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Nice that you stop by and want to learn what I offer in my lectures on "Understanding Nuclear Fuel".
Nuclear fuel behavior covers a large field of science: neutron physics, thermal-hydraulics, material behavior under irradiation, water chemistry and corrosion, neutron microscopic cross sections, static and dynamic mechanical loads on fuel assembies and fuel rods, system behavior under normal, abnormal and accident conditions. If you want to act responsibly in the nuclear industry you have to master a vast variety of details and subjects.
This lecture series was originally prepared at the Technical University of Munich and covers three fields: reactor core design, nuclear fuel design and decommissioning of nuclear facilities.
In the following sections some more details and resources are given on the above topics. A number of videos have been created over the years which are available here . So let's start studying!
Welcome to understanding energy generation by fission from Dr Sdl on Vimeo's fission channel.
Describing and predicting the behaviour of nuclear fuel is at the heart of understanding commercial nuclear power. Whether you want to mine and enrich uranium, or whether you want to design fuel assemblies for light water reactors, or whether you want to study the suitability of geological formations for long term storage, or whether you want to build better and safer nuclear reactor types - you always need to understand the behaviour of nuclear fuel in depth.
Understanding nuclear fuel is truly a multi-discipline challenge. It encompasses material science in order to understand the effects of irradiation and fission product generation and their impact on the fuel's material properties, it is about neutron physics to understand criticality, burnup and power distributions, it is about mechanical engineering to understand the structural behaviour of fuel assemblies under irradiation, it is about thermodynamics and fluid-dynamics to understand the heat transfer mechanisms from the fuel to the coolant or moderator.
Therefore you need a broad set of skills to master this subject. The most important skill is that you like mathematics and that you like programming computers. Many programs which form the licensing basis in the nuclear industry today are from the 1960s and you need to understand Fortran, for example. When you do your own programming you should be able to do it in C++. What French, English, Spanish and Russian is to a good diplomat, here it is C++, Fortran, Matlab, Mathematica or VBA. It is all about solving an interconnected set of differential equations.
From a historical perspective nuclear power is only about 50 years old. That means that it basically is still in its infancy. Technology develops and undergoes its own evolution. This is a vast subject where you can study and learn for the rest of your life. The kind of nuclear power plants which we will have in a 100 years or the solutions for the long-term treatment of fission products which we will have in 200 years will look very different from what we can imagine today. So just keep on inventing!
A typical fuel element of a conventional pressurized water reactor (PWR) today consists of an array of 16x16, 17x17 or 18x18 individual fuel rods. In the most simplest case of an uranium-dioxide (UO2) fuel element all fuel rods have the same enrichment bottom to top and have no additional burnable neutron poisons. There are usually a number of guide tubes in each fuel assembly to enable the insertion of control rods. So when we speak of a 16x16-20 UO2 assembly then this means that all fuel rods contain UO2 pellets without neutron poison and that there are 20 guide tubes in the assembly.
The most common variant is a 16x16-20 UO2-Gd2O3 fuel assembly. Here a couple of fuel rods (typically 8-16) contain UO2 pellets which have the neutron poison Gadolinium mixed into them. The Gadolinium usually burns out during the first cycle and afterwards theses assemblies behave neutronically almost as pure UO2 assemblies. Neutron poison is unusually necessary to better control the power distribution in the core. Then there exist also so called IFBA rods (integral fuel burnable absorber) which do not contain Gadolinium as neutron poison but which have a thin Boron coating. In modern reactor designs there can be many different patters of IFBA or Gadolinium assembly layouts.
A conventional PWR fuel assembly structure consists of the bottom nozzle, the guide tubes, the mixing grids and the top nozzle. They are welded together and form a rigid mechanical structure: the fuel assembly skeleton. The fuel rods are moved into the skeleton but are not rigidly fixed to it. Due to their axial growth under irradiation they need to be able to move to a certain extend freely in the axial direction. The fuel rods are therefore mainly held in place by spring forces exerted by the mechanical structure of the mixing grids.
