development of an improved thermal-hydraulic modeling of the jules horowitz …1053103/... · 2016....

Development of an ImprovedThermal-Hydraulic Modeling of theJules Horowitz Reactor

REIJO PEGONEN

Doctoral Thesis No. 1, 2017KTH Royal Institute of TechnologySchool of Engineering SciencesDepartment of PhysicsNuclear Reactor Technology DivisionSE-106 91 Stockholm, Sweden

TRITA-FYS 2017:01ISSN 0280-316XISRN KTH/FYS/--17:01--SEISBN 978-91-7729-225-8

Akademisk avhandling som med tillstånd av KTH i Stockholm framläggestill offentlig granskning för avläggande av teknologie doktorsexamen ikärnreaktorteknologi tisdagen den 31 januari 2017 kl. 10:00 i sal FA32,AlbaNova Universitetscentrum, KTH, Roslagstullsbacken 21, Stockholm.

© Reijo Pegonen, January 2017Supervisors: Henryk Anglart, Serge Bourdon and Christian Gonnier

Tryck: Universitetsservice US AB

iii

Abstract

The newest European high performance material testing reactor, theJules Horowitz Reactor, is under construction at CEA Cadaracheresearch center in France. The reactor will support existing and futurenuclear reactor technologies, with the first criticality expected at theend of this decade.

The current/reference CEA methodology for simulating the thermal-hydraulic behavior of the reactor gives reliable results. TheCATHARE2 code simulates the full reactor circuit with a simplifiedapproach for the core. The results of this model are used asboundary conditions in a three-dimensional FLICA4 core simulation.However this procedure needs further improvement and simplificationto shorten the computational requirements and give more accuratecore level data. The reactor’s high performance (e.g. high neutronfluxes, high power densities) and its design (e.g. narrow flow channelsin the core) render the reactor modeling challenging compared tomore conventional designs. It is possible via thermal-hydraulic orsolely hydraulic Computational Fluid Dynamics (CFD) simulations toachieve a better insight of the flow and thermal aspects of the reactor’sperformance. This approach is utilized to assess the initial modelingassumptions and to detect if more accurate modeling is necessary.There were no CFD thermal-hydraulic publications available on theJHR prior to the current PhD thesis project.

The improvement process is split into five steps. In the firststep, the state-of-the-art CEA methodology for thermal-hydraulicmodeling of the reactor using the system code CATHARE2 and thecore analysis code FLICA4 is described. In the second and thirdsteps, a CFD thermal-hydraulic simulations of the reactor’s hot fuelelement are undertaken with the code STAR-CCM+. Moreover, aconjugate heat transfer analysis is performed for the hot channel.The knowledge of the flow and temperature fields between differentchannels is important for performing safety analyses and for accuratemodeling. In the fourth step, the flow field of the full reactor vesselis investigated by conducting CFD hydraulic simulations in orderto identify the mass flow split between the 36 fuel elements and todescribe the flow field in the upper and lower plenums. As a sidestudy a thermal-hydraulic calculation, similar to those performed inprevious steps is undertaken utilizing the outcome of the hydrauliccalculation as an input. The final step culminates by producingan improved, more realistic, purely CATHARE2 based, JHR model,incorporating all the new knowledge acquired from the previous steps.

The primary outcome of this four year PhD research project is the

iv

improved, more realistic, CATHARE2 model of the JHR with twoapproaches for the hot fuel element. Furthermore, the project hasled to improved thermal-hydraulic knowledge of the complex reactor(including the hot fuel element), with the most prominent findingspresented.

v

SammanfattningEuropas senaste reaktor för materialtester, Jules Horowitz Reactor(JHR) konstrueras förnärvarande vid CEAs forskningscentrum iCadarache, Frankrike. JHR kommer att stödja nuvarande ochframtida reaktortekniker. Första kriticitet förväntas vid slutet avdetta årtionde.

Nuvarande modellering av reaktorn ger tillförlitliga resultat. Pro-grammet CATHARE2 är kapabelt att simulera hela reaktorkretsen.Dock används en förenklad modell av härden. Resultat av beräkningarmed CATHAR2 används som randvillkor för tre-dimensionellaberäkningar av härden med FLICA4. Denna metodik behöver dockförbättras och förenklas dels för att minska beräkningsresurser somtas i anspråk, dels för att öka noggrannheten på härdnivå. Reaktornshöga prestanda, (dess höga neutronflöde och höga effekttäthet) samtdess design med smala flödesvägar i härden gör härdberäkningarutmanande jämfört med konventionell design. Med hjälp av fluidmekaniska och termohydrauliska beräkningar (Computational FluidDynamics, CFD) kan en större insikt ges i reaktorns termohydrauliskabeteende. CFD används här för att utvärdera tidigare antagande vidmodellering och huruvida noggrannare metoder behövs. Före dennadoktorsavhandling har inga CFD-beräkningar publicerats av JHR.

Processen för att förbättra modelleringen av JHR delas upp ifem steg. I första steget beskrivs CEAs främsta metodik förtermodynamisk modellering med hjälp av systemkoden CATHARE2och programmet för härdanalys, FLICA4. I andra och tredje stegetanvänds termohydrauliska CFD-beräkningar med koden STAR-CCM+ av det bränsle element med högst effekt. Dessutom analyserashetkanalen med kopplad värmeöverföring i bränslet och vätskan.Kunskap både om hastighets- och temperaturfält är viktig förnoggrann modellering. I det fjärde steget används en isoterm CFD-beräkning av hela reaktorkretsen med syfte att studera flödet i övreoch nedre plenum samt flödesfördelningen till de 36 bränsleelementen.Vidare utförs en termodynamisk beräkning, liknande de som utförtsi tidigare steg, med den isotermiska beräkningen som initialvillkor.I det femte och sista steget utvecklas en förbättrad, mer realistiskmodell över JHR som endast kräver CATHARE2 och som utnyttjarden kunskaps som tidigare steg har gett upphov till.

Det huvudsakliga resultatet av denna doktorsavhandling är denförbättrade CATHAR2-modellen av JHR med två metoder förhetkanalen. Projektet har vidare lätt till förbättrad förståelse avden avancerade reaktorn, de främsta upptäckterna presenteras iföreliggande avhandling.

Acknowledgements

First of all, I would like to thank Professor Henryk Anglart for acceptingme as his PhD student in the Nuclear Reactor Technology division at theKTH.

Secondly, I would like to express my sincere gratitude to my threesupervisors, Serge Bourdon (CEA), Christian Gonnier (CEA) and HenrykAnglart, for their guidance, time, support, and constructive criticism. Icould not imagine to have better supervisors and mentors for my DoctoralThesis.

I am grateful to the French Alternative Energies and Atomic EnergyCommission for the opportunity to conduct an international collaborationfor this thesis project. Especially I would like to thank the JHR group forthe friendly atmosphere, inspiring discussions, and providing the necessarycomputational programs, resources and know-how during my three yearexperience at CEA Cadarache research center.

I would like to thank Rob Bamber for fruitful discussion on both CFDand the English language. I wish to extend my thanks to Nicolas Edh fortranslating the English abstract into Swedish.

The financial support obtained from the Swedish Research Council throughthe DEMO-JHR project is gratefully acknowledged.

Finally, I thank my wonderful family.

January 2017

Reijo Pegonen

vii

viii ACKNOWLEDGEMENTS

List of Publications

Included peer-reviewed Papers

I R. Pegonen, S. Bourdon, C. Gonnier, and H. Anglart. A review of thecurrent thermal-hydraulic modeling of the Jules Horowitz Reactor: Aloss of flow accident analysis. Nucl. Eng. Des., 280:294-304, 2014.

II R. Pegonen, S. Bourdon, C. Gonnier, and H. Anglart. Hot fuel elementthermal-hydraulic modeling in the Jules Horowitz Reactor nominaland LOFA conditions. Conference paper, The 16th InternationalTopical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-16), Chicago, USA, 2015.

III R. Pegonen, S. Bourdon, C. Gonnier, and H. Anglart. Hot fuel elementthermal-hydraulics in the Jules Horowitz Reactor. Nucl. Eng. Des.,300:149-160, 2016.

IV R. Pegonen, S. Bourdon, C. Gonnier, and H. Anglart. Hydraulicmodeling of the Jules Horowitz Reactor: Mass flow split between 36fuel elements. Nucl. Eng. Des., 308:9-19, 2016.

V R. Pegonen, S. Bourdon, C. Gonnier, and H. Anglart. An improvedthermal-hydraulic modeling of the Jules Horowitz Reactor using theCATHARE2 system code. Nucl. Eng. Des., 311:156-166, 2017.

Peer-reviewed Paper not included

i R. Pegonen, N. Edh, K. Angele, and H. Anglart. Investigation ofThermal Mixing in the Control Rod Top Tube Using Large EddySimulations. Journal of Power Technologies, 94(1):67-78, 2014.

ix

x LIST OF PUBLICATIONS

Contents

Acknowledgements vii

List of Publications ixIncluded peer-reviewed Papers . . . . . . . . . . . . . . . . . . . . ixPeer-reviewed Paper not included . . . . . . . . . . . . . . . . . . . ix

Contents xi

List of Figures xiii

List of Tables xv

Nomenclature xviiAbbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiDimensionless Symbols . . . . . . . . . . . . . . . . . . . . . . xviiGreek Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . xviiiRoman Letters . . . . . . . . . . . . . . . . . . . . . . . . . . xviii

1 Introduction 11.1 The Jules Horowitz Reactor . . . . . . . . . . . . . . . . . . . 11.2 Thermal-hydraulic codes . . . . . . . . . . . . . . . . . . . . . 4

The CATHARE2 code . . . . . . . . . . . . . . . . . . . . . . 4The FLICA4 code . . . . . . . . . . . . . . . . . . . . . . . . 4The STAR-CCM+ code . . . . . . . . . . . . . . . . . . . . . 5

1.3 Research objective . . . . . . . . . . . . . . . . . . . . . . . . 5

2 The reference CEA methodology for thermal-hydraulicmodeling of the JHR 72.1 CATHARE2 modeling of JHR . . . . . . . . . . . . . . . . . . 72.2 FLICA4 modeling of JHR . . . . . . . . . . . . . . . . . . . . 92.3 CATHARE2 and FLICA4 coupling . . . . . . . . . . . . . . . 92.4 FLICA4 JHR core modeling assumptions . . . . . . . . . . . 102.5 Specific JHR heated channel correlations . . . . . . . . . . . . 11

xi

xii CONTENTS

Safety margin . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 STAR-CCM+ and FLICA4 comparison in the hot channel 133.1 STAR-CCM+ modeling of JHR hot fuel element . . . . . . . 13

Governing equations . . . . . . . . . . . . . . . . . . . . . . . 183.2 STAR-CCM+ and FLICA4 modeling assumptions . . . . . . 203.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Hot fuel element thermal-hydraulics in the JHR 23New assumption . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.1 Mass flow distribution . . . . . . . . . . . . . . . . . . . . . . 23Cold condition . . . . . . . . . . . . . . . . . . . . . . . . . . 23Nominal condition . . . . . . . . . . . . . . . . . . . . . . . . 25Mass flow in the hot sector . . . . . . . . . . . . . . . . . . . 25Mass flow around the bottom end cap . . . . . . . . . . . . . 25Mass flow around the top end cap . . . . . . . . . . . . . . . 27

4.2 Pressure drop . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3 Temperatures and boundary heat flux in the hot channel . . . 294.4 Heat transfer coefficient in the hot channel . . . . . . . . . . 31

5 Hydraulics of the JHR vessel 355.1 STAR-CCM+ modeling of the JHR . . . . . . . . . . . . . . 35

Modeling assumptions . . . . . . . . . . . . . . . . . . . . . . 39Porous media . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2 Mass flow rate distribution between fuel elements . . . . . . . 405.3 Fluid flow description . . . . . . . . . . . . . . . . . . . . . . 415.4 Pressure field in the upper and lower plenum . . . . . . . . . 475.5 Thermal-hydraulic calculation of the hot fuel element with

specified mass flow rate . . . . . . . . . . . . . . . . . . . . . 49

6 An improved JHR modeling using CATHARE2 516.1 Modeling assumptions . . . . . . . . . . . . . . . . . . . . . . 536.2 Fuel element modeling . . . . . . . . . . . . . . . . . . . . . . 53

Hot fuel element channel with the half plate approach . . . . 53Hot fuel element channel with heat exchanger approach . . . 59Mean fuel element channel . . . . . . . . . . . . . . . . . . . . 61

6.3 Full reactor modeling . . . . . . . . . . . . . . . . . . . . . . . 61

7 Conclusions 63

Bibliography 67

List of Figures

1.1 Jules Horowitz Reactor. . . . . . . . . . . . . . . . . . . . . . . . 21.2 Fast neutron flux; thermal neutron flux. . . . . . . . . . . . . . . 31.3 Isometric view of the JHR fuel element with 2D drawings. . . . . 3

2.1 JHR primary and secondary circuits modeled in CATHARE2. . . 72.2 JHR reactor block modeled in CATHARE2; JHR core modeled

in FLICA4; JHR hot fuel assembly modeled in FLICA4. . . . . . 82.3 Normalized power density profiles: axial, radial and azimuthal. . 11

3.1 Isometric views of the following geometries: the hot channel’sassembly (water + metal), the water between the fuel plateswith a simplified annular inlet and outlet (2/3 cut view), thewater between the fuel assembly and the rack and its 2/3 cut view. 14

3.2 Hot channel outlet (z= 0.7 m) temperature distribution in theSTAR-CCM+ simulation. . . . . . . . . . . . . . . . . . . . . . . 21

4.1 Bottom end cap surrounding flow field velocity axial componentsillustrated on multiple plane sections separated by 2.5 cm. . . . . 26

4.2 Velocity axial components around bottom end cap on the planey=0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 Top end cap surrounding flow field velocity axial componentsillustrated on multiple plane sections separated by 2.0 cm. . . . . 28

4.4 Velocity axial components around top end cap on the plane y=0. 284.5 Schematic view of the maximum temperatures in the hot channel

calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.6 The safety margin in the hot channel in a fuel meat zone. . . . . 294.7 Boundary heat flux on the hot channel. . . . . . . . . . . . . . . 304.8 Hot channel calculation azimuthal dependent heat flux and wall

temperature on the first fuel plate and the normalized powerdensity in the fuel meat at the height z= 0.315 m. . . . . . . . . 30

4.9 Temperature distribution in the hot channel and in thesurrounding metal structures on the z= 0.315 m plane. . . . . . . 31

xiii

xiv List of Figures

4.10 Heat transfer coefficient obtained in the hot channel comparedwith the correlations. . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.1 Cut view of the JHR reactor. . . . . . . . . . . . . . . . . . . . . 365.2 Cut view of the water geometry. . . . . . . . . . . . . . . . . . . 365.3 Cross-section views of the fluid geometry. . . . . . . . . . . . . . 375.4 Coupling between subsequent sections. . . . . . . . . . . . . . . . 375.5 Fuel element numbering system. . . . . . . . . . . . . . . . . . . 405.6 Flow streamlines in an outer part of section one, which are

colored by the radial velocity. . . . . . . . . . . . . . . . . . . . . 425.7 Velocity vector field at z=-1550 mm displayed in line integral

convolution mode. . . . . . . . . . . . . . . . . . . . . . . . . . . 435.8 Flow streamlines in an inner part of section one, which are

colored by axial velocity. . . . . . . . . . . . . . . . . . . . . . . . 435.9 Velocity axial profiles of the following cross-sections: z=-1190

mm, z=-1020 mm, z=-800 mm, z=-650 mm, z=-300 mm andz=-15 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.10 Velocity axial profiles of the following cross-sections: z=1020mm, z=1075 mm, z=1350 mm, z=1610 mm, z=1690 mm andz=1725 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.11 Flow streamlines in section four, which are colored correspondingto velocity magnitude. . . . . . . . . . . . . . . . . . . . . . . . . 46

5.12 Absolute pressure in the upper plenum and in the lower plenumon the plane x=0. . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.1 JHR reactor block modeled in CATHARE2. . . . . . . . . . . . . 526.2 JHR hot fuel assembly modeling. . . . . . . . . . . . . . . . . . . 526.3 Fluid cross-sections and perimeters in the fuel assembly. . . . . . 526.4 Normalized power density profiles: axial and azimuthal and radial. 566.5 Safety margin profiles with uncertainties in: undivided hot

channel, sub-channel 1 and sub-channel 2. . . . . . . . . . . . . . 586.6 Hot fuel assembly hot sector modeling in the heat exchanger

approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.7 Safety margin profiles in the hot channel. Heat exchanger

approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

List of Tables

2.1 Reactor meshing. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 STAR-CCM+ and FLICA4 results in the hot channel. . . . . . . 21

4.1 Average mass flow rates. . . . . . . . . . . . . . . . . . . . . . . . 244.2 Mass flow rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3 The change of the averaged mass flow rates due to the power

distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.1 Mesh reference values. . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Physics models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.3 Mass flow rate ratios in the 36 fuel elements. . . . . . . . . . . . 415.4 Absolute pressure results in the upper plenum and in the lower

plenum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.1 Hot fuel element mass flow rates. . . . . . . . . . . . . . . . . . . 556.2 Hot channels minimum safety margins. Half plate approach. . . . 586.3 Power split between channels in the heat exchanger as fuel plate

approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.4 Hot sectors minimum safety margins. Heat exchanger approach. 616.5 Full reactor mass flow rates under cold conditions. . . . . . . . . 62

xv

Nomenclature

Abbreviations

CAE Computer-Aided EngineeringCAD Computer-Aided DesignCATHARE Code for Analysis of THermalhydraulics during an

