Criticality of Nuclear reactors and Geometric Buckling

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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/

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How to understand Nuclear Energy 1. Understand a basic reactor. 2. Understand how the control rods

maintain reactor criticality.

5https://commons.wikimedia.org/wiki/File:Control_rods_schematic.svg

Farther down= more neutrons absorbed & less heatFarther up= less neutrons absorbed & higher heat

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

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maintain reactor criticality. 3. what is criticality?

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Criticality Criticality 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 criticality U235 nucleus Alpha

particle

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Uncontrolled chain reaction:from accidental criticality

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Subcritical- if

more

neutron

s are lost by escape or

nonfission absorption than

are produced, and the chai

n reaction

isn’t self sustaining and dies out

Supercritical- a sustained

chain

reaction

with the rate of

fission

neutron production exceed the rate of

loss

Critical- whe

n exactly one neutron per fission is

available

for initiatin

g another fission.

Criticality

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Sub-critical

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Subcritical- if

more

neutron




n reaction



chain

reaction

with the rate of

fission


loss

Critical- whe


available

for initiatin

g another fission.

Criticality

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Super-Critical

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Subcritical- if

more

neutron




n reaction



chain

reaction

with the rate of

fission


loss

Critical- whe


available

for initiatin

g another fission.

Criticality

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Critical

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Criticality Control Accidental criticality depends on the following:

1. Quantity of the fissile material2. Geometry of the fissile assembly3. Presence or absence of a moderator4. Presence or absence of a neutron reflector5. Presence or absence of a strong neutron absorber

(poison)6. Concentration of fissile material, if the fissile material

is in solution7. Interaction 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

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

2. 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.

3. 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 235U is important to this control.

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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

U235

fission23692

10

23592 UnU

U238

UnU 23992

10

23892

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 6 Fission gamma rays 6 Radioactive decay Beta particle 5 Gamma rays 5 neutrinos 11 200 MeV

U235

QnvFFU AZ

AZ 1

023692

2

2

1

1

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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

221 )( cmmmME nf

15/2 AZ

49/2 AZ

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Uncontrolled chain reaction:from accidental criticality

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Nuclear Fission: Rate of Fission Most 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:

sfiss103.3

sJW1

MeVJ106.1

fissMeV190fissW1

10

13

X

sX

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maintain reactor criticality. 3. what is criticality? 4. Understanding Fission 5.Putting a value on criticality

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Multiplication factor: The Four-Factor Formula Criticality, 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.

system critical0000.1system calsupercriti0000.1

system lsubcritica0000.1:when

eff

eff

effkkk

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FOUR FACTOR FORMULA: INFINITE MULTIPLICATION FACTOR

pfnpfnk

f

f

N

1N

•ηis the mean number of neutrons emitted per absorption of Uranium, so n thermal neutrons will result in ηn 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

1 kkn

kn

llkn

tn

dd

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Reactivity and Reactor Control 0.001s 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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maintain reactor criticality. 3. what is criticality? 4. Understanding Fission 5.Putting a value on criticality 6.Multiplying medium

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 flux

a

f

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maintain reactor criticality. 3. what is criticality? 4. Understanding Fission 5.Putting a value on criticality 6.Multiplying medium 7. Buckling

Bare Slab ReactorCenter line x y

Z

X

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

Extrapolation distance (d)

0)2

()2

(

dada = flux boundaries

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.

0Bdxd 2

12

2

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How to understand Nuclear Energy 1. Understand a basic reactor. 2. Understand how the control rods maintain

reactor criticality. 3. what is criticality? 4. Understanding Fission 5.Putting a value on criticality 6.Multiplying medium 7. Buckling 8. Determination of reactor’s critical dimension

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Reactor’s critical dimension

•Rearranging the Buckling equation we get:

•We can then solve for Rex

2

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M1B

exm R

K

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Sources Ferguson, 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.htm

Hewitt, 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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Criticality of Nuclear reactors and Geometric Buckling