the particle and S is theactual surface area of the particle. The proposed correlation is

CD =24

Rep

(1 + AReBp

)+

C

1 + DRep

(8.12)

The correlation includes four parameters that are functions of the particle sphericity asfollows

A = exp(2.3288− 6.4581φ+ 2.4486φ2)

B = 0.0964 + 0.5565φ

C = exp(4.905− 13.8944φ+ 18.4222φ2 − 10.2599φ3)

D = exp(1.4681 + 12.2584φ− 20.7322φ2 + 15.8855φ3)

The correlation was experimentally validated and the best values of the parameters wereproposed for the particle sphericity in the range of 0.026 < φ < 1.

Debris of a typical shape and size has the sphericity of 0.5 and fits the proposed range.Thus, the drag coefficient presented here is applied to all particle tracking simulations.

8.5 Particle-wall interaction

In this study the particle-wall interaction is assumed as a perfectly elastic collision, no lossof kinetic energy. The assumption is supported by studies discussed below.

Studies done on collisions of a solid particle in fluids found that the particle-wall collision isfunction of a modified Stokes number, Eq (8.13). The modified Stokes number is calculatedbased on the normal component of the particle velocity with relation to the collision wall. Itis also shown that the normal coefficient of restitution in oblique collision is independent ofthe tangential component of velocity and is close to unity for the modified Stokes numbershigher than 1000 (G. Joseph and M. Hunt, 2004).

Stm =2ρpdpvN,imp

9µf(8.13)

Where vN,imp is impact velocity normal to the collision wall.

The value of the modified Stokes number for the modelled particles is calculated in themethodology section, 10.5.

Chapter 9

CFD in OpenFOAM

In this thesis all CFD simulations are conducted in OpenFOAM version 2.3.0

OpenFOAM stands for Open Source Field Operation and Manipulation and is free-to-usenumerical simulation software with extensive CFD and multi-physics capabilities. Open-FOAM is written in object-oriented C++ programming language. The overall structure isschematically illustrated in Figure 9.1.

Figure 9.1: Overview of OpenFOAM structure (OpenFOAM, 2013).

OpenFOAM provides vast number of additional tools called utilities, these are very conve-nient sub-codes that can save a lot of time when used properly. Some of them utilized inthis work are: mirrorMesh, yPlusRAS, particleTracks, probeLocations.

9.1 Case structure

Each simulation is specified in a case folder, which consists of three sub-folders: system,constant and time directories. Contents of these three sub-folders are then specified indi-vidually according to particular simulation.

The basic file structure used with simpleFoam solver for fluid simulation is

43

44 CHAPTER 9. CFD IN OPENFOAM

Init&BoundCond 0

U

p

k

epsilon

nut

Constants constant

polyMesh

triSurface

extendedFeatureEdgeMesh

boundaryData

transportProperties

turbulenceProperties

RASProperties

Numerics system

fvSchemes

fvSolution

controlDict

snappyHexMeshDict

surfaceFeatureExtractDict

decomposeParDict

For the particle-tracking simulation with icoUncoupledKinematicParcelFoam the essentialdata is the velocity field. The kinematicCloudProperties file, located in the constant direc-tory, is essential including all necessary particle properties like: coupling technique, particleforces, injection model, interaction with walls, particle density and dimension.

FieldData 0

U

Constants constant

polyMesh

g

kinematicCloudProperties

particleTrackProperties

transportProperties

turbulenceProperties

RASProperties

Numerics system

fvSchemes

fvSolution

controlDict

9.2. SOLVERS AND NUMERICS 45

9.2 Solvers and numerics

In the current work two solvers were used. simpleFoam which is a steady-state solver forincompressible, turbulent flows, used for all fluid simulations, and icoUncoupledKinematic-ParcelFoam for the passive transport of a kinematic particle cloud. icoUncoupledKinemat-icParcelFoam was run for the obtained velocity field from simpleFoam.

simpleFoam uses Semi-Implicit Method for Pressure Lined Equations to compute U andp in the Navier-Stokes equations. This is an iterative solution strategy for steady-stateproblems which basic steps are as follows (H.K. Versteeg, W. Malalasekera, 2007).