Accident of Reactor and safety EvaluationCEA French Alternative Energies and Atomic Energy

CommissionCFD Computational Fluid DynamicsEdF Electricity of FranceIRSN French Radio-protection and Nuclear Safety InstituteJHR Jules Horowitz ReactorMTR Material Testing ReactorNAB Nuclear Auxiliary BuildingNP Nuclear PowerRANS Reynolds-Averaged Navier-StokesRB Reactor BuildingRUC Reactor core safety cooling systemRUP Reactor pool safety cooling system

Dimensionless Symbols

ξ Local loss coefficientσ Schmidt numberf Wall friction coefficientfD Darcy’s friction coefficientfiso Isothermal friction coefficientF Wall heating correction coefficientF3D Hot channel factor or peaking factorFelement Hot fuel element factorFaxial Axial hot channel axial factorFradial Radial hot channel radial factorFazimuthal Azimuthal hot channel factorNu Nusselt numberPr Prandtl numberPrw Prandtl number at TwRe Reynolds number

xvii

xviii NOMENCLATURE

Greek Symbols

ε Kinetic energy dissipation rate [J/(kg · s)]ε Roughness height [m]λ Thermal conductivity [W/(m ·K)]λs Solid thermal conductivity [W/(m ·K)]µ Dynamic viscosity [Pa · s]µb Bulk dynamic viscosity [Pa · s]µt Turbulence dynamic viscosity [Pa · s]µw Dynamic viscosity at Tw [Pa · s]ρ Density [kg/m3]τ Stress tensor [N/m2]Φ Wall heat flux [W/m2]

Roman Letters

cp Specific heat capacity [J/(kg ·K)]Dh Hydraulic diameter [m]FB Specific total body force [N/m3]g Acceleration of gravity [m/s2]G Mass flux [kg/(m2 · s)]h Heat transfer coefficient [W/(m2 ·K)]hz Elevation [m]kt Specific turbulent kinetic energy [J/kg]L Length [m]Lt Turbulence length scale [m]M Safety margin [K]MI Safety margin with uncertainties [K]p Pressure [Pa]Pf Friction perimeter [m]Ph Heated perimeter [m]Pi Porous inertial resistance coefficient [kg/m4]Pv Porous viscous resistance coefficient [kg/(m3 · s]Tb Fluid bulk temperature [K]Tl Fluid temperature [K]TlSAT

Fluid saturation temperature [K]Ts Solid temperature [K]Tw Wall temperature [K]v Velocity [m/s]∆p Pressure drop [Pa]∆TSAT Wall superheat [K]

Chapter 1

Introduction

1.1 The Jules Horowitz Reactor

The newest European material testing reactor, the Jules Horowitz Reactor,is currently under construction at CEA Cadarache research center inFrance and is expected to start operation at the end of this decade. TheJHR project involves several European and international, industrial andinstitutional partners. This reactor will meet the latest safety standardsand will support both current and future nuclear reactor technologies(generations II, III and IV). The JHR will participate in replacing thecurrent fleet of MTRs, which are typically 50 years old.

This pool-type reactor will have a maximum core power of 100 MWth

and use light water for both cooling and moderation [1]. The JHR willbe used to investigate the behavior of nuclear materials and fuels underirradiation and to produce radioisotopes for medical purposes (e.g. 99Mo)[2, 3]. The reactor’s flexible high-performance experimental capacity isexpected to meet industry’s needs related to generation II, III and IV nuclearreactors [4]. The JHR will provide a high neutron flux, twice as large as themaximum available in contemporary European MTRs [3].

The JHR consists of the reactor and nuclear auxiliary buildings [1, 4], seeFigure 1.1. The RB contains the reactor block, reactor and intermediatestorage pools, experimental rigs in addition to the primary cooling system.Several storage pools, hot cells, control rooms, laboratories and mechanicalworkshop are located in the NAB. The reactor pool is connected with theNAB’s storage pools and with the hot cells through an air and water-tightlock.

The reactor block is situated at the bottom of the reactor pool, with thecore situated approximately 9 meters below the water surface [2], see Figure1.1. The cylindrical core has a diameter of 71 cm and is 70 cm high. Theberyllium reflector (35 cm thick) is located external to the reactor block.The core and reflector have separate cooling systems. The core is cooled viathe primary cooling system (forced convection, 15 m/s in a fuel element)and is fully located inside the RB; the pressure and the flow are on the order

1

2 CHAPTER 1. INTRODUCTION

Figure 1.1: Jules Horowitz Reactor. Courtesy of CEA.

of 1.0 MPa and 7400 m3/h, respectively.

The core is located in an aluminum rack with 37 possible positions forfuel elements. 34 to 37 of these will be occupied by fuel elements dependingupon the core configuration desired. Experimental devices can be placedinto either the core or the reflector, allowing for about 20 simultaneousexperiments. In the core, a maximum of 10 experimental devices can beplaced either in the central hole of a fuel element (7-9 locations, Ø≈ 32 mm)or may replace an entire fuel element (3-1 locations, Ø≈ 70-90 mm) [5].Research presented in this thesis was conducted on the fresh start-up JHRcore configuration containing 36 fuel elements implying one test devise inplace of a fuel element.

In the core, neutron fluxes can reach 5.5·1014 n/cm2/s (E > 1 MeV) and upto 1015 n/cm2/s (E > 0.1 MeV) [5]. In-reflector experiments are performedwith thermal neutron fluxes up to 4.5·1014 n/cm2/s (E < 0.625 eV) [6]. Thedistribution of fast and thermal fluxes can be seen in Figure 1.2. Materialdamage up to 16 dpa/year (with reactor availability of 260 effective full-power days per year) can be achieved for in-core experiments [1].

The JHR fuel element consists of eight circular rings of curved fuel plates(each 1.37 mm thick) assembled with three stiffeners manufactured from6061-T6 aluminum alloy, see Figure 1.3 [6]. The fuel assembly has an

1.1. THE JULES HOROWITZ REACTOR 3

Figure 1.2: (Left) Fast neutron flux; (right) thermal neutron flux. Courtesyof CEA.

external diameter of 97.7 mm (rack hole 98.6 mm) and the hydraulic gapbetween fuel plates is 1.95 mm wide [6]. Each fuel plate comprises of AlFeNicladding, U3Si2/Al fuel and borated aluminum poison at the top end of thefuel element. The thickness of the fuel meat and the poison layer is 0.61 mm[2]. The total height of the fuel plate is 700 mm from which 600 mm is thefuel zone and 30 mm is the poison zone in the upper part. The overallheight of the fuel element is 1015 mm. The top end cap and the bottomend cap have the lengths of 115 mm and 145 mm, respectively.

Figure 1.3: (Top) Isometric view of the JHR fuel element, (bottom) 2Ddrawings with dimensions in millimeters.

The reactor is controlled by 27 control rod mechanisms: 19 for reactivitycompensation, 4 for the reactor power adjustments and 4 for emergencyuse. The reference fuel for the reactor start-up is Silicide Fuel U3Si2, butthe design studies take into account UMo fuel [6, 7].


1.2 Thermal-hydraulic codes

The CATHARE2 code

The CATHARE2 code is a thermal-hydraulic system code designed forPWR safety analysis, accident management, definition of plant operatingprocedures and research & development [8]. In addition it can be usedto quantify conservative analysis margins and for licensing [8]. Thecurrently version (CATHARE2 V2.5_3) is the result of more than 30 yearsdevelopment (the CATHARE project was initiated in 1979) of joint effortby CEA, EdF, AREVA NP and IRSN [8, 9, 10].

The CATHARE2 code is based on a two-fluid six-equation model. Mass,momentum, and energy conservation equations for each phase (liquid andgas) describe the flow fields. The transport of non-condensible gases (upto 4) and radio-chemical components (up to 12) may be described withadditional optional equations [11]. Over 1000 separate effect tests from 45experiments and about 30 integral effect tests have been used to assess theset of physical models/correlations implemented in CATHARE2 [8].

CATHARE2 is a fully modular code [10]. Thermal-hydraulic modelingin CATHARE2 is performed with five main modules: the 1D modulefor pipe flows, the 0D module for volume elements (the pressurizer, theaccumulator, the steam generator dome or the lower plenum of a PWR),the 3D module for multidimensional effects in vessel, the boundary conditionmodule and the double ended break module [11]. Sub-modules are used forsupplementary models (pumps, valves, T-junctions, heat/mass sources andsinks, breaks, etc.) and junctions for connecting modules [9, 11].

The finite volume scheme is used to spatially discretize the mass and energyconservation equations whilst the finite difference scheme in exploited forthe momentum conservation equation [12]. Fully implicit time discretizationis applied for 0D and 1D modules and semi-implicit discretization for 3Delements [9].

The FLICA4 code

FLICA4 is a 3D two-phase compressible flow thermal-hydraulic codedesigned for steady-state and transient reactor core analyses [13, 14].The four-equation model is utilized to model a two-phase mixture. Inaddition to mixture mass, momentum and energy balance equations, afourth, describing the vapor mass balance, is introduced. The velocity

1.3. RESEARCH OBJECTIVE 5

disequilibrium is modeled by a drift flux correlation: the relative velocitybetween phases is taken into account by a kinetic constitutive equation[13, 15]. Both phases are assumed to have the same pressure, with thevapor phase assumed to be saturated [15].

The code includes various closure laws for heat transfer, wall friction anddrift flux and correlations for predicting critical heat flux [13]. A pointkinetics neutron physics model is employed to calculate reactor transientsand a 1D thermal module for fuel temperature fields [16]. FLICA4 uses afinite volume method and is based on an extension of Roe’s approximateRiemann solver [15, 17]. Time discretization can be either explicit or fullyimplicit.

The STAR-CCM+ code

STAR-CCM+ is a commercial computer-aided comprehensive engineeringpackage. It is not just a CFD solver, STAR-CCM+ is an entire engineeringprocess for solving problems involving flow (of fluids or solids), heat transfer,and stress [18]. A single integrated package including a 3D-CAD modeler,CAD embedding, surface preparation tools, automatic meshing technology,several physics and turbulence models, post-processing tools and CAEintegration [18]. It is based on object-oriented programming and providesan easy-to-use robust CFD experience from CAD models to post-processingwith powerful functionality even while tackling multi-physics problems andcomplex geometries. For additional information regarding STAR-CCM+,see [18, 19].

The CFD studies within this PhD thesis were performed using version9 of STAR-CCM+. A significant advantage of utilizing this program(compared to its competitors) was the availability of the polyhedralcell approach, offering faster solutions and requiring less memory thantraditional hexahedral or tetrahedral meshes [20]; it also simplifies meshingof complex geometry. Furthermore, it was possible to generate a conformalgrid for conjugate heat transfer simulation.

1.3 Research objective

The current/reference CEA methodology for calculating the thermal-hydraulic behavior of the reactor during accidental transients providesreliable safety analysis results obtained in sequential applications of theCATHARE2 and FLICA4 codes. The CATHARE2 code simulates the


full reactor circuit, incorporating a simplified approach for the core. Theboundary conditions are transferred into the three-dimensional FLICA4core simulation. However, this procedure should be further simplified andimproved by using only a single tool, namely the CATHARE2 code. Themain reason for developing this new model is to provide more accuratecore level data with reduced computational costs. In addition, best-estimate simulations will help the operators to assess accident managementprocedures and to perform systematic calculations. Producing this new toolwith more realistic assumptions is the main objective for this four year PhDproject.

The high performance of the reactor (e.g. high neutron fluxes, high powerdensities) and its design (e.g. narrow flow channels in the core) render thereactor modeling somewhat challenging when compared to more traditionalreactor designs. One possibility to obtain a better insight into the reactoris to use thermal-hydraulic or solely hydraulic CFD simulations. Thisapproach will be utilized to assess the initial modeling assumptions andto determine if more accurate modeling is required. There were no CFDthermal-hydraulic publications available on the JHR prior to the currentresearch project.

The development process is split into five steps. The outcomes of eachstep will be described in separate chapters of this thesis (Chapters 2 to6). Furthermore, there is a corresponding appended paper included in thisthesis for each chapter. In the first step [21], the state-of-the-art CEAmethodology for thermal-hydraulic modeling of the reactor using the systemcode CATHARE2 and the core analysis code FLICA4, will be described. Inthe second and third steps [22, 23], the CFD thermal-hydraulic simulationof the reactors hot fuel element will be undertaken with the code STAR-CCM+. Moreover, a conjugate heat transfer analysis will be performed forthe hot channel. The knowledge of the flow and temperature fields betweendifferent channels is important for safety analyses and for accurate modeling(e.g. reduction of flow effective area due to local vortices). In the fourthstep [24], the flow field of the full reactor will be investigated by conductingCFD hydraulic simulations in order to identify the mass flow split betweenthe 36 fuel elements and to describe the flow field in the upper and lowerplenums. As a side study a thermal-hydraulic calculation, similar to thoseperformed in previous steps will be carried out utilizing the outcome ofthe hydraulic calculation. The final step [25] will culminate by producingan improved, more realistic, purely CATHARE2 based, JHR model whichincludes all the new knowledge acquired from the previous steps. Chapter7 summarizes the main conclusions of this project.

Chapter 2

The reference CEA methodology forthermal-hydraulic modeling of the JHR

This chapter presents the off-line coupled thermal-hydraulic modeling of thereactor using the CATHARE2 system code and the FLICA4 core analysiscode.

2.1 CATHARE2 modeling of JHR

The modeling of the JHR primary circuit with a reactor pool in CATHARE2is presented in Figures 2.1 and 2.2(left). The reactor block model consistsof 1D and 0D modules connected by junctions. 1D modules are used tomodel a mean core channel (with a weight of 36), a core bypass channel, agap between the vessel and the core, control rods (3 modules representing27 rods) and test devices (2 modules representing 10 devices). The upperand the lower plenum are modeled by 0D modules.

Figure 2.1: JHR primary and secondary circuits modeled in CATHARE2.

7

8CHAPTER 2. THE REFERENCE CEA METHODOLOGY FOR

THERMAL-HYDRAULIC MODELING OF THE JHR

Figure 2.2: (Left) JHR reactor block modeled in CATHARE2; (middle)JHR core modeled in FLICA4; (right) JHR hot fuel assembly modeled inFLICA4.

The modeled cooling system consists of the reactor pool, the pressurizationcircuit, the reactor cooling system (three redundant circuits), the core safetycooling system, the reactor pool safety cooling system and the two additionalsafety circuits, see Figure 2.1. The reactor has two sets of RUC/RUPsystems for redundancy, however only one is modeled. All systems aresimulated by using 1D modules in combination with proper submodules(heat exchanger, pump, T-junction) and junctions. The 0D module isimplemented to model the reactor pool and for connecting several systems(DERIV, JONC, see Figure 2.1).

The RUC and RUP systems are connected through a heat exchangertransferring energy from the reactor block while using forced convection.The pressurization circuit ensures with the pump and the check valvereference pressure for the primary system and provides a means formonitoring water transfer between the reactor pool and the primary system.The first safety circuit is employed in the event of a primary pump failureand the second allows the injection of water from the pool into the primarycircuit in case of depressurization of the primary circuit [26].

The primary circuit consists of 53 hydraulic modules and the total amountof scalar meshes is 3561, see Table 2.1. The simplified JHR secondarycircuit, see Figure 2.1, is modeled using 7 hydraulic modules with 197 totalaccounted scalar meshes. In the secondary circuit model each 1D module isequipped with a heat exchanger sub-module.

2.2. FLICA4 MODELING OF JHR 9

Table 2.1: Reactor meshing.

Primary circuit Secondary circuitPipes 42 3Volumes 10 2Boundary conditions 1 2Tee sub-modules 8 0Volume ports 45 8Pipe meshes 3495 183Total number of hydraulic modules 53 7Total accounted scalar meshes 3561 197

2.2 FLICA4 modeling of JHR

The FLICA4 core simulations are using the two-level method described in[13, 27]. In the first level the whole core with 36 fuel assemblies is calculatedand boundary conditions from the hot fuel assembly are deduced for thesecond level, where only the hot fuel assembly is simulated.

In the first level simulation the core is divided radially into 36 elements(35 mean and one hot fuel assembly) and axially into five zones: inlet,bottom zone, fuel zone, top zone and outlet. The fuel zone has axially 35mesh elements, the rest have 8 elements per zone. Each fuel element isradially divided into three sectors containing 9 water channels and 8 fuelplates. Each sector is further radially divided into four equal parts (36 watercells in total per sector). Three central zones form the fuel element.

In the second level, the hot fuel assembly is divided into three sectors: twomean sectors and the hot sector, see Figure 2.2(middle-right). Thereafterthe hot sector is split into the hot channel and into either one or two meanchannels, depending on where the hot channel is situated. Finally the hotchannel is divided into four sub-channels. In this step the fuel zone has 35axial mesh elements, but in other zones it is reduced by a factor of two.

2.3 CATHARE2 and FLICA4 coupling

CATHARE2 and FLICA4 are off-line coupled, meaning that the codes arerun separately. The thermal-hydraulic system code CATHARE2 is used tocalculate the scenario involving the full JHR. From the results, core power,inlet void fraction, inlet mass flow, inlet enthalphy and outlet pressure fromeach time step are imposed as boundary conditions in the FLICA4 3Dthermal-hydraulic code simulation, where only the reactor core is modeled,



using the two-level method [28].

