BASIC PROFESSIONAL TRAINING COURSE Module I Nuclear physics and reactor theory Version 1a, September 2014 This material was prepared by the IAEA.

BASIC PROFESSIONAL TRAINING COURSE Module I Nuclear physics and reactor theory
Version 1a, September 2014 This material was prepared by the IAEA and co-funded by the European Union.

ATOMIC STRUCTURE OF MATTER
Learning objectives After completing this chapter, the trainee will be able to: Describe the terms element, atom, compound and molecule. Define the atomic mass unit. Define the relative atomic mass Ar. Define the relative molecular mass M and calculate it from the chemical formula. Calculate the mass of elements in a given mass of a compound.

Elements and atoms Elements are basic components of matter
112 elements are currently known, 90 elements naturally occurring Elements have specific names and symbols, e.g.: H – Hydrogen He – Helium Li – Lithium O – Oxygen U – Uranium … Basic constituents of element are atoms: Atom is the smallest particle of an element, having its chemical properties Atoms of different elements have different chemical properties

Compounds Different elements bond together to make a compound
Basic constituents of a compound are molecules: A molecule is the smallest particle of a compound, having its chemical properties Atoms combine into molecules in chemical reactions: Hydrogen + Oxygen → Water (2H2 + O2 → 2H2O) Sodium + Chlorine → Sodium chloride (salt) (2Na + Cl2 → 2NaCl) Uranium + Oxygen → Uranium dioxide (U + O2 → UO2)

Atomic mass unit Atoms are very small and very light
A mass unit used in atomic physics and chemistry: 1 atomic mass unit = 1 amu = 1 u Definition: 1 u = 1/12 of mass of 12C = 1.66∙10-27 kg

Relative atomic mass Ar
Ar is the ratio of atom mass and amu: atom mass = Ar  amu The value of Ar can be found e.g. in periodic system Examples: Hydrogen (H): Ar(H) =  1 Lithium (Li): Ar(Li) =  Boron (B): Ar(B) =  10.8 Carbon (C): Ar(C) =  12 Oxygen (O): Ar(O) =  16 Iron (Fe): Ar(Fe) =  55.8 Uranium (U): Ar(U) =  238

Relative molecular mass Mr
Mr is the ratio of molecular mass and amu: mass of molecule = Mr  amu Mr is calculated as the sum of relative atomic masses of atoms in the molecule: Mr (H2O) = 2  = 18 Exercises: Calculate Mr(H3BO3)! Calculate Mr(C3H5OH)! How many molecules are there in one kg of water?

Exercises Calculate the relative molecular mass of carbon dioxide!
How many atoms of boron there are in 1 kg of boron? How many atoms of hydrogen and how many atoms of oxygen there are in 1 kg of water? What is the mass of hydrogen and the mass of oxygen in 1 kg of water? What is the mass of boron in 10 kg of boric acid H3BO3? How many grams of oxygen need to be added to 2 g of hydrogen, in order that all hydrogen combines with oxygen into water? How much water we would get? How many uranium atoms there are in 1 cm3 of uranium? (which additional information is needed?)

STRUCTURE OF ATOM Learning objectives
After completing this chapter, the trainee will be able to: Describe the structure of an atom. Name the main characteristics of an electron. Define the atomic number, Z. Explain the terms positive and negative ion. Define the binding energy of an electron. Define the unit electron-volt. Describe the energy levels of electrons in an atom. Explain the ground state and excited state of an atom. Explain the transition of an atom from an excited state to the ground state.

Atom Atom: the smallest particle of an element, having it chemical and physical properties Atom is composed of: Nucleus, which has positive electrical charge Negatively charged electrons, which form sort of cloud around the nucleus – the electron envelope Size of atom ~ m Diameter of atom : nucleus ~ : 1 Mass of nucleus > 99,95% of atom mass

Electrons Electrons: light particles with negative electric charge
eelectron = -1.6∙10-19 As = -1.6∙10-19 C ≡ -e0 melectron = 9.1∙10-31 kg  1/1820 u Electrons move in the electron cloud. Electron cloud determines the outer boundary of atom and the chemical, electrical and mechanical properties of an element. Electrons are bound to positively charged nucleus with electrical force.

Atomic number Z Z – atomic number
equal to number of electrons in neutral atom equal to consecutive number of element in the periodic table all atoms of a specific element have the same number of electrons As a rule, atom is electrically neutral negative charge of electrons = positive charge of nucleus charge of electrons in the atom = - Z ∙ e0 charge of nucleus in the atom = Z ∙ e0

Ions Atom becomes: a positive ion, if it loses electrons (positive charge of nucleus prevails) a negative ion, if it gains electrons (negative charge of electrons prevails)

Electron energy Free electrons, when moving, have positive (kinetic) energy Free electrons at rest have zero energy Electron which is bound in atom must be supplied with energy to become free electron Energy of bound electron is negative Binding energy is always negative; the lower (more negative) the binding energy, the stronger electron is bound

Electronvolt Atoms are very small and light  energies of particles within atom are very small The unit for energy on atomic scale is electronvolt (eV): Energy of a particle with elementary charge (e0), accelerated with voltage of 1 V 1 eV = 1.6∙10-19 As ∙ 1 V = 1.6∙10-19 J 1 keV = 103 eV (= 1.6∙10-16 J) 1 MeV = 106 eV (= 1.6∙10-13 J) Binding energies of electrons in atom: ~ eV - ~ keV

Energies of electrons in atom
Electrons moving in electron cloud can have only specific energies Closer the electron to nucleus, lower (more negative) its energy The specific values of energy that electrons can possess, are called energy levels of electrons in atom Any energy level can only be occupied by one electron Energy levels with lowest energies are occupied first Atom is in ground state when the lowest possible energy levels are occupied Atom is in excited state when some energy levels below those occupied are left empty

Transitions between electron energy levels
Transition from excited state to ground state: electron falls from a higher energy level into an empty lower energy level Energy difference is given off in the form of electromagnetic radiation – a photon is emitted Energy difference between levels: ~ eV visible light is emitted ~ keV X-ray of Roentgen radiation is emitted

ATOMIC NUCLEUS Learning objectives
After completing this chapter, the trainee will be able to: Describe the basic properties of protons and neutrons. Define the mass number A and write the relationship between mass number, A, atomic number, Z, and the number of neutrons in the nucleus, N. Define a nuclide and an isotope and describe their notation. Explain the isotopic abundance of an element. Describe the systematic arrangement of nuclei in a table. Describe the energy states of a nucleus. Define the binding energy of a nucleon. Plot the binding energy of a nucleon as a function of mass number, A.