The iteration starts with guess values for the velocity and pressure fields

The guessed pressure field is used to solve the momentum equations

A pressure correction equation, deduced from the continuity equation, is solved toobtain a pressure correction fields

The velocity and pressure fields are updated

Procedure is repeated until convergence

For the fluid simulations second order Gauss discretization scheme was used. Gradient andLaplacian terms were interpolated with central differencing scheme limited with differentoperators in order to take into account the direction of the field, Table 9.1. The divergenceterms were interpolated with second order upwind scheme due to dominant convection.

Scheme Interpolation

Gradient Gauss cellMDLimited linear 0.5Divergence Gauss linearUpwindLaplacian Gauss linear limited 0.777

Table 9.1: Discretization schemes for the fluid simulation.

GAMG (geometric-algebraic multi-grid) method was used for pressure calculation. It isusually faster than standard methods. It generates a quick solution on a mesh with a smallnumber of cells and uses it as an initial guess for a finer mesh. An approximate mesh sizeat the most coarse level in terms of the number of cells is specified by nCoarsestCells entryin fvSolution file.

PBiCG is preconditioned bi-conjugate gradient method for asymmetric matrices used withpreconditioner DILU for LU decomposition, Table 9.2

The calculation stability was controlled by relaxation factors.

Solver Preconditioner

p GAMG GaussSeidelu, k, ε PBiCG DILU

Table 9.2: Solver schemes for the fluid simulation.

46 CHAPTER 9. CFD IN OPENFOAM

Chapter 10

Methodology

The computational simulation of the mixing vane effect is limited to a single flow channelwithout heat sources. Two spacer designs, D and DMV, are modelled. The detaileddescription is provided only for spacer DMV, all procedures for spacer D are analogous.

10.1 Geometry

The geometry of the model was created from the scratch based on the technical drawingsprovided by Westinghouse. The program used for that purpose was Solid Edge ST6. Thegeometry was constructed from three separately prepared elements.

A single fuel rod cell of the D spacer

A mixing vane

A fuel rod

The fuel rod cell and the mixing vane were built in a sheet metal environment, while the fuelrod was built as a solid part. The only difference between spacer D and DMV, consideredin this part, is the mixing vane. Small modification of the D fuel rod cell and addition ofthe mixing vane was the simplest way of creating the DMV fuel rod cell, Figure 10.1.

It must be stressed, that the fuel rod cells (spacer cells) are not identical within a spacergrid and that there are 7 slightly different types depending on the location inside a spacer.However, the differences are minute and mostly concern the central cell. The central cell,together with the rod it holds, are designed to prevent the spacer from sliding along therods.

The final models were created by assembling from the basic parts. Each model consists offour cells and four fuel rods, Figure 10.2.

One modification was applied to the model comparing to the real case. The dimples, whichare the contact points between the spacer grid and the rods, were extruded farther into therods. This allows to avoid meshing complication between the top plane surface of a dimpleand a cylindrical surface of a rod.

47

48 CHAPTER 10. METHODOLOGY

. . .. .

Figure 10.1: Fuel cells of the D spacer (left) and the DMV spacer (right).

...

Figure 10.2: Front view of the final model (left) and its isometric view (right).

Basic dimensions and parameters of the models are presented in Table 10.1.

As in the case of the spacer cells the lattice pitch is not the same within a spacer, itvaries between different rods. The value chosen for this model is the most common for theDMV spacer. Note the thickness of the sheet metal of the spacer grid, it will have seriousconsequences on the mesh generation. Hereinafter, the final model is called geometry.

