lecture 11 - technology of accident analysis 11 - technology of...11/28/2009 7:42 pm lecture 11 –...

11/28/2009 7:42 PMLecture 11 – Technology of

Accident Analysis.ppt Rev. 6 vgs 1

Lecture 11 – Technology of Accident Analysis

Dr. V.G. Snell



Where We Are

Probabilistic RequirementsDeterministic Requirements

Design BasisAccidents

Plant safetyas operated

Safety GoalsExperience

CredibleAccidents

Plant safetyas designed

Safety CultureGood Operating

Practice

MitigatingSystems

ProbabilisticSafety Analysis

SafetyAnalysis

Chapter 2

Chapter 3

Chapter 1

Chapter 2

Chapter 4

Chapter 5

Chapter 6

Chapters 7 & 8

Chapter 9



Reactor Physics - Revisited

n Recall for a point reactor:

dN t

dtk

lN t Cf

pf i i

i

( ) ( )( )=

−+∞

=∑ρ β

λ1

6

dCdt

N t

lCi i f

pi i=

−−

β

ρλ

( )

( )1



CANDU is Not a Point Reactor

n Flux tilts from movement of adjusters, varying zones, fuelling, xenon

n Flux tilt in accidents from half-core void, insertion of shutoff rods from top

n 3-D diffusion + point kineticsn Neutrons are like flow through medium



Continuity Equation -ProductionLet n(r,t) be neutron density at point r and time

tn assume all at same speed

ddt

n t dV production absorption leakageV

( , )r = − −∫Let s(r,t) be # of neutrons/vol/time emitted at point r and time t

production s t dVV

= ∫ ( , )r



Continuity Equation –Absorption

Similarlyabsorption t dVa

V

= ∫ Σ ( ) ( , )r rφ

φ(r,t) is flux•Total rate at which neutrons pass through a given area, regardless of orientation

•Useful for describing neutron reaction rates

Σa(r) is the absorption cross section

Neutrons

Neutron CurrentDensity

Surface dA

J

n



Continuity Equation – LeakageLet J(r,t) =neutron current density vectorn measures the net flow of neutrons across a unit area

in any given directionLet n be a unit normal vector pointing outward from the

surface A around V

leakage t dAA

= •∫ J r n( , )



Continuity Equation

ddt

n t dV s t dV t dV t dVaVVV V

( , ) ( , ) ( ) ( , ) ( , )r r r r J r= − − ∇ •∫∫∫ ∫Σ φ

∂∂

φn t

ts t t ta

( , )( , ) ( ) ( , ) ( , )

rr r r J r= − − ∇ •Σ



Fick’s Lawn Current density

vector ∝ negative gradient of the flux

n Proportionality constant is diffusion coefficient, D

J = − ∇Dr

φ

M

Distance

J

More neutrons percm3 to left of line

Fewer neutrons percm3 to right of line

So neutron current is fromleft to right, proportionalto slope of flux



Neutron Diffusion Equation

n For single energy

n Compare heat conduction

D sv ta∇ − + =2 1

φ φ∂φ∂

Σ

ρ∂∂

cTt

H k T= + ∇ 2



n Pd(t) - power produced by all decaying fission products at time t

n ni(t) - number of atoms decaying per unit time of fission product i at time t

n Ei - average energy produced by the decay of each atom of fission product i

Decay Heat

P t n t Ed ii

i( ) ( )= ∑

1 . 0 0 E - 0 1

1 . 0 0 E + 0 0

1 . 0 0 E + 0 1

1 . 0 0 E + 0 2

1 . 0 0 E + 0 3

1 . 0 0 E + 0 4

1 . 0 0 E + 0 5

1 . 0 0 E + 0 6

1 E - 0 1 1 E + 0 1 1 E + 0 3 1 E + 0 5 1 E + 0 7 1 E + 0 9

T i m e a f t e r s h u t d o w n ( s e c . )

P o w e r ( W )