Composition of the nucleus
Nucleus is composed of particles called nucleons: They are bound together with nuclear force (strongest force in nature) PROTON (p) NEUTRON (n) charge +e0 no charge mass 1, u 1, u

Protons, atomic number Protons are nucleons with positive elementary charge (+ e0) Neutral atom: the number of negative charge carriers (electrons) = the number of positive charge carriers (protons) Atomic number is also the number of protons in nucleus Nuclei of atoms of same element have equal number of protons Nuclei of atoms of different elements have different number of protons

Neutrons, mass number Neutrons are nucleons without electrical charge
Mass number A is the number of all nucleons in nucleus The number of neutrons N is given by N = A - Z Nuclei of the same element can have different number of neutrons

Nuclide Atom with a nucleus containing Nuclide is defined with:
A given number of protons and A given number of neutrons Nuclide is defined with: Number of protons = atomic number Z Number of neutrons = neutron number N Number of all nucleons = mass number A The element that nuclide belongs to = chemical symbol X Nuclide fully defined already with the element and mass number AX examples:

Isotopes Atoms of the same element can differ in weight:
Equal number of protons (and electrons) Equal chemical properties Their nuclei have different masses The difference in masses originates from different number of neutrons Atoms of a given element with different number of neutrons are called isotopes (isotopes are nuclides, belonging to the same element)

Hydrogen isotopes ordinary hydrogen heavy hydrogen superheavy hydrogen
(light hydrogen) deuterium tritium 1 p, 0 n, 1 e p, 1 n, 1 e p, 2 n, 1 e

Isotopic abundance Everywhere on Earth, elements are composed from same isotopes in fixed relative proportions. These proportions are called isotopic abundance of an element. Examples: Element Isotopes and their relative proportions Hydrogen 1H – % 2H – 0.015% Boron 10B – 19.8% 11B – 80.2% Aluminium 27Al – 100% Iron 54Fe – 5.8% 56Fe – 91.72% 57Fe – 2.2% 58Fe – 0.28% Uranium 234U – % 235U – 0.72% 238U – %

Table of stable nuclides
Among ~ 3000 nuclides there are 237 stable nuclides

Energy levels in nuclei
Nucleons can occupy different energy levels All nucleons in lowest possible energy levels: ground state Nucleons in higher energy levels: excited state

Binding energy of a nucleon
Average energy needed to release one nucleon from the nucleus

RADIOACTIVITY Learning objectives
After completing this chapter, the trainee will be able to: Describe the phenomenon of radioactive decay. Describe the random nature of radioactive decay. Define the half-life, average lifetime and the decay constant of a radioactive nuclide. Define the activity of a radioactive nuclide. Write the equation for the decay of activity with time. Calculate using the exponential law of radioactive decay. Explain the terms short-lived, long-lived and stable nuclide. Describe alpha, beta and gamma radioactive decay and give the basic properties of these types of radiation.

Stable and unstable nuclei
There are 81 elements with stable isotopes All together 237 stable nuclides Outside the region of stability, the nuclei are unstable By internal changes and particle emissions unstable nuclei are converted to stable nuclei The process of internal changes → radioactive decay Unstable nuclei → radioactive nuclides or radionuclides Around 3000 radionuclides are known (~ 100 natural, others man-made)

Radioactive decay Decay of unstable atomic nuclei
The internal energy of nucleus is decreased The energy difference is carried away by particles and/or EM radiation  (radioactive) radiation Radioactive decay is a spontaneous process The mode and the rate of decay cannot be influenced from the outside Often, an isotope of one element is converted to an isotope of another element

Statistics of radioactive decay
Unstable nuclei decay randomly and independently One can only predict the probability of decay with time The probability of decay per unit time is called decay constant  (unit s-1) The decay constant is independent of time and external influences

Half-life Half-life t1/2 is the time in which the number of radioactive nuclei decreases by half The number of radioactive nuclei is further halved with each passing of half-life: t = 0: n0 nuclei t = t1/2: ½ (n0) = n0/2 nuclei t = 2 t1/2: ½ (n0/2) = n0/4 nuclei t = 3 t1/2: ½ (n0/4) = n0/8 nuclei … t = m  t1/2: n0/2m nuclei The number of radioactive nuclei decreases exponentially with time

The exponential law of radioactive decay
Mean lifetime τ is the average time from formation of radioactive nucleus to its decay Relation to half-life: τ = 1.44 t1/2 n(t) ... number of nuclei that have not decayed after time t n0 ... number of radioactive nuclei at time t = 0 t1/2 ... half-life

A comparison of nuclides with different t1/2
Long-lived nuclides: large t1/2, small  Short-lived nuclides: small t1/2, large 

Activity Ac =  ∙ n Ac(t) = Ac0 ∙ 2-t/t1/2
Activity Ac is the number of disintegrations per unit time Activity is the product of number of radioactive nuclei and the decay constant Ac =  ∙ n Activity changes with time in the same way as the number of radioactive nuclei – decreasing exponentially: Ac(t) = Ac0 ∙ 2-t/t1/2 Ac0 … initial activity

Units for activity 1 Bq (becquerel) = 1 disintegration per second = 1 s-1 1 Bq is very small activity A human body contains ~ 7000 Bq of natural radionuclides Exemption limit: ~ few 10 kBq Old unit 1 Ci (curie) = 3.7∙1010 Bq = 37 GBq 1 Ci  activity of 1 g of radium (226Ra) 1 μCi = Bq = 37 kBq 1 mCi = 37 MBq

Specific activity Specific activity ac is activity per unit mass or volume units: kg-1 s-1 = Bq/kg or: m-3 s-1 = Bq/m3 Examples: A barrel weighing 460 kg contains 69 MBq of radionuclide 137Cs. Calculate its specific activity! The measured concentration of radon in a room was 125 Bq/m3. What is the total activity of radon in the room which is 6 m long, 4 m wide and its height is 2.2 m?

Types of radioactive decay
the type of radioactive decay is determined by the type of radiation emitted during disintegration most common types of decay are: alpha decay beta decay gamma decay the result of all types of radioactive decay is ionizing radiation: energetic particles or EM radiation that ionizes matter (removes electrons from atoms)

Alpha decay ( decay) 92 238 U → 90 234 Th +𝛼
Alpha decay is a consequence of repulsion between protons heavy nuclei (A > 209) disintegrate with α decay  particle is 4He nucleus energies of  particles are several MeV U → Th +𝛼 𝑧 𝐴 X → 𝑍−2 𝐴−4 Y He

Beta decay ( decay) beta decay is a consequence of ratio between the number of protons and neutrons outside the stability range subtypes of  decay: -, +, and electron capture (ε) nuclei with surplus of neutrons disintegrate with - decay nuclei with surplus of protons disintegrate with + decay or ε - particle is electron, + particle is positron beta decay produces also neutrino ν which carries some energy neutrino has practically no influence on matter or the environment

- decay 1 3 H → 2 3 He + 𝛽 − 𝑍 𝐴 X → 𝑍+1 𝐴 Y + 𝛽 −
during - decay, the following transition occurs inside the nucleus: n → p + e- energies of  particles: ~100 keV - MeV 𝑍 𝐴 X → 𝑍+1 𝐴 Y + 𝛽 −