10.2 Mesh

Due to the complexity of the geometry the unstructured grid arrangement technique isutilized for the mesh generation. The basic cell type is hexahedral element with combinationof prisms and polyhedrons created during the mesh generation. All the needed mesheswere automatically generated by the OpenFOAM utility, SnappyHexMesh. SnappyHexMeshrequires that the geometry surface data are converted to STL (Stereolithography) formatand a background mesh is provided.

The background mesh defines the computational domain with its boundaries and a base

10.2. MESH 49

rod diameter dr 9.84 mmlattice pitch pl 13 mm

hydraulic diameter Dh 12.03 mmsheet metal thickness 0.24 mm

spacer height 26 mm

Table 10.1: Basic dimensions and parameters of the models.

level mesh density. The STL file can be created in Solid Edge, however, by doing this theinformation about the units is not preserved and the STL file need to be scaled by factorof 0.001 before processing further in OpenFOAM.

The mesh generation process in SnappyHexMesh consists of several steps, here are discussedonly those that were extensively used in this work:

Cell splitting at edges and surfaces of the geometry. The splitting process can beimproved by specification of geometry edges. The features can be extracted from theSTL file using surfaceFeatureExtract utility.

Cell removal. After the cell splitting at the prescribed features or surfaces is completedthe cell removal process begins. The cells within the region of the computationaldomain are retained by specifying a location vector within that region.

Cell refinement according to distance to the surface. Cells are refined by specify-ing a distance and a level of refinement. Level zero corresponds to the size of thebackground cell and any higher level has twice shorter cell edge from the previous.

The snapping. The mesh vertices are displaced onto the STL surface. The process isiterative and controlled by quality of the mesh.

The last step is adding mesh layers. However, in our case this step is not utilized,instead the refinement process is extended near the wall regions, which helps toimprove representation of the geometry.

Figure 10.3 shows the background mesh. The mesh is constructed from three blocks:inlet block, spacer region block, outlet block. The difference is in the cell size in the flowdirection, i.e. y direction. Cells in the spacer region have size of 0.4x0.4x0.4 [mm], whilein the inlet and the outlet blocks they change with 0.5 grading in the flow direction, wheregrading is a ratio between largest and smallest cells. The spacer region block starts onehydraulic diameters before the spacer leading edge and ends one hydraulic diameter afterthe spacer, Figure 10.4.

Since the thickness of the sheet metal of the spacer grid is 0.24 mm the level of refinementneed to be at least 2 giving the smallest cells size in the spacer region of 0.1x0.1x0.1 [mm]but ensuring that at least two cells are located at the grid edges. The small size of the nearwall cells will have unfavorable consequences on the boundary conditions, which is discussedin section 10.3. However, this is necessary for good representation of the geometry.


Figure 10.3: Background mesh. Green color denotes the symmetry planes, blue denotesthe inlet.

Figure 10.4: The background mesh and the STL geometry.

The final results of the mesh generation for the spacer region are presented in Figure 10.5and in Appendix A.

In order to minimize influence of boundary conditions the final mesh was generated withprolonged outlet region to 30 Dh, while the inlet boundary conditions were obtained froma separate simulation.

The mesh quality can be controlled by meshQuality utility and improved if necessary. Meshwith bad quality can lead to poor convergence or even to nonphysical results. The basicparameters of the generated meshes are shown in Table 10.3 and Table 10.2.

...

D DMVcells 2.89 · 106 4.44 · 106

fraction [%]hexahedrons 89.6 89.5

prisms 4.7 4.7polyhedrons 5.7 5.8

Table 10.2: Fraction of each fuel cell type in the final mesh.

The inlet boundary conditions of a fully developed flow were obtained separately for the

10.3. INITIAL AND BOUNDARY CONDITIONS 51

Figure 10.5: Representation of the geometry in the final mesh.

D DMVmax average max average

no-orthogonality 60.0 12.3 66.5 12.4skewness 2.9 - 3.8 -

aspect ratio 15.7 - 21.8 -

.

