University Ghent 2015-2016 Reactortheory: Partim I 1 Reactortheory: Partim I G. Janssens-Maenhout Lecture 1 (24/09/2015)

University Ghent 2015-2016 Reactortheory: Partim I

1

Reactortheory: Partim IG. Janssens-Maenhout

Lecture 1 (24/09/2015)


Greet Maenhout (UGENT- European Commission/JRC)greet.maenhout@ugent,be or [email protected] , 0039 0332 78 5831 (or 0039 3348013556)

ExercisesM. Vanderhaegen: discussed during the course/ by email

Exam: written 3hr

theory: 12pt: closed books (no ref. mat.)exercise: 8pt: open book (using ref. mat.)

Lectures: on Thursday afternoons 13:00 Partim I: 24/09 (S9); 15/10 (B913); 22/10; 05/11; 26/11; 3/12

Partim II: 01/10, 08/10, 29/10, 19/11, 10/12SCK.CEN Study trip/ Practicum: 12/11

Traineeship possibilities – JRC – Ispra (https://ec.europa.eu/jrc/en/research-topic/nuclear-safeguards-and-security)BNEN master after master (http://academy.sckcen.be)ESARDA course (https://esarda.jrc.ec.europa.eu/)


History of nuclear fission


Physical characteristics of a nucleus

Chemistry Nuclear physics radius atom: 10E-10m nucleus: 10E-14m

boundary vague clear, Volume~A

model cloud droplet model

proton p

neutron n

elektron e-

1u= 1.7 E-27kg

1.007 1.008 0.00055

1e-= 1.6 E-19 C

+1 0 -1

In a nucleus:

Nuclide X or A = (atomic) mass number

Z : for the chemical element Z = proton number A=Z+N = neutron number

Isotopes : nuclides with same Z : U-233, U-235, U-238,…


5

Eka-rhenium = Neptunium Eka-osmium = Plutonium

Glenn Seaborg (father of radio-

chemistry)

Periodic Table

http://imglib.lbl.gov/ImgLib/COLLECTIONS/BERKELEY-LAB/images/96B05582.lowres.jpeg


Nuclides Chart

N=ZHeavy nucleimore neutrons

decay

decay -emitters


Radioactive decay

Radioactive decay : instable nuclei (in energy state, above their ground energy state) and

decay by emitting , n

time constant for decaying = Decay constant

After a Half life T1/2 only half of the original nuclei number remainedActivity = desintegration / second of the radioactive nuclide

1 Curie = activity of 1 g radium

)(BqNA BqECi 107.31

2N

example

Ground state

Excited states

Decay 1 with

Decay 2 withdttNtdN )()(

)exp()0()( tNtN


8

Relation between Mass and Energy


Mass defect :

Nuclear forces: mass defect

kernmNmZmm np

Nuclear forces are min. 100 x stronger than electromagnetic forces:nuclear fission releases much more energy than chemical reaction

Binding energy :

MeVummmUm nH 4.1789.114392)( A23592

)(931).(. umMeVEB


Nuclear forces: binding energy

NucleonEB ..

A

B.E. steadily increasing

Fe-56max.

fusion fission

Heavy nuclei fission spontaneously:

No natural nuclide with Z²/A>50


Nuclear forces: Bethe-Weiszäcker (emp.) mass formula

4/35

2

431332

21)(21..

Aa

AZAa

AZ²aAaAaEB /

/MeV

Volume term Coulomb term pairing term surface term asymmetric term

Coulombterm ~ 3/1

2

000 4²~

4.

AZ

re

RZeZe

Asymmetric term ~ Bv. He-4, C-6A

ZAZA 2)2(

Pairing term

Z pair A pair N pair = +1 P=155 Z pair A impair N impair = 0 P=53

Z impair A impair N pair = 0 P=50 Z impair A pair N impair = -1 P=4


Nuclear forces: empirical mass formula

3/23/2

4

3

4313

015.022

2max

2142..

AA

AaaAZif

AZa

AZa

ZEB

/

Good agreement between measured mass defect and the mass defect calculated with the empirical mass formulafor heavy nuclei.