+ decay 15 30 P → 14 30 Si + 𝛽 + 𝑍 𝐴 X → 𝑍−1 𝐴 Y + 𝛽 +
during β+ decay, the following transition occurs inside the nucleus: p → n + β+ when positron encounters a regular electron, annihilation occurs e- and e+ disappear, 2 photons with E = 511 keV are created 𝑍 𝐴 X → 𝑍−1 𝐴 Y + 𝛽 +

 decay nucleons in nucleus can occupy only specific energy levels
 decay is a transition from excited state of nucleus to ground state  decay usually follows  or  decays energies of  rays: ~100 keV – MeV

Isomers 43 99𝑚 Tc → 43 99 Tc +γ 43 99 Tc ∗ → 43 99 Tc +γ
some excited nuclei are stable enough to exist in an excited state for a definite time such nucleus is called isomer or 43 99𝑚 Tc → Tc +γ Tc ∗ → Tc +γ 𝑍 𝐴 X ∗ → 𝑍 𝐴 X +γ

Nuclear changes In α and β decays, the structure of nuclei changes
radioactive decay is a spontaneous change of nuclei In any change of structure of nuclei, the following is conserved: number of nucleons electric charge Examples: α decay: β decay: γ decay: 𝑧 𝐴 X → 𝑍−2 𝐴−4 Y He 𝑍 𝐴 X → 𝑍+1 𝐴 Y + −1 0 e 𝑍 𝐴 X ∗ → 𝑍 𝐴 X γ

General facts about radioactive decays
Heavy nuclei decay with alpha decay Nuclei with surplus of neutrons decay with - decay Nuclei with surplus of protons decay with + decay or electron capture (ε) After  or  decay, the daughter nucleus is often in excited state which de-excites by  decay Excited state of the resulting nucleus is usually so short-lived that  rays are attributed to the decayed nucleus

Table of nuclides Other (wall-sized) tables of nuclides provide a number of data for each nuclide

Radiation characteristics
Neutrons do not result from radioactive decay but from nuclear reactions name symbol characteristic mass charge penetration depth alpha  4He nuclei  4 u +2 e0 least penetrating radiation beta β- β+ electrons positrons u –e0 +e0 more penetrating than  gamma γ EM radiation – more penetrating than β neutron n nucleon 1 u

NUCLEAR REACTIONS Learning objectives
After completing this chapter, the trainee will be able to: Explain nuclear reactions. Name the two key conservation laws of nuclear reactions. Define the terms exoergic and endoergic nuclear reaction. List the reactions of neutrons with matter. Write down some important nuclear reactions. Define neutron flux and the reaction cross section.

General description of nuclear reaction
nuclear reactions occur when nuclei are bombarded with particles: a + X → I → Y + b short notation for nuclear reaction: X (a, b) Y

Nuclear reactions often involve nuclear changes
nuclei react with particles or other nuclei new nuclei are created  nuclear changes radioactive decay usually also results in a nuclear change fundamental difference: conservation of charge and the number of nucleons / examples: or nuclear reactions can be controlled radioactive decay is spontaneous 0 1 n B → 3 7 Li α 5 10 B ( 0 1 n , 2 4 α ) 3 7 Li 0 1 n O → 7 16 N p 8 16 O ( 0 1 n , 1 1 p ) 7 16 N

Exoergic and endoergic reactions
Exoergic reaction is accompanied by a release of energy In an endoergic reaction energy is consumed energy must be supplied for the reaction to take place (projectile must have energy larger than threshold energy)

Reactions with neutrons
neutron is a neutral particle neutrons do not interact with electron cloud neutrons get to nucleus without hindrance neutron interactions can be divided into scattering and absorption Scattering neutrons collide with nuclei bounce off them transfer of energy, no creation of new particles the result of the reaction is the initial nucleus and the neutron Absorption nucleus captures the neutron final nucleus and emitted particle are different than the initial nucleus and projectile nuclear change

Neutron scattering neutrons collide with nuclei and bounce off them
“products” of reaction (scattering) neutron and initial nucleus nucleus gains kinetic energy with the collision the kinetic energy of the neutron is decreased the neutron is slowed down → neutrons change from fast neutrons into slow or thermal neutrons can be compared with billiard balls collisions n + X → X + n or (n, n)

Neutron absorption capture fission (neutron induced fission)
radiative capture (n, ) – most typical (n, ), (n, p), … fission (neutron induced fission)

The rate of nuclear reactions
the number of nuclei reacting with neutrons in unit time the number of reactions depends on: The intensity of neutron radiation The probability for neutrons to react with nuclei (type and density of nuclei in the target)

Neutron flux ~ number of neutron per unit area and per unit time
units for flux: 1 m-2 s-1 = 10-4 cm-2 s-1 flux of neutrons in the reactor: 1012 cm-2 s-1 – 1014 cm-2 s-1

Reaction cross section
cross section  ~ effective cross sectional area of a nucleus “seen” by a beam of particles a measure for probability of a reaction on nucleus cross section unit: 1 barn = 1 b = cm2 cross section values change markedly from one nucleus to another, and also relative to neutron energy number of nuclear reactions =   n t

Neutron cross sections
cross sections for individual types of reactions are marked with corresponding index S … scattering a … absorption c … capture f … fission  … radiative capture … some cross sections are related to each other, e.g. a = c + f

Important nuclear reactions in fuel
FISSION: discussed separately in the next chapter Formation of Plutonium: (fuel contains > 95% of 238U which is not fissile) 238U (n, ) 239U 239U → 239Np + - (t1/2 = 24 min) 239Np → 239Pu + - (t1/2 = 2 d)

Important nuclear reactions in coolant
reactor coolant activation: 16O (n, p) 16N this reaction possible only with very fast neutrons (E > 10 MeV) neutron absorption in boric acid (mixed with reactor coolant) 10B (n, ) 7Li reaction 10B (n, ) 7Li important also for thermal neutron detection: 7Li ion and  particle react with the detector material tritium production in coolant: 10B (n, 2) 3H 6Li (n, ) 3H LiOH is added to reactor coolant to control its pH

Corrosion products, neutron sources
Corrosion product formation: 58Fe (n, ) 59Fe 59Co (n, ) 60Co 60Ni (n, p) 60Co 58Ni (n, p) 58Co 50Cr (n, ) 51Cr neutrons are, as a rule, not created during radioactive decay beryllium powder is mixed with -emitting radionuclide (226Ra-Be, 241Am-Be, … neutron source) 9Be (, n) 12C

NUCLEAR FISSION Learning objectives
After completing this chapter, the trainee will be able to: Describe the fission mechanism. Define fissile and fertile nuclides. Illustrate the formation of 239Pu. Name the products of fission. Sketch the dependence of fission fragment yield on mass number A. Explain why fission fragments are unstable. Explain the terms prompt and delayed neutrons. Describe the distribution of energy released by fission. Estimate the consumption of fissile material in a reactor operating at a certain power level. Sketch the time course of decay heat.