2.4 FLICA4 JHR core modeling assumptions

The following assumptions are made in the CEA’s FLICA4 model of the 36fuel assembly JHR core:

1. Turbulence is not modeled.

2. The core reference power is 100 MW·1.065·1.03·0.9916 = 108.77 MW,where the first factor in multiplication is the core nominal power,the second and the third take into account power measurementuncertainties and operating range. The final factor describes 0.84%power loss due to experimental devices and internal structures of thecore. It is assumed that the power arising from the fuel plate is equallydistributed between the channels connected to it (i.e. 50% each).

3. The power is distributed among the 36 fuel elements in such a waythat the hot fuel element and each of the 35 mean fuel elementshave normalized factors of 1.705 and 0.980, respectively [29]. Thefuel element’s axial, radial and azimuthal normalized power densityprofiles can be seen in Figure 2.3. The fuel element is dived into threesectors (one "Hot" and two "Mean") and each sector is azimuthallysubdivided into 4 sub-channels, see Figure 2.2(middle-right). Whendiscussing the radial profile, "1" corresponds to the inner fuel plateand "8" to the outer plate. For normalized power density profiles thehot channel factor or the peaking factor has the following formula:

F3D = Felement · Faxial · Fradial · Fazimuthal, (2.1)

In the case of the JHR, the peaking factor has the value:

F3D = 1.705 · 1.295 · 1.243 · 1.093 = 3.001. (2.2)

Note that the calculation presented in this paper uses a more realisticpower distribution than those utilized in the JHR safety analyses.

4. In the case of a reactor scram, the power evolution profile correspondsto the situation where three emergency stop control rods are inserted.It is assumed that the mechanism of the most effective rod hasmalfunctioned.

5. The hot channel is the second channel from the center of fuel assemblyin the hot sector.

2.5. SPECIFIC JHR HEATED CHANNEL CORRELATIONS 11

0 0.1 0.2 0.3 0.4 0.5 0.60.25

0.5

0.75

1

1.25

(a)

Pow

er d

ensi

ty

Axial position [m]0 2 4 6 8

0.9

1

1.1

1.2

1.3

Plate number

(b)

HotMean

0 1 2 3 40.9

1

1.1

Track number

(c)

HotMean

Figure 2.3: Normalized power density profiles: (a) axial, (b) radial and (c)azimuthal [29].

6. In some FLICA4 calculations, the hot channel’s hydraulic gap isreduced from 1.95 mm to 1.64 mm to take into account manufacturingtolerances and the operational effect on the fuel plates (swelling,oxidation, thermal expansion, etc.) In addition its mass flow is furtherreduced by 4% by increasing the channel’s inlet local pressure losscoefficient. It is calculated in cold conditions under nominal pumpingand is due to the inhomogeneity of the flow in the lower plenum andthe channel’s input velocities [30].

7. The local pressure loss coefficients in the core are calculated froma correlation given in Idel’chik’s handbook of hydraulic resistance[31]. In modeling the head and the foot of a fuel element a simplifiedapproach is used: three segments cross-sectionally varying for the headand two for the foot. The real geometry is accounted for with localpressure loss coefficients.

2.5 Specific JHR heated channel correlations

JHR is designed to work in the single-phase liquid regime. Whilemodeling the heated channels in CATHARE2, a JHR specific private library(RJHCHANL) of physical closure relationships is used. In the case ofturbulent single-phase flows, the RJHCHANL keyword modifies the wallfriction coefficient correlation and the wall superheat correlation at whichthe fully developed subcooled boiling begins. Identical correlations are usedin FLICA4 while modeling the JHR. The wall friction coefficient is expressed



as:f = fiso · F, (2.3)

where the isothermal friction coefficient and the correction for wall heatingare:

fiso = 0.202Re−0.196, (2.4)

F = 1−KPhPf· (Tw − Tl)

1 + 2(Tw+Tl

200 )1.5, (2.5)

where K is a constant (see [32]). For the wall superheat, the Engelberg-Forster & Greif correlation (most suitable for JHR conditions) is utilized[33]:

∆TSAT = 4.44(

Φ104

)0.385·( p

105

)−0.23p < 1 · 106Pa. (2.6)

The Dittus-Boelter correlation [34] for internal flow in pipes is usedfor obtaining heat transfer coefficient in the case of single-phase forcedturbulent flows:

h = 0.023 λ

DhRe0.8Pr0.4. (2.7)

In the case of single-phase forced laminar flows, the following correlation isutilized [35]:

h = 8.235 λ

Dh. (2.8)

Safety margin

Operating the reactor in the single-phase liquid regime requires that the walltemperature must stay below the wall onset of fully developed subcoolednucleate boiling (which precedes onset of significant void) temperature.Therefore, the safety margin can be expressed in the following form:

M = TlSAT+ ∆TSAT − Tw = TlSAT

+ ∆TSAT − (Tl + Φh

) > 0, (2.9)

where the wall superheat at which the fully developed subcooled boilingbegins is given by Equation 2.6. Where the safety margin with uncertaintyis discussed, ∆TSAT and h are assumed to have 15% uncertainty. Theseuncertainties are applied in such a way as to obtain the most pessimisticcase:

MI = TlSAT− Tl + 0.85∆TSAT −

Φ0.85h > 0. (2.10)

In the laminar region the uncertainty for h is 20%. In FLICA4 modeling,uncertainties of 20% and 15% are used for h whenRe < 3000 andRe > 3000,respectively.

Chapter 3

STAR-CCM+ and FLICA4 comparison in thehot channel

The purpose of this chapter is to compare the results of modeling thehot channel in STAR-CCM+ to those obtained using the reference CEAmethodology FLICA4 model (described previously in Chapter 2). Thereduction of the hydraulic gap from 1.95 mm to 1.64 mm has not beenconsidered. Both simulations have been performed with similar mass flowrate in the hot channel (0.924 kg/s, see Chapter 4). In addition the STAR-CCM+ modeling of the JHR hot fuel element is described.

3.1 STAR-CCM+ modeling of JHR hot fuel element

The design of the geometry used in this work is based on the 2011 technicaldrawing of a JHR fuel element [36]. Compared to the original drawingssome minor simplifications had to be made in order to produce a moresuitable CFD model. These simplifications included neglecting extremelysmall irrelevant details/gaps (e.g. part markings, filling internal structuresirrelevant to the flow, merging clearances between parts smaller than 0.5 mm)in order to maintain a reasonably sized mesh.

For this research the following CAD models (by utilizing the commercialsoftware SolidWorks) were created: (i) the water geometry between the fuelplates with a simplified annular inlet and outlet (see Figure 3.1(b)), (ii)the water geometry of the fuel element inside the rack (see Figure 3.1(c-d)), and (iii) the hot channel’s assembly (water + metal parts, see Figure3.1(a)). For completeness, all models are described here, although onlylast two are used in both Chapters 3 and 4 and the first one in Chapter4. The purpose of the first geometry is to simulate the conditions in thecenter of the fuel assembly, uninfluenced by the top and bottom end caps.The second geometry broadens our understanding of the conditions in thehot fuel assembly and determines the boundary conditions for the thirdgeometry, which is in turn utilized to evaluate the conditions in the hotchannel.

13

14CHAPTER 3. STAR-CCM+ AND FLICA4 COMPARISON IN THE HOT

CHANNEL

Figure 3.1: Isometric views of the following geometries: (a) the hot channel’sassembly (water + metal), (b) the water between the fuel plates with asimplified annular inlet and outlet (2/3 cut view), (c) the water betweenthe fuel assembly and the rack and (d) its 2/3 cut view. Sub-figures are notscaled.

The hot channel’s geometry assembly, see Figure 3.1(a), represents thesecond water channel from the center of fuel assembly with its surroundingstructural materials and consists of nine parts: the water, the inner andouter cladding/fuel/poison and two stiffeners. In order to simplify themodel, heat transfer in the center of the fuel is assumed to be radiallysymmetric. Therefore the modeled geometry consists of one water channel;surrounded by structural materials, of which only half is modeled, see Figure3.1(a). The overall height of the assembly is 700 mm.

In the case of the second geometry, see Figure 3.1(b), a 50 mm annuluswas added to both ends of the water geometry between the fuel plates andthe rack. The total height of the geometry is 800 mm. In the case of thethird geometry, water between the fuel assembly and the rack, see Figure3.1(c-d), the geometry’s inlet was prolonged by a 10 mm annulus (givena total height of 1078 mm) in order to avoid direct geometric contraction.The geometric contraction resulted in unwanted turbulent reversed flow atthe inlet boundary. Calculations were performed both with and withoutthe prolongation, which demonstrated that the flow in the main part of thegeometry was unaffected by this change. It is impossible to model only onepart of the geometry due to the asymmetry of the fuel assembly and of thethermal-hydraulic conditions. All parts are considered geometrically newand no manufacturing tolerances or operational effects (oxidation, swelling,

3.1. STAR-CCM+ MODELING OF JHR HOT FUEL ELEMENT 15

etc.) on the fuel plate are taken into account.

In all the simulations, except for the hot channel calculation, only thefluid region is modeled and it is assumed to be three dimensional, steadyand turbulent. Segregated flow, segregated fluid temperature, realizable k-ε turbulence model, and the gravity physics models as well as two-layerall y+ wall treatment are used. The last is designed to give accurateresults regardless of the sub-layer of the turbulent boundary layer in whichthe near-wall centroid is located in. The gravity model in STAR-CCM+changes the working pressure into the piezometric pressure and the bodyforce due to gravity is included in the momentum equations when thesegregated flow model or coupled flow model is utilized [18]. The segregatedflow model solves the flow equations in an uncoupled manner and thelinkage between the momentum and continuity equations is achieved witha predictor-corrector approach [18]. During these simulations a second-order upwind scheme was used for the convection term. In the hot channelsimulation each metallic part has a separate region and they are assumed tohave constant density and to be three dimensional and steady, furthermorea segregated solid energy model is utilized.

The current best practice is to utilize a conformal mesh for conjugate heattransfer and it can only be created by polyhedral mesher when employingthe finite volume method [37]. Furthermore the meshing procedure for thecomplex geometry (fuel assembly) should be fully automatic to producean optimal mesh and save time. Therefore, in this study, an unstructuredpolyhedral mesh with surface remesher and prism layers (except for thesolids) was used to model every geometry.

A major advantage of polyhedral cells is that due to having numerousneighbors, gradients can be better approximated in a complex geometry.In addition to this cells are less sensitive to stretching and are favorablefor handling recirculating flows [38]. Compared to tetrahedral meshes, oneneeds about four times fewer cells, about half the memory and about 10-20% of the computing time to reach a similar level of accuracy [38].

Computational requirements for meshing geometries are substantial. It isunderstood that the maximum number of cells that can be produced isaround 24-26 million cells, with the available computing resources. Threefinal meshes, one for each geometry, were created and two sets of meshingreference values were used in the process. There were five prism layersalong the walls in the fluid domain to resolve the boundary layer and thisis considered sufficient when wall functions are included [18].


CHANNEL

In order to achieve a good quality volume mesh, a surface mesh must be freeof errors and contain only valid elements. Mesh quality can be describedby assessing the face validity and the volume change of the cell. The first isan area-weighted measure of the correctness of the face normals relative totheir attached cell centroid and a value of 1.0 means that all face normalsare correctly pointing away from the cell centroid [18]. Values lower than 0.5point out a negative volume cell. At the same time the volume change metricdescribes the ratio of the volume of a cell to that of its largest neighbor andthe cells with a value of 10−5 or below should be investigated further [18].In all three grids generated the face validity overall value was 1.0 and thevolume change had values above 0.001 and most of the cells above 0.1.

To study the influence of the mesh size several meshes of the third geometrywere created using the same topology and simply reducing the base sizefrom 6 mm to 3 mm. This process created meshes of sizes from 8,516,491cells to 23,211,863 cells. The prism layer performance was kept constantby specifying its parameters in absolute rather than relative terms. As aconvergence criterion the overall pressure drop was monitored with differentmeshes. It was observed that by utilizing the mesh larger than 16.5 millioncells the total pressure drop varies less than 0.3% when compared to thefinest mesh. Although a mesh containing 16.5 million cells would havebeen sufficient, the finest mesh was chosen for the simulation. The secondgeometry represents the center part of the third geometry as well as the firstgeometry is modeling only its channel including the solid parts. Thereforeit is valid to use identical meshing parameters for meshing geometries twoand three. In the case of the first geometry the finest mesh possible wasgenerated.

The total mass flow rate through the fuel elements is 1546.4 kg/s (reactortotal 1727.4 kg/s), from which 42.955 kg/s (1/36th) is assumed to flowthrough the hot fuel element. In future, this value will be corrected accordingto the results of the JHR lower plenum hydraulic CFD calculation (Chapter5).

The thermodynamic properties of the water are obtained from the IAPWS-IF97 (International Association for the Properties of Water and Steam-Industrial Formulation 1997) formulation provided in STAR-CCM+. Forthe cladding and fuel, the same constant values and temperature dependentfunctions as in the FLICA4 calculation described in [21] are utilized. Materialproperties for borated Al poison and for Al 6061-T6 stiffeners are taken from[39] and [40], respectively.

The fuel power distribution profile for the hot fuel assembly is obtained from


the CEA’s 36 assembly JHR core power distribution neutronic calculation[29]. From these data points the following were created: (i) a volumetricpower distribution function for both of the fuel plate meats in the hotchannel calculation, and (ii) a surface power table containing 14,257 pointsfor simulations involving only the water geometry. The power table iscreated in such a way that during the simulation a specific location obtainsits value from the closest data point without interpolation. Walls thatcorrespond to the axial height of the fuel meat have nonzero surface power.In order to describe the water power originating from neutron moderationand gamma heating a simplified approach is used. A full core thermalneutron flux axial profile [41] is utilized for generating power density functionand a 143 point table. Both are used similarly as described above and bothare only dependent upon axial location. It is assumed that the power arisingfrom the fuel plate is equally distributed between the channels adjacent toit (i.e. 50% to each).

Except for the third geometry, all the geometries have one inlet, locatedat the bottom, and one outlet, located at the top, see Figure 3.1. The thirdgeometry outlet consists of four separate surfaces that are merged into oneoutlet surface for the definition of physical conditions. Identical initial andboundary conditions are employed for the second and the third geometries.A mass flow of 42.955 kg/s, a total temperature of 32.1C, a turbulenceintensity of 0.03 with a length scale of 3 mm were specified on the massflow inlets. At the same time the pressure outlet had the following values:a static pressure of 0 Pa, a turbulence intensity of 0.03 and a turbulencelength scale of 3 mm. The no-slip smooth walls thermal conditions wereimposed by heat flux obtained from the table described above. In everysimulation, the reference pressure is adjusted to give an surface-averagedpressure of 600939 Pa at z= 0.7 m. This pressure value was obtained fromthe system code CATHARE2 simulation, described in [21], where the fullJHR circuit with the simplified approach for the core is studied.

The liquid region of the first geometry has similar inlet and outlet boundaryconditions as described above, only the inlet mass flow rate is 0.924 kg/s (seeChapter 4) and the turbulence length scale is 0.374 mm. Furthermore thesmooth non-slip walls were specified to have adiabatic thermal conditions.To allow conjugate heat transfer between different regions a contact interfaceis utilized to connect fluid/solid and solid/solid regions. Fluid and solidequations are implicitly coupled and are solved simultaneously while takinginto account the Dirichlet boundary condition, the Neumann boundarycondition and the Newton boundary condition at the interface [18]. Turbu-lence length scales were evaluated by using hydraulic diameters and commonpractice Lt ≈ 0.1Dh [18].


CHANNEL

Governing equations

The steady-state Navier-Stokes equations for Reynolds-averaged turbulentcompressible flows (also named as the Favre-averaged Navier-Stokesequations) can be written as [42]:

∂

∂xi(ρvi) = 0, (3.1)

∂

∂xj(ρvivj) = − ∂p

∂xi+ ∂τij∂xj

+ FBi , (3.2)

where the stress tensor is given as:

τij = µ

(∂vi∂xj

+ ∂vj∂xi− 2

3∂vk∂xk

δij

)− ρv′iv

′j . (3.3)

The first part of τ represents the viscous stress tensor and −ρv′iv′j is

the Reynolds stress tensor and can be evaluated by using the Boussinesqassumption [43, 44]:

−ρv′iv′j = µt

(∂vi∂xj

+ ∂vj∂xi− 2

3∂vk∂xk

δij

)− 2

3 ρktδij . (3.4)

The steady-state Reynolds-averaged energy equations for the fluid(Equation 3.5) and for the solid (Equation 3.6) are expressed as [45, 42]:

∂

∂xi

(cpρviTl

)= ∂

∂xi

(cp

µ

Pr

∂Tl∂xi

+ cpρv′iT′l

)+ µφ+ q, (3.5)

∂

∂xi

(λs∂Ts∂xi

)+ qs = 0, (3.6)

where q and qs are the power density sources for the fluid and the solid,respectively. In Equation 3.5 cpρv

′iT′l corresponds to the turbulent heat flux

and µφ is the viscous heating dissipation.

