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(1)Faculty of Physics and Applied Computer Science. Doctoral thesis Mikołaj Oettingen. Validation of fuel burnup modelling with MCB Monte Carlo system using destructive assay data from Ohi-2 PWR. Supervisor: Dr hab. inż. Jerzy Cetnar AGH University of Science and Technology, Faculty of Energy and Fuels. Krakow, September 2013.

(2) Declaration of the author of this dissertation: Aware of legal responsibility for making untrue statements I hereby declare that I have written this dissertation myself and all the contents of the dissertation have been obtained by legal means.. date, signature of author. Declaration of the thesis Supervisor: This dissertation is ready to be reviewed.. date, signature of supervisor. i.

(3) Acknowledgments I am extremely grateful to my PhD advisor, Prof. Jerzy Cetnar for his great scientific support, friendly help and loads of patience. I owe a deep sense of gratitude to the supportive staff of the Chair of Nuclear Energy, in particular, to Prof. Stefan Taczanowski, Prof. Jerzy Janczyszyn, Dr Grażyna Domańska and Dr Mariusz Kopeć for their guidance during my graduate and PhD studies. Finally, my thanks go to my family and friends for always encouraging me to reach my goals and for their love and support for my endeavours.. Mikołaj Oettingen. ii.

(4) Abstract The thesis is devoted to the validation of fuel burnup modelling with MCB Monte Carlo system using destructive assay data from Ohi-2 Pressurized Water Reactor. Section 1 describes motivation and objectives of the study as well as its significance for the international scientific community. Section 2 gives the concept of the Pressurized Water Reactor on the basis of the 4loop Westinghouse reactor, which is installed in Ohi nuclear power plant, unit 2. The PWR is described from the technical point of view. Particular attention is given to the explanation of the role of the reactor components which are significant for the core neutronics and thus fuel burnup, e.g. burnable poison. The design and functions of reactor pressure vessel internals as well as in-core components are shown. The engineering design of the 17x17 fuel subassembly used for the development of the numerical model for validation of fuel burnup modelling using the MCB system is explicitly described. Section 3 deals with the principles of the Monte Carlo modelling of the reactor physics. Firstly, general features and possible usage areas of the MCB code are presented. Next, the nuclear data evaluations used for validation of fuel burnup modelling are reviewed. The last two sub-sections focus on the numerical set-up implemented in the MCB code for neutron transport and burnup calculations, respectively. Practical issues related to the construction of the numerical model, including transformation of the engineering specification to the computational geometry are also presented. Section 4 presents results of the fuel burnup validation obtained in the numerical modelling using MCB. First, the methodology developed for the numerical reconstruction of the Ohi-2 irradiation experiment and the characteristics of the developed numerical model are shown. Analytical methods used for the measurements of the final actinide concentrations are also described. Next, the general performances of the investigated fuel sub-assembly obtained in the numerical simulation are evaluated in terms of their consistence with principles of the reactor physics. Finally, the measured and calculated actinide concentrations are compared, which is the main goal of the burnup validation. In addition, obtained calculated-toexperiment ratios are compared with the results of other burnup validation studies. Section 5 concludes the major scientific outcome of the thesis, summarizes presented study and recommends directions for future research in the domain of burnup validation using the MCB system.. iii.

(5) Streszczenie Celem niniejszej pracy jest walidacji modelowania wypalania paliwa za pomocą systemu Monte Carlo MCB z wykorzystaniem danych z pomiarów niszczących paliwa jądrowego z reaktora PWR – Ohi-2. Rozdział 1 opisuje cele przedstawionej monografii jak również istotność wykonanych badań dla międzynarodowego środowiska naukowego. Rozdział 2 przedstawia zasady działania lekko-wodnego ciśnieniowego reaktora PWR na przykładzie 4-pętlowego reaktora firmy Westinghouse. Ten typ rektora jest zainstalowany w drugiej jednostce elektrowni jądrowej Ohi, gdzie została naświetlona kaseta paliwowa z której pobrano próbki do badań niszczących. Rektor jest opisany z technicznego punktu widzenia ze szczególnym uwzględnieniem komponentów mających wpływ na neutronikę rdzenia a tym samym na proces wypalania paliwa jądrowego. Rozdział również opisuje konstrukcję oraz funkcje głównych elementów zbiornika ciśnieniowego oraz rdzenia reaktora, przede wszystkim kasety paliwowej typu 17x17, której model został zaimplementowany numerycznie w celu przeprowadzenia obliczeń walidacyjnych. Rozdział 3 obrazuje teoretyczne podstawy modelowania Monte Carlo fizyki rdzenia reaktorów jądrowych. W pierwszej kolejności autor opisuje właściwości oraz obszary zastosowania systemu MCB. Następnie zaprezentowane są wykorzystane w obliczeniach ewaluacje danych jądrowych. Ostatnie dwie sekcje opisują aparat matematyczny zaimplementowany w systemie MCB do opisu zagadnień transportu neutronów oraz procesu wypalania paliwa jądrowego. Dodatkowo przedstawione są praktyczne aspekty związane z budową modelu numerycznego takie jak transformacja geometrii inżynierskiej na geometrię numeryczną. Rozdział 4 prezentuje wyniki otrzymane podczas symulacji numerycznej wypalania paliwa jądrowego przy pomocy systemy MCB. W pierwszej części pokazana jest metodologia opracowana w celu rekonstrukcji eksperymentu przeprowadzonego w rektorze Ohi-2 oraz zaprojektowany model numeryczny. Następnie przedstawiono metody analityczne związane z pomiarem koncentracji aktynowców w zużytym paliwie jądrowym. Ogólna charakterystyka modelowanej kasty paliwowej otrzymana w symulacji numerycznej oraz analiza spójności otrzymanych wyników z prawidłowościami fizyki reaktorowej jest przedstawiona w kolejnym podrozdziale. Zwieńczeniem rozdziału jest analiza porównawcza zmierzonych i policzonych koncentracji aktynowców, co jest głównym celem walidacji wypalania paliwa jądrowego.. iv.

(6) Ponadto, obliczone współczynniki zgodności zostały porównane ze współczynnikami przedstawionymi w innych pracach naukowych dotyczących walidacji wypalania paliwa jądrowego. Rozdział 5 podsumowuje otrzymane wyniki, uwzględnia najważniejsze wnioski oraz zawiera rekomendacje dalszych badań naukowych w obszarze walidacji wypalania paliwa jądrowego przy użyciu systemu MCB.. v.

(7) Table of Contents Section 1. Introduction ......................................................................................................... 1. 1.1 Motivation ............................................................................................................. 2 1.2 Significance of the Study ...................................................................................... 3 1.3 Objective of the thesis ........................................................................................... 4 1.4 Author’s contribution ............................................................................................ 4 Section 2. Pressurized Water Reactor ................................................................................ 5. 2.1 Introduction ........................................................................................................... 6 2.2 The PWR plant ...................................................................................................... 6 2.3 Reactor internals ................................................................................................... 8 2.3.1 Reactor pressure vessel ................................................................................ 9 2.3.2 Reactor barrel ............................................................................................. 10 2.3.3 Baffle ......................................................................................................... 11 2.3.4 Lower internals .......................................................................................... 12 2.3.5 Upper internals........................................................................................... 12 2.3.6 Neutron reflector ........................................................................................ 13 2.4 Reactivity control ................................................................................................ 14 2.5 Reactor core ........................................................................................................ 16 2.5.1 Fuel sub-assemblies ................................................................................... 17 2.5.2 Fuel pins..................................................................................................... 21 2.5.3 The PWR fuel ............................................................................................ 23 2.5.4 Rod clusters control assembly ................................................................... 25 2.5.5 Burnable poison ......................................................................................... 27 2.6 The PWR in-core fuel management .................................................................... 30 2.6.1 Initial core loading pattern ......................................................................... 31 2.6.2 Some alternate core refuelling patterns ..................................................... 34 2.7 Water chemistry .................................................................................................. 35 Section 3. Monte Carlo modelling of reactor physics ...................................................... 37. 3.1 Introduction ......................................................................................................... 38 3.2 The MCB code .................................................................................................... 39 3.2.1 Program flow chart .................................................................................... 40 3.2.2 Definition of transmutation system ........................................................... 41. vi.

