Monte Carlo Simulations of Bowing Effects Using Realistic Fuel Data

UPTEC F 18062

Examensarbete 30 hp Januari 2019

Monte Carlo Simulations of Bowing Effects Using Realistic Fuel Data

in Nuclear Fuel Assemblies

Marcus Westlund

i

Teknisk- naturvetenskaplig fakultet UTH-enheten

Besöksadress:

Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

Postadress:

Box 536 751 21 Uppsala

Telefon:

018 – 471 30 03

Telefax:

018 – 471 30 00

Hemsida:

http://www.teknat.uu.se/student

Monte Carlo Simulations of Bowing Effects Using Realistic Fuel Data in Nuclear Fuel Assemblies

Marcus Westlund

Deformations of nuclear fuel assemblies have been observed in nuclear power plants since the mid-90s. Such deformations are generally called bowing effects.

Fuel assemblies under high irradiation undergo growth and creep induced by high loading forces and low skeleton stiffness of the assemblies which gives permanent deformations and modifies moderation regions. Hence, giving an unpredicted neutron flux spectrum, power distribution, and isotopic concentrations in the burnt fuel. The aim of this thesis is to study the effects of local fuel bowing in terms of power distribution and isotopic composition changes through simulations of the reactor core.

The reactor is simulated with realistic bowing maps and previous deterministically simulated realistic fuel data from a present reactor by deploying the Monte Carlo method using the nuclear reactor code Serpent 2. Two subparts of a full reactor core with fuel from separate fuel cycles are investigated in 2D using burnup. To quantify the impact of the bowing, the change in power distribution and the induced isotopic composition change are calculated by a relative difference between a nominal case and a simulation with perturbed fuel assemblies. The results are presented in colormaps, for visualization. The isotopic composition for U235, U238, Pu239, Nd148, and Cm244 are investigated.

Also, statistical uncertainty estimations in the composition of the depleted fuel are done by multiple calculations of the same geometry while changing the seed of random variables in the Monte Carlo calculation. The mean value and the standard deviation in the mass density of U235 and Pu239 are calculated for two pins together with histograms with a normal fit for each case to clarify the mathematical distribution of the calculations.

The simulations performed in this thesis have detected clear impacts of the reactor behavior in terms of power distribution and isotopic composition in the burnt fuel introduced by the bowing. Assembly perturbations of about 10 mm may locally introduce a 10 % relative difference in power density and U235 content between the nominal and the bowed case at 15 MWd/kgU burnup. The power and the isotopic composition changes agree with expectations from the bowing maps.

ISSN: 1401-5757, UPTEC F 18062

Examinator: Dr. Tomas Nyberg

Ämnesgranskare: Dr. Henrik Sjöstrand

Handledare: Dr. Dimitri Rochman

iii

Sammanfattning

Deformationer av bränslestavarna i en kärnreaktor är ett problem som varit känt

under de senaste årtiondena. Dessa deformationer refereras generellt som böjning,

med olika tillägg för om det gäller en tryck- eller kokvattenreaktor. Första gången

det officiellt observerades var i Ringhals 4 i södra Sverige. Anledningen till detta

var bland annat att bränslestavarnas fästpunkter och materiella uppbyggnad inte

var tillräckligt styv för att motstå de axiella krafter som uppstår under reaktorns

gång. Åtgärder vidtogs som till viss grad förbättrade dessa fenomen men proble-

men kvarstår fortfarande och beror delvis på att bränslet utnyttjas till högre grad på

senare år. Deformationer och förändringar i bränslets placering påverkar och förän-

drar neutronflödet i reaktorn. Det är fissionen, eller som det kallas kärnklyvningen,

som skapar energin i en kärnreaktor. Detta sker genom att en neutron absorberas

av en uran-atom, som blir ostabil och tillslut delar sig och samtidigt avger 200 MeV

energi. Detta måste ske på ett kontrollerat sätt för att säkerställa en säker drift av

reaktorn. När neutronflödet förändras påverkas i sin tur sannorlikheten för fission

vilket leder till att den lokala effektfördelningen i reaktorn ändras. Förutom vissa

säkerhetsrisker, ger detta upphov till en förändrad isotop-sammansättning av det

använda bränslet. I slutändan leder detta till att det förbrukade bränslet kommer

ha en annan isotop-koncentration än vad reaktorn är designad för. På grund av ra-

dioaktiviteten är detta svårt att kontrollera i efterhand och är inte möjligt att göras

för allt bränsle. Osäkerheterna i det förbrukade bränslets sammansättning betyder

att längden för slutförvar av bränsle kommer justeras. I detta examensarbete har

deformationer av en schweizisk tryckvattenreaktor (PWR - Pressure Water Reac-

tor) studerats med böjningsdata vid två olika cykler av reaktorn. Neutronflödet har

simulerats med den så kallade Monte Carlo metoden genom att använda Serpent 2,

en kod för reaktorfysik. Genom att skriva inputfiler till Serpent kan geometrier och

inställningar för den aktuella reaktorn bli definierad. Speciell vikt har lagts vid att

studera relativa förändringar i effekt- och isotopkoncentration-fördelning genom att

beräkna den relativa förändringen av en nominell (utan böjning) och en beräkning

där böjning introducerats. Två olika delar av reaktorn som uppvisar skilda böjn-

ingsfenomen studeras.

v

Acknowledgements

There are a few people I would to thank a little extra. Fist of all, my girlfriend for letting

me go to Switzerland for 3 months. Dimitri, my sepervisor for all the help and to always be

ready to show some scripting tricks and all other colleagues that I met at PSI. Henrik, my

subject reviewer that introduced me for the opportunity to do the Master thesis at PSI and to

always be up for a quick meeting. . .

vii

Contents

Acknowledgements v

1 Introduction 1

1.1 Background . . . . 1

1.2 Goal . . . . 2

1.3 Reactor physics . . . . 2

1.3.1 Nuclear cross sections . . . . 2

1.3.2 Neutron transport equation . . . . 3

1.3.3 Bateman depletion equation . . . . 4

1.3.4 Nuclear data . . . . 5

1.4 Monte Carlo codes . . . . 5

1.4.1 Serpent . . . . 6

1.5 Bowing effects . . . . 6

1.5.1 Observations . . . . 6

1.5.2 Bowing effects on a PWR - mechanisms and consequences . . . 7

1.6 General methodology . . . . 9

2 Bowing effects on 5 x 5 fuel assemblies 11 2.1 Methodology . . . 11

SERPENT input and fuel data preparation . . . 11

2.1.1 SERPENT settings . . . 13

2.1.2 Data libraries and materials . . . 14

2.1.3 Plotting of data . . . 14

2.2 Simulation results . . . 16

2.2.1 Subpart 1 . . . 17

2.2.2 Subpart 2 . . . 24

3 Discussion and conclusions 33 3.1 Discussion . . . 33

3.2 Conclusion . . . 35

A The CRAM method 37 A.1 CRAM method . . . 37

B Serpent input files 39 B.1 Pin set up . . . 39

C Scripting and written codes 45 C.1 Preprocessing of data . . . 45

C.2 Post-processing of results . . . 46

Bibliography 53

ix

List of Figures

1.1 An arbitrary volume V with surface area S used to illustrate the neu- tron transport (James J. Duderstadt, Louis J. Hamilton, 1976). . . . 3 1.2 An illustrative PWR fuel assembly from Westinghouse with 17x17