A single fuel pellet in a rod for a 16x16 assembly is about 1cm in height and 1cm in diameter. It consists of UO2 at a density of about 10g/cm3. Enrichment today is typically about 4% U235. As the neutron chain reaction begins and the U235 nuclei begin to fission, each pellet at first undergoes a post-sintering phase during which its density increases a bit (densification phase). As the fission gases accumulate in fission gas bubbles inside and at the rim of the grains the pellets begin to swell and their density decreases again (swelling phase).
At the beginning of life (BOL) fuel rods are filled with an inert gas which exerts about 4MPa at operating temperatures. As the chain reactions go on, inside the pellets some of the fission gas will be released into the fuel rod plena so that at the end of life (EOL) the rod inner pressure at operating conditions is of the order of about 16MPa. The mechanism of fission gas release is one of the most important one to understand because of its effect on the mechanical stability of the fuel rods. Very soon after startup at BOL the fuel pellets begin to crack under the thermal stresses. At their centre fuel pellets reach temperatures of about 1500 degreeC while at the outer surfaces temperatures are typically about 500 degreeC. The thermal stresses which are created under theses temperature gradients lead to a handful of fuel fragments which relocate, realign and stick together.
Fission gas atoms initially aggregate into small intragranular fission gas bubbles. Fission gas can diffuse to the grain boundaries where it is trapped and accumulated. As more and more gas accumulates at the grain boundaries an interconnected fission gas bubble network develops which ultimately will release fission gas into the fuel rod plenum. Additionally micro-cracks during power ramps during reactor operation can create additional pathways for fission gas release.
Most fuel rod cladding materials for PWRs consist of the zirconium alloy Zirc-4. It has a low thermal neutron absorption probability, has good corrosion resistance and good ductility. Initially the fuel rod cladding creeps down onto the fuel pellets due to the high outside pressure in the PWR primary circuit. As fuel pellet swelling sets in the cladding is creeping outwards again. During operation the outside of the cladding is oxidized into ZrO2. Typical oxidation layer thickness is 50 micrometre after 4 years of operation. About 10pct of the hydrogen generated from the Zr + H20 -%less ZrO2 oxidation diffuses into the Zirc-4 cladding where it can form zirconium hydrides.
The diffusion and dynamical behaviour of an ensemble of neutral particles was considered by Maxwell as early as 1859 and was more later treated rigorously by Boltzmann. His original formulation of the equation of the transport of neutral particles still very accurately describes the neutron behaviour in nuclear reactors. The first serious attempts to quantitatively describe the slowing down process of neutrons released from fission events were made during the Manhattan project.
The Boltzmann transport equation would be very difficult to solve if the interaction between two neutrons would have to be taken into account which would lead to a non-linear differential equation. Since the interaction between two neutrons is negligible for all practical purposes in a nuclear reactor the equation is linear and can relatively easily been solved. Mathematically speaking the description of the neutron field is therefore much easier than the description of fluid flow.
One of the main ingredients of the Boltzmann transport equation are the neutron interaction cross sections which must be provided by experiment or be estimated theoretically. Broadly speaking neutrons can either be scattered from a nucleus or they can be absorbed. If they are scattered they can either undergo an elastic or an inelastic collision. In elastic scattering the kinetic energies of the two scattering masses are preserved. If a neutron is absorbed by a nucleus then there exist a variety of possibilities: the compound nucleus emits a couple of gamma rays and decays to its ground state. The result can also be a fission event or the re-emission of one or more neutrons, e.g. (n,2n) events and the like. Almost all of the knowledge about the microscopic interaction cross sections which exists is bundled into the so called ENDF data files (evaluated nuclear data files).
The principal elements of a chain reactor are the fuel and the chain carriers. The fuel is the fissionable material; the chain carriers are the neutrons. The chain carriers react with the fuel to liberate energy and produce new chain carriers. The chain carriers can be lost due to parasitic absorption or escape from the reactor. The next generation of new chain carriers can react with more fuel and produce more energy and more chain carriers. The chain reaction will be self-sustaining if the average number of chain carriers, produced by the reaction of one original carrier with the fuel is at least one. If it is exactly one the reactor is said to be critical.
