PDF 5.2 a Taste of Reactor Physics-Part 2

7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2

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1

A Look at Nuclear Scienceand Technology

Larry Foulke

Module 5.2

A Taste of Reactor Physics Part 2


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NuclearEngineeringProgram

Finite System Neutron Balance

Production vs Absorption + Leakage

f = a + Leakage

Note: kkeff (To accommodate leakage)

keff = k =Production

Absorption + Leakage


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Neutron Leakage Effect


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States of criticalitykeff = 1 Critical

keff > 1 Supercritical

keff < 1 Subcritical

No reactor can be constantly critical: Fuel depletion Fission product buildup (absorb neutrons) Temperature changes (changes cross section)

Criticality


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In order to keep an operating nuclear reactor criticalwe will need to adjust terms in the neutron balance

Neutron balance controlled by: ProductionAbsorption Leakage

Criticality Control


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Criticality Control

n Let us consider how we could adjust these parametersto achieve a target keff for two different applications

n Nuclear Power PlantnTarget keff:

nkeff= 1 for steady-state operationnkeff> 1 for start-up, keff< 1 for shutdown

n Nuclear Fuel Processing FacilitynTarget keff:

nkeff< 1 under all possible conditions (including accidents)


7/23NuclearEngineeringProgram

Criticality Control (Reactor)

Nuclear ReactorProduction

Determined by the total fissile content of the core Initial fuel loading Conversion of fertile nuclides (breeding) Refueling

On-line

ShutdownAbsorptionLeakage




Nuclear ReactorProductionAbsorption Fission-Product Absorbers

Cladding, Structure, Coolant Control Rods Soluble Absorbers (poisons) Burnable Absorbers

Leakage




n Nuclear ReactornProductionnAbsorption (Modern reactor designs):

nMoveable control rods (CR) to change power level and maintainsteady state operation.

nMovable safety rods (SR) to quickly shut down reactor andensure keff< 1.

Soluble boron in reactor coolant (PWR only) toshim

keff(liketrim control in an airplane) and fixed burnable poisons (boron or

gadolinium) that deplete during operation to accommodate fuel

burnup.

nLeakage





Absorption

Leakage Core size and shape Reflection of neutrons back into the core Density of core material(s)

(temperature-dependent)


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Water-Reflector

Effect onMinimumCore Size

11

Image Source: See Note 1


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Absorption

LeakageModeration

Controls how effectively neutrons can slow downto thermal energies.

Determined by selection of moderator materialand pin dimensions (diameter and pitch).


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Reactor Criticality Requirements Operation Modes

Power Reactors (Startup / Steady-State / Shutdown) Some Research Reactors (Pulse Mode) All reactors have emergency shutdown (SCRAM) capability

Routine adjustments to reactor criticality are required Account for power fluctuations and feedback effects

Fuel depletion, density changes of moderator Small frequent adjustments: control rods (in PWR) Larger, planned, adjustments: soluble boron (in PWR) BWR reactors use control rods and coolant flow feedback to

adjust criticality.


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nFuel Facility:Always Subcritical!nDesigned subcritical

nVerify that current configuration is subcriticalnConfirm that proposed changes will be subcritical

nkeff< 1 under all conditions; must accountfor:

nUncertainties in Experimental Data and CalculationsnNormal, Anticipated Abnormal & Credible Accident

Scenarios

Criticality Control (Fuel Facility)


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Beyond keff

When designing critical systems (reactors) weneed to know the spatial distribution of neutrons in

the core, in addition to the multiplication factor.


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The Exact Way (Hard)

Write down a neutron balance equation over somedifferential volume element and then solve the resultingintegro-differential equation:

Terms: 1)Time Variance, 2) Leakage, 3) Total Interaction Loss,

4) Fission Source, 5) In-Scattering Source

TR

UTH!


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Typical Core DesignFuel Assemblies

Zoom In on

these 4 assemblies

Core SymmetryImage Source: See Note 2


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Typical Assembly Design

Fuel Pins

Control Rods

Assembly

Symmetry

Zoom In onQuarter Assembly



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Typical, Simplified Assembly Model

Simplified 2-D model of anAP600 quarter assembly.

Contains UO2 fuel, boroncontrol rods, and B4Cburnable absorber rods.

Reflecting boundaryconditions on all sides.



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NuclearEngineeringProgram0 2 4 6 8

0

2

4

6

8

Quarter-Assembly, Control Rods Withdrawn

0 2 4 6 8

0

2

4

6

8

k

= 1.1630



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NuclearEngineeringProgram0 2 4 6 8

0

2

4

6

8

Quarter-Assembly, Control Rods Inserted

0 2 4 6 8

0

2

4

6

8

k

= 0.93287



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A More Approximate Way (Easier)

Write down a neutron balance equation using DiffusionTheory with one energy group

Time Variance, Fission Source, Absorption Loss, Leakage

AL

MOSTTRU

TH!

1

v

(

r,t)

t=

f(

r,t) a(

r,t)+D2(

r,t)


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1. Reprinted with permission from the American Nuclear Society.Nuclear Engineering Theory and Technology of Commercial

Nuclear Powerby Ronald Allen Knief, 2nd Edition. Copyright

2008 by the American Nuclear Society, La Grange Park, Illinois.

2. Reprinted with permission from David Griesheimer. FunctionalExpansion Tallies for Monte Carlo Simulations, PhD

Dissertation, Nuclear Engineering and Radiological Sciences,

University of Michigan (2005). ProQuest/UMI, AAT 3163808.

Image Source Notes

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