In this study realizable k-ε turbulence model [46] were utilized. Comparedto the standard k-ε turbulence model, it uses non-constant Cµ variable inthe turbulence dynamic viscosity formula:

µt = ρCµk2t

ε, (3.7)

Cµ = 14.04 +

√6cosφkv∗ε

, (3.8)


v∗ =√SijSij + ΩijΩij , (3.9)

and there is a new transport equation (Equation 3.11) for the kinetic energydissipation rate:

∂

∂xj(ρktvj) = ∂

∂xj

((µ+ µt

σk

)∂kt∂xj

)+

+ Pk + Pb +Dd − ρε,(3.10)

∂

∂xj(ρεvj) = ∂

∂xj

((µ+ µt

σε

)∂ε

∂xj

)+ ρC1Sε−

− ρC2ε2

kt +√µε/ρ

+ C1εε

ktC3εPb,

(3.11)

where Pk and Pb represent kt production due to mean velocitygradients and buoyancy, respectively. Dd represents the dilatationdissipation, C1=max [0.43, η/ (η + 5)], η=Sk/ε, S=

√2SijSij , Sij =

1/2 (∂vi/∂xj + ∂vj/∂xi), φ = 13cos

−1 (√6W), W = SijSjkSki

S3 ,C1ε=1.44,C2=1.9, σk=1.0, σε=1.2, C3ε=1.0, Ωij = Ωij − 3εijkωk and Ωij is the meanrate of rotation tensor in a reference frame rotating with angular velocity ωk.Pk, Pb and Dd are calculated in the same way as standard k-ε turbulencemodel.

As this is an exploratory study considering realistic assumptions, withlimited time and computational resources, k-ε turbulence model was chosen.The STAR-CCM+ user guide recommends to utilize either standard,standard two-layer, realizable or realizable two-layer k-ε model. If thereis uncertainty as to which turbulence model to use, the user guide advisesthat in a given situation, the realizable two-layer k-ε model would be areasonable choice. If the mesh is coarse, it provides results that are quiteclose to the version without the two-layer formulation. If the mesh is fineenough to resolve the viscous sublayer, it produces results similar to a low-Reynolds number model. The realizable models generally give results atleast as good as the standard models, but typically better [18].

Realizable (two-layer) k-ε turbulence model was chosen because it is alsomost recently developed k-ε model and compared to the standard one, itprovides improved predictions for flows involving: planar and round jets,boundary layers under strong adverse pressure gradients or separations,recirculation, rotation and strong streamline curvatures [47]. In thisstudy one could envisage recirculation and jets; therefore the realizable k-εturbulence model would have advantages over the standard one.


CHANNEL

3.2 STAR-CCM+ and FLICA4 modeling assumptions

The following assumptions are implicit in both models:

• All parts are considered geometrically new, without accounting formanufacturing tolerances and operational effects (oxidation, swelling,etc.) on the fuel plate. The hot channel’s hydraulic gap in FLICA4model is increased for this calculation from 1.64 mm to 1.95 mm.

• Assumptions 2-5, as described in Section 2.4.

Additional assumptions made in the CEA’s FLICA4 model of the 36assembly JHR core are those listed in section 2.4 and not mentioned here.

The following are the additional assumptions made in the CFD simulation:

• Turbulence is modeled.

• The total power of the hot fuel element is 4.900 MW and 0.251 MWis power deposited in the water of the hot channel, originating fromneutron moderation and gamma heating. In addition it is assumedthat only the fuel meat and the water are the source of power. In thehot channel calculation it is assumed that both fuel plates contribute1/2 of the power into the hot channel: 74.5 kW from the first and80.9 kW from the second fuel plate. In addition 6.0 kW is the powerdeposited in the water due to neutrons and gamma rays.

3.3 Comparison

The results of this study are summarized in Table 3.1. Comparisonof the results reveals that the maximum temperatures are smaller andconsequently the minimum safety margin is larger when calculated withCFD. This is because of: i) the heat transfer exchange is enhanced in theCFD calculation compared to the FLICA4 calculation utilizing the Dittus-Boelter correlation, and ii) a smaller maximum heat flux value (-9%), dueto the more accurate modeling of 3D thermal conduction in CFD.

Figure 3.2 shows the hot channel outlet temperature distribution calculatedin the CFD simulations. In the CEA reference methodology the full hotchannel is divided into 4 sub-channels. From Figure 3.2 it can be observedthat the temperature could be considered as piece wise constant in theazimuthal direction and therefore the channel splitting into sub-channels isjustified and a similar method could be used in the future CATHARE2modeling of the JHR with a more accurate core model. At both the

3.3. COMPARISON 21

Table 3.1: STAR-CCM+ and FLICA4 results in the hot channel.

STARCCM+ FLICA4Max wall temperature [K] 394.2 412.5Max cladding temperature [K] 496.6 535.3Max fuel temperature [K] 570.0 604.3Min safety margin [K] M= 71.8 M= 56.1Max heat flux [MW/m2] 4.11 4.52Mass flow rate [kg/s] 0.924 0.925Surface area [MW/m2] 88.7 88.8

edges, thermal gradients are larger; therefore it would be advisable to eitherincrease the channel subdivisions in the full channel or only at the edges.

Figure 3.2: Hot channel outlet (z= 0.7 m) temperature distribution in theSTAR-CCM+ simulation.

There is a difference in the temperatures after the vertical height equal to theupper edge of the fuel meat. In FLICA4 simulation the temperatures in all 4sub-channels stay at the constant temperature, while in the CFD simulationturbulent mixing causes the water temperatures to smooth the temperaturevariations. Therefore the constant maximum water temperature in FLICA4is located vertically within an interval before the outlet and in the CFDmodel at vertical height equal to the upper edge of the fuel meat. Althoughthe current modeling provides reliable results for safety analyses, in futureCATHARE2 modeling of the JHR, with a more accurate core model, thisdifference could be taken into account.

Chapter 4

Hot fuel element thermal-hydraulics in theJHR

In this chapter, a CFD simulation of the reactors hot fuel element ispresented. Moreover a conjugate heat transfer analysis is performed forthe hot channel. The main objective of this work is to improve the thermal-hydraulic knowledge of the complex hot fuel element and to present themost prominent findings.

New assumption

Here it is assumed that the hot fuel assembly and the water in it haveFelement=1.79. The CEA 36 assembly JHR core reference power remains108.77 MW [21], from which now 5.145 MW is the total power of thehot fuel element and 0.264 MW is the power in the water, in the hotchannel, originating from neutron moderation and gamma heating. In thehot channel calculation it is assumed that both fuel plates contribute 1/2of the power into the hot channel: 78.2 kW from the first and 85.0 kW fromthe second fuel plate. In addition 6.3 kW is the power deposited in thewater due to neutrons and gamma rays. Otherwise the CFD modeling isidentical to that described in Chapter 3.

4.1 Mass flow distribution

Cold condition

As a starting point a hand calculation was performed to evaluated themass flow split in cold conditions (32.1C) between the fuel plates in 1/3symmetric geometry by utilizing the Darcy-Weisbach equation:

∆ploss,friction = fDL

Dh

12ρv

2. (4.1)

Darcy’s friction coefficient was evaluated by using the Colebrook (Equation4.2) and the Blasius (Equation 4.3) equations for pipes:

1√fD

= −2log10

(ε

3.7Dh+ 2.51Re√fD

), (4.2)

23

24CHAPTER 4. HOT FUEL ELEMENT THERMAL-HYDRAULICS IN THE

JHR

fD = 0.316Re0.25 . (4.3)

Cold conditions are examined in order to eliminate the change of the flowdistribution that may arise from power distribution. Flow distributionobtained by using Colebrook(ε = 0) or Blasius equations differ by less than0.6%, see Table 4.1. Both correlations underestimate mass flow rate in theinner channels and overestimate it in the outer channels, compared to theCFD calculation. Therefore correction factors should be utilized while usingpipe-based empirical correlations for estimating mass flow rates in the JHRgeometry.

By comparing the mass flow rate average values obtained with the secondand third geometries one can notice that the bottom and the top end capsinfluence the flow field by reducing the mass flow through the inner fivechannels and by increasing it in the outer four channels. The highestaveraged loss is observed in the second channel (-5.9%) and the largestgain in the eighth channel (+3.9%), see Table 4.1. Reduction in the hotchannel (channel 2, sector 2) is 6.8% from 0.987 kg/s to 0.919 kg/s, seeTable 4.2.

Table 4.1: Average mass flow rates [kg/s].

Cold condition (32.1C) Nominal conditionCh. Const. G Colebrook Blasius 2 geom. 3 geom. ∆23 2 geom. 3 geom. ∆23

1 0.933 0.861 0.857 0.883 0.837 -5.2% 0.878 0.829 -5.6%2 1.020 0.974 0.969 0.987 0.929 -5.9% 0.995 0.935 -6.0%3 1.176 1.126 1.121 1.134 1.075 -5.2% 1.142 1.081 -5.3%4 1.332 1.278 1.273 1.281 1.239 -3.2% 1.288 1.246 -3.3%5 1.488 1.432 1.425 1.437 1.420 -1.2% 1.445 1.429 -1.1%6 1.644 1.586 1.579 1.600 1.608 +0.5% 1.607 1.619 +0.7%7 1.800 1.739 1.732 1.757 1.802 +2.6% 1.769 1.815 +2.6%8 1.956 1.893 1.885 1.917 1.991 +3.9% 1.930 2.006 +3.9%9 2.967 3.432 3.441 3.318 3.416 +3.0% 3.263 3.357 +2.9%

There is a deviation between the mass flow rates obtained in the CFDsimulation and those based on the Blasius and Colebrook correlations. FromTable 4.1, it can be observed that in cold conditions, the Blasius correlationover-estimates the averaged mass flow rate in the second channel by 4.1%(0.969 vs 0.929) and the Colebrook correlation by 4.6% (0.974 vs 0.929).The mass flow split obtained by assuming a constant mass flux is addedinto the Table 4.1 as the most inaccurate of the methods discussed.

4.1. MASS FLOW DISTRIBUTION 25

Table 4.2: Mass flow rates [kg/s].

Second geometry, see Figure 3.1(b) Third geometry, see Figure 3.1(c-d)Cold conditions (32.1C) Nominal conditions Cold conditions (32.1C) Nominal conditions

Ch. Sector 1 Sector 2 Sector 3 Sector 1 Sector 2 Sector 3 Sector 1 Sector 2 Sector 3 Sector 1 Sector 2 Sector 31 0.884 0.884 0.883 0.878 0.879 0.877 0.840 0.832 0.838 0.833 0.824 0.8302 0.986 0.987 0.987 0.993 0.996 0.996 0.937 0.919 0.933 0.941 0.924 0.9393 1.131 1.132 1.140 1.138 1.141 1.148 1.082 1.066 1.078 1.087 1.072 1.0844 1.276 1.274 1.291 1.281 1.282 1.300 1.246 1.228 1.242 1.252 1.236 1.2495 1.434 1.434 1.444 1.439 1.442 1.454 1.426 1.408 1.428 1.432 1.418 1.4376 1.600 1.601 1.598 1.603 1.609 1.609 1.613 1.597 1.614 1.620 1.610 1.6267 1.757 1.760 1.756 1.764 1.773 1.769 1.799 1.800 1.807 1.807 1.816 1.8218 1.917 1.918 1.917 1.923 1.935 1.933 1.987 2.003 1.984 1.995 2.023 2.0019 3.318 3.314 3.322 3.260 3.266 3.264 3.395 3.461 3.394 3.332 3.404 3.334The hot channel is marked bold.

Nominal condition

Similar tendencies as described above were also observed under nominalcondition. Here the highest averaged loss in the second channel is -6.0% andthe largest gain in the eighth channel is +3.9%, see Table 4.1. Reductionof mass flow rate in the hot channel is 7.2% from 0.996 kg/s to 0.924 kg/s,see Table 4.2.

Next the change in the mass flow distribution was compared between coldand nominal conditions. As expected it is observed that the mass flow isreduced from the first and the last channels and increased in the others, seeTable 4.3. This can be explained by the fact that these two channels areheated from only one side in comparison to the central channels.

Table 4.3: The change of the averaged mass flow rates due to the powerdistribution.Ch. 1 2 3 4 5 6 7 8 9∆2Geom -0.6% +0.8% +0.7% +0.6% +0.6% +0.4% +0.7% +0.7% -1.7%∆3Geom -1.0% +0.7% +0.6% +0.6% +0.6% +0.7% +0.7% +0.8% -1.7%

Mass flow in the hot sector

In the inner six channels of the hot sector (Sector 2, Table 4.2) the massflow rates are lower than the average values and in the outer three over theaverage values. The nominal mass flow rate for the hot channel is 0.924 kg/s.

Mass flow around the bottom end cap

To demonstrate the mass flow in bottom end cap axial velocity componentsare plotted on nine planes normal to the flow direction in Figure 4.1. The


JHR

planes are separated by 2.5 cm and the final plane is located 1.5 cm inside thefuel plates. For the same reason velocity axial components are plotted on thecentral plane perpendicular to the y-axis, see Figure 4.2. An examination ofthe two figures reveals the same change of flow distribution discussed above.

Figure 4.1: Bottom end cap surrounding flow field velocity axial componentsillustrated on multiple plane sections separated by 2.5 cm.

Figure 4.2: Velocity axial components around bottom end cap on the planey=0.

In Figure 4.2 it can be observed that the initially globally homogeneousflow is modified by the geometrical changes/obstacles. After the geometrychange 12.0 cm from the fuel plates, the flow is bent radially outwards. In

4.2. PRESSURE DROP 27

the same place a flow field similar to a backward-facing step flow with flowseparation and subsequent reattachment is observed. At 9.5 cm from thefuel plates a flow split bends the flow radially outwards to an even greaterextent. After the flow split, a low velocity region in the main flow towardsthe flow splitting wall is formed. In addition there is a re-circulation nearthe flow splitting wall ending 6.0 cm from the fuel plates. The re-circulationareas can be seen in Figure 4.1 in the fifth and sixth cross-sectional planes.There is a nearly stagnant flow field in the flow passage that is separatedfrom the main flow 17.7 cm and reconnected 12.0 cm from the fuel plates.

In conclusion, it is evident that the flow distribution between the fuel platesarises from two main contributions: the natural flow distribution due to thedifferent hydraulic diameters in this geometry (without the influence of thebottom cap) and the jet effect.

Mass flow around the top end cap

For the top end part of the flow field analogue figures as described above arealso produced, see Figures 4.3 and 4.4. Figure 4.3 has ten planes normal tothe flow direction, separated by 2.0 cm, with the first plane located 0.8 cminside the fuel plates. In Figure 4.4 one can notice three locations for theflow split ( 6.5 cm, 7.8 cm and 12.3 cm from the fuel plates) and two flowreunion locations (9.75 cm and 14.0 cm from the fuel plates). At first, theflow in the main passage is bent radially outwards after the first two flowsplits. Thereafter flow split and flow reunions bent the flow in the mainpassage radially towards the center.

At the outlet there are four surfaces: three main passages and one annularpassage. The mass flow is spread in such a way that the annular passagehas 12.0% and each main passage 29.3% of the mass flow on average. Inboth the figures, one can notice areas where the flow is nearly stagnant.

4.2 Pressure drop

Although not strictly valid due to the effect of compressibility, the limitedchange of density (ρmax−ρmin

ρmax≈ 2%) allows the extended Bernoulli equation

to provide a reasonable estimation of the pressure drop:

p1 + 12ρ1v

21 + ρ1ghz1 = p2 + 1

2ρ2v22 + ρ2ghz2 + ∆ploss, (4.4)


JHR

Figure 4.3: Top end cap surrounding flow field velocity axial componentsillustrated on multiple plane sections separated by 2.0 cm.

Figure 4.4: Velocity axial components around top end cap on the planey=0.

where ∆ploss is to account the losses:

∆ploss =∑i

(fD,i

LiDh,i

12ρiv

2i

)+∑j

(ξj

12ρjv

2j

), (4.5)

The first term in Equation 4.5 describes the friction losses and the secondterm describes the local losses. Here index i is referring to a i-th sectionwith constant hydraulic diameter Dh,i and index j is referring to a j-thlocal loss.

4.3. TEMPERATURES AND BOUNDARY HEAT FLUX IN THE HOTCHANNEL 29

Figure 4.5: Schematic view of themaximum temperatures in the hotchannel calculation. The dashedbox marks the water-solid interface.Arrows show only the part and notspecific locations.

Figure 4.6: The safety margin in thehot channel in a fuel meat zone.

The total pressure was measured in five different parts: the bottom end,transition from bottom end to the center, the center, transition from thecenter to the top end and the top end. Area-averaged parameters wereutilized for calculating the pressure drops. The width of the transition areaswas picked to be 1 mm. The area-averaged pressure drops evaluated werethe following: the bottom end - 52.3 kPa, the bottom end/center transition- 27.0 kPa, the center - 205.1 kPa, the center/top transition - 21.4 kPa andthe top end - 24.1 kPa. Transitional drops are purely singular pressure dropsand center drop is purely frictional, others represent the total pressure lossof the part.

4.3 Temperatures and boundary heat flux in the hotchannel

The maximum temperatures obtained in the conjugate heat transfercalculation of the hot channel are shown in Figure 4.5. The maximumcladding temperature was Tcladding,max= 507.3 K and the maximum fueltemperature was Tf,max= 582.7 K. Water reaches a maximum temperatureof Tw,max= 358.4 K (outlet mean temperature Two,mean= 349.0 K) which ishigher than the maximum temperature reached in both the poison Tp,max=353.8 K and the stiffener Ts,max= 335.0 K. The safety margins along theaxial direction (0.5 cm apart) in the zone on fuel meat are calculated andpresented in Figure 4.6. The minimum safety margin achieved was M=68.4 K.

The hot channel boundary wall heat flux is described in Figure 4.7. Thearea where the heat flux is negative corresponds to the influence of the fuelmeat, where heat is transferred from wall to the liquid. Inversely, positivevalues correspond to heat transfer in the opposite direction. Heat transfer


JHR

Figure 4.7: Boundary heat flux on the hot channel. Flow direction is fromleft to right and the boundaries are seen from the center of the fuel assembly.

from the water to the wall is dominant everywhere except for the areas ofthe fuel meat, however the heat flux there is around two orders of magnitudeless and the heat transfer can be considered negligible.