Types of nuclear fission
In fission, heavy nucleus splits – usually into two lighter nuclei spontaneous (a rare type of radioactive decay) induced (a type of nuclear reaction) Spontaneous fission (a rare type of radioactive decay) nuclei split on their own accord neutron source A » 230 242Cm (curium), t1/2 = 163 d 244Cm, t1/2 = 18 y

Induced fission caused by an increase of internal energy of nucleus most frequently when nucleus absorbs a neutron Induced fission is labelled according to energy of neutrons: thermal fission = fission caused by absorption of thermal neutron fast fission = fission caused by absorption of fast neutron

The mechanism of fission
after absorbing a neutron, the intermediate nucleus in excited state increased internal energy causes oscillation and deformation if excitation large enough, the deformation can lead to a dumb-bell shape electric repulsive forces overcome the nuclear attractive forces

Fissile and fertile nuclides
Nuclides that undergo fission after absorption of thermal neutron are called fissile nuclides: 235U and 239Pu fissile nuclides can also split after absorption of fast neutron Nuclides that after absorption of neutron are transformed with radioactive decay into fissile nuclide, are called fertile nuclides: 238U example: U n, γ U β − Np β − Pu fertile nuclides can also undergo fission after absorption of fast neutron

Products of fission Immediate products of nuclear fission:
fission fragments prompt neutrons prompt gamma rays release of energy

Fission fragments medium-sized nuclei with Z: 30 ~ 64 and A: 75 ~ 160
they carry most of energy released (~ 168 MeV) range ~ 10-3 cm  fragments stop within the fuel fission yield: probability of producing a fission fragment with mass number A

Ratio of nucleons in fission fragments

Fission products N/Zfragments  N/Zinitial heavy nucleus
N/Zfragments > N/Zstable medium-sized nuclei Fission fragments are not stable nuclei - decays Fission products fission fragments and their daughter nuclides 3 or 4 - decays to stable nucleus (5 – 20 MeV is released) t1/2 of fission products: from ~0.1 s to several million years

Importance of fission product decay
Large quantities of heat (decay heat) is released after shutdown of the reactor and removal of this heat is necessary Radiation from decay is dangerous to health Emission of delayed neutrons Some fission products are strong neutron absorbers

Prompt neutrons and prompt gamma rays
parameter : average number of neutrons per fission  depends on the nuclide an the neutron energy for most nuclides,  is between 2 and 3 (235U:  = 2.43) average kinetic energy  2 MeV in total they carry away  5 MeV Prompt gamma rays on average, around 8 gamma rays are released per fission in total they carry away  7 MeV

Delayed neutrons emitted after - decay of some fission fragments
daughter nuclides of these fragments emit a neutron -n decay The fission fragment that leads to neutron emission is called delayed neutron precursor The delay time of such neutron is determined by the lifetime of its precursor

Production of delayed neutrons

87Br: example of -n decay
lifetime   80 s 87Br disintegrates after ~ 80 s delayed neutron is born 80 s after fission

Parameters of delayed neutrons
Delay time from fission to release of delayed neutrons: average delay time  ~ 13 s Delayed neutron fraction : fraction of delayed neutrons in the total number of neutrons produced per fission  < 1%, but crucial for successful reactor control  depends on nuclide and neutron energy thermal fission of 235U:  = thermal fission of 239Pu:  = fast fission of 238U:  = due to mixture of nuclides in the fuel, the average delayed neutron fraction changes (decreases) with fuel burn-up

Distribution of energy released by 235U fission
Prompt energy release range fission fragments 168 MeV ~ 10 μm prompt neutrons 5 MeV 0.1 – 1 m prompt gamma rays 7 MeV gamma rays from (n, ) reactions 6 MeV total prompt energy release 186 MeV Delayed energy release β from fission fragment decay 7 MeV ~ mm γ from fission fragment decay 6 MeV β and  from nuclei produced by (n, ) 1 MeV 0.001 – 1 m total delayed energy release 14 MeV total energy release 200 MeV

Consumption of fissile material
reactor operates 1 day at power at 1 MW power energy produced = 1 MWd number of fissions = number of fissioned 235U nuclei the uranium mass that corresponds: m = 2.7·1021 · 235 · 1.66·10-27 kg = 1.05·10-3 kg ≈ 1 g example: 30 days of operation at power of 3000 MW: 90 kg of 235U is consumed 1 MWd= 1 MWd 200 MeV/fission = J s ∙24∙3600 s 200∙ 10 6 ∙1.6∙ 10 −19 J fission =2.7∙ fissions

Decay heat Energy released in the core after reactor shutdown
a consequence of - and  decay of fission products Decay heat proportional to reactor power before shutdown with higher power, more fission products are produced Immediately after shutdown, the decay heat diminishes rapidly consequence of quick decay of short-lived fission products Decay heat diminishes slower, the longer reactor has operated more long/lived fission products have been produced

Time dependence of decay heat decrease
depends on the reactor operating time prior to its shutdown

Decay heat after a long operation at 3000 MWth
Time after shutdown Full power fraction Decay heat 1 s 6.2 % 185 MW 1 min 3.6 % 107 MW 1 hour 1.3 % 38 MW 8 hours 0.6 % 19 MW 1 day 0.4 % 13 MW 1 week 0.2 % 7 MW 1 month 0.1 % 4 MW

Decay heat in the spent fuel pit of a 3000 MWth reactor

NEUTRON CYCLE Learning objectives
After completing this chapter, the trainee will be able to: Explain the slowing down of neutrons in the core. Give the properties of an effective moderator. Define individual factors in the neutron cycle. Define the multiplication factor, k. Explain a chain reaction. Define reactivity and the corresponding units.

Division of neutrons in terms of their energy
Basic division: fast: E > 0.1 MeV epithermal: 1 eV < E < 0.1 MeV thermal E < 1 eV fast neutrons are produced by fission epithermal neutrons are in the slowing-down process slowing-down takes place in the moderator thermal neutrons have completed the slowing-down process their energy (Ek) depends in the temperature of matter they move in

Slowing-down of neutrons in the reactor core
fast neutron loses its energy by scattering on nuclei in the matter most effective is elastic scattering on light nuclei moderator: material that slows down neutrons in the reactor core in light-water reactors the moderator is water (hydrogen) other possible moderators: heavy water (deuterium) graphite (carbon)

Characteristics of moderator
A good moderator has: large probability of scattering, i.e. large scattering x-section s, large average energy loss per collision small probability for neutron absorption, i.e. small absorption x-section a, non-nuclear properties: stable, good thermo-hydraulic properties, low price. Ordinary (light) water is relatively good moderator: however, it is corrosive at high temperatures activated in neutron flux good thermal/hydraulic properties cheap Heavy water is better because of lower neutron absorption.