(8) 3.3 Nuclear data libraries .......................................................................................... 42 3.3.1 The Joint Evaluated Fission and Fusion libraries ...................................... 42 3.3.2 The ENDF format ...................................................................................... 44 3.3.3 The nuclear data libraries of the MCB system .......................................... 45 3.4 Monte Carlo modelling of neutron transport ...................................................... 47 3.4.1 Random sampling ...................................................................................... 49 3.4.2 Physics of interactions ............................................................................... 51 3.4.3 Geometry ................................................................................................... 55 3.4.4 Tallies ........................................................................................................ 60 3.4.5 Monte Carlo statistics ................................................................................ 63 3.4.6 Eigenvalue calculations ............................................................................. 66 3.5 Burnup calculations............................................................................................. 69 3.5.1 The general burnup equation ..................................................................... 70 3.5.2 Theoretical background of the Transmutation Trajectory Analysis ......... 71 Section 4. Validation........................................................................................................... 78. 4.1 Introduction ......................................................................................................... 79 4.1.1 Burnup validation ...................................................................................... 81 4.1.2 Related benchmarks and activities............................................................. 83 4.1.3 Methodology .............................................................................................. 85 4.2 Benchmark verification ....................................................................................... 86 4.2.1 Irradiation history ...................................................................................... 88 4.2.2 Analytical methods .................................................................................... 92 4.2.3 Experimental results .................................................................................. 96 4.3 Numerical model ............................................................................................... 100 4.3.1 Model geometry ....................................................................................... 100 4.3.2 Material composition ............................................................................... 103 4.3.3 System normalization .............................................................................. 107 4.4 System characteristics ....................................................................................... 108 4.4.1 Infinite neutron multiplication factor ....................................................... 109 4.4.2 Burnup ..................................................................................................... 112 4.4.3 Power evolution ....................................................................................... 114 4.4.4 Fuel .......................................................................................................... 118 4.4.5 Absorbers ................................................................................................. 123 4.5 Comparative analysis ........................................................................................ 136 vii.

(9) 4.5.1 Main comparison ..................................................................................... 138 4.5.2 Comparison with other validation studies ............................................... 139 4.5.3 Exact comparison..................................................................................... 143 Section 5. Conclusions ...................................................................................................... 166. 5.1 Summary ........................................................................................................... 167 5.2 Conclusions ....................................................................................................... 168 5.3 Recommendations for future work ................................................................... 172 References…………. ............................................................................................................. 174 Appendix 1 List of figures .................................................................................................... 179 Appendix 2 List of tables ...................................................................................................... 181. viii.

(10) Major nomenclature ADS – Accelerator Driven System AGH – Akademia Górniczo-Hutnicza AIC – Silver-Indium-Cadmium alloy BOL – Beginning of Life EAF – European Activation File EFF – European Fusion File ENDF – Evaluated Nuclear Data File EOL – End of Life FIMA – Fission per Initial Metal Atom GEN-IV – Generation IV nuclear reactors JAERI – Japan Atomic Energy Research Institute JEF – Joint Evaluated File JEFF – Joint Evaluated Fission and Fusion JENDL – Japanese Evaluated Nuclear Data Library KERMA – Kinetic Energy Released per Mass Unit LWR – Light Water Reactor MCB – The Monte Carlo Continuous Energy Burnup Code MCNP – A General Monte Carlo N-Particle Transport Code MOX – Mixed Oxide Fuel MPI – Message Passing Interface NEA – Nuclear Energy Agency OECD – Organization for Economic Co-operation and Development PIE – Post Irradiation Examination PWR – Pressurized Water Reactor RPV – Reactor Pressure Vessel UOX – Uranium Dioxide Fuel VVER – Vodo-Vodyanoi Energetichesky Reactor SFCOMPO – Spent Fuel Composition Database SS – Stainless Steal TTA – Transmutation Trajectory Analysis Code. ix.

(11) Section 1. Introduction. 1.

(12) 1.1. Motivation. In the thesis the author assesses the accuracy of the MCB code in predicting the isotopic composition of the spent nuclear fuel. The establishment of predictable relationship between calculated and measured nuclide concentrations is known as validation of fuel burnup modelling or simply burnup validation. The predictive capabilities of the MCB are essential for the characterization of the nuclear fuel being irradiated in the existing and newly designed nuclear systems including GEN-IV nuclear reactors. The influence of various types of nuclear fuels on reactor core performances, especially in terms of burnup extension and utilization of plutonium and minor actinides has been researched by scientific community. All studies related to the burnup validation enhance knowledge about predictability of numerical simulations in the domain of the nuclear science and engineering. This in turn leads to the extension of the international databases in the new benchmark specifications, which could be used in further burnup validation studies as the existing reference. A comparative analysis between measured and calculated nuclide concentration is an inevitable part of the burnup validation. However, not only the measured actinide concentrations but also additional data related to irradiation history and reactor design are necessary. The more reactor design and operational data are available the more reliable is the numerical reconstruction of the nuclear system. Therefore, the results could be estimated with higher accuracy. In the thesis the Ohi-2 spent fuel assay data were chosen as the reference data for the comparison with the results of the MCB numerical simulation. The spent fuel assay data obtained from Ohi-2 Pressurized Water Reactor were chosen for the burnup validation due to availability of a vast set of operational and design parameters, which was not recognized in other considered benchmarks. The burnup validation was performed using The Monte Carlo Continuous Energy Burnup Code – MCB. The MCB system is under development at the Chair of Nuclear Energy, Faculty of Energy and Fuels, AGH University of Science and Technology, Krakow, Poland. The robustness of the code was proven by series of peer-review scientific papers in the international magazines. Moreover, the code was used in six EURATOM projects related to the design of innovative nuclear systems. The development of MCB is still ongoing and therefore, validation studies are necessary to improve its calculation accuracy and maintain its high scientific value. The thesis significantly contributes to these research activities.. 2.

(13) 1.2. Significance of the Study. The Study presented in the thesis is significant for the three main areas associated with the nuclear science and engineering:. 1. Nuclear safety. Nuclear safety covers all activities related to the prevention of the nuclear and radiation accidents and mitigation of their consequences. The Study is especially important for radiological safety and criticality safety analysis. The spent nuclear fuel radiological properties could not be accurately estimated without knowledge of its final isotopic composition. During irradiation in the nuclear reactor the reactivity of the nuclear fuel is reduced due to the nuclide composition changes in the particle field. Thus, isotopic composition of the nuclear fuel during irradiation is necessary for the reactivity calculations. The composition and associated reactivity could be obtained in the numerical simulation using burnup codes, which is the scope of the criticality safety analysis. The criticality safety analysis is crucial for the nuclear reactor operation.. 2. Advanced simulation and computing of nuclear systems. The high predictive capability of the computational simulation of the high-consequence nuclear system such as nuclear reactor could be provided only with robust and reliable numerical tools. The physical phenomena governing behaviour of the nuclear system have to be reconstructed with high accuracy. The only way to evaluate the capabilities of the numerical tool is its validation.. 3. Back-end nuclear fuel cycle. Technical operations related to the management of the spent nuclear fuel discharged from nuclear reactor are called back-end fuel cycle. The spent nuclear fuel after discharge from the nuclear reactor core, interim dry or wet storage and proper conditioning could be either disposed or reprocessed. Having well validated burnup codes one could calculate final concentrations and compositions of the spent nuclear fuel with high accuracy. This allows for optimization of all steps related to the spent fuel treatment.. 3.

