Transcript QUENCH-06 Preparatory Meeting

FPTRAN: A Volatile Fission
Product and Structural Material
Transport Code for
RELAP/SCDAPSIM

EDUARDO HONAISER (Brazilian Navy
Technological Center)
 SAMIM ANGHAIE (University of Florida)
OUTLINE

Introduction
 Development of the Model
– Numerical Treatment
– Phenomena modeling

Implementation into
RELAP/SCDAPSIM/MOD3.2
 Conclusions

OBJECTIVE
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
Fission Product Behavior
Containment Source
Term
Fission
Products
Release
Fission Products
Transport
11
00
13
00
15
00
17
00
19
00
90
0
70
0
29
8
100000
0.01
1E-09
1E-16
1E-23
1E-30
1E-37
1E-44
1E-51
1E-58
1E-65
1E-72
1E-79
50
0
Chemistry
Pressure (MPa)
Fission
products
initial
inventory
Temperature (K)
BaO
BaI2
Ba
Fission Product Transport (Scope)

Vapor phenomena
– Adsorption
– Condensation
 Onto structures
 Onto aerosol surfaces
– Aerosol nucleation

Aerosol Phenomena
– Deposition
– Agglomeration
– Re-suspension
Characteristics of the Model

Fixed speciation
 Phenomenological and convection model
limited to piping system (upper plenum not
considered)
 Decay heat of deposited FP not considered
 Mechanistic model for aerosol nucleation
Analytical Equations

Vapor species

max
mi ( x, t )  ( v AcCi ( x, t )) N

  k sc, j Asd , j (Ci ,v ( x, t )  Ceqi )   kcar Aard (Ci ,v ( x, t )  Ceqi )dr
t
x
j 1
0
r
N
  k ad ,i , j Asd , j Cv ,i ( x, t )  Sind ,i  J i
j 1

Aerosol Species
ma ,i (r , x, t )
t


 ( v Ac Ca ,i (r , x, t ))
x
r
  kcar 'r Ca ,i (r ' , x, t )dr '  kcar Ca ,i (r , x, t )
0

r
1
  dr ' k agg (r ' , r  r ' )Ca ,i (r ' , x, t ) N a (r  r ' , x, t )  Ca ,i (r , x, t )  k agg (r ' , r ) N a (r ' , x, t )dr '
20
0
N
N
j 1
j 1
  k dep,i , j Asd , j Ca ,i (r , x, t )   k res, j Asd , j Cd ,i , j (r , x, t )
 Sind ,a ,i  J i
Transition Analytical-Numerical
Use fractional
step method to
separate the
convective term
Discrete Ordinate
Approach to treat
Aerosol size
Apply the Gear Method
to solve the ODE system
Hindmarsh (1993)
package
Convert PDE into ODE
2.0E+10
1.8E+10
Change the integral terms
into summation terns
Total Number of Particles
1.6E+10
1.4E+10
1.2E+10
1.0E+10
8.0E+09
Define finite limits for
particle size spectrum
6.0E+09
4.0E+09
2.0E+09
0.0E+00
0.00E+00
5.00E-06
1.00E-05
1.50E-05
2.00E-05
Particle Diameter (m)
2.50E-05
3.00E-05
Numerical Equations

dmi ,vap, z
Bulk states (vapor+aerosol sections)
N
B
N
j 1
l '1
j 1
  ksc, j Asd , j (Ci ,vap  Ceqi , j )   kc,l ',i Aa,l ' Nl ' (Ci ,vap  Ceq ,i )   kch,i , j Asd , j Ci ,vap
dt
l
dmi ,l , z
   f l ' l [
dt
l '1
l
l
M l ',i
t
 kc,l ',i Al ' N l ' (Ci ,vap  Ceq ,i )]  [
M l ,i
t
 kc,l ,i Al N l (Ci ,vap  Ceq ,i )]
B
N
N
m 1
j 1
j 1
 0.5  f mk l kagg,m,k N mCk ,i  0.5 kagg,m,l N mCl ,i   kdep,i , j Asd , j Ci ,l   kres, j Asd , j Cd ,i , j ,l
m 1 k l 1