Lifetime of a generation of neutrons
The majority of fissions in light water reactors is induced by thermal neutrons. In fission, fast neutrons are produced. What happens to a generation of fast neutrons, born in thermal fission?

Fast fission factor ε Some fast neutrons induce fission, mainly on 238U in low-enriched fuel. neutrons, born in fast fission, are fast neutrons, as well fast fission increases the number of fast neutrons for a factor of ε: The initial generation of n fast neutrons, born in thermal fissions, is increased to (ε ∙ n) fast neutrons, born in both, thermal and fast fissions. 𝜀= number of fast neutrons produced by fission with neutrons of all energies number of fast neutrons produced by fission with thermal neutrons

Fast fission: factor ε Fast fission factor is always greater than one.
LWRs: ε ~ 1.1

Fast non-leakage factor Pf
Probability that a fast neutron will not escape from the core: From (ε ∙ n) fast neutrons, (Pf ∙ ε ∙ n) remain in the core. Pf= number of fast neutrons which remain in the core number of fast neutrons produced by fission with neutrons of all energies

Fast neutron leakage: factor Pf
Fast non-leakage factor is always smaller than one typical PWR: Pf  0.98

Resonance escape probability p
As fast neutrons slow down, same of them are absorbed. The highest probability for neutron absorption is in the epithermal energy range (resonance absorption) most resonance absorption occurs in 238U and 240Pu Probability that fast neutrons that slow down will not be absorbed in resonances: From (Pf ∙ ε ∙ n) fast neutrons that start slowing down, (p ∙ Pf ∙ ε ∙ n) slow down to thermal energies. p= number of fast neutrons slowed down to thermal energies number of fast neutrons that start slowing down

Resonance escape: factor p
resonance escape probability is always smaller than 1 depends on the fuel enrichment

Thermal non-leakage factor Pt
Probability that a thermal neutron will not escape from the core: From (p ∙ Pf ∙ ε ∙ n) neutrons that slowed down to thermal energies, (Pt ∙ p ∙ Pf ∙ ε ∙ n) remain in the core. Pt= number of thermal neutrons which remain in the core number of neutrons which slow down to thermal energies

Thermal neutron leakage: factor Pt
Thermal non-leakage factor is always smaller than one typical PWR: Pt  0.99

Thermal utilisation factor f
Fraction of thermal neutrons absorbed in fuel relative to absorption elsewhere the core: From (Pt ∙ p ∙ Pf ∙ ε ∙ n) thermal neutrons that remain in the core, (f ∙ Pt ∙ p ∙ Pf ∙ ε ∙ n) thermal neutrons are absorbed in the fuel f= number of thermal neutrons absorbed in the fuel number of thermal neutrons absorbed in all core materials

Utilisation of thermal neutrons: factor f
The value of factor f can change significantly it is changed intentionally, in order to control the operation of reactor

Neutron yield per absorption 
Number of fast neutrons which are released in thermal fission per thermal neutron absorbed in fuel: From (f ∙ Pt ∙ p ∙ Pf ∙ ε ∙ n) thermal neutrons absorbed in the fuel, ( ∙ f ∙ Pt ∙ p ∙ Pf ∙ ε ∙ n) fast neutrons are produced in fission. = number of fast neutrons from thermal fission number of thermal neutrons absorbed in fuel

Neutron reproduction: factor 
Neutron yield per absorption is always greater than one. depends significantly on fuel enrichment: natural uranium:  = 1.34, 3% enrichment:  = 1.84, pure 235U:  = 2.08.

Neutron cycle

Multiplication factor k
Multiplication factor, k, is the defined as the radio of the number of neutrons in one generation to the number of neutrons in the previous generation: In the neutron cycle, as described previously, k can be expressed as a product of six factors: k= number of neutrons in given generation number of neutrons in the previous generation k =  ∙ f ∙ Pt ∙ p ∙ Pf ∙ ε

Chain reaction each generation of neutrons leads to the birth of next generation of neutrons chain reaction in the case k = 2: 1st generation 2nd generation 3rd generation of neutrons of neutrons of neutrons

Criticality k = 1: critical chain reaction
the number of neutrons in the core does not change with time, the number of fissions per unit time is constant, reactor power is constant. k > 1: supercritical chain reaction the number of neutrons in the core increases with time, the number of fissions per unit time increases with time, reactor power increases. k < 1: critical chain reaction the number of neutrons in the core does decreases with time, the number of fissions per unit time decreases with time, reactor power decreases.

Reactivity We are usually interested in reactor conditions where k  1
we want to avoid using a large number of decimal places Let us introduce reactivity, which represents departure from criticality: k < 1  ρ < 0  reactor is subcritical, k = 1  ρ = 0  reactor is critical, k > 1  ρ > 0  reactor is supercritical.

Notations for reactivity
reactivity is dimensionless quantity several notations are used: k/k: reactivity is calculated and the number is followed by k/k % k/k: 1% k/k = 0.01 k/k pcm: 1 pcm = k/k $: 1 $ = k/k

Positive and negative reactivity
Any change of the core properties modifies k and ρ: burnup of fuel, production of fission products, operator actions (boron concentration, control rods). If changes in the core decrease the multiplication factor k: negative reactivity has been added in the core. If changes in the core increase the multiplication factor k: positive reactivity has been added in the core.

Reactivity and change of reactor power
During operation at constant power: the reactor is critical, multiplication factor k = 1, core reactivity ρ = 0. If we want to increase the power, positive reactivity has to be added in the core. If we want to decrease the power, negative reactivity has to be added in the core.

REACTOR KINETICS Learning objectives
After completing this chapter, the trainee will be able to: Explain the exponential increase in reactor power. Define the period T. Define the start-up rate or SUR. Describe the relationship between the multiplication factor, reactivity, the period and start-up rate and sketch how power changes for different k values. Explain a chain reaction by taking and without taking delayed neutrons into account. Define prompt criticality. Sketch the reactor power response to a step change in reactivity.

Operation ranges of reactor

Reactor operation at low power range
Thermal power negligible  the temperature of fuel and coolant does not change perceptibly with change of power no temperature feedback effects on reactivity Any change of reactivity is cause exclusively with external actions, e.g. withdrawal or lowering the control rods

Time dependence of reactor power
time for one neutron cycle to pass = average lifetime of neutrons = l change in the number of neutrons in one cycle: N = k ∙ N – N = (k – 1) ∙ N = k ∙ N change per unit time: ∆𝑁 ∆𝑡 = ∆𝑘∙𝑁 𝑙 solution: 𝑁= 𝑁 0 ∙ 𝑒 ∆𝑘 𝑙 ∙𝑡 N0 … number of neutrons at time t = 0 N … number of neutrons at time t

Reactor period T introducing 𝑙 ∆𝑘 =𝑇: 𝑁= 𝑁 0 ∙ 𝑒 𝑡 𝑇 ⇒𝑃= 𝑃 0 ∙ 𝑒 𝑡 𝑇
𝑁= 𝑁 0 ∙ 𝑒 𝑡 𝑇 ⇒𝑃= 𝑃 0 ∙ 𝑒 𝑡 𝑇 T is the reactor period – in this time the reactor power changes for a factor of e.