pins (Dahlheimer et al., 1984). . . . 7 1.3 A sketch of different bowing shapes (Li, 2016). . . . 8 2.1 Left: A geometry output of the nominal 5x5 assemblies for one sub-

part studied. Right: A geometry output with the perturbed 5x5 as- semblies from one of the bowing maps. . . 12 2.2 Left: The bowing map for subpart 1 of the reactor core. Right: The

bowing map for subpart 2 of the reactor core. . . 13 2.3 The yellow arrows show the direction and amplitude of the bowing,

the scale is noted in the lower left corner. Left: The relative power difference between the nominal and the bowed assemblies for bur- nup at 0.1 MWd/kgU of subpart 1. Right: The relative power differ- ence between the nominal and the bowed assemblies for burnup at 15 MWd/kgU of subpart 1. . . 17 2.4 The yellow arrows show the direction and amplitude of the bowing,

the scale is noted in the lower left corner. Left: The relative isotopic mass density difference of U

between the nominal and the bowed assemblies for burnup at 0.1 MWd/kgU of subpart 1. Right: The rela- tive isotopic mass density difference of U

between the nominal and the bowed assemblies for burnup at 15 MWd/kgU of subpart 1. . . 18 2.5 The relative difference in isotopic mass density between the nominal

and the bowed assemblies with burnup. The results are for 4 pins in the central assembly and the most affected region. . . 19 2.6 The relative uncertainty in power change for figure 2.3 at 15 MWd/kgU

burnup. . . 20 2.7 A Serpent output plot of the power distribution within subpart 1 at

15 MWd/kgU. The power distribution is normalized, darker regions corresponds to less power and less fission and brighter to regions to higher power and more fission events. . . 21 2.8 The relative uncertainty in power change (from 2.3) with burnup for

4 pins in a region of high/low absolute power. . . 22 2.9 The relative difference in mass density as a function of the pin posi-

tion. Pin 1 is at the assembly edge and pin 7 is at the center. . . 23 2.10 The relative difference in mass density for U

, Pu

, Nd

, and

Cm

for burnup step 10 at 15 MWd/kgU. . . 24

2.11 The yellow arrows show the direction and amplitude of the bowing, the scale is noted in the lower left corner. Left: The relative power difference between the nominal and the bowed assemblies for bur- nup at 0.1 MWd/kgU of subpart 2. Right: The relative power differ- ence between the nominal and the bowed assemblies for burnup at 15 MWd/kgU of subpart 2. . . 25 2.12 The yellow arrows show the direction and amplitude of the bowing,

the scale is noted in the lower left corner. Left: The relative isotopic mass density difference between the nominal and the bowed assem- blies for burnup at 0.1 MWd/kgU of subpart 2. Right: The relative isotopic mass density difference between the nominal and the bowed assemblies for burnup at 15 MWd/kgU of subpart 2. . . 26 2.13 The relative difference in isotopic mass density for the nominal and

the bowed assemblies with burnup for 4 pins in the central subpart and the most affected region. . . 26 2.14 The relative uncertainty in power change for subpart 2 in figure 2.11

at 15 MWd/kgU burnup. . . 27 2.15 The relative uncertainty of power change for 4 pins in a lower and a

higher power region. . . 28 2.16 The Serpent output for the normalized absolute power distribution

within subpart 2. Darker regions corresponds to less power density and less fission, the opposite applies for brighter regions. Left: 0.1 MWd/kgU burnup. Right: 15 MWd/kgU burnup. . . 28 2.17 The relative difference of mass density as a function of the pin posi-

tion. Pin 1 at the assembly edge and pin 7 in the center. . . 29 2.18 The relative difference of mass density for U

, Pu

, Nd

, and

Cm

at 15 MWd/kgU burnup of subpart 2. . . 30 2.19 Four histograms of 50 independent simulations for the mass densities

of U

and Pu

in two separate pins. (A) for U

in the lower, (B) for U

in the top, (C) for Pu

in the lower and (D) for Pu

in the top part of the central assembly. The mean value and the standard deviation are calculated for each case. . . 31 B.1 The assembly-core definition for one assembly. . . 39 B.2 The pin geometrics and the material definitions (A) and the division

setting for a few pins (B). . . 39 B.3 (A) the fuel material card definition with normalized isotopic densi-

ties for one pin and (B) the material definitions for a few pins. . . 40

xi

List of Abbreviations

MC Monte Carlo

FA Fuel assembly

JEFF Joint Evaluated Fission and Fusion ENDF Evaluated Nuclear Data File

CRAM Chebyshev Rational Approximation Method IAEA International Atomic Energy Agency

NDS Nuclear Data Services NEA Nuclear Energy Agency

TENDL TALYS-based evaluated nuclear data library

1

Chapter 1

Introduction

This chapter introduces a general background, the purpose and aim for this thesis, a brief history of the field together with bowing observations.

The chapter will also cover general theory related to reactor physics and specific theory of the simulation code used.

1.1 Background

Deformation of fuel assemblies in nuclear power plants has been observed in oper- ating reactors around the world since the mid-90s. Ringhals 4 was the first where this phenomenon was publicly reported in 1994 (Inozemtsev, 2010). One control rod was not fully inserted during a reactor trip and four Rod Cluster Control Assemblies (RCCAs) were stuck in the dashpoint region during a drop down test (Inozemtsev, 2010).

For pressurized water reactors (PWR) these deformations are called assembly bow- ing and for boiling water reactors (BWR) channel or box bowing (Inozemtsev, 2010).

Deformations of the fuel assemblies (FAs) might lead to contact between subassem- blies, introducing sub-channel moderation regions. As a result, this modifies the neutron flux spectrum around the fuel assemblies giving an unexpected power dis- tributions of the reactor core. Moreover, power anomalies impact the isotopic con- centrations in the burnt fuel giving unpredicted contents in the spent fuel which in the long run may affect storage limits in final depositories.

Fuel bowing effects are well studied and these effects have previously been simu- lated using fresh fuel data, one example is (Li, 2016). As a continuation, bowing effects are now studied using realistic fuel data from a present Swiss nuclear reactor.

Spent fuel in Sweden and Switzerland are used to determine the number of assem- blies that can be stored in final depositories. Uncertainties in the spent fuel content are translated into storage limits. This study is meant to be part of this research by investigating and developing a method for simulating the impacts of the fuel bow- ing with realistic fuel data and geometrics from a present reactor.