Figure 4.8: Hot channel calculationazimuthal dependent heat flux (a)and wall temperature (b) on the firstfuel plate and the normalized powerdensity (c) in the fuel meat at theheight z= 0.315 m. All parameters areplotted in the azimuthal interval thatcorresponds to the fuel meat location.

The maximum volumetric heatsource is located at z= 0.315 m andthe corresponding heatflux distribution along azimuthaldirection (parallel to the fuel meat)on the inner wall (wall towardsthe center of the fuel assembly) isillustrated in Figure 4.8(a). ThereSTAR-CCM+ results are comparedwith the case where the axial andazimuthal conduction is neglectedand the heat flux is calculatedfrom the power distribution, seeFigure 4.8(c). There is a smallreduction, less than 4.8%, in aheat flux in the central part (90

in azimuthal angle) if the axialand azimuthal conduction is notaccounted for. At both endsof the fuel meat sections (4.35

in azimuthal angle) the heat fluxencounters a noteworthy reductioncaused by thermal conduction inthe cladding towards the stiffeners.The azimuthal heat conduction can

be found in Figure 4.9, where the temperature distribution is shown. Theinfluence of the azimuthal heat conduction can be observed by the gradualtemperature reduction in the azimuthal direction in the cladding nearthe fuel meat. The heat flux at the ends of the fuel meat sections is

4.4. HEAT TRANSFER COEFFICIENT IN THE HOT CHANNEL 31

Figure 4.9: Temperature distributionin the hot channel and in thesurrounding metal structures on thez= 0.315 m plane.

Figure 4.10: Heat transfer coef-ficient obtained in the hot channelcompared with the correlations.

reduced by 52-55% of its value without axial and azimuthal conduction.Accordingly the wall temperature decreases by 34-39 K compared to thecentral "plateau". Similar findings to those discussed above have beenreported in [48] while investigating a BR2 fuel assembly geometry.

The azimuthal wall temperature distribution on the inner wall, see Figure4.8(b), follows the azimuthal boundary heat fluxes distribution. Inthe central part the temperature is within interval of 2.8 K. The walltemperature as the heat flux has a tendency to peak toward the edges,not in the center of the fuel plate.

4.4 Heat transfer coefficient in the hot channel

Convective heat transfer from a heated wall into the adjacent fluid can bedescribed by the Newton’s law of cooling:

h = ΦTw − Tb

. (4.6)

On the other hand h can be expressed in terms of the non-dimensionalNusselt number as follows:

h = Nu · λDh

. (4.7)

There are several empirical Nu form correlations available for calculating hin the case of a forced convection turbulent flow. The correlations evaluatedin this thesis are the following:(i) Dittus-Boelter correlation for pipes [34]:

Nu = 0.023Re0.8Pr0.4. (4.8)


JHR

(ii) Modified Dittus-Boelter correlation for pipes proposed in [48]:

Nu = 0.023Re0.8Pr0.4(µbµw

)0.11. (4.9)

(iii) Sieder-Tate correlation for pipes [49]:

Nu = 0.027Re0.8Pr1/3(µbµw

)0.14. (4.10)

(iv) Petukhov-Popov correlation for pipes [50]:

Nu = (fD/8)RePr1.07 + 12.7 (fD/8)1/2 (

Pr2/3 − 1) ( µb

µw

)0.14. (4.11)

(v) Gnielinski correlation for pipes [51]:

Nu = (fD/8) (Re− 1000)Pr1.07 + 12.7 (fD/8)1/2 (

Pr2/3 − 1) ·

·

[1 +

(Dh

L

)2/3](

Pr

Prw

)0.11.

(4.12)

(vi) Gnielinski correlation for annulus [52]:

Nu = (fD/8) (Re− 1000)Pr1.07 + 12.7 (fD/8)1/2 (

Pr2/3 − 1) ·

·

[1 +

(Dh

L

)2/3][

1− 0.14(Din

Dout

)0.6](

Pr

Prw

)0.11.

(4.13)

In Equations 4.11-4.13 the Darcy friction factor is obtained from Filonenko’scorrelation [53]:

fD = (1.821 log10 Re− 1.64)−2. (4.14)

By using Equation 4.6 the mean heat transfer coefficient (dependent uponaxial location) in the hot channel was evaluated by using the meanheat flux of the heated wall, its mean temperature and the bulk fluidtemperature. The wall parameters were taken from the wall interfaces. Thevalue of h obtained is compared with those estimated by the correlationsdescribed above. Figure 4.10 illustrates that the Gnielinski and thePetukhov-Popov correlations clearly overestimate and both Dittus-Boeltercorrelations underestimate the heat transfer coefficient. The Sieder-Tatecorrelation over-predicts h, aside from a small region at the entrance of the

4.4. HEAT TRANSFER COEFFICIENT IN THE HOT CHANNEL 33

channel, where it slightly under-predicts h. Currently in thermal-hydraulicmodeling of the JHR, see [21], the Dittus-Boelter correlation is utilizedfor conservative estimation of h. In light of the present results, a modifiedDittus-Boelter correlation could be used to produce less conservative resultsand the correlation could be improved by accounting for the entrance effectas it is done in the Gnielinski correlations.

Chapter 5

Hydraulics of the JHR vessel

The aim of this chapter is four-fold: (i) to determine the mass flow ratedistribution between the 36 fuel elements in the rack and to analyze why itis split in this specific manner, (ii) to describe the flow field in the reactor,(iii) to report the absolute pressure range and its average value in specificvolumes defined in the lower and upper plenums of the reactor, and (iv) topresent some of the results obtained from the thermal-hydraulic researchdescribed in [23] with specified mass flow rate value, determined in thecurrent research.

5.1 STAR-CCM+ modeling of the JHR

For this chapter, the commercial CAD tool SolidWorks was used to createthe complex geometry for the liquid-filled regions. Thereafter, the CFD codeSTAR-CCM+ was utilized for generating a mesh, describing the physics tobe modeled, solving and post-processing the results.

The geometry used in the numerical model was generated by manuallycreating the fluid domain primarily for this analysis, based on the CATIACAD model of the JHR (see Figure 5.1). Several simplifications wereintroduced during this process, the most significant of these were: (i)inside the test devices and control rod guide tubes, the complex geometrymandated simplification into tubes with a diameter defined as the hydraulicdiameter used in the JHR’s CATHARE2 model described in [21], and (ii)two perforated cylinders in the lower plenum (colored orange in Figure 5.2)and the 36 fuel assemblies (colored red in Figure 5.2) were modeled as porousmedia (described later). Other simplifications included neglecting extremelysmall irrelevant details/gaps (e.g. part markings, filling internal structuresirrelevant to the flow) and smoothing immensely complicated details. It isimpossible to model only 1/2 of the geometry due to the asymmetry of thedesign. The geometry utilized in this research can be seen in Figure 5.2with some of its cross-section views shown in Figure 5.3.

The geometry had to be split into four sections due to the limitedcomputational resources available for meshing and solving. The cutting

35

36 CHAPTER 5. HYDRAULICS OF THE JHR VESSEL

Figure 5.1: Cut view of the JHRreactor with vertical positions of thecross-sections illustrated in Figures5.9-5.10 (dimensions in millimeters).Courtesy of CEA.

Figure 5.2: Cut view of thewater geometry. Cross-section viewsindicated by letters (a)-(f) areillustrated in Figure 5.3.

strategy is illustrated in Figure 5.2 by the various coloring: (i) section one-blue, orange and green, (ii) section two- yellow, (iii) section three- light grayand red, and (iii) section four- dark gray. Splitting is done in such a way asto give an overlapping region between two subsequent sections, see Figure5.4. This is performed in order to retrieve the inlet boundary conditions forthe next section (taken 15 cm below the outlet), without having significantinfluence of the outlet boundary conditions applied to this section. Couplingbetween sections is explained in more detail later.

The meshing procedure for the complex geometry should be fully automaticin order to produce an optimal mesh and save time. Therefore, in thisstudy an unstructured polyhedral mesh with the surface remesher optionand prism layers was applied. Table 5.1 shows the parameters used in

5.1. STAR-CCM+ MODELING OF THE JHR 37

Figure 5.3: Cross-section views ofthe fluid geometry (Figure 5.2).

Figure 5.4: Coupling betweensubsequent sections.

this meshing procedure. Default parameters were utilized for the optionsnot mentioned in Table 5.1. The total number of cells used to model thefull reactor is 70,150,212 cells. The mesh quality can be determined byassessing the face validity and the volume change of the mesh. In all thegrids generated for different sections of the reactor, all the faces had avalidity of 1.0 and the majority of cells had a volume change greater than0.1. The majority of cells adjacent to the wall had values of y+ between30 and 150. Except for in regions of stagnant flow (e.g. base of the lowerplenum) where the y+ is obviously low, all cells had a value of y+ between13 and 300. The wall functions with the models chosen in STAR-CCM+are reasonably accurate for values of 12 and above [18].

Table 5.1: Mesh reference values.Surface remesherBase size 7.0 mmCAD projection EnabledPolyhedral mesherOptimization cycles 8Quality threshold 1Prism layer mesherNumber of prism layers 5Prism layer stretching 1.5Prism layer absolute thickness 3.5 mm**5.275 mm in the inlet manifold (colored blue in Figure 5.2) + refinement onspecific surfaces. Default values were used for unspecified parameters.


In order to ensure that the results obtained are independent of the grid size,different meshes created for section one (see Figure 5.2) were compared.This section was chosen due to the full range of different length scalesthat can be found in this geometry. In this section the highest velocitygradients can be found. Grids were created automatically by changing thebase size from 10 mm to 7 mm. The prism layers were left unchanged byspecifying them in the absolute units. The resulting grids had cell countsfrom 9.9 million cells to 19.1 million cells. The pressure drop was utilizedto determine the mesh independence and it was observed that by using thegrid larger than 16.7 million cells the relative error is less than 1% comparedto the finest mesh, which is sufficiently accurate. At the same time, themass flow distribution at the section edge was found by splitting it into16 equally sized sectors. A maximum relative error of less than 0.6% wasfound between the different meshes. However, for the present calculation,the finest mesh and base size of 7 mm were chosen. Base size 7 mm wasconserved throughout the geometry to yield similar overall topology.

Table 5.2: Physics models.

Model SpecificationSpace model Three dimensionalTime model Steady stateMaterial model LiquidEquation of state model IAPWS-IF97 (Water)Flow model Segregated flowEnergy model Segregated fluid isothermal (32.1C)Viscous regime model TurbulentTurbulence model k-epsilonk-epsilon model Realizable two-layerWall treatment All y+Wall type No-slip smooth wallsOptional model GravityConvection scheme Second order upwind (default)Material properties IAPWS-IF97(Water)

The physics models utilized in the present study are summarized in Table4.1. The turbulence parameters, 0.03 (≈0.16Re− 1

8 [54]) for the turbulenceintensity and 58 mm (10% of the inlet diameter [54]) for the inlet turbulencelength scale, were deployed in the calculation with the first section on themass flow inlet. Thereafter turbulence kinetic energy and the turbulentdissipation rate profiles from the previous section’s converged solution(taken 15 cm below the outlet) are imposed to the next section as inletboundary conditions in addition to the three velocity components, seeFigure 5.4. At the pressure outlet of the first section a constant staticpressure of 0 Pa was imposed and the reference pressure was adjusted inorder to have at the outlet of the first section an area-averaged pressure

5.1. STAR-CCM+ MODELING OF THE JHR 39

equal to that acquired by the system-code CATHARE2 simulation [21] atthe same location. In the other sections the reference pressure was adjustedin order to have an equal area-averaged absolute pressure on a surface 15 cmbelow the outlet surface of the previous section and on the inlet surface ofthe next section.

Next, with each set of subsequent sections, the following section’s inletpressure profile is compared to the pressure profile of the previous section atthe location from where the inlet conditions were taken (at the beginning ofthe overlapping region). As a result, an additional calculation was requiredon section three by imposing the pressure profile obtained from section four(taken 15 cm above the inlet) on the outlet in order to take into accountthe asymmetric influences of the primary outlet. At the same time, theinlet boundary conditions acquired from section two remained uninfluenced.Also an additional run was performed with section four with the new inletconditions and it was verified, that the converged solution was obtainedwith no need for additional calculations.

Modeling assumptions

The following assumptions are made in this research:

1. The reactor has CEA 36 assembly core configuration under coldconditions (32.1C, [21]).

2. The total mass flow rate in the reactor is 1,727.43 kg/s, from which69.85 kg/s is assumed to flow within 27 control rods and 9 test devices[21].

3. All parts are considered geometrically new and no manufacturingtolerances or operational effects (oxidation, swelling, etc.) on the fuelplate are taken into account.

4. The fluid is assumed to be stagnant in a volume occupied in areactor core vessel above primary coolant outlet above the horizontalstructural plate (colored light blue in Figure 5.1) due to the extremelysmall flow channels in the plate. In addition, the volume above theplate is a trapped zone. Therefore the fluid domain is only modeledup to this plate (compare Figures 5.1 and 5.2).

Porous media

The two perforated cylinders (with uniform hole distribution) in the lowerplenum and 36 water geometries between the fuel assembly and the rack


are modeled as porous media where the pressure drop is specified as follows[18]:

∆p = − (Pi|vn|+ Pv) vnL. (5.1)

The coefficients Pi and Pv for each porous media were evaluated byadditional CFD simulations where the original geometries were modeledunder different flow conditions and the pressure drop values were recorded.By using a second order polynomial regression on the obtained results, theconstant coefficients in Equation 5.1 were obtained. In the case of theperforated cylinders Pi= 94,970 kg/m4 and Pv= 14,410 kg/(m3s). In thecase of water between the fuel element and the rack Pi= 3,190 kg/m4 andPv= 6,810 kg/(m3s). All acquired values were tested in CFD simulationswhere the original geometries were substituted by porous media and similarresults were obtained, showing this approximation to be acceptable. Allcalculations were undertaken under the assumption of velocity normal to thesurface and the Pi and Pv components in the cross-flow directions were givenvalues 2-3 orders of magnitude greater than those in the normal direction.

5.2 Mass flow rate distribution between fuel elements

Figure 5.5: Fuel element numberingsystem (top view) relevant to Table5.3. Location 103 is occupied by thetest device (instead of a fuel element)and the flow primary inlet/outlet islocated horizontally right from thecenter point. Courtesy of CEA.

The mass flow rates within differentfuel elements are shown in Table 5.3with the corresponding locationsdescribed in Figure 5.5. The resultsare normalized using the averagemass flow rate.

One can notice that the lowestmass flow rate is in the centralposition (001), whilst the secondlowest is in position 106. Position106 corresponds to the fuel elementlocation that obtained the highestpower factor in the neutroniccalculation [29] and is therefore thehot fuel element. The mass flowratio of 0.9811 is one importantoutcome of this study. In previousresearches [22, 23] the exact massflow rate through the hot fuel

element was assumed to be an average value (42.955 kg/s). Now similarCFD thermal-hydraulic studies can be undertaken with specified value of

5.3. FLUID FLOW DESCRIPTION 41

0.9811·42.955=42.143 kg/s.

By averaging the ratios in fuel assemblies of the same radial distance fromthe center it was observed that a slight increase in flow exists toward the edgeof the reactor: 0.9792(0-ring), 0.9943(1-ring), 0.9976(2-ring) and 1.0044(3-ring). Compared to the average mass flow rate the highest overflow is 3.5%(FE 303) and underflow is -2.1% (FE 001). In a next subsection the flowfield in the reactor will be described in order to explain the reason whythere is an overflow (compared to the average) in fuel assemblies 101, 105,203, 207, 211, 301, 303, 307, 313, and nearly average flow or underflow inthe others. In advance it should be noted that all nine locations where theoverflow was observed, correspond to the locations where an experimentaldevice is placed into the central hole of the fuel element.

Table 5.3: Mass flow rate ratios in the 36 fuel elements.

FE Ratio FE Ratio FE Ratio001 0.979 207 1.022 307 1.032101 1.012 208 0.986 308 0.998102 0.982 209 0.988 309 0.994104 0.982 210 0.998 310 0.995105 1.015 211 1.021 311 0.996106 0.981 212 0.989 312 0.995201 0.983 301 1.032 313 1.030202 0.989 302 0.994 314 1.000203 1.021 303 1.035 315 0.999204 0.991 304 0.993 316 1.000205 0.989 305 0.996 317 0.998206 0.995 306 0.994 318 0.998The location of the hot fuel element is marked bold.

5.3 Fluid flow description

This research is focused on the main part of the primary flow which passesthrough the fuel elements. The descending primary flow (in the inlet pipe),after passing the 90 degree bend, hits the flow deflector and splits into twoparts surrounding the two perforated cylinders, see Figure 5.6. After hittingthe flow deflector, the flow is highly turbulent. The perforated cylinders arerequired in order to rehomogenize the flow.

Figure 5.7 shows the velocity vector field at the specified plane. There wecan see that in the space directly behind the flow deflector (tangentially20 deg in both directions from the center) there are vortices and the flow


Figure 5.6: Flow streamlines in an outer part of section one, which arecolored by the radial velocity (the radial component of velocity relative tothe axis of the core).

in the perforated cylinders can be found radially flowing both toward andaway from the axis of the core. It is followed by the area of an angular widthof 20 deg, where the deflected jets hit the cylindrical perforated plates andthe inward mass flow is maximum. Next, tangentially 40-90 deg, thereis an area where the mass flow can be found in both radial directions,mostly inwards. In the 180 deg section opposite the inlet pipe, the radialflow through the perforated cylinder is only towards the center. 64.15%(1,108.1 kg/s; 1,801.9 kg/(s · m2)) of the mass flow is entering through theupper perforated cylinder and 35.85% (619.33 kg/s; 768.12 kg/(s · m2))through the lower perforated cylinder.