For light nuclei and for magic nuclei, which are more stable: The shell model is more appropriate than the droplet model.


Fission and Fusion Reactions

)1(3,205421 0

001

10

13654

9842

10

23592

eVMeVQnXeMonU

fission

fusion

)1(6.17111 4

210

21

31

MeVMeVQHenHH


Nuclear reaction

4 Conservation laws

Conservation of number of nucleons

Conservation of electric charge

Conservation of momentum

Conservation of energy

Nuclear reactions and energy

dcbadcba ),(or

2331232::),( 23390

23290 nucleonsThnTh

UpnNp 23892

23893 ),( ),(235

92 fnUThnTh 23390

23290 ),(

19293::),( 23892

23893 chargeUpnNp


Mechanism to fission nucleus

Droplet model

If the nucleus deforms with contraction

then the nucleus fissions by repulsion of Coulomb forces


Fission threshold

Fission threshold:

minimal excitation energy

Q-value:

reaction energy

abd EEE

ac EEQ


Q-value of a nuclear reaction:

Q>0: exothermal reaction

Q<0: endothermal reaction

Examples: fission (reaction)

fusion (reaction)

chemical reaction

Nuclear reactions and energy: Q-value

22 )()( cmmcmmQ dcba

MeVQnDT 20

MeVQnXeMonU 200421 00

01

10

13654

9842

10

23592

eVQCOOC 422


Fission mechanism: fission parameter

Fission parameter x: = ratio Z² / (50A)

1. if (deformation remains constant and x increases) then E decreases2. if (A is large and x constant) then the impact of A is small

3. The height of fission threshold ~ deformation energy (surfaceterm+Coulombterm); experimentally determined as

AZ

MeVEd

²36.019

)( Z even A even N even = 0 Z even A odd N odd = 0.4

Z odd A odd N even = 0.4 Z odd A even N odd = 0.7

Bi-209 Th-232 U-235 U-238 Pu-239 Fm-254 x=0.66 x=0.70 x=0.72 x=0.71 x=0.74 x=0.79


Fission induced by absorbing neutrons

Heavy nuclei fission if excitation energy Ex > threshold Ed

Addition of excitation energy: with a neutron, approaching the nucleus and having the neutron taken up.

If (binding energy of latest n En (= 7 MeV) >

threshold energy (for U-235 (Z²/A=36) Ed =6 MeV)

then fission

QAZAZAZ

AZnAZ

),,(),(),()1,(

)1,(),(

2211*

*


Excitation energy of nucleus

Excitation energy = binding energy of last neutron absorbed

4/3

543/4

3313/1

232

1

4/34/315

22

4

3/13/13

3/23/221

1

)²/2(1²

)1(

211

21)1(

)1(²)1(

),.(.)1,.(.)(931)(

AaAZaAZaAaa

AAa

AZA

AZAa

AAZaAAaa

AZEBAZEBmmmMeVE

AA

AnAn

0.5MeV~33.5’A-3/4N even: ’=-1 ; N odd ’=+1


Thermal and fast fissioning

Thermal fissionable nuclide: if En Ed then the absorption of a thermal n suffices for fission (e.g. U233, U235, Pu239)

Fast fission: if En< Ed then additional energy is needed for excitation, for which n receives additional kinetic energy

Conservation of momentum

Energy

kinetic threshold energy: (Ed - En ) (A+1) /A

vMm

mV

nKEA

AmvA

A

mvMm

MVMmmvEK

1²

1

²²².).(

21

21

21

21


Fissile / fertile

Non-fissile nuclide not fissionable by thermal n, but possibly by fast n with KE > Ed

(fast fission)

Fissile nuclide is a thermally fissionable nuclide

(fissionable by thermal n with KE < 0.5eV )

U-233, U-235, Pu-239, …

Fertile nuclide: absorption of thermal n leads to a fissile nuclide, so that absorption of a second n induces fission U-238, Th-232, Pu-240, …