The thesis was proposed by Paul Sherrer Institute (PSI) in Villigen, Switzerland as a

collaboration with Uppsala University in Sweden. The main work has been done at

PSI facility at the Reactor Physics and Systems Behaviour Laboratory.

1.2 Goal

The aim of this thesis is to achieve a better understanding of the change in neutron flux and power density and predict their consequences due to local fuel bowing ef- fects using the Monte Carlo method with realistic fuel and bowing data. The goal is to predict the change in power distribution and the effect on the isotopic composi- tion of the burnt fuel.

Generally, there is a need to predict the fuel content (actinides, and important fis- sion products) at the end of the assembly life, after the last irradiation.

1.3 Reactor physics

The basic concept of nuclear reactor design is to create an environment where a con- trolled and sustained nuclear chain reaction can take place (Bahman, 2017). In general, slow (thermal energy) neutrons can initiate fission by neutron capture of a U

nu- cleus. The fission process produces fission products, fast neutrons and ∼ 200 MeV of additional energy. The newly released neutrons are essential for the chain reaction to take place but the probability for fission induced by fast neutrons are very low. In order to slow down the neutrons, one adds a moderator material inside the reactor, which may consist of water. When the neutrons interact with the molecules of the moderation medium, they lose energy, and in the end neutrons of a certain energy range will initiate fission once again.

Moreover, the reactor design need to consider the production rate of neutrons and balance it by the absorption and leakage of neutrons out of the reactor system (James J. Duderstadt, Louis J. Hamilton, 1976).

Some basic concepts (relevant for this thesis) and necessities for a self-sustained nuclear chain reaction is covered in this section, although some are omitted (mul- tiplication factor, criticality etc.) due to less relevance for this thesis.

1.3.1 Nuclear cross sections

In nuclear physics, the concept of cross sections describes the fundamental probabil- ity of a certain process (Wikipedia, 2017). Nuclear cross sections are divided into microscopic and macroscopic cross sections. Microscopic cross sections describe the probability for particular events of a single nucleus, like fission, elastic and inelastic scattering or neutron capture. It measures in the unit of barns, where one barn equals 10

cm

and it is denoted as σ.

Macroscopic cross sections describe the probability of a particular reaction character- ized by the target (and the macroscopic chunk of material) (James J. Duderstadt, Louis J. Hamilton, 1976), the unit is cm

and is denoted Σ. The macroscopic cross section is calculated via (Bahman, 2017),

Σ = Nσ, (1.1)

where N is the atomic density of a particular nuclide.

1.3. Reactor physics 3

Large libraries containing nuclear cross sections of different nuclides over a wide energy rage are used in nuclear physics and are important in reactor design. Such libraries and the continues development of them are further described in 1.3.4.

1.3.2 Neutron transport equation

The nuclear reactions and fission events inside a nuclear reactor and the rates at which these reactions take place depend on the neutron distribution inside the reac- tor core (James J. Duderstadt, Louis J. Hamilton, 1976). The neutron distribution is determined by studying the neutron transport with loss and gain mechanisms of neu- trons. By representing the neutron population as a dilute gas and with kinetic theory of statistical mechanics, the distribution can be calculated using the Boltzmann equa- tion. However, the Boltzmann equation is non-linear and therefore hard to solve. In reactor physics one often uses its linear counterpart, the neutron transport equation, to determine the neutron distribution (James J. Duderstadt, Louis J. Hamilton, 1976).

F

1.1: An arbitrary volume V with surface area S used to illus- trate the neutron transport (James J. Duderstadt, Louis J. Hamilton,

1976).

Generally the population of neutrons inside a reactor are described by gain and loss mechanisms, meaning neutrons that entering or leaving the reactor system (James J. Duderstadt, Louis J. Hamilton, 1976). Imagine an arbitrary volume V with surface area S and neutrons travelling in direction ˆ Ω, seen in 1.1. The gain and loss mecha- nisms for a neutron of a specific energy E entering or leaving V are then translated into:

Gain mechanisms:

i. Neutron sources in V (fission) ii. Neutrons entering the system

iii. Neutron scattering that changes the neutron energy into the point of interest

Loss mechanisms:

v. Neutron leakage out of V

vi. Neutron scattering changing the energy from the desired energy E to E

or neutron absorption.

A balance relation is created by balancing the different mechanisms by which neutrons are gained or lost within the system (James J. Duderstadt, Louis J. Hamil- ton, 1976), the relation is later translated into the Boltzmann equation (or the neutron transport equation in this case),

the rate of change of neutrons inside V = _i + _ii + _iii − _iv − _{v (1.2)} For an arbitrary volume V in 1.1 and using 1.2 one finds for the neutron transport (James J. Duderstadt, Louis J. Hamilton, 1976),

Z

V

d

r

"

∂n

∂t + v ˆ Ω ·∇ n + v ∑

t

n ( r, E, ˆ Ω, t ))

−

Z

0

dE

Z

4π

d ˆ Ω

v

∑

S

( E

→ E, ˆ Ω

→ _Ω ^ˆ ) n ( r, E

, ˆ Ω

, t ) − s ( r, E, ˆ Ω, t ))

#

dEd ˆ Ω = 0, (1.3) Since the volume V is arbitrary chosen one can make the integral vanish by putting its integrand to zero,

Z

anyV

d

r f ( _r = 0 ) ⇒ f ( _r ≡ 0 ) . (1.4) The balance relation of the neutron transport equation is written,

∂n

∂t

+ v ˆ Ω ·∇ n + v ∑

t

n ( _{r, E, ˆ Ω, t} ) =

Z

4π

d ˆ Ω

^Z

0

dE

v

∑

s

( E

→ E, ˆ Ω → _Ω ^ˆ ) n ( r, E

, ˆ Ω

, t ) + s ( r, E, ˆ Ω, t ) .

(1.5)

Even with the addition of adequate initial and boundary conditions the neutron transport equation is often impossible to solve analytically for most reactor type structures due to its seven independent variables x, y, z, θ, φ, E, t (James J. Duder- stadt, Louis J. Hamilton, 1976). Normally, it is approximated by deterministic meth- ods using the neutron defuse model (James J. Duderstadt, Louis J. Hamilton, 1976) or modelled based on stochastic Monte Carlo methods (nuclear-power, 2018) . In this thesis the neutron transport is solved with a Monte Carlo code, described in 1.4.1.

1.3.3 Bateman depletion equation

The isotopic composition inside a nuclear reactor is constantly changing due to fis- sion, decay and production of new isotopes. A model for the decay chain was pos- tulated by E. Rutherford in 1904-1905 (Rutherford, 1904). The equation was later solved by H. Bateman in 1910 (Bateman, 1910).