(14) 1.3. Objective of the thesis. 1. Assessment of the burnup capabilities of the MCB system in PWR modelling. 2. Numerical reconstruction of the Ohi-2 irradiation experiment using MCB system. 3. Evaluation of the MCB performances in predicting the isotopic compositions using Ohi-2 destructive assay data. 4. Verification of the MCB system with respect to other burnup codes and nuclear data libraries. 5. Review of the Ohi-2 destructive assay data in terms of their quality for burnup validation.. 1.4. Author’s contribution The author of the thesis developed the general framework of the Study, in particular,. found and elaborated operational and design data about Ohi-2 Pressurized Water Reactor including associated spent fuel assay data. The author built numerical model for MCB simulation, performed neutronics and burnup calculations, analyzed and interpreted the results. In general, the author has created the methodology for validation of fuel burnup modelling with the MCB system using destructive assay data from Ohi-2 PWR.. 4.

(15) Section 2. Pressurized Water Reactor. 5.

(16) 2.1. Introduction The section describes the general layout of the Western type1 Pressurized Water. Reactor (PWR) on the basis of the 4-loop Westinghouse reactor. The spent fuel samples for validation of fuel burnup modelling were taken from the fuel sub-assembly irradiated in this type of PWR at Ohi nuclear power plant – unit two. Some in-core components, which do not have significant influence on the reactor core neutronics and thus do not influence burnup performances, but are important from the technological point of view, are also described. The aim of describing these components is to present not only physical aspects of the PWR reactor but also technological ones. This approach should facilitate the understanding of the PWR not only from the theoretical point of view but also from the practical one. Section 2.2 explains the role of both primary and secondary cooling circuits of the PWR plant and their components. The main aim of section 2.3 is to describe the most important internals of the reactor pressure vessel (RPV) from the technological point of view. Section 2.4 makes reader familiar with the basis of the criticality analysis and reactivity control. The components of the reactor core and their influence on the core neutronics are explicitly described in section 2.5. The basics of the in-core fuel management are presented in section 2.6 and aspects of water chemistry in section 2.7.. 2.2. The PWR plant In general a nuclear reactor is a system producing energy from the nuclear fission of. heavy nuclei. There are many types of the nuclear reactors classified by their unique physical features, including neutron spectrum; specific material issues such as type of fuel, coolant, moderator; purpose of usage, namely, power generation, industrial heat production, research, naval propulsion systems; and many others. The most common type of the nuclear reactor used worldwide, mainly for power generation is the Pressurized Water Reactor, which was chosen as a dedicated system to perform validation of fuel burnup modelling. Nowadays, about 432 PWR reactors are in operation, 68 under construction, 162 planed and 316 proposed, all over the world [1]. Under the term Pressurized Water Reactor one understands a nuclear reactor cooled and moderated with light water under high pressure, characterized by thermal neutron 1. Term used to distinguish between Russian VVER-type reactors and Western-type reactors. A good example of. 6.

(17) spectrum. Typically, the main fuel of this kind of reactors is uranium dioxide enriched in the fissile U235. The PWR reactors contain two cooling systems, primary and secondary one. Generally, the whole cooling system may consist of two to four loops. It means that primary cooling system is connected to the reactor pressure vessel using two to four cooling loops as depicted in Fig. 1. The reactor pressure vessel, reactor coolant pumps, pressurizer, steam generator and interconnecting piping are the main components of the primary cooling system. The secondary system consists of the feed-water pumps, high and low pressure turbines, condenser and piping.. Figure 1. Cooling system of the 4-loop Westinghouse PWR [2]. Heat generated in the fission reaction of heavy nuclei is passed to the working medium (light water) in the cooling channels of the fuel sub-assemblies. Then, the water flows through the hot legs of primary cooling system to steam generator, where the heat is transferred to the feed-water of the secondary cooling system. Due to low pressure in the secondary system, the water boils and steam is generated. The steam flows through the turbines, which are coupled with electric generators. This leads to the transformation of the fission energy to the electricity. The steam exiting the turbines is directed to condensers, where it changes the state of aggregation to the water and is pumped to steam generators. The piping located after the steam generator in the primary cooling system is called the cold leg. After giving back a part 7.

(18) of the heat in steam generator the water enters the cold leg and is pumped again into the reactor core. The inlet temperature of the water in the primary cooling system is between 291oC and 293 oC, and rises to about 325oC - 330oC, so temperature difference of water between the hot and cold leg equals about 32oC - 39 oC. High pressure at the level of 15.5 MPa in the primary cooling system prevents water from boiling. The mass density of water under these conditions is about 0.7 g/cm3. The working temperature and pressure of water in the secondary cooling system are lower than in the primary one, and equal about 277 oC and 7.5 - 7.9 MPa, respectively. The thermal power2 for conventional Western-design reactors varies from about 3411 to 4270 MWth [3, 4]. The thermal efficiency of the plant, which is the ratio of the gross electrical power3 to the thermal power, for PWR is about 33%. The net electrical efficiency denoted as the ratio of net electrical power4 to the thermal power typically equals about 30% 32% and characterizes the plant efficiency in the straightforward manner [5, 2]. It should be noted, that the detailed conditions of the working medium and plant parameters depend on the particular features of the plant, but do not differ much from the specifications mentioned.. 2.3. Reactor internals The following sub-sections describe the most important in-core components of the. PWR reactor. Sections from 2.3.1 to 2.3.5 explain the role of the reactor pressure vessel, reactor barrel, baffle, lower internals and upper internals. All components listed above, comprise the reactor reflector, which is significant for the core neutronics and thus burnup. The reflector itself is described in detail in sub-section 2.3.6.. 2. Power produced in the nuclear reactor core [MW th]. It depends on the reactor type and specific engineering features as well as on the quantity and quality of the steam produced. 3 Power produced by electric generators attached to the set of steam turbines [MW e]. It considers the ambient temperature of the condenser circuit. 4 Power, which could be sent out from the plant to the grid discarding electric power, needed for running the plant.. 8.

(19) 2.3.1 Reactor pressure vessel The description of the reactor pressure vessel is based on the Westinghouse 4-loop plant, which is a good example of the Western-type RPV. The reactor pressure vessel encloses the nuclear reactor core and other auxiliary in-vessel components. It is the primary containment of the core and main component5 of one out of four physical safety barriers of the whole plant according to the defence in depth safety strategy [6]. Therefore, RPV must meet the highest quality and reliability standards to withstand normal operation conditions and abnormal transient conditions.. Figure 2. Internals of the Westinghouse 4-loop RPV [7]. The vessel has a cylindrical shape with hemispherical bottom and the upper head as plotted in Fig. 2. The bottom head is welded to the cylindrical body, whilst the upper one is bolted, which enables its removal during outages in the reactor operation for refuelling or 5. The whole barrier consists of the primary coolant boundary and all its components.. 9.