Experimental results of nuclear fission reactions

Experimental observations of a nuclear fission reaction:

a. Direct release: - 2 primary fission products with high Ex - 2-3 prompt neutrons (1.E-12s after fission) - prompt -photons (1.E-8s after fission)

b. Indirect release: primary fission products decay to secondary fission products with - - decay: n p + - + - delayed neutrons, fraction 0.2% - 0.6%

Summarising: a fission reaction creates:

1. fission products, 2. energy, 3. prompt n, 4. delayed n

_


Experimental results: 1. Fission products

Yield: asymmetric fission

Remark:

- symmetric fission: rare

- Peaks at A=140 and A=95

- Z2/A only left peakA shifts to higher A

- If KE of n sym. fission more probable

- Evolution towards stable nucleithrough av. 3 decay (+)

U-235 Pu-239


Experimental results: 2. Energy released at fission

Energy Released

Kinetic energy of fission products

Energy of neutronsprompt -radiationFission products‘decay - - radiation - - radiation - Neutrino‘s

Secondary –radiationSecondary -radiation

168 MeV

5 MeV

7 MeV

8 MeV 7 MeV 12 MeV

(2 ~ 4 MeV)(3 ~ 6 MeV)

Total 200 MeV

Range (in U+air)

<0.01cm prompt

>10 cm prompt 100 cm prompt

<0.1 cm delayed100 cm delayed>100cm delayed

100 cm delayed<0.1cm delayed

About 1 gram fissile material supplies 1 MWth per day


Experimental results: 3. Fission neutrons

With the fission neutrons n we can control a chain reaction

Total number of free n: depends on - excitation energy Ex - deformation of the nucleus - fission products

Averaged total free n /fission:

Types of free n: - prompt n (fraction > 99%) - delayed n (fraction = 0.65%)

X-A(E)=0,X-A+aX-AE

2.9Pu-239

2.4U-2350

~1/8 ~1/7 E>1MeV ~1/15 E<1MeVa (1/MeV)


Experimental fission results: 3 Prompt fission neutrons

Kinetic energy of prompt n shows a continuous spectrum.

Fission spectrum (E)spectrum of which (E)dE represents the fraction of n with energy between E and E+dE.

properties of (E):

Independent of:- X-A- K.E. of n

max(E=0.72MeV)

E 2 MeV

cEbEa sinhexp


28

Einstein – Slizard:

Chain reaction

Basis for criticality: 1 neutron keeps reactions ongoing

System/mixture can be: subcritical: decliningcritical: stablesupercritical: exponentially growing

Chain Reaction

http://images.google.co.uk/imgres?imgurl=http://img214.imageshack.us/img214/1210/56398649dl5.jpg&imgrefurl=http://yusufonline2.blogcu.com/Einstein/&h=379&w=485&sz=38&hl=en&start=6&um=1&usg=__ackSIyVGaSH3FzqlI9x-eZBSkxM=&tbnid=-zBQDwF-xDRvdM:&tbnh=101&tbnw=129&prev=/images%3Fq%3DSlizard%2BEinstein%2Bphoto%26um%3D1%26hl%3Den%26rls%3DRNWE,RNWE:2005-40,RNWE:en%26sa%3DX


29

History of Nuclear Non-ProliferationFrom Einstein to Eisenhower

If the idea of world government is not realistic, then there is only one realistic view of our future: wholesale destruction of man by man A. Einstein


Mean neutron cycle: six factors model

Effective multiplication factor keff : number of thermal n

re-absorbed in fissile material after a mean cyclefthpLfLek

keff < 1 keff = 1 ke>1

Subcritical Supercritical mixture mixture

Critical mixture

Production factor

Fast fission factor

Fast neutron leakage

Resonance escape probability

Thermal neutron leakage

Thermal utilization factorfLp

L

th

f


31

n-leak

used n

2.4 kg 16 kg

Moderator: water

water left n-poison: B

geometry size mass

Water-reflector More leaking n N poisoning

Controlling a mixture of nuclear material around criticality


fast reactor: c = Na, Pb, PbBi s = Fe f = UO2, PuO2

The reactor as critical mixture: composition

coolant cstructure-material sfuel with

fissile material f

Fuel pin

thermal reactor: c = H2O, D2O, gas (CO2, He) s = Zr f = UO2,MOX m= H2O, C, D2O

moderator m


33

Chicago Pile 1

Rods were manually lifted on 2/12/42 9:45

History of nuclear fission reactors


Four generations of nuclear power plants

I

1942Prototype reactors:Chicago Pile

1,Dresden,Magnox

II

1965commercial

reactors:LWR

CANDUWWERRBMK...