To ensure a safe operation of a nuclear reactor it is important to predict its behaviour

1.4. Monte Carlo codes 5

by estimating nuclei concentrations. This is done via the Bateman depletion equation (Bateman, 1910) ,

dN

dt = ∑

i6=j

( S

− λ

N

− φσ

N

) , (1.6) S

is the source term and the production rate of nuclide j, λ

N

is the radioac- tive decay and φσ

N

is the rate of transmutation of nuclide j, including fission. Dif- ferent methods of solving this equation are implemented in nuclear reactor codes.

One method that Serpent uses is further described in Appendix A.

1.3.4 Nuclear data

The IAEA (International Atomic Energy Agency) serves as an international coordi- nator for scientific collaborations and activities within the nuclear field under the United Nations regime (World Nuclear, 2018). There are many different nuclear organizations around the world, some are responsible for nuclear research and co- operations and others based on regulatory purposes. A few of them are international based, whereas others are country specific.

One example of such an activity is the continuous development of reliable and im- proved nuclear data libraries. Reliable nuclear data is essential for nuclear energy production, research and waste management but are also used in medical dosime- try and diagnostics, laser and accelerator applications, environmental monitoring, and fusion energy research (IAEA/NDS, 2018). Thus, a continuous development of better nuclear data for future libraries is still important. Two organisations responsi- ble for development of nuclear data and establishment of international networks are the NDS (Nuclear Data Section) though the IAEA (NDS, 2018) and the NEA (Nu- clear Energy Agency) (NEA, 2018) based on the OECD countries. A few examples of nuclear data libraries are JEFF (Joint Evaluated Fission and Fusion) (Nuclear En- ergy Agency, 2018), ENDF (Evaluated Nuclear Data File) (NNDC, 2018) and TENDL (TALYS-based evaluated nuclear data library) (Koning and Rochman, 2012).

The libraries cover different aspects depending on the purpose. Some cover nu- clear structure and decay data whereas others contain cross section for fundamental collision processes.

In this thesis is the U.S library ENDF/B-VII.1 (Chadwick et al., 2011) used, where the Cross Section Evaluation Working Group (CSEWG) in nuclear data evaluation is responsible for the evaluation.

1.4 Monte Carlo codes

The particle reaction and transport in the reactor core is simulated with the Monte

Carlo method. There are several public available Monte Carlo codes for reactor cal-

culations, such as MCNP (Los Alamos National Laboratory, 1957). A relatively new

one is Serpent (Leppänen et al., 2015), written at VTT Technical Research Center in

Finland by Jaakko Leppänen. Serpent 1 was first distributed by the OECD/NEA

Data bank in 2009 and is nowadays widely used at institutions and in research

world-wide (Leppänen et al., 2015)

Due to limitations of Serpent 1, Serpent 2 (montecarlo.vtt, 2018) was initiated and is still under continuous development. Serpent 2 is more adopted for three dimen- sional analysis and is not only suitable for reactor physics. It has a possibility to cou- ple with multi-physics calculations like thermal hydraulics, CFD (Computer Fluid Dynamics) and fuel performance codes. Moreover, it can be used for neutron and photon transport simulations for a range of applications, such as medical physics and fusion research. Serpent 2 is used in this thesis.

1.4.1 Serpent

Serpent uses a continuous energy approach and solves two- and three-dimensional particle transport equations with the use of external nuclear data libraries containing continuous neutron energy cross sections, described in 1.3.4. Separate libraries are used for moderation regions containing thermal scattering cross sections (Leppänen et al., 2015). A Doppler broadening preprocessor routine adjusts the nuclide tem- peratures (Viitanen, 2009) and a Doppler broadening Rejection Correction (Becker, Dagan, and Lohnert, 2009) accounts for the temperature dependences in the reso- nant scattering kernels. Meaning that Serpent adjusts for irregularities in the actual temperatures and the temperature specified by the nuclear data libraries.

The geometries can be defined in multiple layer structure where subparts are de- fined individually and later imported in the main input file (Leppänen, 2010). This feature is adopted in this thesis which simplifies the file structure of the model.

The particle transport equations are solved using a combination of surface track- ing and Woodcock delta tracking methods (Woodcock, E.R., et al., 1965). The Bate- man depletion equation described in 1.3.3 is solved with two options, Transmuta- tion Trajectory Analysis (TTR) (Cetnar, 2006) or Chebyshev Rational Approxima- tion Method (CRAM) (Pusa, 2011). TTR solves the particle decays based on a linear chain method and provides the analytic solution of the depletion chains. CRAM (de- scribed in Appendix A by applying CRAM to first order linear equation) applies a matrix exponential method developed for Serpent. The method handles a system of nuclides and accounts for short lived isotopes without any approximation for step length or numerical precision.

Serpent is adopted for burnup calculations and can handle a large number of iso- topes and depletion zones in an efficient way (Isotalo and Aarnio, 2011). This is one reason why Serpent was considered in this thesis.

Most of the theory in this section apply for both Serpent 1 and 2.

1.5 Bowing effects

1.5.1 Observations

Incomplete Rod Cluster Control Assembly (RCCA) insertions (IRI) was reported by

several operators around the world in the mid 1990s during emergency shuts down

or drop time tests, developed for reactor safety analysis. The root cause reported

for the fail of such tests was extensive fuel assembly deformations causing sticking

of control rods during the drop down (Inozemtsev, 2010). As stated in the Back-

ground section 1.1 such deformations are refereed as Bowing effects. The Bowing

1.5. Bowing effects 7

effects were first publicly reported for Ringhals 4 1994 (Inozemtsev, 2010) in Swe- den. Investigations showed that FAs (fuel assemblies) bowed in an S-shape with displacement amplitudes reaching 20 mm. Because of that, several monitoring and preventive actions were implemented by the safety regulators. Such as limitation of fuel burnup in the assemblies close to the RCCA position and introduction of ad- ditional drop tests at the end of the fuel cycle. Such drop tests of RCCAs are an effective way to find deformation issues of the nuclear fuel (Inozemtsev, 2010).

In recent years, extensive investigations and safety arrangements have made the bowing effects of FAs less critical but FA shape measurements are still performed by utilities in the reactor core and storage pools (IAEA, 2005). A higher utilization of the nuclear fuel nowadays (related to economy etc.) impacts the bowing, since the amplitude of the displacement is related to the fuel burnup (among other things).

Implying that, it is still important to study the consequences of fuel bowing effects.

1.5.2 Bowing effects on a PWR - mechanisms and consequences

A typical pressure water reactor (PWR) fuel assembly is shown in figure 1.2 from a Westinghouse 17x17 pin assembly design and with the corresponding definitions of its parts. Although a 15x15 pin assembly design is used in this thesis, the main features are the same.

F

1.2: An illustrative PWR fuel assembly from Westinghouse

with 17x17 pins (Dahlheimer et al., 1984).

Beside handling damages on fuel and grid spacers during transport, investiga- tions showed a few root causes to the fuel deformations. One major contributor was low skeleton stiffness of the FAs together with high hold down forces from the ending springs (IAEA, 2005) (Inozemtsev, 2010). This phenomenon is illustrated in figure 1.3 and shows the basic concept causing the deformations.

