QUENCH-06 Preparatory Meeting
Download
Report
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 4r 2 4 r 3 R T ln S
0
l
-1
3
M
850 K, S=20: O(10 m)
Experimental evidence: Winfrith
3M
*
r
Laboratories (1986): 0.50.9 m
l RT ln S
Homogeneous Nucleation Models
Analytical Models
– Classical theory (Becker-Doring (1935)
S1
kT
– Kinetic theory (Girshick et al (1990)
S1,1n 2 s
Kinetic theoryJhas
12
better performance
43
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 4Di ,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
3b 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
TbT
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 (100500m)
– 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