FPTRAN: A Volatile Fission Product and Structural Material Transport Code for RELAP/SCDAPSIM EDUARDO HONAISER (Brazilian Navy Technological Center) SAMIM.

FPTRAN: A Volatile Fission FPTRAN: A Volatile Fission Product and Structural Material Product and Structural Material

Transport Code for Transport Code for RELAP/SCDAPSIMRELAP/SCDAPSIM

EDUARDO HONAISER (Brazilian Navy Technological Center)

SAMIM ANGHAIE (University of Florida)

OUTLINEOUTLINE Introduction Development of the Model

– Numerical Treatment– Phenomena modeling

Implementation into RELAP/SCDAPSIM/MOD3.2

Conclusions

Development of a model to predict the transport of released fission products through the RCS, and to calculate the quantities each FP product deposited in the RCS and released to the containment

OBJECTIVEOBJECTIVE

Fission Product BehaviorFission Product Behavior

Fission productsinitial

inventory

Fission Products Release

ChemistryFission Products

Transport

Containment SourceTerm

1E-79

1E-721E-65

1E-58

1E-51

1E-441E-37

1E-30

1E-23

1E-161E-09

0.01

100000

Temperature (K)

Pres

sure

(MPa

)BaO

BaI2

Ba

Fission Product Transport (Scope)Fission Product Transport (Scope)

Vapor phenomena– Adsorption– Condensation

Onto structures Onto aerosol surfaces

– Aerosol nucleation

Aerosol Phenomena– Deposition– Agglomeration– Re-suspension

Characteristics of the ModelCharacteristics of the Model

Fixed speciationPhenomenological and convection model

limited to piping system (upper plenum not considered)

Decay heat of deposited FP not consideredMechanistic model for aerosol nucleation

iiaindjidjsdjres

N

jiajsdjidep

N

j

aaggiaaia

r

agg

iacar

r

iarcariacia

JStxrCAktxrCAk

drtxrNrrktxrCtxrrNtxrCrrrkdr

txrCkdrtxrCkx

txrCAv

t

txrm

,,,,,,1

,,,,1

0

,,

0

,

0

,',,

),,(),,(

'),,'(),'(),,(),,'(),,'()','('2

1

),,('),,'()),,((),,(

Analytical EquationsAnalytical Equations Vapor species

Aerosol Speciesiiindivjsdjiad

N

j

r

eqviardcareqvijsdjsc

N

j

ici

JStxCAk

drCtxCAkCtxCAkx

txCAv

t

txmii

,,,,,1

0

,,,,1

),(

)),(()),(()),((),( max

Transition Analytical-NumericalTransition Analytical-Numerical

0.0E+00

2.0E+09

4.0E+09

6.0E+09

8.0E+09

1.0E+10

1.2E+10

1.4E+10

1.6E+10

1.8E+10

2.0E+10

0.00E+00 5.00E-06 1.00E-05 1.50E-05 2.00E-05 2.50E-05 3.00E-05

Particle Diameter (m)

Tota

l Nu

mb

er o

f Par

ticle

s

Use fractionalstep method toseparate the

convective term

Discrete OrdinateApproach to treat

Aerosol size

Convert PDE into ODE

Apply the Gear Method to solve the ODE system

Hindmarsh (1993)package

Change the integral termsinto summation terns

Define finite limits for particle size spectrum

Numerical EquationsNumerical Equations Bulk states (vapor+aerosol sections)

Surface states (condensed, absorbed, and deposited) Total number of equations of the system: Sx(B+1+3N)

vapijsdjich

N

jieqvapi

B

lllailcjeqvapijsdjsc

N

j

zvapi CAkCCNAkCCAkdt

dmi ,,,,

1,,

1''',,',,,,,

1

,, )()(

ljidjsdjres

N

jlijsdjidep

N

j

B

milmlmagg

l

m

l

lkikmkmagglmk

ieqvapillilcil

ieqvapi

l

lllilc

illl

zli

CAkCAkCNkCNkf

CCNAkt

MCCNAk

t

Mf

dt

dm

,,,,,1

,,,,11

,,,1 1

,,,

,,,,,

,,1'

'',',,'

',,

5.05.0

)]([)]([

Vapor-Structural SurfaceVapor-Structural Surface Laminar flow (Re<2300)

– Leifshitz model (1962)