F

1.3: A sketch of different bowing shapes (Li, 2016).

It is observed that the bowing shape has a strong dependence of the FA location within the core at the end of a fuel cycle whereas the burnup has a milder impor- tance to the global deformations. Hence, the bowing effects evolves as a stepwise function of its positioning in the core throughout its lifetime. As a consequence of this were fuel shifting schemes invented, relaxing such effects. The bowing effects are basically seen as something that evolves with increased deformations over time.

Actions, such as design changes and improvement of structural materials in reac- tors and fuel assemblies were recommended by utilities. Generally, materials with enhanced mechanical properties were implemented by reactor operators and fuel manufacturers based on the recommendations (Inozemtsev, 2010). A few actions proposed by suppliers to enhance the structural behaviours and attenuate the bow- ing effect were an advanced cladding and guide thimble material with low growth rate and high creep resistance and increasing the grid width to reduce inter assem- bly lateral gaps (Inozemtsev, 2010). A low growth recrystallized zircaloy-4 cladding material was implemented, which increased the skeleton stiffness.

As a consequence of the deformations, the friction between control rods and the

guide thimbles may increase. Which in the end could break or cause sticking of

RCCAs during drop-down tests or result in incomplete RCCA insertion during an

emergency shut down, as mentioned in 1.5.1.

1.6. General methodology 9

Moreover, the increased/ decreased water gap due to the bowing redistributes the local power distribution within the reactor core in respect with nominal conditions and thus it is critical to assure that the perturbations in power do not exceed limita- tions in the reference safety analysis (Inozemtsev, 2010) of the reactor.

1.6 General methodology

Realistic data from an operating Swiss reactor is used both regarding fuel composi- tion and bowing data. The dimensions, the fuel data and direction and amplitudes of the bowing come from the same PWR.

The fuel contents are previously simulated for the full core using two determinis- tic codes (CASMO5 and SIMULATE3). The fuel data for a specific height of the reactor core are extracted by the supervisor of this thesis and the data are provided as a starting point. However, all nuclear data generated from the deterministic sim- ulations is not essential for this thesis and is therefore not used. The isotopic mass densities are used and are extracted from the simulated fuel data (at the specific height), formatted in a Serpent readable way and used as input for the Monte Carlo simulations. Isotopic contents less than 10 g/t fuel are not considered and assumed to have a minor effect of the reactor behaviour.

Each pin within the subparts simulated is defined with its own unique fuel com- position and all calculations in this thesis are done in 2 dimensions using Serpent 2.

Since already a 2D calculation with burnup and separate depletion zones in each pin is memory demanding, only two subparts of the full reactor core are chosen for the study and presented in this report. The Serpent input files are constructed in such a way that these regions can easily be moved throughout the reactor core, thus more interesting parts can be isolated, such as larger bowing regions. The bowing maps of these subparts are presented in chapter 2. Generally, the 2D bowing maps show the extreme displacement in one plane of each FA together with its corresponding direction.

By using Bash scripting, the fuel data for the subparts is extracted and formatted for each pin which makes the analysis efficient and less time-consuming. The dis- placement of the bowing map is however read and updated manually. Examples of the Bash scripts are found in Appendix C.

All result data are post-processed with Bash and plotted in Matlab.

11

Chapter 2

Bowing effects on 5 x 5 fuel assemblies

This chapter covers the methodology used together with the main results.

2.1 Methodology

Two subparts of the full reactor core with different bowing characteristics are in- vestigated and presented in this report. The bowing maps 2.2 are measured from different fuel cycles, one quite recent and another a bit older, but both of them come from the same Swiss reactor.

SERPENT input and fuel data preparation

All fuel data for each FA used is first simulated and validated for the full core and the corresponding fuel cycle. As stated in 1.6, these initial calculations were performed with deterministic codes (CASMO5 and SIMULATE3) before the start of the thesis.

The simulated fuel data for one assembly is stored into a separate file containing fuel content for each pin at a specific height of the reactor core. Fresh fuel is considered for the FAs that are being replaced in the present fuel cycle.

The amount of simulated nuclear- and isotopic-data is large and before one can use it in Serpent it needs prepossessing and formatting. Initially, the fuel mass density is in the unit of g/t but it is normalized to 1 during the formatting. Serpent handles a large number of different isotopes and their corresponding distribution better if the isotopic contents are first normalized. For simplicity, materials with low content are omitted and assumed to a have minor impact.

Each pin is separated from each other by creating individual names and depletion zones. All pins are associated with a unique file containing the fuel data. The extract- ing, the normalizing, the renaming of isotopes in Serpent readable way, and prepar- ing of the material card definition for each pin is programmed with Bash scripting in the Linux environment. A few scripting examples are found in Appendix C and a file with fuel contents in Appendix B.

For simplicity, each fuel assembly is also separated in a two-file layer structure. Files

are constructed for material pin inputs, pin layouts and definitions and for deple-

tion zones with the possibility to add several depletion zones of each pin. The pin

radius and the assembly size and distances are set accordingly of the reactor under

consideration. Definitions are set for pins in a first layer. The pin definitions are col-

lected and formed as assembly definitions in a second layer, forming assembly files.

The assembly files are later imported into the main Serpent input file, where a 5x5 assembly matrix and all specific simulation settings are defined. Examples of each file type and the main input file are found in Appendix B. Keeping a file structure like this makes the structure easier to follow and possible errors easier to find.

For the chosen subparts, the 5x5 assembly matrix is first simulated with a nominal distance of the adjacent FAs and later with a perturbed. The assembly perturbations are in accordance with the bowing maps in figure 2.2 of each subpart. The physical behaviour of a bowed assembly in 2 dimensions is represented by using the nominal and the perturbed case and calculate the relative difference between in terms of the desired quantities one like to study.

Figure 2.1 shows a geometry output plot of the 5x5 assemblies from Serpent. The small circles are the fuel pins with random colors due to the specific fuel data defini- tion of each pin (a feature of Serpent). The blue background is water and the empty circles are the channels for the control rods. To the left is the nominal case with the unperturbed assemblies and to the right the case with perturbed assemblies.

F

2.1: Left: A geometry output of the nominal 5x5 assemblies for one subpart studied. Right: A geometry output with the per-

turbed 5x5 assemblies from one of the bowing maps.

The bowing maps for the two subparts under consideration are seen in figure 2.2 with the scale of the perturbations marked in the lower left corner. As before mentioned these maps do not come from the same fuel cycle of the reactor. Meaning that some assemblies are replaced or at least moved during their lifetime, according to the fuel shifting scheme of the reactor.

As seen, displacement measurements are not taken for each FA and even for the two subparts under consideration some measurements are missing. Since these positions are not measured, it does not mean that no displacements occurs at these positions.