Table 10.3: Mesh quality.

inlet of 60 Dh length. In order to avoid asymmetry mesh was generated for one quarter ofthe domain and mirror around two planes of symmetry.

10.3 Initial and boundary conditions

10.3.1 Inlet boundary conditions

The inlet conditions were simulated with simpleFoam solver.

A preliminary value for the required channel entrance length for fully developed turbulentflow can be calculated according to Eq.(10.1)(D. Wilcox, 2006).

lh = 4.4Re16 (10.1)

Where lh is expressed in hydraulic diameters. For our simulation it gives approximately38Dh, however, that distance was not long enough and at least 50Dh were necessary to getfully converged velocity profile. The required distance was inferred from the developmentof the velocity along the channel axis, Figure 10.6.

It can be seen that at the distance of 38Dh the velocity is still increasing. Thus, the fluidproperties are taken from the distance of 60Dh.

Figure 7 depicts the outlet velocity obtained from the simulation at the distance of 60Dh.For the sake of clarity the zero velocities from the walls are not included in the plot. Velocityvalues as well as the turbulence kinematic energy and the dissipation are used as the inletcondition for the fluid simulation.


Figure 10.6: Streamwise component of the velocity along the channel axis.

10.3.2 Setup of boundary conditions

Due to relatively low cross-flows in BWR fuel assemblies, symmetry boundary conditionsare applied at the rod gap regions. Setups of the inlet, outlet and geometry boundaryconditions are shown in Table 10.4 and Table 10.5.

Inlettype value

u timeVaryingMappedFixedValue tablep zeroGradient -k timeVaryingMappedFixedValue tableε timeVaryingMappedFixedValue tableνt calculated -

...

Outlettype value

u inletOutlet 10−11

p fixedValue 10−11

k zeroGradient -ε zeroGradient -νt calculated -

Table 10.4: Setup of boundary conditions at the inlet and the outlet.

timeVaryingMappedFixedValue - This boundary provides field values according to spec-ified values in a table. Here the values from the developed flow are tabulated.

.

inletOutlet - This boundary works as a zero gradient for the out flow and as a fixedvalue for the case of return flow. Setting zero prevents from return flows.

.

LowReWallFunction - This boundary condition works as scalable wall functions providinga wall function for low- and high-Reynolds number turbulent flow. It operates in two modes,based on the y+ value and switches between at y+ = 11.53. It is necessary due to very smallcells at the spacer edges.

10.4. FLUID PROPERTIES 53

Figure 10.7: The outlet velocity.

.Geometrytype value

u fixedValue (0, 0, 0)p zeroGradient -k kLowReWallFunction 10−11

ε epsilonLowReWallFunction 10000νt nutLowReWallFunction 10−11

Table 10.5: Setup of boundary conditions at the geometry.

10.4 Fluid properties

Fluid is treated as a mixture of steam and water with properties near the core outlet forBWRs. The fluid velocity is approximated for a high power assembly at the elevation ofspacer 7 according to Figure 10.8.

The fluid properties at that location are derived based on the core inlet conditions andDrift Flux Model. The fluid at the inlet is assumed to be 10oC subcooled water withcross-section averaged velocity of uin = 2m

s. From the above and according to Eq. (10.2)

and Eq. (10.3) the mixture density and the void fraction can be obtained.

G ≡ ρmum = ρinuin (10.2)

ρm = αρg + (1− α)ρf (10.3)


Figure 10.8: An example of the flow velocity along the fuel assembly in a peripheral, anaverage power, and a high power assembly (K. Ryttersson, et al., 2007).

Where um is the mixture velocity, subscripts f and g denote saturation condition for liquidand gas, respectively.