• Turbulent flow

3/2

0

07.41 hC

C

Heat Transfer (empirical) Mass Transfer

Nu=hdh/k=0.023Re0.83Pr0.33 Sh=Vddh/D=0.023Re0.83Sc0.33

fluidh

n

Vr

DLh

2 fluid

n

hdL V

L

r

C

Cv

0

1

Vapor-Aerosol ProcessesVapor-Aerosol Processes

– Homogeneous nucleation

– Heterogeneous nucleation

Monomers Unstable Clusters Aerosol (stable) and monomers from clusters “break”

Soluble or Insoluble Nuclei

Soluble nuclei (S<1)

Vapor Molecules

Insoluble nuclei (S>1)

Nucleation PatternNucleation Pattern Experimental evidence

– PBF-SFD and Phebus-FP

experiments Procedure

– Calculate selectively

nucleation rate for Ag and U– Select a model for

homogeneous nucleation– Obtain the particle critical size, defining lower particle size as

spectrum limitCritical radius for Ag-U particles : 850 K, S=20: O(10-1m)Experimental evidence: Winfrith

Laboratories (1986): 0.50.9 m

STM

RrrG l ln

3

44 32

0

SRT

Mr

l ln

3*

Homogeneous Nucleation ModelsHomogeneous Nucleation ModelsAnalytical Models

– Classical theory (Becker-Doring (1935)– Kinetic theory (Girshick et al (1990)

kT

S1

Kinetic theory has better performance

2

321,1

)(ln27

4exp

212 S

nSJ

s

Heterogeneous NucleationHeterogeneous NucleationApproach

– Diffusion– Continuum region (Kn<<1)

– Near Continuum region (Fuchs and Stuggin correction)

rp

J- J+

0)(1 2

2

rCdr

dr

dr

d

r

dr

rdCDJ

)(

2,333.171.11

1)(4

vv

veqipbulkiv

KnKn

KnCCNrDm

Aerosol Processes Assumptions Aerosol Processes Assumptions Aerosol spherical shape Empirical evidence

– PBF-SFD and Phebus experiments

Synergy– Mathematical

Sticking coefficientSteady stateStokes Region (Rep<<1)Continuum region (Kn<<1)

inertialgravThermLTdep VVVVV / 0J

pb

c

d

CB

3

Aerosol-SurfaceAerosol-SurfaceGravitationalUsing the concept of mobilityUpper limit of the spectrum: 50 mLaminar diffusion

– Gormley and Kennedy (1954)

ppdg gBmv

r

cr

rrPex

cu

11

......0325.00975.08191.0 1146.44314.7

0

hhh eeeC

C fluidh

n

Vr

DLh

2

fluidn

hdL V

L

r

C

Cv

0

1

Early Models (theoretical)– Friedlander (1957), Davies (1966) and Beal (1968)

Semi-empirical model (Sehmel-1970) Empirical Models

– Liu (1974), Iam and Chung (1983), Chiang (1996)

Aerosol-Surface (Turbulent)Aerosol-Surface (Turbulent)

Model Chi-SquareFriedlander (1957) 0.308Sehmel (1970) 0.111Davies (1966) 0.342Liu and Agarwal (1974) 0.306Iam and Chung (1983) 0.231Chiang (1996) 0.039

*73.0

223.2249.0

Re13.27 Vd

dv

h

p

b

pdT

Chiang Correlation

Aerosol-Surface (Thermophoresis)Aerosol-Surface (Thermophoresis)Principle (Continuum)Brock Solution (1962)

GRADIENT DE

TEMPERATURE

Springer (1970) Talbot (1980) Assessments

– Dumaz (1994)

Experiment Knudsen Deposition(%) Talbot(%) Springer(%)1 0.15 38 21.4 13.22 0.29 45 31.7 21.7

3 0.16 39 24.2 16.5

4 0.67 7.8 8.72 9.55

5 2.67 9.5 9.05 9.42

Error 25% 40%

)(221))(31(

)(2

ptp

gpm

Tbbcpt

p

gs

dTr

rKnCk

krKnC

T

TCrKnC

k

kC

v

Other ModelsOther ModelsBends deposition Pui el al. (1989)

Contractions Muishondt (1996)

Steam separators driers RAFT model

Adsorption Empirical models from Sandia and Winfrith experiments

Re-suspension Parozzi model (2000)

Aerosol-Aerosol (Agglomeration)Aerosol-Aerosol (Agglomeration)Brownian agglomeration