These assemblies are perturbed as the assembly straight above or below, wherever

measurements exist. Additionally, for the methodology to work, the displacement

in 2D cannot be greater than the corresponding distance to the adjacent assembly,

since physically they cannot overlap. As confirmed in 2.2, most assemblies perform

2.1. Methodology 13

a collective displacement behaviour, although some deviations are seen. Some as- semblies at the left border in the left map of 2.2 move more than their inner neigh- bours, which is not physically allowed in 2D. To avoid collisions, these are perturbed as much as allowed by the distance of the adjacent FAs. In reality, the extreme dis- placement of the FAs in the bowing maps may occur at different heights, which are not covered in the 2D plots. Meaning that the amplitude maxima of the s- and c- shape perturbations showed in figure 1.3 varies at different heights throughout the reactor core.

F

2.2: Left: The bowing map for subpart 1 of the reactor core.

Right: The bowing map for subpart 2 of the reactor core.

2.1.1 SERPENT settings

Two general phenomena are investigated, power and isotopic composition changes induced by FA displacements. The power calculation in Serpent is performed by placing power detectors covering each assembly. These detectors produce an output file with power content and uncertainty for each pin.

The fuel is depleted with 10 burnup steps from 0.1 - 15 MWd/KgU and a set of isotopes is defined in the Serpent input file, which is followed. Serpent generates isotopic data with burnup in output files for the defined isotopes. Since all pins are separately defined, the output allows a study of isotopic data with burnup for each pin.

The nominal calculation, described in section 2.1, is first performed and later is the same calculation performed again but with perturbed assemblies and a different seed. The seed is changed manually to ensure that the random variables come from a different set.

A periodic boundary condition is used, periodic means that the defined geometry of the subpart is copied and repeated periodically at the boundary of each side of the 5x5 assemblies.

Serpent performs the MC calculation in a set of cycles with the defined number of

neutrons for each set. The uncertainty of the calculation depends on the size of the

neutron population and the number of cycles. The number of neutrons and cycles have been changed and steadily increased during the simulation process, in order to improve the statistical uncertainties. However, due to the statistical importance are all the simulations kept and used in the analysis. The results are weighted and averaged according to the number of cycles and neutrons, as described in 2.1.3.

The assembly linear power density is set to 38.6

kW/g. This value (the total av- erage power density in the system) is not substantial for a relative study but is used as a normalization factor. Serpent provides normalized power data based on this factor in the result output files.

A possibility to investigate subdivisions of every pin are defined. Every pin are divided into radial- or section-wise divisions (or both), allowing radial or azimuthal investigation with burnup. Results for this feature are not presented in this report but it may be used for pins of specific interest. This feature is preferably not used for all pins since sub-divisions in each pins are very memory demanding and all pins are already defined with separate depletion zones.

The predictor-corrector method is used to solve the neutronics with depletion (bur- nup). A linear extrapolation on the predictor and a linear interpolation on the cor- rector in 10 steps (with the command set pcc leli 10 10) is used.

The material volumes are crucial for the burnup calculation and these are estimated by sampling 10

random points inside the geometry (with the command set mcvol 100000000).

2.1.2 Data libraries and materials

Light-water is used as moderator. Thermal scattering data for hydrogen at 600 K is used via lwe7.12t in the ENDF/B-VII.1 evaluation (Chadwick et al., 2011). The nuclear decay data for the burnup calculation and the neutron induced fission yields are used via endfb7.dec and endfb.nfy libraries in the ENDF/B-VII.1 evaluation.

Zircaloy-4 at 610 K is used as cladding material (PNNL-15870, Rev.1).

2.1.3 Plotting of data

As described in section 2.1.1, are two general phenomena investigated, a power and an isotopic composition change induced by the bowing impact.

As discussed, Serpent produces output files with power distribution and isotopic composition data for each pin and burnup step. Results from several separate cal- culations of the same geometry but with different seed are combined to increase the statistics. The nominal and the bowed simulations are combined independently with Bash scripting and one example is found in Appendix C. All results are plotted with MATLAB.

One power detector is defined for each of the 5x5 assemblies which calculates the power dissipation in each pin. The output from the power detectors are straightfor- ward to plot and one output file is generated for each burnup step.

One assembly is defined by 15x15 pins and the power detectors produces power

2.1. Methodology 15

outputs for those 225 positions. Thus, the positions for control rods with zero power are also detected. However, these positions are distinguished by plotting them as black squares in the color maps that show the relative difference between the nomi- nal and perturbed calculation. The color maps are seen in 2.2.

The power files contain matrices with normalized power densities and the corre- sponding relative power uncertainty of each pin. Results with different neutron population and number of cycles, discussed in 2.1.1, are combined and weighted according to their significance. The total weighting factor for the number of cycles and the number of neutrons are calculated as,

ω

= ∑

n

( w

w

) , (2.1)

for all simulations. Where ω

is the total weighting factor of all simulations combined, w

is the number of cycles and w

, n the size of the neutron population of simulation n, respectively.

The average power density of all simulations is calculated as, P

= ¹

ω

∑

n

w

w

a

, (2.2)

a

is the power density in pin j, burnup m and simulation n. The pin index j

is increased by moving to the next pin. The power density is calculated for the nom- inal and bowed simulation case (described in section 2.1) and a relative difference between them are plotted using equation 2.4 (see result section 2.2).

It is not straight forward to use the result files containing isotopic composition data from Serpent. The output files contain more than 3 million rows for the 80 different isotopes that are followed, in this case. The files consist of matrices with composition data for each burnup step and every fuel pin. The rows are for different isotopes and the columns are for burnup steps. Naturally, no data is generated in places where control rods are, since these cells do not contain any fuel. In this sense, some modifi- cation of the output files simplifies the plotting while plotting the relative change of the nominal and perturbed simulation in color maps, similar as for the power results.

Matrices with zeroes of the same size are added at the same position as the empty cells with a corresponding name. Thus, can control rods easily be distinguished in the color maps.

The output files with composition results contains various data, but the isotopic mass density is only studied here. The mass densities are extracted from the rest by creating one new file for each assembly that contains the isotopic mass density for the different burnups and pins.

As for the power density, results form several runs are combined with a weighted average for each burnup step,

M

= ¹ ω

∑

n

w

w

b

, (2.3)

where b

is the mass density in pin j, burnup step m and simulation n.

The statistical uncertainty of the calculation improves by combining results from several independent simulations using equation (2.2) and (2.3).

The bowing effects are illustrated in MATLAB by using equation (2.2) and (2.3) and by calculating the relative change in power and isotopic mass density between the nominal and the perturbed case with Bash. Hence,

∆

= C

j/bj

− C

j/bj

C

j/bj

, (2.4)

where i applies for the mass density of isotope i, C

j/b_j

and C

j/b_j

are the case for the nominal and the perturbed power or mass densities of the fuel assemblies, re- spectively. The bowing maps used are considered constant as a function of burnup.