(20) inspection. The thickness of the cylindrical body equals about 21.6 cm, of the upper head about 16.5 cm and of the lower head about 14 cm. The height of the vessel is about 13 m, the diameter about 4.8 m and the weight amounts to approximately 410 metric tonnes without internals. The design pressure between 17.0 - 17.5 MPa and temperature between 340 - 350 oC characterize the Western-type vessels and these parameters stand for the main design criteria of the RPV. The vessel body and both heads, are penetrated by numerous outlet and inlet nozzles, elements of the control rod drive mechanism, safety inspection nozzles and other instrumentation. In general, fine-grained low-alloy ferritic steels are used for the vessel fabrication. The inner surfaces of the vessel are cladded with 3 to 10 mm of the austenitic stainless steel to minimize corrosion caused be the aggressive environment, especially borated water. This also reduces buildup of the corrosion products and their circulation in the primary cooling system. The cylindrical body of the vessel as well as of the both heads may be fabricated in two ways. The first method concerns welding the rolled steel plates into the radial courses and then welding them together. In the method the longitudinal and circumferential welds are used. The second method concerns only welding large ring forgings without any longitudinal welds. The region around the fuel is usually made from one large ring forging to minimize the number of welds around the fuel regions because the weld material has lower resistance to the neutron radiation than the base one [3]. The usage of one solid forging around the fuel region improves the reliability of the vessel.. 2.3.2 Reactor barrel The core (reactor) barrel is the first component installed in the RPV. Its function is to separate the inlet water flow from the core. The water coming through the cold leg enters the RPV at inlet nozzles and hits against the core barrel, where it is directed downwards and fills space between core barrel and RPV. At the bottom of the RPV water flow is reversed and directed upwards. Then, it reaches the fuel sub-assemblies, flows through cooling channels and recovers heat produced in the reactor core. At the end the hot water enters the region of the upper internals and is directed to the outlet nozzles and through the hot leg to the steam generators as mentioned in section 2.2. In some designs on the outer surface of the core barrel, the steel plates, called thermal shields or neutron pads, are located. They could encompass the whole barrel or just be placed. 10.

(21) in the strategic locations with the highest particle flux-gradients. Their function is to absorb the particle flux from the reactor core and reduce the exposure of the RPV and its embrittlement, especially in the region of the RPV welds. Hence, the life-time of the vessel is enhanced. In the 4-looop Westinghouse plants core barrel as well as thermal shields are usually fabricated using 304 SS steel. The thickness of the barrel is about 5 - 6 cm and of the thermal shield about 6 - 7 cm. The barrel is manufactured using rolled and welded steel plates. The thermal shields are fastened to the barrel by means of dowels and bolts [8].. 2.3.3 Baffle Core baffle has three important functions in the reactor core. First of all, it directs and stabilizes water flow in the core, secondly it is the carrier of the fuel sub-assemblies, lastly it assures the transition between the cylindrical core barrel and the polygonal structure of the core. The horizontal plates, called formers are the connecting elements between core barrel and core baffle, as depicted in Fig. 3. The baffle is composed of the individual plates with thickness of about 3 cm and manufactured from the carbon steel. The baffle is the in-vessel component, which must be characterized by the high reliability and accuracy of manufacturing. The baffle plates are the first solid structure around the fuel sub-assemblies. Therefore, baffle is exposed to high thermal gradients developing from the neutron and gamma heating as well as from the heat transfer into the coolant. In addition, the pressure difference between bypass and core causes the additional load. The precise positioning of the baffles is required because it is located just a few mm from the fuel sub-assemblies. The integrity of the whole structure, composed of barrel, formers and baffle plates, is ensured by the numerous bolts (1000 - 1500), see Fig. 3. The bolts are tightened with the well-defined pre-stress. During the irradiation the bolts undergo deformations caused by the thermal and mechanical stresses and the integrity of the whole structure could be violated. This causes the instability of the coolant flow and consequently some vibration of the fuel rods may occur.. 11.

(22) Figure 3. Core baffle and its connection to the core barrel using bolts [9].. 2.3.4 Lower internals The core baffle and fuel sub-assemblies are supported by the lower support structure whose main component is the lower core plate, which positions the lower end of the fuel subassemblies. Its thickness equals about 7 - 8 cm and it is manufactured from the 304 SS steel. It is mounted in the RPV using a system of bolts, clevis and pads. It has many holes to promote coolant flow upwards the core through each fuel sub-assembly. The loads caused by the core are transmitted through the lower core plate to the lower core forging and support columns, located below. The radial and circumferential movement of the core barrel inside the RPV is restrained by clevis attached at the bottom forgings. The clevis are uniformly distributed around the forging and fix it to the RPV. This allows axial and radial thermal expansion but prevents rotation of the barrel.. 2.3.5 Upper internals Just above the fuel sub-assemblies the holed upper core plate is located. It determines the boundary between core and upper plenum. Its main function is to position the upper end of the fuel sub-assemblies and lower end of the control rod guide tubes and instrument thimbles. The thickness of the upper core plate equals about 10 cm and it is made of the 304 SS steel. 12.

(23) The control rod clusters, neutron source clusters6 and other instrumentations such as neutron detector sets, surveillance vessels and thermocouples, are inserted into reactor core through the holes in the upper core plate. The upper plenum is the space between upper core plate and upper support plate filled with the hot water exiting the core. To ensure the stability and to control the path of the control rod insertion or withdrawal, the guide tubes are mounted along the upper core plenum, between the upper core plate and upper support plate. They are similar to the square shaped sleeves and encompass the control rod clusters. Their function is to provide straight, lowfriction path for the control rods during their withdrawal or insertion. Additionally, during refuelling they provide a storage place for the control rod clusters drive lines. The vertical movements of the upper core structures are allowed because of refuelling and inspection.. 2.3.6 Neutron reflector The fuel sub-assemblies are surrounded by the baffle, barrel with thermal shields and RPV. The gaps between the said components are filled with water. The lateral layers of steel and water about 40 cm thick are denoted as a side reflector. All components above and below the fuel pins with thickness about 25 cm stand for the top and bottom reflector, respectively [10]. The idea of the neutrons reflector is to reflect neutrons escaping the core, so the neutron reflector should be made from material having low absorption and large scattering cross section. In case of PWR water reflects mostly thermal neutrons while iron based elements reflect fast neutrons [11]. In general, the steel components of the reflector are treated as spectrum adaptation zones, which slow down and reflect fast neutrons to the epithermal ones, thereby decreasing the exposure of the RPV. The neutrons coming back from the reflector region to the core cause additional fissions increasing the power at the core peripheries. Therefore, the reflector is used as a flux shaping element in the reactor core. The flatter flux profile the more uniform the distribution of the temperature and fuel burnup. In addition, the isotopic composition of the reflector forms the neutron spectrum at the core peripheries, which in turn, influences the isotopic composition of the fuel. Some isotopes of Fe, Ni and Cr used as compounds of the reflector have significant influence on the neutron flux. These isotopes have large resonance in the medium energy range, which increases the resonance shielding effects in the reflector. 6. The neutron source clusters (assemblies) are used for the sub-criticality monitoring and supplying neutrons by the reactor start-up. They contain californium as a neutron source material.. 13.