Flow in the inner part of section one is illustrated in Figure 5.8. Afterentering through the perforated cylinders the flow is redirected upwards andat the outlet level of section one a nearly symmetric flow field is formed,see Figure 5.9(a). The higher axial velocities at the outer edge are due tothe cylindrical contraction preceding the vertical location depicted. Theflow field is next altered by three contractions 120 deg apart, see Figure5.9(b). These two contractions and the flow entering location (through theperforated cylinders and not from the bottom of the reactor) should bemainly responsible for the slight mass flow radial increase towards the edgediscussed in the previous subsection.

Before reaching the grid, see Figure 5.9(c), the primary flow is split into themain flow, the annular flow between the vessel and the rack, and the flowwithin the the 27 control rods and 9 test devices. The split is visualized in


Figure 5.7: Velocity vector field at z=-1550 mm displayed in line integralconvolution mode. Position z=0 mm corresponding to the lower edge of theporous fuel elements (colored red in Figure 5.2).

Figure 5.8: Flow streamlines in an inner part of section one, which arecolored by axial velocity (the axial component of velocity relative to theaxis of the core).

Figure 5.2 near marker (c). The main flow is colored red, the flow withincontrol rods and test devices is colored yellow and the annular flow betweenthe vessel and the rack is colored light grey.

The grid (colored dark green in Figure 5.1 and marked with z=-800) influences the flow field further. One important influence on theflow distribution between the fuel elements arises from the geometrical


Figure 5.9: Velocity axial profiles of the following cross-sections: (a) z=-1190 mm, (b) z=-1020 mm, (c) z=-800 mm, (d) z=-650 mm, (e) z=-300mm and (f) z=-15 mm. The vertical positions are marked in Figure 5.1In cross-sections (e) and (f) the flow within the 27 control rods and 10test devices is not included (but are modeled in the calculation). The flowprimary inlet/outlet is located vertically upwards from the center point.


Figure 5.10: Velocity axial profiles of the following cross-sections: (a)z=1020 mm, (b) z=1075 mm, (c) z=1350 mm, (d) z=1610 mm, (e) z=1690mm and (f) z=1725 mm. The vertical positions are marked in Figure 5.1. Incross-sections (a)-(c) the flow within the 27 control rods and 10 test devicesis not included (but are modeled in the calculation). The flow primaryinlet/outlet is located vertically up from the center point.


differences after the grid. In 27 locations, there are larger geometricobstacles (colored purple and green in Figure 5.1 and marked with z=-650) instead of pipes. The resulting flow field can be seen in Figure 5.9(d).Lower flow obstacle results in higher velocities near these 9 locations andthe flow field maximums conserve their locations even at the higher verticalheight (see Figure 5.9(e)) where there is no geometric difference betweenthe 36 locations. The last sub-figure (f) in Figure 5.9 shows a flow fieldwhere one can distinctly see the flow distribution 4 mm before the lowerend of the rack.

The geometrical differences at the rack outlet, also partly responsible forincreasing the flow within those 9 fuel elements containing test devices canbe seen in Figure 5.10(a). Test device containing locations have outletswith a higher surface area (+4.8 %) and therefore lower flow resistancecorresponding to a higher mass flow.

Figure 5.11: Flow streamlines insection four, which are coloredcorresponding to velocity magnitude.

The flow field in the upper plenumof the reactor is shown in Figure5.11 and specific cross-sectionsare illustrated in Figure 5.10(b-f). It should be noted thatin the upper plenum the flow isinfluenced mainly by six factors: (i)the location of the primary outlet,(ii) the grid, (iii) the flow cross-sectional area reduction due to thegeometric enlargement of the testdevices, (iv) rejoining flow fromwithin 27 control rods and 9 testdevices, (v) flow jets rising fromthe fuel elements, and (vi) rejoiningflow from the annulus between thevessel and the core.

At first, the primary outlet influences the flow field by creating a highermass flow region near the outlet. The effect can be observed until around200 mm below of the lower edge of the grid (colored orange in Figure 5.1 andmarked with z=1690). At the same time, the flow below the grid is partlyhomogenized by the reconnecting flow that was flowing within test devicesand control rods. The reconnecting area starts approximately 120 mm belowthe grid and includes several reconnecting streams perpendicular to themain flow at multiple vertical positions (some can be seen in Figure 5.10(d)).

5.4. PRESSURE FIELD IN THE UPPER AND LOWER PLENUM 47

The influence of primary outlet’s location on the mass flow split between thefuel elements was estimated by comparing the distributions obtained, seeTable 5.3, with the calculation where the influence from geometric sectionfour (see Figure 5.2) would not be taken into account in geometric sectionthree. Instead of utilizing the pressure profile obtained from geometricsection four as an outlet boundary condition in geometric section three, aconstant outlet pressure was used. The results show that the outlet increasesthe mass flow in the geometric half closest to it whilst reducing it in theother half. In the central fuel element the mass flow rate is reduced (-0.23%). The fuel elements can be divided into three groups based on thesize of the influence. The higher increase takes place in a group that islocated closest to the primary outlet (FE-s: 102, 106, 201, 202, 211, 212,301-303, 317, 318). There the mass flow increases by 0.22-0.50%, havingthe highest increase at the outer edge and closer to the axis of the primaryoutlet. In the second group (FE-s: 104, 204-208, 308-310) the mass flow isdecreased by 0.24-0.54%. In the other fuel elements, except for FE 001, themass flow change is below 0.19%. Compared to the heterogeneity observedbetween the fuel elements in Table 5.3, the influence of the outlet positionis small (by one order of magnitude).

5.4 Pressure field in the upper and lower plenum

In the reference CATHARE2 model of the JHR the upper and the lowerplenums are modeled by volume elements. In the lower plenum a singlevolume element is used to model the geometry illustrated in Figure 5.6(excluding the primary inlet pipe) and one for the geometry shown in Figure5.8. In a new model the inner part of the lower plenum could be splitvertically into two parts and the volumes could be divided by the grid plate(colored light green in Figure 5.1, nearly level with the axis of the inletpipe). The second part would be vertically limited by the lower edge ofthe contraction seen in Figure 5.12(b). The upper plenum in the referenceCATHARE2 model is also modeled by a single volume element occupyingthe volume between the grid and the primary outlet.

The CFD results will help to improve the reactor’s description in theCATHARE2 model in order to increase the accuracy of the prediction ofthe flow and pressure distribution. Therefore, it is important to know theaverage absolute pressure (the sum of the piezometric pressure and thereference pressure, [18]) values in the volumes which were described earlier.In each volume, the range of values should also be known. The latter will


be useful when modeling accidental scenarios, as instead of using a singlevalue from the volume element, a more realistic value could be applied as aninitial value. In addition, the pressure field could also be used to estimatethe forces acting on the control rods and other structural components. Itshould be noted that in CATHARE2, the variable pressure represents thepiezometric pressure. The distribution of absolute pressures in the lowerand upper plenums is illustrated in Figure 5.12, whilst its range and thevolume average values are collected into Table 5.4.

Figure 5.12: Absolute pressure in theupper plenum (a) and in the lowerplenum (b) on the plane x=0. Figuresare not in scale.

The volume average absolutepressure in the outer part of thelower plenum (LPout) is 1064.6 kPaand the absolute pressure valueslie within a range of 172.2 kPa,out of which 90% of the cellvalues are varying within 21.1 kPa.Most of the outlying values areconcentrated in the region near theflow deflector- the higher valuesare located near the splitting edgeof the flow deflector, in the areaswhere the deflected jets hit theperforated cylinders and in somelocations at the bottom of thevolume; the lower values can befound mostly near the trailing edgeof the flow deflector.

In the lower inner part of the lowerplenum (LPin,low) and in the upperpart of the lower plenum (LPin,up)the absolute pressure is decreasing

vertically upward. The absolute pressure is distributed there in a relativelyhomogeneous way, see Table 5.4. In the upper plenum above the grid (UP )the volume averaged absolute pressure is 497.6 kPa. Although the absolutepressure there has values within a 211.3 kPa range, 90% of the cells havea value from 490.6 kPa to 531.2 kPa. Lower values found in regions withhigher velocities and vice versa.

5.5. THERMAL-HYDRAULIC CALCULATION OF THE HOT FUELELEMENT WITH SPECIFIED MASS FLOW RATE 49

Table 5.4: Absolute pressure results in the upper plenum and in the lowerplenum.

LPout LPin,low LPin,up UP

pabs (kPa) 1,064.6 1,064.9 1,047.4 497.6100% cellsRange (kPa) 172.2 29.1 52.0 211.3Max value (kPa) 1,108.1 1,071.3 1,065.0 535.0Min value (kPa) 935.9 1,042.2 1,013.0 323.799% cellsRange (kPa) 57.6 13.9 28.8 109.1Max value (kPa) 1,097.0 1,069.1 1,058.6 531.7Min value (kPa) 1,039.4 1,055.2 1,029.8 422.690% cellsRange (kPa) 21.1 9.6 21.3 40.6Max value (kPa) 1,073.8 1,069.1 1,055.4 531.2Min value (kPa) 1,052.7 1,059.5 1,034.1 490.6

5.5 Thermal-hydraulic calculation of the hot fuel elementwith specified mass flow rate

The results of the main study were used in a thermal-hydraulic sub-modelof a single hot fuel element as previously described in Chapter 4. It can beseen from Table 5.3 that the minimum mass flow rate in the fuel assemblyis about 98% of the one used these studies. Taking into account this recentevolution, the mass flow rate for the hot fuel element was reduced from42.955 kg/s to 42.143 kg/s, with other parameters were left unchanged. Thecomputed mass flow rate through the hot channel reduced proportionallyfrom 0.924 kg/s to 0.907 kg/s and the total pressure loss in the hot channelreduced at the same time from 3.30 bar to 3.18 bar (-3.6%). The decreasedpressure difference across the studied fuel element is caused by the increasedlosses (found in this main study) at the inlet and outlet of the hydraulicallyunfavorably positioned fuel elements. This decreased pressure drop isconsistent with the reduced mass flow rate in certain fuel elements. Thenew minimum safety margin under the nominal conditions is 67.0 K (change-1.4 K). The new surface averaged temperature increase in the hot channelis 44.6 K (change +0.8 K) and in the full hot fuel element is 30.0 K (change+0.6 K).

Chapter 6

An improved JHR modeling usingCATHARE2

The objective of this chapter is to introduce an improved thermal-hydraulicmodel of the reactor using solely the CATHARE2 system code.

The modeling process was improved in two stages. In the first stage, amean core channel with a weight of 36, was split into a mean core channelwith a weight of 35 and a hot fuel element channel. In the reference model,the core channel is modeled using three 1D modules axially aligned andadjacent: one for the flow across the fuel plates and other two for eachextremity of the channel. In the new approach, both ends ("foot" & "head")are modeled with a 0D module situated at either end of the fuel plates zone,and 1D modules at the extremities, see Figures 6.1 and 6.2.

For the fuel plate zone two different approaches are used: (i) the half plateand (ii) the heat exchanger approach. In the former it is assumed thatthe power arising from the fuel plate is equally distributed between thechannels connected to it (i.e. 50% to each). In the second approach the fuelplate is modeled via a heat exchanger element with radial conduction inorder to obtain a more realistic power split. This stage produced separateCATHARE2 models containing either the mean core channel or the hot fuelelement channel (total of four different models). These separate models werecreated by using the knowledge obtained in previous steps of this research[21, 22, 23] and the reader should note that while creating these models amass flow rate of 42.955 kg/s (1/36th of the total mass flow rate through thefuel elements) was utilized. Detailed descriptions are given in the specificsubsections of this thesis.

In the second stage, the previously created separate models wereimplemented in the full reactor model, see Figure 6.1. The full reactormodeling was improved by using the latest knowledge [24] in addition tothose discussed above. The outcome of this stage was two full reactormodels (one for each approach) and is described in more detail later inthis thesis.

51

52 CHAPTER 6. AN IMPROVED JHR MODELING USING CATHARE2

Figure 6.1: JHR reactor blockmodeled in CATHARE2. Color-map: 1D modules- palegreen, 0Dmodules- beepskyblue and junctions-red.

Figure 6.2: JHR hot fuel assemblymodeling.

Figure 6.3: Fluid cross-sections andperimeters in the fuel assembly.Color-map: 1D modules- green and0D modules- blue.

6.1. MODELING ASSUMPTIONS 53

6.1 Modeling assumptions

The following assumptions are inherent in this work:

1. The core reference power is 100 MW·1.065·1.03·0.9916 = 108.77 MW.This is made up of the nominal power (100 MW) multiplied by thepower measurement uncertainties (1.065) and operating range (1.03).A final multiplication factor of 0.9916 accounts for the power deposedin the experimental devices and internal structures of the core. Outof the 108.77 MW, 103.47 MW is distributed into the fuel plates, with5.3 MW dissipated in the water, originating from neutron moderationand gamma heating.

2. It is assumed that the hot fuel element has a mean power factor of1.79 compared to the average value. The total power within the hotfuel element channel is 5.408 MW and 2.953 MW in the case of themean fuel element channel.

3. The reactor is in the CEA 36 fuel assembly start-up core configurationand the corresponding hot channel is the second channel (from thecenter of the fuel element) in the hot sector of the hottest fuelassembly.

4. All parts are considered geometrically new and neither manufacturingtolerances nor operational effects (oxidation, swelling, thermalexpansion, etc.) on the fuel plate are taken into account. The hotchannels hydraulic gap is 1.95 mm.

5. The total liquid mass flow rate through the reactor is 1727.44 kg/s,of which 1546.38 kg/s is the total mass flow rate through the fuelelements. The remaining part of flow is split between the experimentaldevices, the control rods, the annular gap between the vessel and therack, and the bypasses in the rack.

6.2 Fuel element modeling

Hot fuel element channel with the half plate approach

In this approach, flow through the hot fuel element is modeled as per theprevious FLICA4 model [21], including the assumption that the powerarising from the fuel plate is equally distributed between the channelsconnected to it. The fuel plate zone is divided into three parallel axialelements, see Figure 6.2. Element ECCSM with a weight of 2, represents amean sector, whilst element SPCC models a hot channel and the remainderof the hot sector (excluding the hot channel) corresponds to SCCM. In


order to improve the modeling of the hot channel, it is further subdividedazimuthally into eight sub-channels, each represented by a 1D module.These eight sub-channels include six central sectors with an angular widthof 15 and two edging sectors. The fuel meat in the fuel plates is subdividedin a identical manner. In the subdivided model, adjacent sub-channels arethermally connected via a heat exchanger in an axial interval from the endof the fuel meat zone to the end of the fuel plates. The heat exchanger hasa perimeter equal to the hydraulic gap between fuel plates and uses thermalproperties of water. Seven heat exchangers are utilized in order to give amore realistic temperature profile within the sub-channels after passing thefuel meat zone. No cross-flow is modeled between adjacent sub-channels.The half plate approach finally provides two JHR CATHARE2 models: onewith a full hot channel and other with a subdivided hot channel, otherwiseidentical. The CFD results from [22, 23] were utilized in order to create thehot fuel element modelings.

In the previous modeling [21] the fuel plate zone was axially divided into70 elements, the "foot" had 35 elements and the "head" 32 elements. In thenew model, all corresponding 1D modules have axially 149 elements (defaultCATHARE2 limit). Cross-sectional areas and perimeters used in the newmodel are shown in Figure 6.3. In the fuel plate zone, 99 elements (defaultCATHARE2 limit) correspond to the fuel meat zone, defining the powerprofile.

Mass flow rates and pressures

After defining the geometrical parameters in the CATHARE2 models, thecorrect mass flow split and pressure profile should be obtained. Themass flow split adjustment and pressure profile corrections were made byintroducing singular pressure drops where necessary. The CFD results undercold conditions (32.1C), with a mass flow rate of 42.955 kg/s (1/36th ofthe total mass flow rate through the fuel elements), were used for thispurpose. Adjustments were first made on a model containing an undividedhot channel.

Initially the mass flow split and pressure drop profile within the fuel channelswere adjusted. The mass flow split calculated by CFD within the hot fuelelement is collected into Table 6.1. In order to obtain the desired mass flowsplit, singular pressure drop coefficients to the ECCSM and SPCC wereintroduced. At the same time core pressure drop values (including singulardrops at the both ends) were monitored. The resulting mass flow split can beseen in Table 6.1. By comparing the core pressure drop values between the

6.2. FUEL ELEMENT MODELING 55

CFD and CATHARE2 results after obtaining the desired mass flow rates,one can conclude that CATHARE2 is overestimating this value by less than1%. Next, the frictional and singular pressure drops were compared. InCATHARE2 a wall friction coefficient is given by Equation 2.3 and thefrictional pressure drop values are overestimated by: 20.2% (47.0 kPa) inECCSM, 20.8% (48.4 kPa) in SCCM and 17.2% (36.8 kPa) in SPCC. At thesame time, absolute values were lacking from the singular pressure drops.Overall CATHARE2 overestimates the pressure drops by less than 3 kPa.

Table 6.1: Hot fuel element mass flow rates [kg/s].