– Approach (continuum)– Target particle flux from other

particles – Equation

– Boundary conditions Continuum/near continuum region

0),(2

),(2

2

trCrr

trCr

Dab

abba

ba

abba

ba

bababaG

Vrr

DD

rr

rrDDrr

rrK

)(4

)(4),(

Aerosol-Aerosol (Agglomeration)Aerosol-Aerosol (Agglomeration)Differential gravitational

– Simplified model

– Realistic model Consider the fluid trajectories Approximations

– Fuchs (1964)

– Pruppacher and Klett (1978)

jijijiagg vvrrK )( 22,,

22

,,

),min(

2

1

ji

jijiPK

rr

rr

Turbulent agglomeration– Processes

Diffusivity (small particles) Inertial (large particles)

– Approaches Leifshitz (1962)

– Solution of diffusion equation

Saffman and Turner (1956)– Statistic approach for turbulence

Aerosol-Aerosol (Agglomeration)Aerosol-Aerosol (Agglomeration)

๑ ๑ ๑ ๑ ๑ ๑ ๑ ๑๑ ๑ ๑ ๑ ๑ ๑

๑ ๑ ๑ ๑ ๑Eddy Scale

Length (100-500m)

5.03)(65.5),(

T

babaT rrrrK

ImplementationImplementation

RELAP5

TRCNL

TRAN

FPTRAN

INPUTD

FPREAD

FPINIT

Implementation in RELAP/SCDAPSIM/MOD 3.2

VerificationVerification

Robustness of the math solver, positive masses

Global mass error (OK) Sensitive studies

Synergy

111 TDV

11 PCS2 13

Geometry PWR Primary CircuitTime 500 sBoundary ConditionsInlet Gases T 1500 K

Composition 0.5 mass concentrationVelocity 0.5 m/s

Struc. Surfaces Initial Temp 560 KPCS1 SS Hout 2 W/m2K

110 10 Source CsI 0.001 Kg/sCsOH 0.0001 Kg/s

3 TDV Ru 0.001 Kg/s1 TDV Ag 0.01 Kg/s

UO2 0.001 Kg/s

Stability StudiesRe-nodalizationNumber of Sections

StabilityStability

0.00E+00

5.00E+09

1.00E+10

1.50E+10

2.00E+10

2.50E+10

3.00E+10

0.00E+00 5.00E-06 1.00E-05 1.50E-05 2.00E-05 2.50E-05 3.00E-05

Particle Diameter (m)

Nu

mb

er o

f P

arti

cles

N=15

N=5

N=10

N=20

TDV

11--01 11--10 13

10--02

31

0.00E+00

2.00E+10

4.00E+10

6.00E+10

8.00E+10

1.00E+11

1.20E+11

1.40E+11

5 10 15 20 25 30 35 40 45 50

Number of Sections

Tota

l Num

ber o

f Par

ticle

s

1

10

100

1000

10000

100000

1E+06

1E+07

1E+08

1E+09

1E+10

1E+11

Va

po

r

1.1

4

1.5

8

2.2

0

3.0

5

4.2

4

5.8

9

8.1

9

11

.38

15

.81

21

.97

30

.53

42

.42

Co

nd

en

se

d

De

po

site

d

No

rma

lize

d m

as

s

20 nodes

40 nodes

ConclusionsConclusions A FP transport model was developed, using a system of mass

balance equations of first order Aerosol size was treated by a discrete ordinate approach, the

convective term was treated using the fractional step method ODE system was solved using Hindmarsh package Phenomenological models:

– Condensation onto structural surfaces– Condensation onto aerosol surfaces– Aerosol homogeneous nucleation– Aerosol deposition

Gravitational settling, laminar diffusion, turbulent diffusion, thermophoresis

– Aerosol Agglomeration Diffusive, turbulent, and due to gravitational difference

– Additional models Aerosol Re-suspension, deposition onto singularities, vapor adsorption

ConclusionsConclusionsThe model was implemented, and verified regarding:

– Global mass balance

– StabilityFor aerosol size discretizationFor spatial discretization

Prior Activity

1. Develop a model for speciation, with a consistent thermo-chemical database

2. Implementation of upper plenum model

3. Review of release models in RELAP/SCDAPSIM/MOD3.2. Make it consistent with the developed speciation

4. Decay heat model review

AcknowledgmentsAcknowledgments

Dr. Chris Allison and Dick Wagner for their support and the use of RELAP/SCDAPSIM for this project