Surface states (condensed, absorbed, and deposited)
 Total number of equations of the system: Sx(B+1+3N)
Vapor-Structural Surface

Laminar flow (Re<2300)
– Leifshitz model (1962)
C
 1  4.07 h 2 / 3
C0
h
Ln D
rh2V fluid

C  rh
vdL  1   V fluid
 C0  Ln
• Turbulent flow
Heat Transfer (empirical)
Mass Transfer
Nu=hdh/k=0.023Re0.83Pr0.33 Sh=Vddh/D=0.023Re0.83Sc0.33
Vapor-Aerosol Processes
– Homogeneous nucleation
Monomers
Unstable Clusters
Aerosol (stable) and monomers from clusters
“break”
– Heterogeneous nucleation
Soluble or Insoluble Nuclei
Soluble nuclei (S<1)
Vapor Molecules
Insoluble nuclei (S>1)
Nucleation 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 limit
 Critical radius for Ag-U particles : G  4r 2  4 r 3  R T ln S
0
l
-1
3
M
850 K, S=20: O(10 m)
 Experimental evidence: Winfrith
3M
*
r

Laboratories (1986): 0.50.9 m
l RT ln S
Homogeneous Nucleation Models

Analytical Models
– Classical theory (Becker-Doring (1935)

S1
kT
– Kinetic theory (Girshick et al (1990)
S1,1n 2 s

Kinetic theoryJhas
12
better performance


43 
exp 
2
2
27
(ln
S
)


Heterogeneous Nucleation

Approach
– Diffusion
J+
J-
rp
– Continuum region (Kn<<1)
1 d  2 d 
r
C (r )  0
2
r dr  dr 
dC ( r )
J  D
dr
– Near Continuum region (Fuchs and Stuggin correction)


1  Knv
m v  4Di ,bulk rp N (Ci  Ceq ) 
2
1  1.71Knv  1.333Knv 

Aerosol Processes Assumptions

Aerosol spherical shape
 Empirical evidence
– PBF-SFD and Phebus
experiments
 Synergy
– Mathematical
Vdep  VT / L VTherm Vgrav Vinertial
 Sticking coefficient
 Steady state
 Stokes Region (Rep<<1)
 Continuum region (Kn<<1)
J  0
Cc
B
3b d p
Aerosol-Surface

Gravitational
 Using the concept of mobility
dg
 Upper limit of the spectrum: 50 m
 Laminar diffusion
v  m p gB p
c 1 1   c 
u 
r 
x Pe r r  r 

C  rh
vdL  1   V fluid
 C0  Ln
– Gormley and Kennedy (1954)
C
 0.8191e 7.314h  0.0975e 44.6 h  0.0325e 114h ......
C0
h
Ln D
rh2V fluid
Aerosol-Surface (Turbulent)

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)
Model
Friedlander (1957)
Sehmel (1970)
Davies (1966)
Liu and Agarwal (1974)
Iam and Chung (1983)
Chiang (1996)
 p 
vdT  27.13 
 b 
0.249
 dp 
 
 dh 
Chi-Square
0.308
0.111
0.342
0.306
0.231
0.039
2.223
Re 0.73 V *
Chiang Correlation
Aerosol-Surface (Thermophoresis)

