lec02

Operational Reactor Safety

22.091 /22.903

Professor Andrew C. Kadak Professor of the Practice

Spring 2008

Lecture 2: Reactor Physics Review

Topics to Be Covered

– C ross Sections

– F ission Process

– I nfinite Reactor Systems

– F inite Reactor Systems

– Four Factor Formula

– C riticality Control

– D iffusion Theory

– N eutron Transport (Boltzman Equation)

Nuclear Reactor Physics Review

Cross Sections

Uranium Cross Sections

Fission Chain Reaction

Fission Neutron Energy

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Fission Energy

Fission Product Decay Chain

Fission Yield by Mass Number

Chart of the Nuclides

Conversion Chain: Fertile  Fissile

Reaction Rates*

• How do we make power?

• Factors to consider in design

– C hanges in fuel material

– Life of reactor core

– R eactivity swing

– Refueling strategies


	RF.ACTOR PHYSICS OVFRYfEW	Page 13

ENERGY DEPE N DENC E OF TYPCIAL TARGET NUCLEUS NEUTRON REACTOR CRO S S SE C TION

- l/v reg io n

resonance

reg;on

0,001 eV

l og E

l MeV 10 McV

Neutron Moderation Parameters

Infinite & Finite Reactor Systems*

• Infinite Systems

– N eutron Multiplication

– Four Factor Formula

• Finite Systems

– L eakage

– Six Factor Formula

• Diffusion Theory

Courtesy of John A. Bernard. Used with permission.

John A. Deniard Subcrizi al klulhplicalion und Reactor plan up

Com e Mult i licatio n Factor

I . It is useful to define a ’core multiplication faclor' W lCh is denoted by ihc symbol 'K’ and which is ihc prDduct of the siK factors that definc ihe neutron life cycle. Titos,

2. The abo v c expression, which lS Gdlled the 'six-faclor ftirrnul a, ha.s physical mo.ariing:

K = Neutron s Produce d fro m Fissio n or

Neurons Absorbed + Neutron LRakage

_ Numbe r Neuron s i n Presen t Generatlof l

K

Number Neutrons in Preceding Generation

K= n , n 2 . n when n is the number of

I l p T ) j f t - 2 neutrons in each generation.

3. If K is unity, the reactor is critical.

4 If we know thc K-vfiluc for a reactor core, we Can determine lhc rate of ch.ange of its neutron populatlon. This is mosl useful in reactor startups.

Definitions of Neu

t = Tot £ Numbe r o f Pas t Neutron s Produce d ño n Fas t an d Therma l Fi ssio n

Number of Fast Neutrnns Produced from ¥hemal Fission

L

Tota l Nu mbe r o f Fas t Neuiron s Reapin g Leakag e

f * Total Number of Fart Neutrons Produced ñoin Fast and Thermal Fissinn

Total Number of %ermalized Neuirons

Total Numbsr of Past Neutrons Hscaping L ea kage

p Tola l Numbe r o f Them d Neuron s Escapin g Leakage

L,

TDtal Number of ThermalIzed Neutrons

John A. Dam:nd

SutrnotñMuliplcatonaV RcJLlor Sl up

Definition s o f Neutro n Lif e Cycl e Fac t or s ( cont. )

f = Th e rma l Neuro n s Absorbe d i n Fu el TDtal Number of Thermal Neutrons Escaping Leakage

Themal Neurons Captured in FuRl Which Cause Flssion

Of

Thermal Neutrons Absorbed in Fuel

Number of Fast Neutrons Roduccd from Thermal Fission

Thermal Neutrons AbSorbed in the Fuel

Of the above factors, the reactor operator can alter 'I by changing the contr ol rod position or by ad justin g the soluble poison content. The leakage terms zlso var y durlflQ r ou tine operation whenever coolant temperature changes. The olher terms are fixed by the fucl type.

REACTOR PHYSICS OVERVIEW

NEUTR ON L OSS M ECHA N I S M S

• Escape From Reactor

- Reactor length scale: L - m

- Neutron length scale: i£ - 0.1 m

- Probability of Escape Grows as ( l7L ) Grows

• Capture By React o r Materials

- Control materials

Control rods ( e.g., B, Cd )

Bunable poison s ( e.g„ Gd, 5m )

- Structural materials ( Fe, Zr )

- Moderator, used to slow down neutrons ( H, C )

- Coolant, used to remove heat from reactor ( H2O, He, Na )

Courtesy of Michael W. Golay. Used with permission.

Criticality Control

• K should = 1 for 18 to 24 months

– H o w ?

• F uel excess reactivity (fuel)

• Balance with control rods or soluble boron

• Burnable poisons in fuel to deplete with time

• Leakage

• O n-line refueling – C ANDU – Pebble Beds

Diffusion Theory*

• O ne group

– N eutron Balance for critical reactor

– C onsider production absorption and leakage

• M ulti-group

– Include different energy groups

Diffusion Theory Fluxes and Bucklings

Department of Nuclea r S c ien ce & Engineering

Prof. Andrew C. Kadak, 2008 Page 28

Multigroup Calculations

Diffusion Theory Flux Shapes

Fast and Thermal Flux Shapes

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Boltzman Equation

• Neutron Transport Theory

• Fundamental Equation of neutron interaction

Homework

• Knief Chapter 4

– Problems: 4.3, 5, 8, 10, 11, 14, 15

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22.091 Nuclear Reactor Safety

Spring 200 8

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