The actual quality was calculated according to Eq. (10.4)

xa =1

1 + (1−α)α

ρfρgSp

(10.4)

Where the slip ratio Sp, which is a ratio of phasic velocities uvul

, was obtained from the

drift-flux void correlation for an annular flow with the known void fraction (H. Anglart,2010), Eq. (10.5). Here, the void fraction is expressed in terms of channel mean superficialvelocity of gas Jg, total superficial velocity J , and two parameters C0 and Uvj.

α =Jg

C0J + Uvj(10.5)

The drift-flux parameters are not constant and depend on flow condition. For an annularflow they are expressed as follows.

C0 = 1.05 (10.6)

Uvj = 23

(µfJfρgDh

)0.5(ρf − ρg)

ρf(10.7)

Since the mass flux G is known and is related to the superficial velocities and the phasicvelocities as follows

10.4. FLUID PROPERTIES 55

G = Jg + Jf = αuv + (1− α)ul (10.8)

The slip ratio can be iteratively obtained combining Equations (10.5) (10.6) (10.7) andrelation (10.8).

The calculated mixture properties are listed in Table 10.6.

pressure 70 bartemperature 287 oC

velocity 10.5 ms

calculatedvoid fraction 0.848 -actual quality 0.338 -

mixture density 143.9 kgm3

mixture kinematic viscosity 2.771 · 10−7 m2

s

Table 10.6: Mixture properties.

The mixture kinematic viscosity is computed according to Equations (10.9) and (10.10).

νm =µmρm

(10.9)

1

µm=xaµg

+1− xaµf

(10.10)

One study is also conducted for fluid with low void fraction to capture higher burnupassemblies. The mixture velocity at the elevation of spacer 7 is assumed to be 5 m

s, corre-

sponding to void fraction of 0.62. The flow has slug pattern and the drift-flux parametersare different and should be adopted accordingly, for details see (H. Anglart, 2010). Thecalculated fluid properties are listed in Table 10.7. The detailed steps of this study are notpresented only results.

pressure 70 bartemperature 287 oC

velocity 5 ms

calculatedvoid fraction 0.622 -actual quality 0.118 -

mixture density 302.2 kgm3

mixture kinematic viscosity 2.0815 · 10−7 m2

s

Table 10.7: Fluid properties for a high burnup assembly.

For the fluid simulation only the mixture kinematic viscosity need to be provided. For theparticle tracking simulation also mixture density is required.


10.5 Particle properties

The modelled debris is assumed to be of wire type. The dimension is adopted from theexperimental measurement of a terminal velocity conducted by Westinghouse (K. Rytters-son, et al., 2007) and according to the efficiency of DF filter reported in (B. Helmersson,et al., Paris 2009), where the threshold for passing the filter corresponds to bits of wiremeasuring approximately 15 mm. Here, some particles are expected thus the length of themodelled debris is shortened. Particle properties are listed in Table 10.8.

density (steel) 7800 kgm3

dimensions Φ0.5x12 mmsphericity 0.445 -

Stokes number 25 859 -modified Stokes number ∼ 106 -

Table 10.8: Particle properties.

The Stokes number, in Table 10.8, was calculated for the Stokes type of flow. In order toconfirm high order of the Stokes number for wide range of particle velocities. The correction(8.4) was applied for a particle having much lower velocity than in the Stokes flow, up = 7m

s,

with the particle Reynolds number, Rep = 20853. The resulting value is St = 67 which isstill much higher than unity. Thus, as it was stated in section 8.1, the particle flow will bedominated by particle-wall interactions.

Further, assuming that the particle velocity, near the point of collision with the mixingvane, is close to the fluid velocity the modified Stokes number is in order of 106, see section8.5. Where, the incident angle is 68o (90o − 22o) and is formed by the trajectory of aparticle and the wall’s normal. Here, 22o is the angle that the mixing vane forms withthe flow direction. From the above and according to (G. Joseph and M. Hunt, 2004) therestitution coefficient is one and the particle-wall interaction maybe assumed of an elasticrebound type.