Half plate approachΣ=42.955 Cold condition (32.1C) Nominal conditionUndividedCh CFD CATHARE2 CFD CATHARE2 ∆ [%]ECCSM 14.3205 14.3205 14.3130 14.3253 +0.09SCCM 13.3950 13.3950 13.4050 13.3738 -0.23SPCC 0.9190 0.9190 0.9241 0.9306 +0.71SubdividedCh CFD CATHARE2 CFD CATHARE2 ∆ [%]ECCSM 14.3205 14.3205 14.3130 14.3246 +0.08SCCM 13.3950 13.3950 13.4050 13.3783 -0.20ΣSubCh 0.9190 0.9190 0.9241 0.9275 +0.37→SubCh1 0.0685 0.0685 0.0682 0.0664 -2.71→SubCh2 0.1290 0.1290 0.1297 0.1310 +1.00→SubCh3 0.1306 0.1306 0.1317 0.1328 +0.84→SubCh4 0.1310 0.1310 0.1322 0.1332 +0.76→SubCh5 0.1311 0.1311 0.1323 0.1333 +0.76→SubCh6 0.1308 0.1308 0.1319 0.1330 +0.83→SubCh7 0.1293 0.1293 0.1300 0.1312 +0.92→SubCh8 0.0687 0.0687 0.0684 0.0665 -2.78

Heat exchanger approachCFD CATHARE2 CFD0.5plate CATHARE2 ∆ [%]

ECCSM 14.3205 14.3203 14.313 14.625 +2.18Channel1 0.832 0.832 0.825 0.792 -4.00Channel2 0.919 0.919 0.924 0.883 -4.43Channel3 1.066 1.066 1.072 1.024 -4.48Channel4 1.228 1.228 1.236 1.179 -4.61Channel5 1.408 1.408 1.418 1.352 -4.65Channel6 1.597 1.597 1.610 1.536 -4.60Channel7 1.800 1.800 1.816 1.733 -4.57Channel8 2.003 2.004 2.023 1.931 -4.55Channel9 3.461 3.461 3.405 3.274 -3.85*see Figs. 1.1-1.2 for part names.

The highest power density and the minimum safety margins are locatedaxially in the central part of the fuel plates and it is important to havethere the most realistic pressure values. Therefore the core pressure rangeis arranged in such a way that at the entrance the pressure is overestimatedand at the exit it is underestimated by a similar amount, resulting in thecorrect pressure (or minimum possible deviation) in the center. In thecase of the hot channel (SPCC) entrance, the pressure is overestimated


by 18.4 kPa (in abs. pressure values +2.22%) and at the exit pressure isunderestimated by 18.4 kPa (in abs. pressure values -2.99%).

Next, the pressure drop values in the "head" and the "foot" were comparedand any missing pressure drops were introduced into the CATHARE2model. This allows for nearly identical pressure drops between the CFD andCATHARE2 models to be obtained and replication of the CFD pressureprofile as closely as possible in the "head" and "foot". The hydrostaticpressure drop in the CATHARE2 hot fuel element model (with a mass flowrate of 42.955 kg/s) is 388.5 kPa (+0.01% compared to CFD) and the totalpressure drop is 348.4 kPa (+0.75% compared to CFD).

Finally, the hot channel was split into eight sub-channels, with the correctmass flow rates obtained by adjusting singular pressure drop values in eachsub-channel. Otherwise the model was left unaltered.

Hot fuel element channel under nominal conditions

Power is defined in a power density form, having 99 axial elements in themeat zone of the fuel plates. The axial and the azimuthal normalized powerdensity profiles are illustrated in Figure 6.4. In the case of a subdividedhot channel azimuthal factors seen in Figure 6.4 are used and in the case ofan undivided hot channel an azimuthal factor of 1.055 is utilized in orderto give a limiting envelope case. In both models, the hot channels radialnormalized power factor is 1.243 and the power is split in such a way thatexactly 1/3rd of it is deposed in each sector of the hot fuel element.

Figure 6.4: Normalized power density profiles: (a) axial and (b) azimuthaland (c) radial. In case of the undivided hot channel model an azimuthalfactor of 1.055 is used.

This conservatism used here (similar to that described in [21]) results in thehot channel power peaking factor of 3.039 for both models. Accordingly,


the total power distributed into the hot channel in the subdivided case is187.9 kW and in the case of undivided model 198.3 kW (187.9·1.055). Inthe CFD calculations a more realistic power distribution [29, 23] was used,resulting in a total power of 169.5 kW distributed into the hot channel.The heat exchanger approach described in the following subsection has amore realistic power distribution, with the total power distributed into thehot channel being 168.1 kW. The total power within the hot fuel elementschannel is 5.408 MW in all models.

Under nominal condition, there is a small difference between the CFDand CATHARE2 models mass flow splits, see Table 2.1. There is a slightoverflow in the ECCSM and SPCC channels and an underflow in the SCCM.

Next, the thermal results will be compared. One of prominent parametersto compare is the safety margin. While calculating the safety margin, oneshould take note of the heat transfer coefficient uncertainty in Equation 2.9.The uncertainty arises from using the Dittus-Boelter correlation (Equation2.7). In [23] the Dittus-Boelter correlation was compared with the heattransfer coefficient obtained in the hot channel under nominal conditionand it was observed that the Dittus-Boelter correlation underestimates hby an average of 15.9%, varying axially (min= 3.8%, max= 25.6%). TheDittus-Boelter correlation also does not account for entrance effects andtherefore one possibility is to use an axial dependent uncertainty functionf(z), that can be obtained by using the results from [23].

On the other hand, in another recently published study [32] the Dittus-Boelter correlation was compared to the SULTAN-JHR experimentalresults. The experimental conditions were selected to be as close aspossible to those in the JHR and rectangular channels were used as a goodapproximation to the JHR channels. From their results it can be concludedthat the Dittus-Boelter correlation underestimates h by at least 20%. Thisvalue of 20% corresponds to the channel gap size of 2.1 mm and in case ofJHR, it is smaller. The uncertainty value increases as the channels gap sizedecreases and reaches 50% in the case of a 1.5 mm. In our calculation 20%is used as a conservative value, giving a lower safety margin value. Whencalculating safety margin in transition zone (2000<Re<4000) a Reynoldsnumber dependent linear interpolation function for h is utilized.

Minimum safety margin values with different approaches to the uncertaintyare summarized in Table 6.2. The results clearly show that the minimumsafety margins without uncertainty are underestimated by upto nearly 20C(68.4C VS 48.6C in SubCh1) and indicate the need to utilize the heattransfer coefficient uncertainty for obtaining more realistic values. By


comparing values obtained with a constant 20% uncertainty with the axiallydependent ones, one can see that the latter approach gives smaller absolutevalues and that both have minimum values in the second sub-channel. Inthe full channel approach the minimum safety margin is underestimatedby 8.3-10.2% and the corresponding underestimation in the sub-channelapproach is 7.2-9.2%. In order to exactly match the minimum safetymargin value, an uncertainty of 30% should be used, see Table 6.2. It wasverified that by using the conservative approach for estimating h (20%) weare underestimating the minimum safety margin values. Minimum safetymargin axial profiles for the undivided channel and for the two sub-channelscontaining the lowest values are illustrated in Figure 6.5.

Table 6.2: Hot channels minimum safety margins [C]. Half plate approach.

CFD SPCC SubCh1 SubCh2 SubCh3 SubCh4 SubCh5 SubCh6 SubCh7 SubCh8 Min(SubCh)M(0%) 68.4 48.9 48.6 50.4 53.3 54.2 54.6 54.3 51.7 50.6 48.6M(20%) 62.7 64.9 63.5 66.0 66.8 67.2 66.9 64.6 66.6 63.5M(f(z)%) 61.4 64.3 62.1 64.6 65.4 65.8 65.4 63.2 65.9 62.1M(30%) 68.0 71.29 68.4 70.8 71.5 71.9 71.6 69.5 72.8 68.4

Figure 6.5: Safety margin profileswith uncertainties in: (a) undividedhot channel, (b) sub-channel 1 and (c)sub-channel 2.

Another parameter to compareis the temperature rise in thehot fuel element channel. Inboth of the CATHARE2 models,the fluid temperature increased by30.3C, this is 3.0% greater thanin the CFD (29.4C). The hotchannel’s temperature increase inthe undivided approach is 51.0C,which is 16.4% more than in theCFD (43.8C). In the subdividedapproach, the increase is sub-channel dependent having a valueof around 31C in the outer sub-channels and around 51C in theinner six sub-channels, giving amass flow averageincrease of 48.5C for the entire hotchannel. The differences in the hotchannel temperature increase fordifferent models is approximatelyproportional to the different powerdepositions (198.3 kW VS 187.9 kW


Figure 6.6: Hot fuel assemblyhot sector modeling in the heatexchanger approach. Nine waterchannels are colored blue and theeight heat exchangers, representingthe heated part of the fuel plates, arecolored red.

Figure 6.7: Safety margin profilesin the hot channel. Heat exchangerapproach.

VS 169.5 kW).

The final value to compare is the hot channel’s outlet temperature. In theundivided hot channel case the maximum temperature is 83.2C and in thesubdivided approach 85.2C. The former overestimates the CFD surface-averaged value (75.9C) by 7.3C and second one by 9.3C.

This comparison has shown that the conservative assumptions of thereference modeling significantly change the results with respect to the morerealistic hypotheses used in the CFD modeling. Next, a more realisticCATHARE2 model will be introduced.

Hot fuel element channel with heat exchanger approach

In this approach a more realistic modeling is utilized. Compared to theprevious models, the hot sector modeling has been modified. The fuel platezone is modeled using nine 1D modules, one per channel, and adjacentchannels are thermally connected via heat exchangers, representing the fuelplates. A schematic of the hot sector modeling in this approach can be seenin Figure 6.6.

No assumptions are made on the fuel plate power distribution between thechannels adjacent to it and the power within the sectors of the hot fuelelement is based upon the results of neutronic calculation [29]. Now, insteadof an equal 1/3rd division of power between the sectors, the hot sector haspower equal to 1.06 times the average sector power and the correspondingfactor for the mean sector is 0.97. As in the other CATHARE2 models,each 1D element has axially 149 elements where 99 of these represent the


fuel meat zone.

In addition, a CATHARE2 subroutine used for the computation of heattransfer from wall to liquid in case of a heat exchanger had to be modifiedin order to utilize the same correlations as described in RJHCHANL, seeEquations. 2.3-2.8.

Mass flow distribution between the flow channels and pressure drops wereadjusted under cold conditions using a methodology described above,with the results shown in Table 6.1. After introducing hot conditionsit was possible to compare the CATHARE2 results obtained with theheat exchanger approach to the CFD results obtained with the half plateapproach. The most noticeable difference lies in the mass flow split, seeTable 6.1. Mass flow through the average sector (ECCSM) is increased by2.18% and is reduced in the hot sector 4.35%. The reduction in the hotchannel is 4.43%.

The power split between channels in the heat exchanger approach aresummarized in Table 6.3. For the first plate, the half plate approach nearlyperfectly valid. The next three plates have an approximately 49%-51% split,the majority of the power deposited in the channel furthest from the fuelassembly center. In plates five to seven the power split slightly homogenizeswith each plate. Plate eight has the most heterogeneous power split 46.6%-53.4% due to the ninth channel, which has the highest mass flow through itand therefore providing more effective cooling. The total power depositioninto the hot channel is 168.1 kW (-1.4 kW compared to the CFD).

Table 6.3: Power split between channels in the heat exchanger as fuel plateapproach.HeatExch.i HeatExch.1 HeatExch.2 HeatExch.3 HeatExch.4 HeatExch.5 HeatExch.6 HeatExch.7 HeatExch.8Chan.i 49.98% 48.94% 48.99% 49.03% 49.16% 49.25% 49.35% 46.60%Chan.i+1 50.02% 51.06% 51.01% 50.97% 50.84% 50.75% 50.65% 53.40%

The minimum safety margin values for each of the nine channels arecollected into Table 6.4. The hot channels safety margin without uncertaintyis 55.4C (-13.0C) and 68.8C (+0.4C) with the 20% uncertainty asdescribed above. This model overestimates the minimum safety marginvalue by less than 0.6%, whilst using uncertainty. Minimum safety marginaxial profiles in the hot channel are shown in Figure 6.7. The temperatureincrease in the hot fuel element is 30.3C (+0.9C) and in the hot channel45.6C (+1.8C), whilst the hot channel outlet temperature is 77.8C. Withthis approach, the temperature increase in the hot channel differs from theCFD by 4.1%.

6.3. FULL REACTOR MODELING 61

Table 6.4: Hot sectors minimum safety margins [C]. Heat exchangerapproach.

CFD0.5plate Chan.1 Chan.2 Chan.3 Chan.4 Chan.5 Chan.6 Chan.7 Chan.8 Chan.9 Min(Chan.)M(0%) 68.4 57.9 55.4 86.8 89.2 91.2 92.4 92.8 93.5 105.5 55.4M(20%) 73.1 68.8 90.3 92.3 93.8 94.7 95.0 95.6 112.0 68.8

Mean fuel element channel

The mean fuel element channel is modeled in a manner similar to that ofthe hot fuel element channel, with the only difference being in the fuel platezone. The fuel plate zone is modeled with only one axial element (ECMOY).The cross-sectional area and perimeter values used in ECMOY can be seenin Figure 6.3. Hydraulically, the "foot" and the "head" in the mean fuelelement channel are identical to those utilized in the case of the hot fuelelement channel. Pressure drops in cold conditions are also similar. Undernominal conditions, the minimum safety margin values in the mean fuelelement’s channel are 106.7C, 112.7C and 111.7C, for uncertainties of0%, 20% and f(z)%, respectively.

6.3 Full reactor modeling

The previous subsections described three different hot fuel element channelmodeling methods in addition to the mean fuel element channel model.From these three, the models with undivided hot channels (one for eachapproach) were chosen for implementation into the reference CATHARE2full reactor model [21]. While introducing the hot fuel element channeland mean fuel element channel models into the full reactor model, asseen in Figures 6.1 and 6.2, the mass flow split within the reactor wasadjusted, under cold conditions (32.1C), in order to obtain the distributionsummarized in Table 4.3 by fine-tuning singular pressure drops. At thesame time it was ensured that the most realistic possible pressure rangewas produced within the hot channel. The resulting mass flow split withinthe reactor (with both approaches) is shown in Table 6.5. There it can beseen that the mass flow within the hot fuel element channel is 0.9811 [24] ofthe average value (42.955 kg/s) with the reminder of the total (1546.38 kg/s)passing through the mean fuel element channel. The relative error limit foran acceptable mass flow split was fixed at 0.05%. Finally, the pressurein the lower plenum (BOITE, see Figure 6.1) and in the upper plenum(SUP_CAI, see Figure 6.1) was modified to give identical values to those


found in [24]. All the improvements made are located within the JHRreactor block (Figure 6.1). The primary and secondary circuit modelingwas left unchanged from that described in [21].

Table 6.5: Full reactor mass flow rates [kg/s] under cold conditions (32.1C).

Aim 0.5 plate appr. ∆ [%] Heat exch. appr. ∆ [%]DISPO 22.350 22.357 +0.03 22.357 +0.03DISPO3 12.070 12.074 +0.03 12.076 +0.05ECMOY 1505.237 1504.255 +0.00 1504.248 +0.00HFEC 42.143 42.143 +0.00 42.143 +0.00BIPASSE 50.830 50.839 +0.02 50.839 +0.02LAMCAI 60.370 60.363 -0.01 60.363 -0.01AC 25.080 25.069 -0.04 25.069 -0.04AP 5.280 5.278 -0.04 5.278 -0.04AS 5.070 5.067 -0.05 5.067 -0.05*see Figs. 1.1-1.2 for part names. HFEC- hot fuel element channel.

Next, some parameters are quantified in the format result1|result2, wherethe former originates from the half plate approach and the latter from theheat exchanger approach. Under nominal conditions, the mass flow ratethrough the hot channel is 0.94|0.88 kg/s. The maximum water temperaturein the hot channel, the maximum cladding outer (wet) surface temperature,the maximum cladding temperature and the maximum fuel temperature arerespectively 82.7|78.1C, 146.1|140.1C, 210.2|197.8C and 283.1|261.8C.Furthermore, the minimum safety margins are having the following valuesof M=50.3|55.3C and M(20%)=64.2|68.7C.

By comparing the two different approaches, it can be seen that the first onegives results closer (although still more realistic) to the previous approach[21] due to the conservatism applied (e.g. maximum azimuthal powerpeaking factor 1.055 used in the full hot channel, 50-50 power split in fuelplates). The second approach should give more realistic results. As for thesafety margins, M and M(20%), M(20%) is producing more realistic valuesdue to Dittus-Boelter underestimating h by at least 20%. Lastly, it shouldbe pointed out that under the nominal steady-state conditions, the newaverage pressure in the lower plenum exceeds the one in the previous fullreactor model [21] by 1% with both approaches.

Chapter 7

Conclusions

The JHR’s high performance (e.g. high neutron fluxes, high power densities)and its design (e.g. narrow flow channels in the core) render the reactormodeling challenging compared to more conventional designs, requiringmore sophisticated tools and adapted models/meshing. The initial thermal-hydraulic methodology for designing the reactor was based on two codes: thesystem code CATHARE2 which simulates the full reactor with a simplifiedapproach for the core. The results are used as boundary conditions forthe three-dimensional FLICA4 core simulation. This initial modelingwas undertaken by a design team by using their expertise, state-of-artrecommendations and code utilization guidelines.