Start-up rate the rate at which reactor power changes is usually expressed by the start-up rate, SUR, defined by the equation: 𝑃= 𝑃 0 ∙ 10 𝑆𝑈𝑅 P0 … initial reactor power P … reactor power after t minutes SUR is measured in DPM (decades per minute) or min-1 relationship between SUR and the reactor period T: 𝑆𝑈𝑅= 26 𝑇 T is in seconds, SUR in DPM!

Supercritical reactor
k > 1  ρ > 0  T > 0  SUR > 0 Reactor power increases exponentially with time. The higher k, the higher the core reactivity ρ and the faster reactor power increases: higher is SUR and shorter the reactor period T. When increasing the power, the reactor is supercritical. The operators must increase reactor power slowly and in accordance with the procedure which specifies the maximum start-up rate.

Supercritical reactor dynamics

Critical reactor k = 1  ρ = 0  T = ∞  SUR = 0
At higher power levels, the number of fissions per unit of time (or number of neutrons) is higher than at lower power levels, but constant in a critical reactor (it does not change with time).

k < 1  ρ < 0  T < 0  SUR < 0
Subcritical reactor k < 1  ρ < 0  T < 0  SUR < 0 Reactor power decreases exponentially with time. The smaller k, the smaller the core reactivity ρ (more negative) and the faster reactor power decreases: shorter negative period T and higher negative SUR. When decreasing the power, the reactor is always subcritical.

Subcritical reactor dynamics

Neutron lifetime Time from the birth to the disappearance of a neutron (escape, absorption). It is divided into: birth time: the time from fission to neutron release ~ s, slowing-down time: the average time from neutron’s release to its thermalization ~ 10-5 s, diffusion time: the average time from a neutron’s thermalization to its disappearance ~ 10-5 s.

Phases of neutron lifetime
lifetime of prompt neutrons in a pressurized water reactor core is of the order of magnitude of 10‑4 s.

Chain reaction with prompt neutrons
Reactor operates at 10 kW constant power. The operator withdraws the control rods few steps, i.e., adds positive reactivity ρ = 70 pcm. k  𝑇= 𝑙 ∆𝑘 = 10 −4 s =0.143 s after 1 second: 𝑃= 𝑃 0 ∙ 𝑒 𝑡 𝑇 = 𝑃 0 ∙ 𝑒 1 s s ≈1100 𝑃 0 If the chain reaction is maintained with prompt neutrons only, the corresponding fast changes of power are impossible to control.

Average lifetime of prompt and delayed neutrons
Slowing-down and diffusion times of delayed neutrons are comparable to those of prompt neutrons Birth time of delayed neutron is the life time  of its precursor (for 235U fission ~ 13 s) and is much longer that diffusion or slowing/down time. Lifetime of delayed neutrons is essentially the lifetime  of their precursors. Average lifetime of all neutrons: l = (1 – β) ∙ lp + β ∙  l = (1 – ) ∙ 10-4 s ∙ 13 s  0.1 s

Chain reaction with prompt and delayed neutrons
Reactor at 10 kW constant power, positive reactivity ρ = 70 pcm 𝑇= 𝑙 ∆𝑘 = 0.1 s =143 s after 1 second: 𝑃= 𝑃 0 ∙ 𝑒 𝑡 𝑇 = 𝑃 0 ∙ 𝑒 1 s 143 s ≈1.007 𝑃 0 after 100 seconds: 𝑃= 𝑃 0 ∙ 𝑒 𝑡 𝑇 = 𝑃 0 ∙ 𝑒 100 s 143 s ≈2.0 𝑃 0 In 1 s, the power increases by 0.7% and in 100 s it doubles. Such slow changes, due to contribution of delayed neutrons, are well within the operator’s control.

Dependence of reactor period on reactivity
the graph shows absolute values of reactivity and reactor period the shortest negative period is ‑80 s. reactor can not shut down faster than the decay of most long-lived precursors

Prompt criticality in case 𝜌≥ 𝛽 : reactor period determined by the lifetime of prompt neutrons reactor period becomes very short reactor is said to be prompt critical Rule: reactor reactivity must always be kept smaller than 𝜷 (1$) both during start-up and power increase.

Reactor power response to a positive step change in reactivity

Reactor response to a negative step change in reactivity

REACTIVITY CHANGES Learning objectives
After completing this chapter, the trainee will be able to: Give a qualitative explanation of the temperature coefficients of reactivity. Describe the impact of power change on reactivity. Sketch reactor power response to a step change in reactivity. Describe the formation and removal of 135Xe and 149Sm. Sketch the reactivity due to Xe and Sm as a function of time after start-up. Sketch the reactivity due to Xe and Sm after shutdown. Sketch how the critical concentration of boron, CB, changes relative to its burn-up rate. Describe the principle of reactor control.

Classification of reactivity changes
During reactor operation, the core properties and consequently its reactivity change. Based on how fast the core properties or its reactivity change during reactor operation, reactivity changes are classified as: short-term changes (~ seconds, minutes) medium-term changes (~ hours) long-term changes (~ months)

Short-term reactivity changes
when reactor is in operating power range (0% - 100%), fuel and coolant temperatures change change of temperature influences: density of the moderator resonance absorption in fuel void fraction in the coolant

Impact of coolant (moderator) temperature on reactivity
The moderator temperature coefficient, αm, is defined as the change in reactivity per degree change in the average moderator temperature. increase in coolant (moderator) temperature decreases its density mass of water in the core decreases, mass of fuel remains constant: increase in neutron absorption in fuel relative to absorption in water increase of the thermal utilization factor f slowing down distance of neutrons increases resonance absorption increases: resonance escape factor p decreases Depending on which of the two effects prevails: αm is negative or positive. LWRs usually constructed for a negative αm

Impact of fuel temperature on reactivity
The fuel temperature coefficient, αf, is defined as the change in reactivity per degree change in the fuel temperature. Increase in fuel temperature increases the resonance absorption of neutrons. Commercial reactors have low enriched fuel  parasitic resonance absorption in 238U (and 240Pu) predominates. The fuel temperature coefficient αf is always negative.

Impact of void fraction on reactivity
The void coefficient, αv, is the reactivity change per percent change in the void fraction. Increase in fraction of voids (steam bubbles) in the core reduces the moderator density. Impact on reactivity is similar to the impact of the moderator temperature. Due to small total void fraction formed in the core of a PWR, the associated total reactivity change is small. Void coefficient is important in BWRs.