(24) Therefore, neutron reflector has a big impact on the flux and consequently, on the power distribution at the core peripheries and should be taken into account in the neutronic analysis of the reactor core. In the presented studies neutron reflector based on the material and geometrical features of the Westinghouse 4-loop plant was modelled. A good design of the reflector improves the neutron economy, decreases power peeking at the core peripheries and exposure of the RPV. The 5 cm thick layer of the stainless steel reduces the fluence at the RPV by a factor of about 1.5. Furthermore, the fuel cycle cost benefit of about 2 - 3% is achieved using neutron reflector. The thickness of the neutron reflector is limited by space available between the barrel and RPV. Some problems are also caused by the high deposition of gamma heating at some reflector components, e.g. thermal shields [12]. In the new reactor designs, so called heavy reflector was introduced. Reflectors of this type are assembled from the stainless steel blocks locked axially one on the other. The heavy reflector has the axial holes for water cooling, which is necessary because of the high heat deposition due to gamma radiation. Neither bolts nor welds are used in its assembling and installation process, which improves the mechanical behaviour of the whole reactor lower internals. The. heavy reflector is mostly manufactured using the stainless steel, which. improves its reflecting properties, neutron economics and finally reduces cost of the fuel cycle.. 2.4. Reactivity control The role of some in-core components is important not only from the technological but. also from the physical point of view. The interface between mechanical and physical aspect of the reactor core is very tight. Many in-core components have multiple functions. Some of them are used for reactivity control and power adjustment. Hence, the introduction of the theoretical background about reactivity control appears necessary. Furthermore, the presented Monte Carlo calculations are performed in so called kcode mode, which estimates the reactivity of the system. Nuclear reactor operates at the desired, constant power level only if the effective neutron multiplication factor (Keff) equals unity. A more convenient quantity describing neutron balance in the reactor core is reactivity. The reactivity describes the amount by which Keff differs from unity and is defined as:. 14.

(25) . K eff  1. (1). K eff. In other words, it is a measure of the imbalance between neutron removal and production over entire core [13]. According to Eq.(1), reactivity depends on the value of Keff and may be positive, negative or zero. The former corresponds to the supercritical reactor, next to the subcritical reactor and the latter to the steady-state critical reactor. Generally, the larger absolute value of the reactivity, the further from criticality the reactor is. During the reactor operation the Keff decreases due to the fuel burnup and fission product production. The former refers to the consumption of the fissionable material, which naturally decreases Keff. The latter is related to the effect of the neutron absorption in some fission and decay products like Xe135 or Sm149, see section 4.4.5. The strong absorbing fission and decay products are called neutron poisons. To assure the operation at the desired power level during the whole reactor cycle the initial core must provide sufficient amount of the excess reactivity7. This excess reactivity depends on the fuel enrichment, fuel load and loading pattern. The introduction of the negative reactivity is necessary to compensate for the excess reactivity. Otherwise the initial core would be supercritical. The adjustment of the negative reactivity should be possible during the whole reactor cycle. The negative reactivity is also used to regulate short-time reactivity changes like power control, reactor shut-down and start-up. In the reactivity control, one also have to take into account constrains according to power peaking factors8 and ensure sufficient shutdown margin9. The negative reactivity is provided by the insertion of the neutron absorbing materials into reactor core, usually in the form of the movable control rods (see section 2.5.4), burnable poison rods (see section 2.5.5) or chemical shim (see section 2.7). In some reactor designs the movable elements of reflector or movable fuel sub-assemblies may be used for reactivity control. The coolant flow also may be used for the reactivity adjustment. During reactor operation the reactivity may be affected by many parameters namely, pressure, temperature, fuel depletion, load of burnable poison, etc. To quantify the change in the reactivity due to the change in some parameter, the reactivity coefficients were introduced. They are defined as the amount of reactivity change for a given change in the parameter [14]. 7. The reactivity of the fresh core, when all control elements are withdrawn. Set of parameters defining the conditions in the hottest location (hot spot) in the reactor core. The parameters are defined as several ratios of local conditions to average conditions (usually power or power density). e. g. radial peaking factor, axial peaking factor, total peaking factor, axially integrated peaking factor etc. 9 The negative reactivity of the fresh core when all control rods, apart from the most reactive one, are wholly inserted. 8. 15.

(26) The most important reactivity coefficients are: moderator temperature coefficient, fuel temperature coefficient, pressure coefficient and void coefficient.. 2.5. Reactor core Section 2.5 describes the components of the reactor core using specification of the. Westinghouse 4-loop plant. Since modelling of the reactor core is the most important aspect of the thesis, a deep knowledge about its geometry and material composition is necessary. Sections 2.5.1 and 2.5.2 explain the layout of the fuel sub-assemblies and fuel pins. The focus of these sections is to present the main components of the reactor core and some design criteria from the technological point of view. The reader should. focus mainly on the. geometry of the structural components. Section 2.5.3 describes the fuel used in the PWR reactors. The fuel manufacturing process is also briefly described. Section 2.5.4 and 2.5.5 focus on all aspects of the rod cluster control assemblies and burnable poison. These elements are described in detail because of their big impact on the reactor core neutronics and burnup. The nuclear reactor core is located in the centre of the RPV and consists of the array of the fuel, moderator and control elements [15]. The heat from the nuclear fission and other nuclear reactions is produced mainly in the ceramic fuel pellets enclosed by metal tubes, called fuel pins, rods or elements. Fuel pins are assembled and mounted in the carriers called fuel bundles or fuel sub-assemblies. Fuel sub-assemblies are arranged in the square fuel lattice, which builds the reactor core. The fuel sub-assemblies contain a few axial penetration holes for the control rods. Most commonly, in the middle of the sub-assembly the instrument thimble is located. It serves as a penetration channel for the surveillance vessels and other instrumentation. In some cases the fuel sub-assemblies may contain burnable poison rods to compensate the long-term changes in the reactivity. The regions around fuel pins are filled with the cooling water and are called the cooling channels. The equivalent diameter10 of the reactor core in case of the 4-loop Westinghouse plant equals about 340 cm. The height of the core is equivalent to the height of the fuel subassembly, and is about 400 cm. The active height defined as the cumulative length of the pellets in the fuel pin equals 366 cm. The 193 fuel sub-assemblies of the design 17x17 are comprised in the reactor core. Each fuel sub-assembly contains 289 locations for 264 fuel pins, 24 locations for control rods guide tubes and one location for the instrument thimble.. 10. Assumes the cylindrical shape of the lattice of the fuel sub-assemblies.. 16.

(27) The total weight of the UO2 fuel located in the reactor core equals about 100 tonnes, of which 90 is heavy metal11. The cumulative weight of the structural materials equals about 35 tonnes, of which approx. 25 is zirconium cladding of the fuel. Remaining 10 tonnes are attributed to the weight of the stainless steel elements of the fuel sub-assembly and zirconium spacers. Thus, the total weight of the core is approx. 135 tonnes.. 2.5.1 Fuel sub-assemblies Fuel sub-assemblies are the smallest units combining fuel pins into a precise grid pattern. There are many types of the fuel sub-assemblies, which are characterized by a lot of individual features like shape, size and configuration. The section describes general features of the fuel sub-assemblies and their design criteria. The sub-assemblies used in the Japanese 4-loops plants are described more precisely. The specification of such a sub-assembly was used to build the numerical model, needed for burnup validation. The sub-assemblies are characterized by some common features from the operational, mechanical and physical point of view. Firstly, the positioning of the fuel pins under normal and off-normal operation conditions must be assured. Thus, the spacer grids of the fuel subassemblies restrict the movement and vibration of the fuel pins in all directions and enable good coolant mixing and low resistance of the coolant flow. The construction of the fuel subassembly must also provide excellent positioning of the control rods and other instrument vessels during their insertion and withdrawal into control rod channels or instrument thimbles. Other important aspects concern fuel handling during refuelling and transport before and after irradiation. The refuelling of the reactor core should be done as fast as possible in order to minimize the outage time. Proper construction of the sub-assembly and fuel handling machine speed-up core reloading and refuelling significantly. Therefore, on the top of each subassembly the connecting point for the refuelling equipment is attached. Moreover, in offnormal condition the structure of the fuel sub-assembly must enable sufficient removal of decay heat. From the neutronic point of view the fuel sub-assembly materials should provide low neutron absorption cross section, for the sake of the neutron economy. The failure of the fuel sub-assembly may occur as the result of dimensional changes caused by creep, structural growth and stress relaxation. The loss of geometry of the fuel subassembly may cause a lot of undesirable effects, namely fuel rod bow and growth, guide tube 11. Weight of all actinides presented in the fuel composition, no oxygen included. The initial uranium fuel contains U234, U235, U236 and U238.. 17.