III

1995advanced reactors:

AP600System 80+

ABWREPR ...

IV

2020Future reactors:• economically performant• inherently safe (passive systems, operator-friendly)• minimal waste (with solution for HLR waste)• proliferation-resistent


Schematics: PWR: Pressurised Water Reactor

fuel:

cladding:moderator:

coolant:

UO2 , MOXU-235 3,2%ZrH2OH2O

efficiency=33% 4 circuitspprim= 150 bar, Tin=290°C, Tout=320°C

P / V = 100 MW/m³example T.M. I. ReactorSuccessor: APWR


Reactor vessel: internals

1 Control rod drive mechanism3 Vessel head 4 outlet (+ seal)6 Fuel assembly7 Internal basket (fuel support barrel)8 Bolds (fixing vessel head )10 Control rod cluster voor 1 bundel11 Reactor vessel12 Support plate 13 Guide thimbles for core instrumentation

14


Primaire circuit: Primary pump

1 Flywheel 2-3 Radial upper bearings4-5 Motor rotor and stator7 Radial lower bearing8 Seal No. 3 with controlled leak 9 Seal No. 2 with controlled leak 10 Pump axis11 Coolant inlet (thermal barrier)12 Orifice 13 Suction14-15 Motor 16 Seals17 Seal No. 1 with controlled leak 20-22 Metallic can protecting pump23 Diffuser


Primary Circuit: Pressurizer

To regulate 150 bar in the primary circuit


Primary circuit: Steam generator

1 Steam outlet2 Steam dryers (pos. entrainment)3 Upper shell4 Cyclone5 Moisture separator (scrubbers)6 Bottom shell 7 Bundle of steam generator tubes8 Support plates 9 Feedwater inlet 10 Lower tube sheet 11 Divider plate (separating primary water inlet and outlet)12 Outlet primary coolant 13 Inlet primary coolant


Heat transfer from primary circuit to secondary circuit


Cooling of secundary circuit


BWR: Boiling Water Reactor

Fuel:

Cladding:Moderator:

Coolant:

UO2

U-235 2,6%ZrH2OH2O

Efficiency=33% 3 Circuitspprim= 70 bar, Tin=290°C, Tout=320°C

P / V = 60 MW/m³Successor: ABWR


SGHWR: Steam Generating Heavy Water Reactor

Fuel:

Cladding:Moderator:

Coolant:

UO2

U-235 2,24%ZrD2OH2O

P / V = 15 MW/m³

Efficiency=32% Pressure Tubespprim= 60 bar, Tin=240°C, Tout=270°C


CANDU: Canadian Deuterium Reactor

Fuel:

Cladding:Moderator:

Coolant:

UO2

U nat: U-235 0,7%ZrD2OD2O

P / V = 11 MW/m³Successor: CANDU-3

Efficiency=30% Pressure Tubespprim= 85 bar, Tin=270°C, Tout=300°C


Fuel:

Cladding:Moderator:

Coolant:

U MetalU MetalU nat.U nat.Magn.Ox.Magn.Ox.CCCOCO22

Magnox: Gas Cooled Graphite Reactor

P / V = 1 MW/m³

Efficiency=31% 14mx8m C-Blockpprim= 20 bar, Tin=200°C, Tout=370°C


AGR: Advanced Graphite Reactor

Fuel:

Cladding:Moderator:

Coolant:

UO2U-235 2,3%aust. steelCCO2

P / V = 2,8 MW/m³


CO2 gas evaporates water

steam drives turbine


HTR: High Temperature Reactor

Fuel:

Cladding:Moderator:

Coolant:

UO2 - UCU-235 10%SiCCHe

P / V = 6,3 MW/m³Successor: MHTGR



FBR: Fast Breeding Reactor

Fuel:

Cladding: Moderator:

Coolant:

UO2 - PuO2

Pu-239 20%aust. steel----Na

P / V = 650 MW/m³Successor: EFR, BREST

Efficiency=43% Blancket enriched Upprim= 5 bar, Tin=500°C, Tout=600°C


RBMK: Water Cooled Graphite Reactor

Fuel:

Cladding:Moderator:

Coolant:

UO2

U-235 2,0%ZrCH2O

P / V = 1,3 MW/m³

e.g. Tschernobyl Unit 4



Nuclear Power Plants in Europe

LWR

WWERRBMK

GCR, FR,...


51

Where to situate the Nuclear Power ?


52

The Nuclear Club


Belgian Reactors

Nuclear share48%

Permanent shutdown


Reactor core: refueling

Pressurised Water Reactor: refueling after 12-18 months

RBMK large graphite watercooled reactor: online refueling

Fuel Assembly of a Pressurised Water Reactor


Reactor vessel : vertical cross section

1 Reactor vessel head bolt 2 Upper support plate3 1 of the 4 hot legs (outlet)4 Reactorsteel sample 5 radial support6 Control rod guiding tube 7 Spring to counteract lift force 8 O-ring for reactor vessel head9 Support column10 Lower control rod guiding tube 11 Support barrel 12 Core shell (+ rad. refl. / therm. shield)13 Lower support plate14 Diffuser plate (vortex)15 Secondary support

1

2

3

4

5

7

8

9

10

11

12

13

14

6

15


Reactor core : horizontal cross sectionPWR core

radial reflector (thermal shield)Support barrelReactor vessel

Zone 1: 1e cycle:Fresh fuel: UO2/MOX

Zone 2: 2e cycle

Zone 3: 3e cycle

With control rods

157 fuel assemblies


Reactor core: fuel assemblies configuration

Fuel assembly

(typical MOX: UO2 +PuO2)

17x17Pin lattice

o o oo o

o o o oo o

o o o o o o oo o o o

o o o oo o o o

o o o o o o oo o

o o o oo o

o o o

zone 1 nieuwe splijtstof UO2/MOX

zone 2 2e cyclus

zone 3 3e cyclus

o met controlestaven

o o oo o

o o o o o

o o x o o

o o o o o

o oo o o

zone 1 12 stiften 4.12 % Pu

zone 2 68 stiften 5.54 % Pu

zone 3 8.70 % Pu

o geleidingsbuis voor controlestaaf

x geleiding voor instrumentatiebuis

PWR core

Fresh fuel

2nd cycle fuel

3rd cycle fuel

pin

pin

Guiding tube for control rod

Guide thimble for core instrumentationWith control rods


Reactor core: fuel pin1

2

3

4

5

78

6

Pin of 9.5-12 mm thickness, 4m lengthUnder pressure (in cold condition 20-30 bar)Filled with He (heat conducting tracer gas)

1 Upper plug 2 Expansion room with spring3 Zircaloy cladding (0.5 mm)4 Isolating upper pellet5 Fuel pellets6 Isolating lower pellet 7 Supporting tube 8 Lower plug

Quality requires no leak (controlled by means of Sippingtest)


Reactor core: fuel assembly or fuel element

1 Control rod cluster 2 Control rods3 Head with spring4 Upper lattice5 Intermediate lattice support keeping fuel pins in position6 Guiding tube for control rods 7 Lower lattice8 Sole with damper

1

2

3 4

5

6

7 8


Example of Sellafield reprocessing plant: spent fuel storage

Reactor core: refueling

University Ghent 2015-2016 Reactortheory: Partim I 1 Reactortheory: Partim I G. Janssens-Maenhout Lecture 1 (24/09/2015)

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