Criticality of Nuclear - PowerPoint Presentation

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Criticality of Nuclear reactorsand Geometric Buckling

Eastern Illinois University

Derek Smith

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How do you make Nuclear energy safe?1. Understand a basic reactor.

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http://www.cameco.com/uranium_101/uranium_science/nuclear_reactors/Slide4

How to understand Nuclear Energy1. Understand a basic reactor.

2. Understand how the control rods maintain reactor criticality.

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https://commons.wikimedia.org/wiki/File:Control_rods_schematic.svg

Farther down= more neutrons absorbed & less heat

Farther up= less neutrons absorbed & higher heatSlide6

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http://www.lanl.gov/quarterly/q_fall03/reactor.shtmlSlide7

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How to understand Nuclear Energy1. Understand a basic reactor.

2. Understand how the control rods maintain reactor criticality.3. what is criticality?

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CriticalityCriticality may be defined as the “attainment of physical conditions such that a fissile material will sustain a chain reaction”

Accidental criticality is the highest hazard a health physicist deals with.

This can be maintained with efforts to prevent accidental criticality with Criticality control or Nuclear safety

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Accidental criticalityU235 nucleus

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Alpha particleSlide11

Uncontrolled chain reaction:from accidental criticality

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Criticality

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Sub-critical13Slide14

Criticality

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Super-Critical

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Criticality

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Critical

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Criticality Control

Accidental criticality depends on the following:Quantity of the fissile material

Geometry of the fissile assemblyPresence or absence of a moderator

Presence or absence of a neutron reflectorPresence or absence of a strong neutron absorber (poison)

Concentration of fissile material, if the fissile material is in solutionInteraction between two or more assemblies or arrays of fissile material, each one of which is subcritical by itself. Consideration of this possibility is important in

the transport and storage of fissile materials.

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Criticality control

Nuclear safety can be assured by limiting at least one of the factors that determines criticality

Mass control- limiting the mass of fissile material to less than the critical mass under any conceivable condition

Geometry control- having a geometric configuration that can never become critical because the surface-to-volume ratio is such that excessive neutron leakage makes it impossible to attain a multiplication factor as great as 1.

Concentration control- if the solution of fissile material is sufficiently dilute, absorption of neutrons by the hydrogen atoms makes a sustained chain reaction impossible. The degree of enrichment of

235

U is important to this control.

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How to understand Nuclear Energy1. Understand a basic reactor.

2. Understand how the control rods maintain reactor criticality.3. what is criticality?4. Understanding Fission

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Nuclear Fission: Uranium relation

Nuclei with odd numbers of nucleons are more easily fissioned than those with an even number of nucleons. For example which fissions after capturing a thermal neutron,

Whereas which can also capture a thermal neutron, is transformed into an even-odd nucleus and rids itself of its excitation energy by emitting a gamma ray

http://scienceblogs.com/startswithabang/2009/04/is_uranium_the_heaviest_natura.php

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Nuclear Fission: fission fragments

When an atom fissions, it splits into two fission fragments plus several neutrons (the mean number of neutrons per fission of is 2.5) plus gamma rays according to the conservation equation:

An approximate distribution of this energy is as follows:Fission fragments, kinetic energy 167 MeV

Neutron kinetic energy 6Fission gamma rays 6Radioactive decay

Beta particle 5 Gamma rays 5 neutrinos 11

200 MeV

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Nuclear Fission: Spontaneous fission

For the possibility of fission the following mass- energy relationship must hold:This condition can only be met by isotopes whose atomic number and atomic mass are such that:

Although its likelihood is very small spontaneous fission (can cause accidental criticality) is very important in criticality control.If an isotope : the nucleus is unstable toward fission and would undergo spontaneous fission.

http://acadine.physics.jmu.edu/main/phys215_transparencies/12.nuclear_fission/61_liquid_drop_model.JPG

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Uncontrolled chain reaction:from accidental criticality

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Nuclear Fission: Rate of FissionMost of the energy dissipated in the critical assembly is heat energy. Using a mean value of 190

MeV (million- electron volts) heat energy per fission, the rate of fission to generate one watt of power is calculated as follows:

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How to understand Nuclear Energy1. Understand a basic reactor.