Impact of power change on reactivity
The power coefficient, αp, is defined as the change in reactivity per percent power change. Change of power changes the coolant temperature, the fuel temperature, and the void fraction. The combined effects of moderator, fuel and axial power redistribution are accounted for in the total power coefficient. In PWRs, power coefficient is always negative. The power defect tells us how much core reactivity changes if reactor power is changed by a given value of P.

Response to a step change in reactivity at operating power
At operating power range, temperature feedback effects are present (neglected in chapter “Reactor kinetics”). Operator withdraws the control rods for a few steps Power is stabilized at higher level

Mid-term changes of reactivity
Fissions in the core result in over 200 different fission products. Two fission products important for reactor operation: 135Xe – absorption cross-section for thermal neutrons a = 2∙106 b 149Sm – absorption cross-section for thermal neutrons a = 4∙104 b

Production and removal of Xenon-135
135Xe is produced: as a direct product of fission from the decay of 135I which decays with a half-life of 6.6 hours and is a daughter products of the fission fragments 135Sb and/or 135Te Te β − , s I β − , h fission → Xe 135Xe is removed: by burn-up via the neutron capture reaction decays with a half-life of 9.1 hours Xe β − , h Cs β − , 2∙ y Ba n,γ Xe

135Xe during reactor start-up
After reactor start-up, 135Xe concentration starts to grow Equilibrium concentration of 135Xe approx h after start-up equilibrium conc. depends on reactor power, but dependence not linear

135Xe during reactor shutdown
after shut-down, 135Xe in produced by the decay of 135I (t1/2 = 6.6 h), and is removed by its own decay (t1/2 = 9.1 h) maximum 135Xe concentration reached ~ 9 h after shutdown (depending on reactor power) after ~24 h 135Xe concentration roughly equal to its level at shutdown after ~ 80 – 90 h there is practically no 135Xe in the core during 135Xe decay, positive reactivity is inserted into the core – possible recriticality of reactor!

Reactivity due to 135Xe after shutdown

Production and removal of Samarium-149
149Sm is produced: from the decay of 149Pm (promethium) which decays with t1/2 = 53.1 h Ce β − , 5 s Pr β − , min Nd β − , ℎ Pm β − , h Sm 149Sm is removed: by burn-up via the neutron capture reaction Sm n,γ Sm

149Sm during reactor start-up
After reactor start-up and with a fresh core, 149Sm concentration starts to grow. Equilibrium concentration of 135Xe approx. 400 h after start-up and is independent of reactor power.

149Sm during reactor shutdown
after shut-down, 149Sm burn-up by neutron absorption ceases, but 149Sm is still produced by the decay of 149Pm maximum 149Sm concentration reached ~ 400 h after shutdown (depending on reactor power)

149Sm during reactor restart
As the reactor is restarted on power, the equilibrium concentration of 149Sm equal to its value prior to shut-down is re-established.

Long-term changes of reactivity
With operation of a LWR through a fuel cycle: burn-up of 235U burn-up of 238U (negligible importance) production of 239Pu and other Plutonium isotopes production of fission products, some of which are important neutron absorbers With core burn-up, the reactivity of core decreases.

Excess reactivity Excess reactivity is defined as the amount of surplus reactivity over that needed to enable reactor operation at zero power. Excess reactivity is compensated by adding boron to the coolant and by burnable poisons. Since core reactivity decreases with burn-up, the concentration of boron CB in the moderator is gradually reduced over the fuel cycle.

Critical boron concentration
The critical boron concentration (CB) is defined as the concentration of boron required for the reactor to be critical on full power with the control rods withdrawn. Typical course of critical boron concentration over the fuel cycle:

Reactor control Operators primarily influence core reactivity in two ways: by control rods alloy of 80% Ag, 15% In and 5% Cd good absorber of thermal and epithermal neutrons compensation of short-term reactivity changes ensure a negative reactivity reserve needed for fast reactor shut-down by changing the boric acid concentration in the coolant good absorber of thermal neutrons compensation of mid-term and long-term reactivity changes

SUBCRITICAL MULTIPLICATION
Learning objectives After completing this chapter, the trainee will be able to: Explain subcritical multiplication. Define the subcritical multiplication factor, M. Explain the 1/M curve for core loading.

Neutron sources Neutron population in core measured by excore detectors they measure neutrons that leak out of the core when reactor is shut down, the neutron population is low Independent neutron sources in the core are needed: control of the reactivity changes in the subcritical reactor, signal on the detectors high enough for controlled approach to criticality, verification that the excore detectors are operational.

Types of neutron sources
Nonregenerative neutron sources: (Pu-Be) source: α particle emitted by Pu triggers reaction 9Be(α,n)12C 252Cf: spontaneous fission Regenerative neutron source: (Sb-Be) source: antimony is activated in neutron flux: 123Sb(n,)124Sb; gammas from the decay of 124Sb trigger reaction 9Be(,n)2 α Reactors that have operated for several cycles: no need for additional neutron sources in the core old fuel elements contain sufficient amount of 242Cm and 244Cm which fission spontaneously and emit neutrons

Population of neutrons in subcritical reactor
Number of neutrons per unit time in a subcritical reactor: 𝑁= 𝑆 0 1−𝑘 S0 … number of neutrons emitted by source per time unit A subcritical reactor with an independent source creates an equilibrium neutron population, N, even when k < 1. If the independent source were removed from a subcritical reactor, the neutron population would drop to zero.

Response to a step change of reactivity in subcritical reactor

Subcritical multiplication factor
𝑀= 1 1−𝑘 ratio between the total neutron population per unit time and the number of neutrons per unit time emitted by the neutron source when approaching criticality (e.g. core loading) k → 1  M → ∞ or: 𝑘⟶1⟹ 1 𝑀 ⟶0 Core loading should be managed with great care, and the neutron population must be continuously monitored → by using the 1/M value

Example: loading of empty core
In an empty core, k = 0. Count rate co (base count rate) results exclusively from the independent sources. 1/M is calculated: 1 𝑀 = 𝑐 0 𝑐 0 =1 a few fuel elements are added to the core. This makes k ≠ 0. The detector counts c1 impulses and 1/M is: 1 𝑀 = 𝑐 0 𝑐 1 <1 both values are entered on a graph and a line is drawn through extrapolation of this line to horizontal axis gives an estimate how many more fuel elements are needed

Loading of empty core (cont’d)
each step (adding a few more elements) gives better estimate how many more elements are needed to reach criticality step Number of inserted elements ci c0/ci 100 1 10 125 0.8 2 20 166 0.6 3 30 250 0.4 4 40 500 0.2 5 45 1000 0.1

Inverse Count Rate Ratio – ICRR
base count rate can be placed anywhere 1/M curve is renormalized to a new base count in this case we rather speak of the ICRR curve prediction of the criticality (ICRR = 0) remains the same

Loading of a power reactor
ICRR is determined after loading of each fuel element if ICRR deviates abnormally, stop all activities in the core and act in accordance with the relevant procedures for safety reasons, the core is heavily poisoned with boric acid even after loading all fuel elements, reactor remain subcritical

HEAT REMOVAL FROM NUCLEAR REACTORS
Learning objectives After completing this chapter, the trainee will be able to: Name three modes of heat transfer. Describe heat conduction. Describe forced and natural convection. Describe heat transfer to a fluid with phase change. Explain the formation of steam bubbles. Sketch and describe the boiling curve. Define the boiling crisis. Describe the average and maximum thermal power of a fuel rod in a PWR. Describe hot channel factors and explain the reasons for their limits.