Particles are to be injected with zero initial velocity. It is important that they reach anequilibrium with the fluid and stop accelerating before reaching the spacer. For this reasonall the fluid simulations are conducted with the inlet block of 10 Dh length. The accelerationof particles was checked. Figure 10.9 shows an asymptotic trend of the particle velocityfrom the inlet to the spacer region. The velocity changes little between 7Dh and 10 Dh,thus the distance of 10 Dh is considered as sufficient.

It should be stressed that Figure 10.9 represents a particle injected at the center of thechannel where the fluid velocity and the change of the particle velocity is the highest.

A particle collector is used for counting particles passing through a region of interest. Itcan be specified by a polygon of arbitrarily chosen vertices. For the purpose of this worktwo particle collectors were defined. One to count particles at the lower edge of the spacerand one at the upper edge of the spacer. Each of them covers only the flow channel area,Figure 10.10 clarifies what is meant by the flow channel area.

The total number of injected particles is defined at the beginning of the simulation. Hence,the number of particles passing through other region than the flow channel must balance

10.5. PARTICLE PROPERTIES 57

Figure 10.9: Particle velocity along the channel axis measured from the inlet to the spacerregion.

the number of particles measured at the collector and the number of injected particles.

Figure 10.10: Flow channel with particle collector marked in blue. The near rods region ismarked in red.

Chapter 11

Results

The results for the fluid simulation are presented and discussed at first, then the resultsfor the particle tracking simulation followed.

11.1 Fluid phase

The resolved fluid flow allows to check the actual value of y+ for each simulation.

For the spacer D, y+ : ....min: 1.21, max: 56.35, average: 30.26

For the spacer DMV, y+ : ..min: 1.11, max: 65.20 average: 28.90

The minimum y+ values, for both simulations, are lower than 5, which justifies use ofscalable wall functions.

The final residuals are listed in Table 11.1. These values are in acceptable range, however,to gain higher confidence in the results the flow properties were monitored during eachsimulation. A probe located in the center of the flow channel at the upper edge, recordedstreamwise velocity and turbulence kinetic energy. Here, only the outcome for the DMVsimulation is shown in Figure 11.1. The flow properties are oscillating but within acceptablerange.

Figure 11.2 and Figure 11.3 show cross-sections with the velocity at the upper edge forspacer D and DMV, respectively. In addition, for each cross-section the velocity is plottedover a horizontal line located in the middle of each cross-section, Figure 11.4 and Figure11.5.

The mixing vane affects the flow velocity. In some parts of the flow channel velocitydecreases to approximately 5m

s, while in two regions close to the rods velocity reaches

15.9ms

. In this case, higher velocity may promote higher debris vibrations (with higherfrequency) and faster through-wall fretting and fuel failure (K. Rytterson et al., 2007).

For the spacer without mixing vane the flow is nearly undisturbed. The velocity is approx-imately 12m

sacross the flow channel decreasing near the spacer grid.

59

60 CHAPTER 11. RESULTS

DMV D

variable residualux 5 · 10−4 5 · 10−4

uy 2 · 10−4 1 · 10−4

uz 4 · 10−4 5 · 10−4

p 6 · 10−3 5 · 10−3

ε 2 · 10−4 1 · 10−4

k 3 · 10−4 1 · 10−4

Table 11.1: Final residuals for the fluid simulation of spacer DMV and D.

Figure 11.1: Streamwise velocity (left) and turbulent kinetic energy (right) recorded duringthe spacer DMV simulation in the channel center at the upper edge.

11.2 Particle tracking

Since the particle-particle interactions are not applied, the one-way coupling technique isused, all particles are injected at the same time through the inlet patch. The injectionmodel provides fairly good initial dispersion, as can be seen in Figure 11.6. It is importantthat the particles do not form any pattern or clusters, depending on the mesh at theinjection point, which could then preserve for long time and false results.

