7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

1/17

1

A Look at Nuclear Scienceand Technology

Larry Foulke

Module 5.1

A Taste of Reactor Physics Part 1

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

2/17

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

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

3/17

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

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

4/17

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

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

5/17

NuclearEngineeringProgram

5

What Now ?

Put it all togetherTime dependenceReactivityDepletionPlant OperationsVirtual Plant TourDesign andDesign Interfaces

Image Source: See Note 3

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

6/17

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

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

7/17NuclearEngineeringProgram

Nuclear Reactions

Production = Fission Rate (f)

Neutrons producedper fission ()

Destruction Rate = Absorption Rate (a)

What aboutenergy

dependence?

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

8/17NuclearEngineeringProgram

235U

238U

Cross

Section

(Energy

Dependence)

Fission

238UAbsorption

Image Source: See Note 4

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

9/17NuclearEngineeringProgram

Neutron Scattering

Image Source: See Note 4

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

10/17NuclearEngineeringProgram

Increasingly High-Z MaterialsLower Average Energy Loss

Decreasingly Effective Moderation

Moderator Materials

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

11/17

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 )

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

12/17

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

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

13/17

NuclearEngineeringProgram

238U Absorption Cross Section

Importance of Resonance Escape

Jump Resonances

Image Source: See Note 4

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

14/17

NuclearEngineeringProgram

Effect of

Heterogeneityof Fuel &

Moderator

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

15/17

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

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

16/17

7/28/2019 PDF 5.1 a Taste of Reactor Physics-Part 1

17/17

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