Principle (Continuum)
 Brock Solution (1962)
vdTr



GRADIENT DE
TEMPERATURE
 kg

T


2Cs
 Ct Kn(rp ) Cc b
k

TbT
p





kg

(1  3Cm Kn(rp )) 1  2
 2Ct Kn(rp ) 


k
p


Springer (1970)
Talbot (1980)
Assessments
– Dumaz (1994)
Experiment Knudsen
Deposition(%) Talbot(%) Springer(%)
1
0.15
38
21.4
13.2
2
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
25%
40%
Error
Other Models
Bends deposition
Pui el al. (1989)
Contractions
Muishondt (1996)
Steam separators driers
RAFT model
Adsorption
Empirical models from
Sandia and Winfrith
experiments
Parozzi model (2000)
Re-suspension
Aerosol-Aerosol (Agglomeration)

Brownian agglomeration
– Approach (continuum)
– Target particle flux from other
particles
– Equation
 2

2 
Dab  2 C (r , t ) 
C (r , t )  0
r r
 r

– Boundary conditions
 Continuum/near continuum region
4 (ra  rb )Da  Db 
K G (ra , rb ) 
ra  rb
4( Da  Db )

ra  rb   ab ra  rb Vab
Aerosol-Aerosol (Agglomeration)

Differential gravitational
– Simplified model
K agg,i , j   (ri 2  rj2 ) vi  v j
– Realistic model
 Consider the fluid trajectories
 Approximations
– Fuchs (1964)
– Pruppacher and Klett (1978)
 PK ,i , j
1 min( ri , rj )

2 ri  rj 2
2
Aerosol-Aerosol (Agglomeration)

Turbulent agglomeration
– Processes
 Diffusivity (small particles)
 Inertial (large particles)
๑๑๑๑๑๑๑๑
๑๑๑๑๑๑
๑๑๑๑๑
– Approaches
 Leifshitz (1962)
Eddy Scale
Length (100500m)
– Solution of diffusion equation

Saffman and Turner (1956)
– Statistic approach for turbulence
 T 
KT (ra , rb )  5.65(ra  rb )  
 
3
0.5
Implementation
RELAP5
INPUTD
TRCNL
FPREAD
TRAN
FPINIT
FPTRAN
Implementation in RELAP/SCDAPSIM/MOD 3.2
Verification
111
TDV
11 PCS2
PCS1
110
10
1 TDV
13
Geometry
PWR Primary Circuit
Time
500 s
Boundary Conditions
Inlet Gases
T
1500 K
Composition 0.5 mass concentration
Velocity
0.5 m/s
Struc. Surfaces Initial Temp 560 K
2
SS
Hout
2 W/m K
Source
CsI
0.001 Kg/s
CsOH
0.0001 Kg/s
3 TDV
Ru
0.001 Kg/s
Ag
0.01 Kg/s
UO2
0.001 Kg/s
 Robustness of the math solver,
positive masses
 Global mass error (OK)
 Sensitive studies
Synergy
 Stability Studies
Re-nodalization
Number of Sections
Stability
1E+11
TDV
20 nodes
1E+10
40 nodes
11--01
1E+09
11--10
13
1E+07
1E+06
100000
10000
1000
100
10
10--02
1
Deposited
Condensed
42.42
30.53
21.97
15.81
11.38
8.19
5.89
4.24
3.05
2.20
1.58
1.14
Vapor
3
1
3.00E+10
Total Number of Particles
1.40E+11
2.50E+10
N=15
N=5
N=10
N=20
2.00E+10
Number of Particles
Normalized mass
1E+08
1.50E+10
1.00E+10
1.20E+11
1.00E+11
8.00E+10
6.00E+10
4.00E+10
2.00E+10
5.00E+09
0.00E+00
5
0.00E+00
0.00E+00
5.00E-06
1.00E-05
1.50E-05
Particle Diameter (m)
2.00E-05
2.50E-05
3.00E-05
10
15
20
25
30
35
Number of Sections
40
45
50
Conclusions

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
Conclusions
 The model was implemented, and verified regarding:
– Global mass balance
– Stability
 For aerosol size discretization
 For 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
Acknowledgments
 Dr.
Chris Allison and Dick Wagner for
their support and the use of
RELAP/SCDAPSIM for this project