In each simulation 10 000 particles were tracked and counted while passing through theparticle collector. The results are summarized in Table 11.2.

An increase of particles passing the near rod region is observed for the spacer DMV andequals 9.25 percent points compering to the spacer D. The shares of the particles passingthe near rods region where the increased velocity is observed is 26.27% for the left regionand 4.87% for the bottom region, see Figure 11.3.

The lower edge is not affected by the mixing vane, the particle proportions between tworegions are nearly equal for both spacer designs.

The lower void fraction has negligible effect on particle distribution.

The exact particle dispersion at the upper edge for both spacers is shown in Figure 11.7

11.2. PARTICLE TRACKING 61

Figure 11.2: Velocity at the upper edge of the D spacer.

and Figure 11.8.

The stream lines of the fluid were compared to particle tracks. The high curvature of thefluid stream lines is not reflected in the particle tracks. Particles are affected by the flowchanges to very low extent, see Appendix B.

Total number of injected particles 10 000D DMV

Voidfraction

Channelregion

Near rodsregion

Channelregion

Near rodsregion

α = 0.85Upper edge 58.72% 41.28% 49.47% 50.53%Lower edge 57.34% 42.66% 57.76% 42.24%

α = 0.62 Upper edge - - 49.82% 50.18%

Table 11.2: Particle distribution at the upper and lower edge of the spacers D and DMV.


Figure 11.3: Velocity at the upper edge of the DMV spacer.

Figure 11.4: Velocity plotted over the horizontal line for D.

11.2. PARTICLE TRACKING 63

Figure 11.5: Velocity plotted over the horizontal line for spacer DMV.

Figure 11.6: Particle dispersion at the point of the injection.


Figure 11.7: Particle dispersion for the spacer D at the upper edge.

Figure 11.8: Particle dispersion for the spacer DMV at the upper edge.

Chapter 12

Conclusions on Part II

The main conclusions of the part II of this thesis are:

The mixing vane significantly affects the fluid velocity. For DMV the are two regionsclose to the spacer grid with much higher fluid velocity than in corresponding regionsof D. In these regions higher debris vibration are suspected and faster through-wallfretting.

The particle fraction passing the near rod region for the spacer DMV is approximately9.25 percent points higher than for the same region in the spacer D. The confinementof this region and higher concentration of particles increase the probability of debriscapture.

It is concluded, based on the negligible differences for the DMV spacer design, that thevoid fraction, in the range investigated in this work, do not affect particle distribution.

The modelled particles, relatively dense and big, are affected by the changes in theflow field to very low extent. Particle flow is dictated by the interaction with spacerstructure, manly mixing vane.

The higher particle concentration and the increased flow velocity in the upper part ofDMV, while comparing to D, confirm suspections, raised in part I, of the unfavourableeffect of mixing vanes on debris capture and fuel failure. This explains higher proprtion offuel filures for the upper edge of spacer DMV but also implicates higher frequency of fuelfailures for spacers with mixing vanes compared to spacers without mixing vanes.

65

66 CHAPTER 12. CONCLUSIONS ON PART II

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Appendix A

Figure .1: Mesh refinement seen from the inlet side.

Figure .2: Mesh refinement seen in the spacer region.

69


Figure .3: Mesh refinement around the mixing vane. The lines going through the meshcells are due to wrong interpretation of the tetrahedral cells, cut with a plane, by thevisualization software and have no representation in the mesh.

Appendix B

Figure .4: Stream lines from the DMV simulation seen from upstream.

Figure .5: Stream lines from the DMV simulation seen from downstream.

Figure .6 and Figure .7 serve only as an illustration of particle tracks around the mixingvane. The number of injected particles differs from the number of particles injected in thefinal simulation.

71


Figure .6: Particles path lines (tracks) around the mixing vane, seen from downstream.

Figure .7: Particles path lines (tracks) around the mixing vane, seen from upstream.

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