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1
A Look at Nuclear Scienceand Technology
Larry Foulke
Module 5.1
A Taste of Reactor Physics Part 1
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NuclearEngineeringProgram
What Now ?
What weve learned so far:
The fuel cycleSource of nuclear energyTypes of radiation
interactions
Reaction ratesFission and its productsBasis for reactor corecalculations
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NuclearEngineeringProgram
3
What Now ?Lets address the calculation of the spatial distribution of the neutronflux in the reactor
0 2 4 6 8
0
2
4
6
8
d
dt
1
v r ,,E,t( )
=
r ,,E,t( ) t r ,E, t( ) r ,,E,t( )+ s r ,t, E E, ( ) r , , E ,t( )d E d
0
4
+1
k
E( )4
f r , E , t( ) r , E , , t( )d E d 0
4
Fuel rod
Control rod (rodwithdrawn)
Fixed burnableAbsorber rod
Image Source: See Note 1
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NuclearEngineeringProgram
What Now ?Will also address the removal of the energy from fission and theconversion of that energy to electricity
Image Source: See Note 2
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NuclearEngineeringProgram
5
What Now ?
Put it all togetherTime dependenceReactivityDepletionPlant OperationsVirtual Plant TourDesign andDesign Interfaces
Image Source: See Note 3
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NuclearEngineeringProgram
Rate of Increase
in Number
of Neutrons
=
Rate of
Production
of Neutrons
Rate of
Absorption
of Neutrons
Rate of
Leakage
of Neutrons
Accumulation = Production - Absorption - Leakage
If Accumulation:
= 0 Critical Steady State Static
> 0 Supercritical Increasing Kinetic/ Dynamic
< 0 Subcritical Decreasing Kinetic/ Dynamic
Neutron Balance
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Nuclear Reactions
Production = Fission Rate (f)
Neutrons producedper fission ()
Destruction Rate = Absorption Rate (a)
What aboutenergy
dependence?
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235U
238U
Cross
Section
(Energy
Dependence)
Fission
238UAbsorption
Image Source: See Note 4
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Neutron Scattering
Image Source: See Note 4
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Increasingly High-Z MaterialsLower Average Energy Loss
Decreasingly Effective Moderation
Moderator Materials
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NuclearEngineeringProgram
Moderator Materials
Hydrogen Highest average energy loss per collision of any target
atom.
Small, but noticeable, absorption cross section( a 0.332 barns )
DeuteriumAlmost as effective as hydrogen at moderation. Smaller absorption cross section than hydrogen
( a 0.0005 barns )
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NuclearEngineeringProgram
Neutron Moderator MaterialsNeutronModerationPropertiesofSelectedAtomsandMolecules
ModeratorTarget AtomicMass(A) ScatteringRatio() (1-) CollisionstoThermal
H 1 0.000 1.000 18
H2O 20
D 2 0.111 0.889 25
D2O 35
Be 9 0.640 0.360 86
C 12 0.716 0.284 114
O 16 0.779 0.221 150
Na 23 0.840 0.160 218
U 238 0.983 0.017 2148Averagenumberofcollisionstomoderateafast(1MeV)neutrontoathermalequilibriumenergyof0.025eV.
Low Z atoms are more effective moderators than high Z atomsMost modern reactors use H, D, or C as moderators
Image Source: See Note 4
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NuclearEngineeringProgram
238U Absorption Cross Section
Importance of Resonance Escape
Jump Resonances
Image Source: See Note 4
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NuclearEngineeringProgram
Effect of
Heterogeneityof Fuel &
Moderator
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NuclearEngineeringProgram
For fissile isotopes (U235, Pu239, etc.), fission is mostefficiently caused by thermal neutrons (energy < 1 eV).
However, neutrons produced by fission are born withhigh energy (energy 2 MeV).
In order for the chain reaction to continue, these high-energy fission neutrons must be slowed down to thermal
energies (7 orders of magnitude).
Neutrons can lose energy through elastic collisions with targetatoms in the material.
We also want to minimize the number of neutrons that areabsorbed before they reach thermal energies and can cause
fission events.
Importance of neutron moderation
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1. Reprinted with permission from David Griesheimer. FunctionalExpansion Tallies for Monte Carlo Simulations, PhDDissertation, Nuclear Engineering and Radiological Sciences,University of Michigan (2005). ProQuest/UMI, AAT 3163808.
2. Reprinted with permission from World Nuclear Association.3. Reprinted with permission from Nuclear Engineering
International UK. Source: World Nuclear Industry Handbook2013.
4. Adapted with permission from the American Nuclear Society.Nuclear Engineering Theory and Technology of CommercialNuclear Powerby Ronald Allen Knief, 2nd Edition. Copyright2008 by the American Nuclear Society, La Grange Park, Illinois.Figure 2-12 (slide 8), 2-11 (slide 8 and 13), 4-2 (slide 9). Table4-1 (slide 12).
Image Source Notes