(28) bow and growth, cooling channel deformation, grid and top fitting force relaxation, etc. To provide sufficient dimensional stability, the following requirements must be met: . sufficient top fitting spring forces to ensure that the fuel sub-assembly is not elevated by the hydraulic forces of coolant flow.. . sufficient thickness of the fuel sub-assembly structural components.. . the lowest possible radial uniform hydriding and corrosion.. . low and uniform irradiation growth and creep.. The most dangerous failure is a general bow of the sub-assembly causing also the bow of the control rod guide tube. This, in turn can cause decrease in the control rod drop time and even blockage of the control rod insertion. This was observed with some fuel sub-assemblies designs by Westinghouse and Framatome. The reasons of this were too large hold-down forces, too low coolant flow, too small sub-assembly stiffness and too high irradiation growth [16].. Figure 4. Fuel 17x17 sub-assembly for the PWR.. 18.

(29) For the Western-type reactors the square configuration12 of the fuel pins in the subassemblies, is used. Over years the array dimensions have increased from 14x14 to 17x17 and in some new designs even up to 18x18. The reason for this was to reduce linear heat generation rate, which gives some benefits in fuel performances, e.g. lower fission gas release. The fuel sub-assemblies are positioned between lower and upper core plates by the top and bottom fittings. The design of fittings differs depending on the fuel manufacturer. Fig. 4 presents the 17x17 sub-assembly fabricated by Nuclear Fuel Industries in Japan [17]. In this design the upper fitting is provided by hold-down springs and integral pads located on the top nozzle, whilst the lower one by simple placement of the bottom nozzle bearing pads on the lower core plate. The radial positioning is provided by contact between sub-assemblies at the spacer-grid level. It is worth noting, that there is a clearance between both the nozzles and the ends of fuel rods. Fuel rods are fixed only to the grid spacers. The proper orientation of the sub-assemblies is assured by the pin inserted into the indexing hole located in the top nozzle and by the visual check-up of the engraved identification number. The 17x17 fuel subassembly is structured by the top and bottom nozzles, spacer grids, guide tubes and fuel rods.. Top nozzle The welded top nozzle assembly contains three main components, i.e. an adapter plate, an enclosure and a top plate. The first refers to the bottom of the top nozzles and contains semicircular slots to promote upward coolant flow and rounded holes for locking the guide tubes. The axial movement of the fuel rod from the fuel sub-assembly is restricted by ligaments in the adapter plate, which enclose the top of the fuel rods. The enclosure is the space between the adapter plate and the top plate. The four sets of hold-down springs are attached to the top plate by screws and clamps. The screws are located at the diagonally opposite corners of the top plate. The connection between the upper core plate and top nozzles is done using integral pads with the alignment holes placed at the two remaining corners of the top plate. The large square holes in the middle of the top plate provide the access of the control rod cluster assemblies and other instrumentation. The top nozzle could be removed for inspection fuel rod examination or replacement. The top nozzle assemblies are usually manufactured from the stainless steel.. 12. Russian type PWR use hexagonal fuel array.. 19.

(30) Bottom nozzle The bottom nozzle is the bottom component of the fuel sub-assemblies. Its function is to direct the coolant flow into the sub-assemblies. The bottom nozzle assembly consists of four angle legs equipped with the bearing pads and a skirt. The upper plate of the bottom nozzle prevents the off-normal downward ejection of fuel rod. The holes promoting the coolant flow are located between the rows of the fuel rods. The bottom nozzle also serves as a debris filter preventing the debris particles, present in the coolant, from entering the core active region. The transmission of the axial loads to the lower core plate is provided by the bottom nozzle. The bottom nozzle is placed on the lower core plate using connection between the two diagonally opposite bearing pads with alignment holes and locating pins of the lower core plate. The bottom nozzle is fabricated from the stainless steel.. Spacer grids The radial spacing of the fuel sub-assemblies is provided by the spacer grids assemblies located at the specified intervals along the entire sub-assembly length. Typically, for the 17x17 sub-assembly nine spacer grids are applied. The fuel rods are attached to the spacer grids using a combination of dimples and springs. The forces of the connection should not be too large in order to avoid fretting. The design of the spacer grids allows axial and radial thermal expansion of the fuel rods in order to minimize their deformation. Some spacer grids may contain mixing vanes to promote coolant flow. The spacer grids are fabricated from the Zircaloy but some components may be made from nickel-chromium-iron alloys. Techniques of welding and brazing are used for their fabrication.. Guide tubes and instrument thimble For the 17x17 design the rigidity of the fuel sub-assembly is assured by 24 guide tubes and one instrument thimble attached to the spacer grids using bulge joints. In addition, the guide tubes are attached to the bottom nozzle by a screw connection and locked in the top nozzle. The guide tubes are the load bearing support of the fuel sub-assemblies. The vertical forces acting on the guide tubes are determined by the sub-assembly weight, hold down forces, coolant flow forces and differential thermal growth and expansion forces between the 20.

(31) guide tubes and the fuel pins. The inner and outer diameters of the tubes are constant over the entire sub-assembly length. The large inner diameter facilitates the rapid control rod insertion during a reactor scram and stable coolant flow during normal operation. The instrument thimble, located in the middle of the fuel sub-assembly has the same layout as the guide tubes. However, it is not used for the control rod operation but for the insertion of the auxiliary instrumentation including neutron detector sets. The tubes are fabricated from the Zircaloy or Iconel.. 2.5.2 Fuel pins The geometry and material composition of the fuel pin are necessary to build the numerical model of the fuel sub-assembly. The presented description of the fuel pin is based on the pins applied to the 17x17 fuel sub-assemblies fabricated by the Nuclear Fuel Industries in Japan and widely used in the Japanese 4-loop Westinghouse plants. The fuel pin is the smallest sealed unit of the fuel. In the PWR technology it is usually zirconium-based alloy tube filled with the numerous fuel pellets and sealed from the both ends. The gap between the fuel and zirconium-based cladding is filled with helium to enhance heat transfer to the cladding and then to the cooling water. The gap diameter is about 0.09 mm and helium gas is pressurized to about 3.0 MPa. The gap accommodates thermal expansion between fuel pellets and cladding as well as fuel density changes due to fuel swelling. In addition, it provides space to accumulate fission and decay gases released during irradiation. The overall length of the fuel pin is at the level of 385 cm, the diameter about 0.9 cm and cladding thickness about 0.6 mm. Between the fuel pellet stack, top-end plug and bottom-end plug two plena for the fission and decay gases are located. The fuel pellets are fastened by two plenum springs located below and over fuel pellet stack. Springs are usually fabricated from the Iconel alloy. Between springs and fuel pellets two isolators13 are placed. This prevents direct contact between the fuel pellets and springs, so the chemical interaction between them is eliminated. The upper plenum is usually longer than the lower one. To facilitate manufacturing and handling of the fuel rods the bottom-end and top-end plugs are given helical or tapered profile. Both of them are welded to the fuel rod. The active height of the fuel in the 17x17 sub-assembly equals 366 cm. The height of the single fuel pellet equals about 1 cm and diameter about 0.8 cm, see Fig. 5. The PWR fuel pellets are fabricated from. 13. For instance Al2O3.. 21.