The macroscopic cross sections (XS) are calculated by multiplying the microscopic cross sections with the appropriate particle densities. When multiplied by the scalar neutron flux the macroscopic XS yield the reaction rate for a certain interaction type (i.e. absorption, fission etc.) The Boltzmann equation in its integral form is simply a volume balance of neutrons entering and leaving the volume:
Rate of change of number of neutrons with energy E and direction O in a volume element V equals:
(1) number of neutrons generated by neutron sources (i.e. fission)
(2) plus neutrons streaming into V through its surface S
(3) minus neutrons leaking out of V through S
(4) plus neutrons of different energy E' and direction O' scattered into E and O
(5) minus neutrons of E and O scattered into some different E' and O'.
The solution of the Boltzmann equation for a typical PWR in operation today typically proceeds in three steps. First of all the neutron flux of a single fuel rod cell is calculated with comparatively high precision in an infinite array of similar fuel rod cells. This allows the calculation of an effective macroscopic cross section for the fuel rod cell regions (e.g. moderator, cladding and fuel) in which the neutron flux is assumed to be constant. In the second step a fuel assembly is put together consisting of different types of averaged fuel rod cells (e.g. different enrichments, water rods etc.) Again a relatively precise solution of the whole assembly neutron flux is calculated in an infinite array of similar fuel assemblies. This then is followed by the creation of an effective macroscopic fuel assembly cross section (many modern codes offer to split the assembly in 4 or 8 symmetric regions with separate, average macroscopic cross sections). Finally in the reactor simulator the average assembly cross sections are put together to simulate the full nuclear core and burnup behaviour.
The instrumentation and control system (I&C) of nuclear power plants have to fulfil much higher reliability and safety requirements than any other computerized system. Whereas your personal computer or tablet may crash a few times per week these systems have to continuously run for months and years flawlessly without affecting plant operation. In order to achieve these high standards a number of methods are employed: redundant availability of subsystems and of electronic modules; redundant and diverse measurement of plant data (i.e. the reactor power is measured independently by four neutron detectors which are located in different parts of the reactor building and possibly come from different suppliers, for example); classification of subsystems according to priority (i.e. reactors scram system with highest priority, reactor parameter limitation system with intermediate priority and reactor control system with lowest priority); physical separation of systems of different priority; independent power bus for systems of different priority; autarkic and redundant power bus for systems of highest priority; use of self-health-check circuits and of keep-alive-check circuits; physical protection of I&C through reinforced building construction.
In order to design the I&C a number of events which have the potential to damage the system has to be considered: (1) damages originating from within the system, e.g. stochastic failure of modules or components, systematic failure of components due to manufacturing errors (2) damages from within the plant, e.g. fire, flooding, human error (3) damages originating from outside, e.g. lightning.
The reactor scram system is required to bring the plant into a safe state under the following conditions: (1) prevent events which could lead to a beyond-design release of energy into the reactor (2) prevent events that lead to a beyond-design blockage of heat removal from the reactor (3) prevent events that lead to a beyond-design release of radioactive materials (4) bring the reactor into a safe state during events which originate from outside the plant. In order to achieve these objectives the I&C has the task to take care of the following requirements: (1) enable a fast enough power reduction of the reactor (2) ensure sufficient reactor coolant inventory (3) guarantee the heat-removal from the reactor core (4) ensure availability of secondary heat sink (5) limit reactor vessel pressure (6) enable steam generator feed water supply (7) guarantee enclosure of radioactive materials.
In order to ensure that the reactor scram system reliably recognizes a design basis accident the instrumentation of the reactor is designed in such a way that at least two independent safety variables are measured, i.e. the reactor power and the reactor pressure; if the reactor power protection sub-module does not recognize an over-power accident then the reactor pressure protection module acts independently to scram the reactor. This design also prevents against failure of reactor scram due to passive failures of control modules. The following failure modes are considered: (1) systematic failure of I&C modules (2) stochastic failure (3) failure in a row (4) maintenance. Once the I&C is designed an independent accident simulation analysis of the reactor has to show that all the safety protection goals can be achieved. In these kind of analyses it is usually assumed that one stochastic failure, one systematic failure and a failure in a row happen.
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