The Serpent input file is prepared in such a way that the power and the relative uncertainty in power are calculated for each pin. The combined mean absolute un- certainty in power is calculated for the nominal and the perturbed case of several independent simulations,

e

= ¹ ω

∑

n

q

( w

w

a

e

)

_{, (2.5)}

where e

is the relative uncertainty for one pin and one simulation. The com- bined absolute uncertainty is used to propagate and calculate the relative uncer- tainty of the relative change in power between the nominal and the bowed calcula- tion, described in equation 2.4,

e

= v u u t

( P

e

)

+ ( P

e

)

( P

)

^{, (2.6)}

P

and P

are the nominal and bowed mean power distributions from (2.2) whereas e

and e

are the nominal and bowed mean absolute uncertainty from (2.5).

The relative uncertainty of the relative change between the nominal and the bowed calculation is illustrated with a colormap for each subpart of the reactor core (see result section 2.2).

Serpent does not provide any uncertainty data for the isotopic composition. Instead an uncertainty estimation is done for subpart 2 (in section 2.2.2) by running 50 in- dependent simulations, calculating the standard deviation in mass density between them and plotting mass densities in a histogram. One can consider the statistics to be enough, if the standard deviation is low and the distribution of the histogram is Gaussian.

2.2 Simulation results

The results of the two 5x5 assembly subparts from figure 2.2 of the reactor core, both

with different characteristics, are presented separately in this section. The two parts

are denoted as subpart 1 and 2, respectively. The bowing direction and amplitude

2.2. Simulation results 17

of each subpart are denoted by yellow arrows in some of the result plots that show the global distribution of a relative power or a mass density change induced by the bowing effects. The arrows allow for a better understanding of the impact from the displacement of the fuel assemblies.

2.2.1 Subpart 1

The corresponding bowing map of subpart 1 is to the left in 2.2.

The relative power difference between the nominal and the perturbed assemblies is calculated using equation 2.4 and the result is plotted in figure 2.3. The left col- ormap corresponds to the first burnup step at 0.1 MWd/KgU and the right figure to the last burnup step at 15 MWd/KgU. Each simulation is performed with burnup in 10 steps, but only the two extremes are shown here. The red regions refer to an increase of power dissipation and blue regions to a power decrease, introduced by the displacement of the FAs in respect with the nominal non-displaced case. The yellow arrows show the 2D direction and amplitude of the perturbations from the corresponding bowing map, with the scale noted in the lower left corner.

The relative difference in power is directly comparable with the expected behaviour by the displacement of the FAs. An increased water gap in-between adjacent as- semblies results in an increased moderation region, meaning that the neutrons are more efficiently thermalized, which increases the probability of fission and thus in- creases the power dissipation in that region. The opposite applies to regions with a decreased moderation region. The relative difference is greatest for the first bur- nup step. However, the central part of the FAs at the first burnup are whiter than at higher burnup, meaning that the power dissipation of the central parts is not af- fected, as much, at low burnup. The central parts of the FAs are affected for the highest burnup, where one sees a blue-shift (decrease) of the FAs in the center of the subpart whereas the assemblies at the top and bottom row are red-shifted (increase).

The cause for this might be related to the periodic boundary condition used (and the input settings), but also a result of the FA perturbations. Possible reasons are further discussed in the discussion3.1.

Relative change in power [%]

-10 -8 -6 -4 -2 0 2 4 6 8 10

10 mm

Relative change in power [%]

-10 -8 -6 -4 -2 0 2 4 6 8 10

10 mm

F

2.3: The yellow arrows show the direction and amplitude of the bowing, the scale is noted in the lower left corner. Left: The rela- tive power difference between the nominal and the bowed assemblies for burnup at 0.1 MWd/kgU of subpart 1. Right: The relative power difference between the nominal and the bowed assemblies for burnup

at 15 MWd/kgU of subpart 1.

The isotopic concentration and depletion of U

are closely related to the power distribution inside the reactor, regions of high power dissipation corresponds to high depletion of U

. Figure 2.4 shows the relative mass density difference of U

for the first and last burnup step. Note that the scales are not the same in this cases, the first burnup step has a very low relative difference, but still notable. The relative difference is at least 100 times higher for the last burnup step.

Regions of an increased relative power corresponds to a decrease of U

mass den- sity, as expected, by comparing the relative power difference in figure 2.3 with the relative change of U

mass density in figure 2.4. The color settings are adopted for showcasing this phenomenon, where the red regions for increased power becomes blue for the relative decrease in U

content. Generally is the power map directly translated into the mass density map of U

, except for a few places. In the cen- tral FA of the second row form the bottom are all pins in the bottom row dark blue.

That should, with the discussed logics, correspond to a red region in figure 2.3 of increased power, which is not the case.

Relative change in isotopic massdensity for U235 [%]

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

10 mm

Relative change in isotopic massdensity for U235 [%]

-10 -8 -6 -4 -2 0 2 4 6 8 10

10 mm

F

2.4: The yellow arrows show the direction and amplitude

of the bowing, the scale is noted in the lower left corner. Left: The relative isotopic mass density difference of U

between the nominal and the bowed assemblies for burnup at 0.1 MWd/kgU of subpart 1.

Right: The relative isotopic mass density difference of U

between the nominal and the bowed assemblies for burnup at 15 MWd/kgU

of subpart 1.

Figure 2.5 shows the relative mass density difference with burnup for U

, U

,

Pu

, Cm

, and Nd

. The results are for the 4 most affected pins in the central

assembly. Two pins are at the border of the FA and the other two are adjacent (inner)

to them. The ones at the border exhibit the greatest difference and are most affected

by the bowing. Naturally, the relative mass density of U

and Pu

decreases with

depletion whereas Cm

and Nd

increases since more isotopes are produced with

depletion. The mass density of U

stays roughly the same depending on its low

fission cross section in the present energy region.

2.2. Simulation results 19

0 5 10 15

Burn up [MWd/kgU]

-15 -10 -5 0 5 10

"

mass density [%]

U²³⁸ Pu²³⁹ Cm²⁴⁴ Nd¹⁴⁸

Burnup

F

2.5: The relative difference in isotopic mass density between the nominal and the bowed assemblies with burnup. The results are

for 4 pins in the central assembly and the most affected region.

The relative uncertainty for the relative power change is calculated and propa- gated for each pin of the combined simulations results, as mentioned in section 2.1.3.

The global distribution of uncertainty is plotted in a colormap to easily display the differences. Figure 2.6 shows the relative uncertainty of figure 2.3 at 15 MWd/kgU.

The uncertainty is generally low ( ∼ 0.2%) for all FAs, although some differences

are seen. The assemblies in the second column from the left together with the two

assemblies, one in the end of the first row and the other in the end of the last row,

originates from fresh fuel at the start of the simulation and these show the lowest

relative uncertainty. The power dissipation is highest in these fresh assemblies (com-

paring with others from older fuel cycles), meaning that there might be a absolute

power relation to the relative uncertainty of the power change. The absolute power

distribution is shown in figure 2.7. However, it could also be related to the number

of different isotopes considered in the beginning of the simulation, comparing the

fresh fuel with previously used fuel.