(32) uranium or plutonium dioxide. The top and bottom surfaces of every pellet are dished at the centreline to provide some space for the axial expansion as well as for the fission and decay gases accumulation. The edges of each pellet are chamfered to improve manufacturability and handling. For the PWR containing 193 sub-assemblies with 264 fuel rods in each of them, number of pellets equals about 19 millions.. Figure 5. Fuel pin and fuel pellet of the Japanese 17x17 fuel sub-assembly. Zirconium-based alloys are perfect material for fuel rod cladding due to their low thermal neutron capture cross section, high mechanical strength and corrosion resistance in aggressive hot-water environment. The fuel rod cladding is one of the barriers preventing the release of the radioactive products to the outside reactor systems. Therefore, the integrity of the cladding must be maintained during normal operation, rector trip as well as after irradiation, during interim wet and dry storage. To ensure the integrity some limits of heat transfer, maximum cladding temperature, cladding oxidation and chemical hydrogen production from the reaction between water/steam and cladding, were established. For instance, the temperature limit for the zirconium-based cladding equals about 1200oC. The 22.

(33) zirconium-based alloys contain some additional components of oxygen, tin, niobium, iron, chromium and nickel to improve their properties. The density of the zirconium-based alloys equals about 6.4 to 6.6 g/cm3 and the melting temperature is about 1800oC [18].. 2.5.3 The PWR fuel The reactor selected for the burnup validation works on the uranium fuel enriched to the 3.2 wt% in U235. Some pins contain also gadolinia (see section 2.5.5) and are enriched only to the 1.7% wt% in U235. The initial isotopic composition of the fuel and its neutronic behaviour under irradiation play important role in the reactor core modelling. The section describes briefly properties of the nuclear fuel and the methods of its fabrication thereby providing general outlook on the fuel technology. The energy produced in the nuclear reactor core comes from the fission process of heavy nuclei. The fuel usually contains both, fissile isotopes, namely U233, U235, Pu239, Pu241 and fissionable isotopes such as Th232, U238, Pu240. The fuel containing these isotopes may be fabricated in oxide, carbide, nitride or metallic forms, depending on the core design. Understanding of the in-pile behaviour of the nuclear fuel is a prerequisite of safe and efficient reactor operation. The phenomena related to heat transfer, neutronics, mass transport, thermo-mechanics and hydro-mechanics must be investigated before the commercial implementation of a new kind of nuclear fuel is launched. All processes concerning preparation of the nuclear fuel, before loading it into the reactor core are named head-end fuel cycle. In the majority of PWR reactors the nuclear fuel is in a form of compact, ceramic pellet of UO2 or (U,Pu)O2 (MOX). The microstructure as well as the physicochemical properties of the fuel change as a function of particle fluence. For instance, the thermal conductivity of the nuclear fuel decreases due to the accumulation of the fission products and the radiation damage. Thus, the fuel material must fulfil some constrains in accordance with physical properties during in-pile operation. First of all, the density of UO2 has to be about 95% of the theoretical density, which equals 10.96 g/cm3. The lower density has negative impact on the thermal conductivity. On the contrary, higher density causes some problems with the accumulation of the fission/decay gases and related matrix-swelling. Fuel swelling originates, mostly from production of helium from α-decay. Fuel porosity must be at least at the level of 5% and the pores, with dimensions from 1 to 10 μm, should be uniformly. 23.

(34) distributed in order to mitigate fuel swelling. Additionally, the thermal conductivity of the fuel material must be high enough to provide efficient heat transfer to the coolant and prevent local overheating and melting. The other important parameter is the melting temperature of the nuclear fuel, which should exceed the in-core temperatures, even in the accident conditions. In case of uranium dioxide it equals 3120 ± 20K. Finally, the dimensions and surface roughness must be within specified tolerations.. Fabrication of UO2 fuel The starting point of the fuel production is the mining of uranium ore. The uranium ore contains about 0.25% uranium oxide U3O8. The uranium ore is milled and leached with the sulphuric acid and then the methods based on solvent extraction or ion exchange are used to recover dissolved U3O8. After calcination process a crude uranium oxide containing 70 to 90% U3O8, called the yellow cake is obtained. In additional post processing, the yellow cake is refined to pure UO3. Next, the hydrogenation process is used to convert UO3 to UO2. The reaction between UO2 and hydrogen fluoride produces UF4, which is converted to the gaseous uranium hexafluoride UF6. The UF6 is used in the enrichment process, in which the concentration of the U235 is increased. The natural abundance of the fissile U235 equals 0.7% but the PWR reactors use uranium fuel enriched to about 3 - 5 wt.% U235. Many enrichment techniques, namely gaseous diffusion, electromagnetic separation, ultracentrifugs, laser excitation, have been developed and used worldwide. After enrichment gaseous UF6 must be converted to UO2 pellets. First, in wet or dry process the UF6 is converted to the UO2 powder. In the wet process UF6 reacts with water and ammonia, which results in precipitation of the uranium as a ammoniadiurante. In the further calcinations U3O8 is formed and at the end, reduced to the UO2. In the dry process UF6 reacts with the superheated steam and flows through the rotating kiln, which results in the formation of the UO2. Then, the UO2 powder, characterized by grains of about 8 - 12 μm, is mixed with the lubricants, binder materials, pore formers, and cold pressed at the pressure 150 - 300 MPa to form pellets of 50 - 60% theoretical density. The pellets are sintered in the hydrogen-argon atmosphere for about 5 - 10 h at temperature 1600oC - 1700oC, to form pellets with 95 - 96% theoretical density.. 24.

(35) 2.5.4 Rod clusters control assembly The applied numerical model of the fuel sub-assembly does not contain any control rods. The reference fuel sub-assembly during two following reactor cycles was located in the in-core position, which does not correspond to any control rod bank. Nevertheless, the exact description of the control rods from the technological and physical point of view is necessary to understand the basics of the reactivity control mechanism. The movable rod cluster control assemblies contain neutron absorbing material to control core reactivity and rate of power production. Hafnium, boron, silver, cadmium and indium are the neutron absorbing materials used for the control rod fabrication. The materials for control rods should be characterized by long life-times. It means that they should not burn out rapidly due to high neutron absorption cross sections. According to the absorber material, there are two main kinds of the control rods, grey and black ones. The grey control rods are less absorbing and in many cases absorb only neutrons in some specified energy range. Sometimes pure stainless steel is used for their fabrication. The black rods absorb more neutrons and consequently burn out faster. From the operational point of view the grey rods are usually used for the reactivity control and power adjustment, because they do not cause any high flux depression around the control rod, so the flux profile is flatter. Generally, the flat flux profile may also be achieved using so called epithermal absorbers rather than thermal absorbers. The area of the influence of the epithermal absorber around the control rod is larger than that of the thermal absorbers because the mean free path of the thermal neutrons in the reactor core is shorter than the path of the epithermal neutrons. Therefore, epithermal absorbers absorb neutrons which are more distant from the control rod. Rod clusters control assemblies may be designed for the reactor shutdown, fine control and coarse control. The shutdown rods, also called safety rods, provide negative reactivity to very fast reactor shutdown in case of off-normal operation conditions. The fast rector shutdown is called scram. The fine control rods are used to adjust desired power level or temperature in the core and provide small amounts of negative reactivity. The coarse control rods provide negative reactivity in the large amounts and act as intermediate regulating elements, between fine and shutdown rods. In the modern reactors the coarse and fine reactivity adjustment is done by the same control rods sets. Sometimes, the same rod cluster control assembly may be used for the three aforesaid purposes.. 25.