CANDU Bundle Power after Shutdown



Fueln Key safety parameters

n Fuel temperaturen Drives fission product transportn Drives pressure tube deformationn Potential sheath failuren Potential pressure-tube failuren Limited effect on physics

n Fuel sheath integrityn Fission product inventory & release



Location of Fission Productsn Fission products

formed within fuel grains

n Diffusen Bound inventory

– in grainsn Grain boundary

inventoryn Gap inventory

<10% >90%Fission products move this way with increasing temperature & burnup



Behaviour With Irradiationn Crackingn Swellingn Dishing/ridgingn Gas pressure increasen Pellet-clad interaction

Un-irradiatedFuel

IrradiatedFuel (exaggerated)



Fuel Heat Conduction

Q kAdTdx

= −One dimension

Three dimensions

(Rate of change of internal energy) =(rate of energy release) - (rate of energy loss from conduction)

ρ∂∂

cTt

H k T= + ∇ 2



Integrate (let )

Cylindrical Fuel Pin

d Tdr r

dTdr

HkF

2

2

1+ = −

T r THr

kF

( ) ( )= −04

2drdTru =

Steady state heat conduction



Sheath and Gap

Apply same equation to sheath

∆ T T THa a b a

kS Si SoS

= − =+2

2log[( ) / ]

And gap

q h T Tg F Si= −( )

And coolant

q h T TSo C= −( )



Sheath-to-Coolant ∆T

qH a

a b=

+π

π

2

2l

l( )

T THa

h a bC So− =+

2

2 ( )

Steady State –

All heat produced in fuel is transferred to coolant, so for length l :



Safety Importance

Heat CapacityMelting PointThermal ConductivityCharacteristic

LowHighLowHighHighLowMetal FuelUO2 Fuel



Dryoutn Sudden drop in

sheath-to-coolant heat transfer when “Critical Heat Flux” is reached

n Temperature jump strongly dependent on subcooling

CHF



Flow Regimes in Horizontal Heated Channel (High Flow)

SubcooledBoiling

SaturatedNucleateBioling

ForcedConvectiveEvaporation

FilmBoiling

ForcedConvection toVapour

Flow



Progressive Effects of Overpowern Dryoutn Sheath temperature risen Zircaloy annealingn Oxidation embrittlement of sheathn Braze melting and attack on Zircaloyn Zirconium-water reaction (exothermic)n Bundle collapsen Sheath meltingn Fuel melting (extremely unlikely)n Pressure tube balloon or burstn Heat transfer to moderator



CHF in a CANDU Channeln CHF determined

experimentallyn no reliable theory for

needed accuracyn Local flux shape

means dryout is not at the end

n How can we change the flux shape to improve margins?

Distance along channelInlet Outlet

Heat flux(normal)

Heat flux(overpower)

CHF

Quality

Dryout



Gas Pressure

n Driving force for sheath strain in accidents

n Affects sheath liftoffn Therefore fuel-to-sheath heat transfern Therefore fuel temperature

n Model via ideal gas law



n Relevant to large LOCAn Transverse stress:

n P is the pressure differential across the tuben r is the tube radiusn w is the tube thickness

Strain

σ =Prw



Strain Rate Equations

& / /εε

σ σ= = +− −ddt

A e B en k T m Tl

All parameters determined from experiment

Sheath may fail by ballooning if ε > 5%

What is fission product release?• fraction of gap inventory• small % of grain-boundary & bound inventory

- at high temperatures only



Fission Product ReleaseMCE2-T03 (Fragment in Argon)

0

20

40

60

80

100

0 5000 10000 15000 20000

Time (s)

Cs-

137

Rel

ease

(%)

0

500

1000

1500

2000

Tem

pera

ture

(C

)

Measured TemperatureHCE2-BM5 (Mini Element exposed to Steam)

0

20

40

60

80

100

0 5000 10000 15000 20000

Time (s)

Cs-

137

Rel

ease

(%)

02004006008001000120014001600

Tem

pera

ture

(C)

Measured Steam on Steam off Temperature

Release is a strong function of temperature, atmosphere

lecture 11 - technology of accident analysis 11 - technology of...11/28/2009 7:42 pm lecture 11 –...

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