2. Understand how the control rods maintain reactor criticality.3. what is criticality?4. Understanding Fission5.Putting a value on criticality

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Multiplication factor: The Four-Factor FormulaCriticality, also known as the value of

Keff depends on the supply of neutrons of proper energy to initiate fission and also on the availability of fissile atoms.

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Four factor Formula: Infinite Multiplication Factor

η

is the mean number of neutrons emitted per

absorption of Uranium, so n

thermal neutrons will result in

η

n

fission neutrons.

Є

=

fast fission factor with max value= 1.29

p=Resonance capture is called Resonance escape probability

or

p

and is defined as the fraction of the fast, fission produced neutrons that finally become

thermalized

. The value of

p

depends on the ratio of moderator to fuel.

f=The fraction of the total number of

thermalized

neutrons absorbed by the fuel (including all the uranium) is called the

thermal utilization factor, f

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Reactivity and Reactor Control Increase in the

neutron multiplication factor >1 is called excess reactivity, defined by: For neutrons in one generation, we have additional neutrons in succeeding generation. The time rate of change of neutrons is:

, is the lifetime of the neutron generation

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Reactivity and Reactor Control0.001s is the mean lifetime of a neutron from its birth to its absorption in pure

235U When the excess reactivity is 0.1%, that is ∆

k = 0.001, the reactor period is: T=0.001/0.001= 1s and the power level increases by a factor of e, or 2.718 each second.

If ∆k were increased to 5% then: T= 0.001/0.005= 0.2s ,and the power lever increases in 1s would be by a factor of 150.

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How to understand Nuclear Energy1. Understand a basic reactor.

2. Understand how the control rods maintain reactor criticality.3. what is criticality?4. Understanding Fission5.Putting a value on criticality

6.Multiplying medium

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Reactor PhysicsMultiplying Medium

A multiplying medium is one in which fission, either thermal or fast or both, does occur. = absorption = fission

both terms have the same mathematical form cross section times a fluxSlide33

How to understand Nuclear Energy1. Understand a basic reactor.

2. Understand how the control rods maintain reactor criticality.3. what is criticality?4. Understanding Fission5.Putting a value on criticality

6.Multiplying medium7. Buckling

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Bare Slab Reactor

Center line x

y

Z

X

(-a/2-d) -a/2 0 a/2 (a/2+d)

Extrapolation distance (d)

= flux boundariesSlide35

Buckling

The neutron diffusion equation for the bare slab reactor can be written as would be:      

       in which B1 is called Buckling.

Buckling is the measurement of extent to which the flux curves or "buckles".buckling can be used to infer leakage. The greater the curvature the more leakage expected. For critical reactivity the material buckling should be equal to geometrical buckling.

Hence reactivity can be controlled with proper buckling incorporated in reactor’ s design. Slide36

How to understand Nuclear Energy1. Understand a basic reactor.

2. Understand how the control rods maintain reactor criticality.3. what is criticality?4. Understanding Fission5.Putting a value on criticality

6.Multiplying medium7. Buckling8. Determination of reactor’s critical dimension

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Reactor’s critical dimension37

Rearranging the Buckling equation we get:

We can then solve for R

ex Slide38

SourcesFerguson, C. D. (2011).

Nuclear Energy- what everyone needs to know. New York, New York: Oxford University Press, Inc.Cotton, S. (n.d.). Uranium Hexafluoride - UF6

. Retrieved February 26, 2012, from chm.bris.ac.uk: www.chm.bris.ac.uk/motm/uf6/uf6v.htmHewitt, P. G. (2006). Conceptual Physics 10th edition. St. Petersburg: Pearson-Addison Wesley.

Moniz, E. (2011). Why We Still Need Nuclear Power. Foreign Affairs , 83-94.  Nuclearfiles.org. (n.d.). from nuclear proliferation to nuclear testing

. Retrieved February 25, 2012, from Nuclearfiles: project of the nuclear age peace foundation: http://www.nuclearfiles.org/?gclid=CN2AvL3vyK4CFQzGKgod62OzBg

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