Definition of basic quantities
Heat is energy which passes from a point of higher temperature to a point of lower temperature. If there is no difference in temperature, there can be no heat transfer. Heat flux is defined as the quantity of heat per unit time: 𝑄 = ∆𝑄 ∆𝑡 [J/s = W] Heat flux density is heat flux per unit surface area [W/m2].

Modes of heat transfer heat conduction through matter (diffusion)
heat transfer by means of fluid flows (convection) radiation convection conduction radiation

Heat conduction process which takes place at the atomic level

Heat conduction equation
𝑄 = 𝜆 𝐴 Δ𝑇 Δ𝑥  heat conductivity [W/mK] A surface area of the wall [m2] T temperature difference [K] x wall thickness [m]

Temperature profile in a wall made of various materials

Temperature profile in fuel rod
CL r1 r2 r3 coolant fuel pellet gap cladding T TW TB ~8 mm 0.01 ~0.6 mm

Convection Convection involves heat transferred by the flow of fluid.
Convection can be natural or forced. Example of natural convection in PWR: core cooling after primary pumps have been shut down heat source heat sink Δh

Natural convection Convection is heat transfer by the flow of fluid.
Natural convection: the fluid moves due to a difference in fluid density (temperature difference or phase change) Example of natural convection due to difference in liquid density is PWR core cooling after shut down of primary pumps. Example of natural convection due to phase change is the circulation of secondary water inside a steam generator.

Forced convection Fluid is forced to move by means of a pump or fan.
Example in PWR: the flow of the primary coolant through the core driven by the operation of reactor coolant pumps.

Equation of heat transfer
𝑄 = ℎ c 𝐴 Δ𝑇 hc heat transfer coefficient [W/m2K] A wall surface area [m2] T temperature difference between wall and fluid [K] hc depends on fluid velocity, pressure, temperature, the flow regimes of potential two-phase flow, etc. It is determined experimentally.

Radiative heat transfer
Emission of internal energy by electromagnetic waves. Radiation can spread through empty space (a vacuum), as well. Stefan-Boltzmann law: 𝑄 =𝜀 𝜎 𝐴 𝑇 4 ε emission coefficient (1 for a black body) σ Stefan-Boltzmann constant A total area of the body radiating heat T absolute temperature Examples: solar radiation uncovered reactor core in case of Loss-Of-Coolant-Accident (LOCA)

Boiling heat transfer When heat is transferred from a solid body to a liquid and the temperature of solid body is high enough, the liquid may boil phase change heat flux is significantly higher than in the case of natural or forced convection similar applies for condensation, as well saturated boiling: water is at the boiling point temperature throughout its bulk subcooled boiling: temperature lower than boiling point, bubbles collapse when they break away from the heating surface

Bubble formation Bubbles break away from the heating surface, “mixing” the liquid and “breaking” the laminar layer of liquid which would otherwise cause much lower heat transfer.

Boiling curve

4 regions of the boiling curve
Natural convection: small T Nucleate boiling: beginning of boiling subcooled nucleate boiling saturated nucleate boiling Partial film boiling: bubbles combine into layers next to the wall this layer of vapour insulates the surface and reduces heat transfer in this region, the vapour layers are not stable Film boiling and radiation: stable layers of vapour form next to the heating body poor heat transfer despite a relatively large temperature difference

Departure from Nucleate Boiling
Point c: boiling crisis or Departure from Nucleate Boiling – DNB nucleate boiling switches over to film boiling heat flux at point c is called the critical or DNB heat flux. Departure from Nucleate Boiling Ratio – DNBR: DNBR should always be greater than 1 DNBR limit value is set down in the Technical Specifications DNBR = critical heat flux actual heat flux

Heat transfer in the reactor core
During normal operation and during incidents, the integrity of the reactor core must be maintained. Design limits for the fuel pellet temperature and the boiling crisis Power distribution in the core is uneven and depends on: nuclear properties thermodynamic parameters fabrication parameters Power distribution is described by using peaking factors maximum value of certain parameter is a product of average value and respective peaking factor

Average linear power density
thermal power released per unit fuel rod length [kW/m] Example: thermal power of a PWR: MW number of fuel elements in the core: 121 number of fuel rods in each element: 235 length of fuel rod: m fraction of heat released in the fuel: 97.4% 𝑞 = 1994∙1000 kW ∙ ∙235 ∙3.6 m =18.7 kW/m Linear power density is not equal for all the rods in a fuel element varies among individual elements varies with the height of a fuel rod in the core

Heat flux hot channel factor FQ
maximum allowed FQ set in the operational limits example: FQ = maximum heat flux in the core average heat flux in the core

Maximum allowed linear power density
example: 𝑞 max = 𝐹 𝑄 ∙ 𝑞 =2.35∙18.7 kW/m=44 kW/m The FQ limit ensures that: the maximum temperature in the middle of a fuel pellet (centreline temperature) during normal operation is lower than the melting point temperature, the maximum temperature of fuel rod cladding during a loss of coolant accident is lower than 1200° C.

Enthalpy rise hot channel factor, FΔH
example: Hot channel factors calculated from periodic (~ every 1000 MWd/t) measurements of thermal neutron flux with movable neutron detectors. FH = maximum fuel rod integral power average fuel rod integral power The FH limit ensures that a boiling crisis does not occur during normal operation and moderately frequent incidents.

Operating conditions and DNBR
during operation, DNBR > 2.0 DNBR = critical heat flux actual heat flux DNBR is reduced when: the pressure in the primary system falls, the flow in the primary system decreases, the temperature of the primary coolant rises The views expressed in this document do not necessarily reflect the views of the European Commission.

BASIC PROFESSIONAL TRAINING COURSE Module I Nuclear physics and reactor theory Version 1a, September 2014 This material was prepared by the IAEA.

Similar presentations

Presentation on theme: "BASIC PROFESSIONAL TRAINING COURSE Module I Nuclear physics and reactor theory Version 1a, September 2014 This material was prepared by the IAEA."— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

BASIC PROFESSIONAL TRAINING COURSE Module I Nuclear physics and reactor theory Version 1a, September 2014 This material was prepared by the IAEA.

Similar presentations

Presentation on theme: "BASIC PROFESSIONAL TRAINING COURSE Module I Nuclear physics and reactor theory Version 1a, September 2014 This material was prepared by the IAEA."— Presentation transcript:

Similar presentations

About project

Feedback