"0rel [%]

#10^-3

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 -1

F

2.6: The relative uncertainty in power change for figure 2.3 at 15 MWd/kgU burnup.

Since the FAs have separate fuel composition and some originates from differ- ent fuel cycles, i.e consisting of fuel of different age, which implies that the power distribution inside the reactor is not uniform. Unfortunately, this behaviour is not realised in figure 2.3, since only the relative difference is calculated and the differ- ences introduced by the bowing are only covered.

The absolute power distribution within subpart 1 (for one simulation run) is shown

by the Serpent generated geometry plot in figure 2.7, for the perturbed assemblies

at 15 MWd/kgU. Brighter regions corresponds to higher absolute power and the

opposite for the darker regions. Basically, one sees a similar pattern for the relative

uncertainty and the absolute power distribution comparing figure 2.6 and figure 2.7.

2.2. Simulation results 21

F

2.7: A Serpent output plot of the power distribution within subpart 1 at 15 MWd/kgU. The power distribution is normalized, darker regions corresponds to less power and less fission and brighter

to regions to higher power and more fission events.

The previous reasoning of a power dependency for the uncertainty is confirmed by figure 2.8. The figure shows the relative uncertainty of 4 pins in a high (with fresh fuel) respective a low (with older fuel) absolute power region plotted with burnup.

The high power region corresponds to one assembly in the second column and the

central assembly (of the subpart) is used as the low power region. The variation with

burnup is very little, but there is a distinct difference between the two regions, i.e the

investigation indicates that the absolute power impacts the relative uncertainty, but

other effects are also possible.

0 5 10 15 Burn up [MWd/kgU]

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2

0

power density [%]

#10

High power region Lower power region Mean 0_rel

Low power region High power region

-1

Power change[%]

Burnup

F

2.8: The relative uncertainty in power change (from 2.3) with burnup for 4 pins in a region of high/low absolute power.

Figure 2.4 shows that the relative difference of U

mass density is most severe

at the border of the perturbed assemblies. In figure 2.9 is the relative difference in the

mass density of 2 pins at each distance from the border plotted for U

, U

, Pu

,

Cm

and, Nd

, by starting from the border of the central assembly and move

towards the center. One realizes that the bowing effects of the isotopic composition

become less with the distance from the assembly edge, which are seen for all isotopes

plotted. Hence, the bowing affects the border regions of the FAs mostly.

2.2. Simulation results 23

1 2 3 4 5 6 7

Pin position from assembly edge -15

-10 -5 0 5 10

"

mass density [%]

U²³⁸ Pu²³⁹ Cm²⁴⁴ Nd¹⁴⁸

F

2.9: The relative difference in mass density as a function of the pin position. Pin 1 is at the assembly edge and pin 7 is at the

center.

The global distribution of the relative mass density difference is also plotted for U

, Pu

, Cm

, and Nd

at 15MWd/kgU burnup, the results are shown in fig- ure 2.10. Note that the colorbar scales in these plots are not the same since the iso- topic composition does not change equally.

The difference in (A) for U

is about 100 times less than for U

in figure 2.4, but

the bowing impacts are still seen. Some random noise is present in the center of the

assemblies which may be related to the low rate of neutron-induced fission for U

.

Pu

in (B) shows good statistics and low noise, hence all color transitions between

adjacent pins are smooth. The impacts at the assembly centres is very little for Pu

and almost everything occurs at the borders. Nd

in (C) and Cm

in (D) exhibit

similar, but different patterns from what are seen before and the relative difference

in mass density is not directly deduced from the bowing maps 2.2. Some random

noise is also present, especially for (D), which indicates less statistics.

Relative change in isotopic massdensity for U238 [%]

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

(A)

Relative change in isotopic massdensity for Pu239 [%]

-10 -8 -6 -4 -2 0 2 4 6 8 10

(B)

Relative change in isotopic massdensity for Nd148 [%]

-10 -8 -6 -4 -2 0 2 4 6 8 10

(C)

Relative change in isotopic massdensity for Cm244 [%]

-20 -15 -10 -5 0 5 10 15 20

(D)

F

2.10: The relative difference in mass density for U

, Pu

, Nd

, and Cm

for burnup step 10 at 15 MWd/kgU.

2.2.2 Subpart 2

The corresponding bowing map of subpart 2 is to the right in figure 2.2. The bowing characteristics of subpart 2 are different from what are seen for subpart 1. All FAs in subpart 2 perform a collective displacement towards the right with similar but different amplitudes, which is different from subpart 1, where all central assemblies were displaced away from each other.

The relative power difference between the nominal and the perturbed FAs of sub-

part 2 is calculated according to equation 2.4 and the results are plotted in figure

2.11. As previously, the yellow arrows show the 2D direction and amplitude of the

perturbations from the corresponding bowing map, with the scale noted in the lower

left corner. The same blue-shift of the central assemblies in subpart 1 is also noted

here, with a relative power decrease in the middle of the assemblies for burnup at

15 MWd/kgU. The relative effect of the assembly-border regions become less severe

as the fuel is depleted (comparing burnup at 0.1 and 15 MWd/kgU), which is also

seen for subpart 1.

2.2. Simulation results 25

Relative change in power [%]

-10 -8 -6 -4 -2 0 2 4 6 8 10

10 mm

Relative change in power [%]

-10 -8 -6 -4 -2 0 2 4 6 8 10

10 mm

F

2.11: The yellow arrows show the direction and amplitude of the bowing, the scale is noted in the lower left corner. Left: The rela- tive power difference between the nominal and the bowed assemblies for burnup at 0.1 MWd/kgU of subpart 2. Right: The relative power difference between the nominal and the bowed assemblies for burnup

at 15 MWd/kgU of subpart 2.

Figure 2.12 shows the relative mass density difference of U

between the nom- inal and the perturbed FAs for the first and last burnup step. The power maps in 2.11 are consistent with the mass density difference, except for one FA in the first burnup step. The middle assembly at the left border shows random (noisy) changes between adjacent assemblies with higher amplitudes than seen for the rest. This is not realized for the higher burnup case and since the effect is quite low for the first burnup step no major importance is made (thinking of the scale difference between the two figures). As for 2.4 there is a 100 times difference between the first and last burnup step.

The statistics are less in the simulation of subpart 2 than for subpart 1, which is believed to be one reason why more noise is present in figure 2.12, than seen before.

Although, Serpent does not provide any uncertainty for the isotopic composition,

random changes between adjacent pins, without uniformity and smooth transitions,

especially in the central assemblies and less affected regions, may indicate less statis-

tics. Thus, implying higher uncertainty in the composition data.