(36) The number of control rods in the cluster depends on the fuel sub-assembly array. For the 17x17 design each cluster contains 24 control rods. The 24 stainless steel tubes (rodlets) are brazed or welded to the arms of the spider assembly, which is the central interface to the control rod drive mechanism. Each tube contains pellets of the absorbing material. The tapered control rod tip ensures precise insertion into the fuel sub-assembly guide tube. The gap between control rod tube and absorber pellets provides space for possible thermal expansion. The control rod gap is filled with the helium gas as is the case with fuel rod. The spider assembly and the control rod tubes are made from the stainless steel. The heat generated by the neutron absorption and other reactions is removed by water flowing between guide tubes and control rod tubes. During normal operation control rods are always inserted into the guide tubes. The lowest possible insertion depth corresponds to the location of the control rods tips just above the active height. The diameter of the absorber pellet equals about 0.7 cm and the length about 30 cm. The diameter of the control rod tube is about 1 cm and the gap width between the control rod tube and guide tube equals about 0.05 cm. In some designs rod cluster control assemblies may contain some stainless steel rods as well as absorber rods. The length of the control rods in the cluster is the function of the rector type. Some rods may be shorter than other ones.. Figure 6. Control rod cluster assembly. 26.

(37) The Westinghouse 4-loop plants contain 28 shutdown rods assemblies and 23 control rods assemblies. The first group is used just for reactor shut-down or start-up. The second group is used for compensating reactivity changes due to the change in the reactor operation conditions, such as burnup, formation of fission and decay products, power defects, void formations and changes in the coolant temperature. The control rods assemblies are arranged into control rods banks, as depicted in Fig. 8. The symmetric location of the control rod banks around the core provides flat flux and power distributions. The banks can be operated separately. The control rods absorbing material is fabricated from the silver-indium-cadmium alloy (AIC). The composition of the alloy is 80% Ag, 15% In and 5% Cd by weight, which allows absorption of the neutrons having wide energy range. The density of the absorbing material equals about 10.17 g/cm3 and melting point is about 800oC.. 2.5.5 Burnable poison For the purpose of the thesis the 17x17 fuel sub-assembly was modelled. The reference sub-assembly contains burnable poison in the form of Gd2O3, incorporated in the 16 fuel pins. The section explains the role of the burnable poison in the PWR technology and reasons for its usage. The physical and technological aspects of the burnable poison are presented. For the reactors with the conversion ratio14 less than 1.0 the reactivity decreases during the reactor operation. Hence, the initial core must provide some excess reactivity to keep the reactor critical at the desired power level (see section 2.4). In the PWR reactor, one could compensate the reactivity decrease utilizing burnable poison, control rods or soluble boron. The reactivity adjustment using control rods causes higher fuel demand owing to the flux depressions around inserted control rods (see section 2.5.4). The concentration of the soluble boron is limited due to some safety issues in accident conditions (see section 2.7). Thus, the reactivity control mechanism based on the burnable poison was introduced. The burnable poison is neutron-absorbing material, that depletes during the reactor operation due to neutron capture incorporated absorbing isotopes. This is how the isotopes characterized by the lower neutron capture cross section are formed. The burnable poison material transmutes faster than the fuel burnup due to the larger absorption cross section, so it exerts the highest influence at the beginning of the reactor cycle. The behaviour of the 14. Conversion ratio also known as a breeding ratio is the average rate of fissile atoms produced to the average rate of fissile atoms consumed during the reactor cycle.. 27.

(38) burnable poison during reactor operation is presented in Fig.7. The most effective absorption for the burnable poison materials usually occurs in the thermal energy range. Therefore, the introduction of the burnable poison is the most effective in thermal reactors. The reactivity introduced by the burnable poison should compensate the reactivity lost due to the fuel depletion and absorption in fission products. In practice, ideal reactivity adjustment using burnable poison is not possible. One of the problems is incomplete depletion of the neutron absorbing-material. This causes undeliberate introduction of the negative reactivity until the end of the irradiation cycle. The other problem is that burnable poison material partly replaces the fuel material thereby decreasing the fuel load. The solution is to increase the fuel enrichment to provide enough fuel to conduct the reactor on the desired power level during the whole cycle. The burnable poison is also used for shaping power profiles. Generally, its application helps to avoid formation of the hot spots in the reactor core. In addition, the usage of the burnable poison allows the larger initial fuel inventories and resulting longer duration of the reactor cycles without any violation of the control requirements.. Figure 7. Neutron flux depression in the burnable poison material in time function. One can distinguish between discrete and integral burnable poisons. The difference lies in the method of its introduction into the reactor core. The former concerns the burnable poison pins without any fissile component located in the fuel sub-assembly. In this design pure burnable poison pins replace some fuel pins in the fuel sub-assembly. The latter refers to the design, where burnable poison material is coated on the surface of the fuel pellet or incorporated in the fuel material. The coating is usually put on the fuel pellet surface using spraying technologies. The introduction of the burnable poison material into the fuel material. 28.

(39) is done at the level of the fuel fabrication. As a rule, the uranium powder is mixed with burnable poison material and then standard fabrication technology is applied. The most common isotopes used as burnable poisons are B10, Gd155, Gd157 and Er167. The B10 could be incorporated in the natural boron in ZrB2 coating on the surface of the fuel pellet or in the separate B4C rods. The natural abundance of B10 equals about 20%. The isotope burns out in reaction (n,α), in contrast to other burnable poison isotopes which burn in reaction (n,γ). This specific feature causes increase of the fuel pellet internal pressure and may disturb its integrity [19]. The B10 cross section in the thermal15 energy range is about 3.84E3 barns. Erbium oxide Er2O3, known as an erbia is used as an integral burnable absorber. Er167 has a thermal neutron absorption cross section of 670 barns and its natural abundance equals about 23%. It burns out to Er168 with the thermal absorption cross section of about 2.5 barns. The unique feature of the erbia is the large resonance in the upper part of the thermal spectrum. This provides negative component to the reactivity moderator coefficient. The slowest depletion of erbia in comparison with other burnable absorbers may cause some problems with the large reactivity penalty at the end of the cycle. Gadolinia Gd2O3 is the most widely used burnable absorber. It is used in boiling water reactors as well as in PWR reactors. In general, the Westinghouse PWR plants operate on the fuel containing gadolinia fraction. The natural gadolinium contains two isotopes with high thermal absorption cross sections. The natural abundance of the G155 equals 15% and thermal absorption cross section 6.1E4 barns, whilst natural abundance of Gd157 is 16% and thermal absorption cross section about 2.25E5 barns. The gadolinia is utilized as the integral burnable absorber. Most commonly, the fuel rods contain from 6 to 12 wt% of gadolinia. The gadolinia pins are symmetrically located in specified fuel sub-assemblies. From 8 even to 24 pins containing gadolinia may be placed in a single fuel sub-assembly. The flexibility in the number of gadolinia pins and fraction allows design of the fuel sub-assemblies with different reactivity worth, which further facilitates the core optimization. The gadolinia component in the fuel causes some negative effect, i.e. decrease of thermal conductivity and melting temperature.. 15. At energy 0.025 eV.. 29.