Experience has shown that this modeling could be further simplifiedand improved by using solely CATHARE2 and introducing more realisticparameters in the calculations. This would both shorten the computationaltime and give more accurate core level data. The CFD simulations wereused to achieve a better insight of the hydraulic and thermal aspects ofthe reactor’s performance. This would also assess the initial modelingassumptions (and accordingly the design, the improvement of the model,a new evaluation of the safety margin, etc.) and detect the possiblerequirement for more accurate physical modeling. This is first time in Francethat CFD has been used to validate reactor modeling with a system code.CFD analysis also helps to assess the conservatism inherent in the referenceCEA methodology.

The primary outcome of this four year PhD research project is an improvedCATHARE2 model of the JHR with two modeling approaches for the coreand the hot fuel element. In order to achieve this, significant work has beenrequired in diverse subjects as described in the following paragraphs.

The CATHARE2 and STAR-CCM+ codes were mastered whilst a basiclevel of competence was gained with the FLICA4 code. The referencestate-of-the-art CEA methodology for modeling and the main JHR relatedcorrelations were studied and are described in Chapter 2. The reactorperformance during a loss of flow accident was analyzed [21].

63

64 CHAPTER 7. CONCLUSIONS

CFD simulations of the reactor internals were performed to allow forbenchmarking as described above. In order to do this, CAD modelswere produced, representing the entire reactor vessel, the hot fuel elementand the hot channel (+ surrounding structural material). The meshingof these models was demanding due to the size and complexity of thedesign, exacerbated by the asymmetry. CFD simulations performed includehydraulic, thermal-hydraulic and thermal-hydraulic with conjugate heattransfer.

A large part of the work involved physical interpretation of the CFD results.The FLICA4 and STAR-CCM+ descriptions of the hot channel performancewere compared, see Chapter 3.

As detailed in Chapter 4, the mass flow distribution in the hot fuel elementwas compared and described under both cold and nominal conditions. Thisallows the mass flow rate of the hot channel to be determined. The flowfield around the bottom and top end caps was described and its influence onthe mass flow split between the fuel channels investigated. Pressure dropsand temperature distributions in the various hot fuel element sections wereevaluated. Maximum temperatures and the safety margin within the hotfuel channel and surrounding material were reported. The heat transfercoefficient calculated within the hot channel was compared to prominentcorrelations and the results analyzed.

Chapter 5 discusses the work performed in order to study and describe thehydraulic flow within the reactor vessel. An important outcome of this isthe determination of the mass flow distribution between the fuel elements,including the mass flow rate within the hot fuel element. The pressurefield in the upper and lower plenums of the reactor is described. A specificthermal-hydraulic calculation of the hot fuel element with the reduced massflow rate was undertaken.

All the acquired understanding was utilized in order to produce animproved, more realistic and purely CATHARE2 based JHR model, seeChapter 6. This study shows that more precise core modeling includingadaption of the local thermal-hydraulic conditions to better describe theaverage behavior of the core and hot fuel assembly can improve the referenceCATHARE2 model and consequently more accurately evaluate the safetymargin. However, one can conclude that there is no need for fundamentalmodification of the physical model(s), because the reference CATHARE2model is consistent with the phenomena observed in the CFD calculations.

The following major improvements of the CATHARE2 model of the JHR

65

have been shown to produce more realistic results:

• Modifications were carried out only within the reactor block. Therewas no need to change the primary circuit modeling.

• The mean core channel with a weight of 36 was split into a hot fuelelement channel and a mean core channel with a weight of 35. Thehot fuel element’s fuel zone was divided into a hot sector and a meansector with a weight of two.

• All nine channels in the hot sector were modeled and each fuelplate was modeled via a heat exchanger element. This allows fora more realistic prediction of the power split into the adjacent coolingchannels when compared to the 50%-50% power split assumed in thehalf plate approach. The CATHARE2 subroutine related to heatexchangers had to be modified in order to utilize the JHR channelrelated correlations.

• It was found that it is not necessary to split the hot channelazimuthally into sub-channels, provided that the maximum azimuthalfactor is utilized to give a limiting envelope case.

• Flow and pressure distributions within the reactor block (including ineach channel of the hot fuel element) were adjusted in order to matchthe latest CFD findings. The mass flow rate heterogeneities betweenthe fuel elements are shown to be small. An important conclusion isthat under cold conditions, the mass flow rate through the hot fuelelement is 98.1% of the average one.

• The mesh count within each fuel element’s sub-model was increasedin order to better represent the geometry and the flow/pressuredistribution.

• The power split within the reactor has been given a more realisticdistribution.

• The latest evaluation of the heat transfer coefficient was taken intoaccount.

This improved CATHARE2 model compares well to the CFD descriptionof the reactor’s performance. Under nominal reactor operating conditions,these modifications led to a significant increase in the safety margin of about23.7C when compared to the more conservative reference model. Wheninvestigating a loss of flow accident scenario, the corresponding increase is27.8C, as described in [21, 25].

66 CHAPTER 7. CONCLUSIONS

The following observations were made regarding different empiricalcorrelations:

• Under cold conditions (32.1C), it has been shown that the Blasiusand Colebrook correlations underestimate the pressure drop andconsequently overestimate the average mass flow rate in the secondchannel (the hot channel) of the JHR fuel assembly by 4.1% and 4.6%,respectively.

• The standard Dittus-Boelter correlation underestimates heat transfercoefficient by at least 20% compared to the CFD results [23]. A similarconclusion was reached from the SULTAN-JHR experiments [32].

• Compared to the CFD results [23] the wall friction coefficient derivedfrom the SULTAN-JHR experiments and used in CATHARE2 for theJHR heated channels overestimates frictional pressure drop in the hotchannel by 17.2%.

The improved CATHARE2 model of the JHR will be used to re-evaluatethe impact of manufacturing tolerances and to analyze the core behaviorunder both nominal conditions and accidental situations while using morerealistic assumptions than in the reference model. The obtained CFDresults could be used in order to split the upper and lower plenums intosmaller subdomains and to improve their description. The reactor coremodeling could be further improved by explicitly modeling the 36 fuelelements separately as opposed to grouping them and modeling the averageparameters. If more accurate modeling of the temperature distribution isrequired, each channel in the hot fuel element could be divided into multiplesub-channels.

As for the CFD model of the full reactor, future work could investigatethe influence of the turbulence model on the results. In addition, the powerdistribution could be added to the CFD model, allowing it to be employedfor simulating a reactor design basis accident in transient mode. The currentCFD model could be improved by accounting for manufacturing tolerancesand the operational effects on the fuel plates (oxidation, thermal expansion,swelling, etc...).

Bibliography

[1] CEA. The Jules Horowitz Reactor (JHR). http://www.cad.cea.fr/rjh, 2013. Accessed 22 September 2013.

[2] J.P. Dupuy, G. Perotto, G. Ithurralde, C. Leydier, and X. Bravo.Jules Horowitz Reactor General layout, main design options result-ing from safety options, technical performances and operating con-straints. Joint meeting paper, TRTR-2005/IGORR-10, Gaithersburg,Maryland, USA, 2005.

[3] G. Bignan, P.M. Lemoine, and X. Bravo. Jules Horowitz Reactor: ANew European MTR (Material Testing Reactor) Open to InternationalCollaboration: Description and Status. Conference paper, RRFM 2011,Rome, Italy, 2011.

[4] D. Iracane, P. Chaix, and A. Alamo. Jules Horowitz Reactor: ahigh performance material testing reactor. Comptes Rendus Physique,9:445–456, 2008.

[5] Christian Gonnier. The Jules Horowitz research reactor. A new highperformance MTR in Europe. Seminar presentation, IVA Seminar,Stockholm, Sweden, 2013.

[6] P. Lemoine. Fuel design and LEU development for the Jules HorowitzReactor. Symposium presentation, NAS-RAS Symposium on the Con-version of RR to LEU fuel, Moscow, Russia, 2011.

[7] Patrizio Console Camprini. Power Transient Analysis of ExperimentalDevices for Jules Horowitz Testing Reactor (JHR). PhD dissertation,University of Bologna, Engineering Faculty, 2013.

[8] CEA. CATHARE : Advanced Safety Code for Pressurized Water Re-actors. http://www-cathare.cea.fr, 2006. Accessed 22 September2013.

[9] G. Geffraye, O. Antoni, M. Farvacque, D. Kadri, G. Lavialle,B. Rameau, and A. Ruby. CATHARE 2 v2.5_2: A single version forvarious applications. Nuclear Engineering and Design, 241:4456–4463,2011.

[10] F. Barre and M. Bernard. The CATHARE code strategy and assess-ment. Nuclear Engineering and Design, 124:257–284, 1990.

67

68 BIBLIOGRAPHY

[11] CEA. CATHARE 2 User Guide - General Description of theCATHARE 2 V2.5_2mod8.1 System Code, 2012.

[12] M. Polidori. Implementation of Thermo-Physical Properties andThermal-Hydraulic Characteristics of Lead-Bismuth Eutectic and Leadon CATHARE Code. Report rds/2010/51, ENEA, 2010.

[13] S. Aniel, A. Bergeron, P. Fillion, D. Gallo, F. Gaudier, O. Gré-goire, M. Martin, E. Richebois, E. Royer, P. Salvatore, S. Zimmer,T. Chataing, P. Clément, and F. Francois. FLICA4: Status of nu-merical and physical models and overview of applications. Conferencepaper, The 11th International Topical Meeting on Nuclear ReactorThermal-Hydraulics (NURETH-11), Avignon, France, 2005.

[14] E. Royer and N. Todorova. Computation of BWR Turbine Trip withCRONOS2 and FLICA4. Conference paper, PHYSOR 2002, Seoul,Korea, 2002.

[15] André Bergeron, Daniel Caruge, and Philippe Clémen. Assessment ofthe 3-D Thermal-Hydraulic Nuclear Core Computer Code FLICA-IVon Rod Bundle Experiment. Nuclear Technology, 134(1):71–83, 2001.

[16] A.-M. Baudron, N. Crouzet, C. Döderlein, A. Geay, J.-J. Lau-tard, E. Richebois, E. Royer, and P. Siréta. Unstructured 3D MI-NOS/FLICA4 coupling in SALOME. Application to JHR transientanalysis. Conference paper, International Conference on the Physics ofReactors "Nuclear Power: A Sustainable Resource", Interlaken, Swiz-erland, 2008.

[17] I. Toumi, A. Bergeron, D. Gallo, E. Royer, and D. Caruge. FLICA-4: a three-dimensional two-phase flow computer code with advancednumerical methods for nuclear applications. Nuclear Engineering andDesign, 200:139–155, 2000.

[18] CD-adapco. STAR-CCM+ Version 9.06 User Guide, 2014.

[19] CD-adapco. STAR-CCM+ website. http://www.cd-adapco.com/products/star-ccm, 2016. Accessed 22 September 2016.

[20] Viable Computing. CD adapco Group Releases STAR-CCM+. http://www.cfdreview.com/newsoftware/04/05/06/1358254.shtml,2004. Accessed 22 September 2016.

[21] R. Pegonen, S. Bourdon, C. Gonnier, and H. Anglart. A review of thecurrent thermal-hydraulic modeling of the Jules Horowitz Reactor: Aloss of flow accident analysis. Nucl. Eng. Des., 280:294–304, 2014.

BIBLIOGRAPHY 69

[22] R. Pegonen, S. Bourdon, C. Gonnier, and H. Anglart. Hot fuel ele-ment thermal-hydraulic modeling in the Jules Horowitz Reactor nom-inal and LOFA conditions. Conference paper, The 16th InternationalTopical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-16), Chicago, USA, 2015.

[23] R. Pegonen, S. Bourdon, C. Gonnier, and H. Anglart. Hot fuel elementthermal-hydraulics in the Jules Horowitz Reactor. Nucl. Eng. Des.,300:149–160, 2016.

[24] R. Pegonen, S. Bourdon, C. Gonnier, and H. Anglart. Hydraulic mod-eling of the Jules Horowitz Reactor: Mass flow split between 36 fuelelements. Nucl. Eng. Des., 308:9–19, 2016.

[25] R. Pegonen, S. Bourdon, C. Gonnier, and H. Anglart. An improvedthermal-hydraulic modeling of the Jules Horowitz Reactor using theCATHARE2 system code. Nucl. Eng. Des., 311:156–166, 2017.

[26] M. Boyard, J. M. Cherel, C. Pascal, and B. Guidon. The Jules HorowitzReactor core and cooling system design. Joint meeting paper, TRTR-2005/IGORR-10, Gaithersburg, Maryland, USA, 2005.

[27] E. Royer. Private communications, 2013.

[28] E. Royer and I. Toumi. CATHARE-CRONOS-FLICA, Coupling withISAS: a Powerful Tool for Nuclear Studies. Conference paper, 6thInternational Conference on Nuclear Engineering , San Diego, USA,1998.

[29] B. Pouchin. Private communications, 2013.

[30] J.-F. Pages. Private communications, 2013.

[31] I. E. Idel’cik. Memento des pertes de charge. Idel’chik éditions Eyrolles,1986.

[32] A. Ghione, B. Noel, P. Vinai, and C. Demaziere. Assessment ofthermal-hydraulic correlations for narrow rectangular channels withhigh heat flux and coolant velocity. International Journal of Heat andMass Transfer, 99:344–356, 2016.

[33] K. Engelberg-Forster and R. Greif. Heat Transfer to a Boiling Liquid:Mechanism and Correlation. Transactions of the ASME, Journal ofHeat Transfer, 81:43–53, 1959.

[34] F. W. Dittus and L. M. K. Boelter. Heat transfer in automobile ra-diators of the turbular type. University of California Publications inEngineering, 2:443–461, 1930.

70 BIBLIOGRAPHY

[35] R. K. Shah and A. L. London. Laminar Flow Forced Convection HeatTransfer and Flow Friction in Straight and Curved Ducts- A Summaryof Analytical Solutions. Report, Stanford University, Stanford, USA,1971.

[36] AREVA TA. Project RJH. Fuel element technical drawings, 2011.

[37] CD-adapco. Best Practice Workshop: Heat Transfer. Workshop pre-sentation, STAR South East Asian Conference 2012, Singapore, 2012.

[38] M. Peric. Flow simulation using control volumes of arbitary polyhedralshape. ERCOFTAC Bulletin, 62, 2004.

[39] NRC. Appendix A. Material Properties for COBRA-SFS Model of TN-68 Cask. http://pbadupws.nrc.org/docs/ML0524/ML052490246.pdf, 2001. Accessed 6 January 2015.

[40] ASM Aerospace Specification Metals, Inc. Aluminium 6061-t6; 6061-t651. http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6, 2015. Accessed 6 January 2015.

[41] P. Sireta. Private communications, 2014.

[42] David C. Wilcox. Turbulence Modeling for CFD. DCW Industries,California, USA, third edition, November 2006.

[43] J. Boussinesq. Essai sur la théorie des eaux courantes. Mémoiresprésentés par divers savants à l’Académie des Sciences XXIII, 1:1–680,1877.

[44] R. Pegonen, N. Edh, K. Angele, and H. Anglart. Investigation of Ther-mal Mixing in the Control Rod Top Tube Using Large Eddy Simula-tions. Journal of Power Technologies, 94(1):67–78, 2014.

[45] Armando Gallegos-Muñoz, Nicolás C. Uzárraga-Rodriquez, and Fran-cisco Elizalde-Blancas. Conjugate heat transfer in ribbed cylindricalchannels. In Salim N. Kazi, editor, An Overview of Heat Transfer Phe-nomena, chapter 16, pages 469–496. InTech, Rijeka, 2012.

[46] T.-H. Shih, W. W. Liou, A. Shabbir, Z. Yang, and J. Zhu. A newk-epsilon eddy viscosity model for high reynolds number turbulentflows: Model development and validation. Technical report, NASATM 106721, NASA Lewis Research Centert, Cleveland, OH, UnitedStates, 1994.

[47] Andre Bakker. Applied Computational Fluid Dynamics, Lecture10- Turbulence models. http://www.bakker.org/dartmouth06/engs150/, 2008. Accessed 8 January 2016.

BIBLIOGRAPHY 71

[48] C. P. Tzanos and B. Dionne. Computational Fluid Dynamics Analy-ses of Lateral Heat Conduction, Coolant Azimuthal Mixing and HeatTransfer Predictions in BR2 Fuel Assembly Geometry. Technical re-port, Argonne National Laboratory, May 2011. ANL/RERTR/TM-11-21.

[49] E. N. Sieder and G. E. Tate. Heat Transfer and Pressure Drop ofLiquids in Tubes. Ind. Eng. Chem, 28:1429–1436, 1936.

[50] B. S. Petukhov and V. N. Popov. Theoretical Calculation of Heat Ex-change in Turbulent Flow in Tubes of an Incompressible Fluid withVariable Physical Properties. High Temp., 1(1):69–83, 1963.

[51] V. Gnielinski. New Equations for Heat and Mass Transfer in TurbulentPipe and Channel Flows. Int. Chem. Eng., 16:359–368, 1976.

[52] V. Gnielinski. Wärmeübertragung im konzentrischen Ringspalt und imebenen Spalt. In VDI Wärmeatlas, 8. Auflage, pages S Ga 1–GA 9.Springer-Verlag, Berlin, 1997.

[53] G. K. Filonenko. Hydraulic resistance in pipes. Teploenergetika,1(4):40–44, 1954.

[54] Compass Ingenieria y Sistemas. Turbulence Handbook, 2015.

72 BIBLIOGRAPHY

development of an improved thermal-hydraulic modeling of the jules horowitz …1053103/... · 2016....

Documents