Download RISØ-M-2257 USER MANUAL For the Probabilistic Fuel

RISØ-M-2257
USER MANUAL
For the Probabilistic Fuel Performance Code FRP
John Friis Jensen and lb Misfeldt
Abstract
This report describes the use of the probabilistic
fuel performance code FRP. Detailed descriptions of both input
to and output from the program are given. The use of the
program is illustrated by an example.
INIS-descriptors; BWR TYPE REACTORS; F CODES; FAILURES;
FUEL PINS; MANUALS; PERFORMANCE; PROBABILITY; PWR TYPE
REACTORS; RELIABILITY
UDC 621.039.548 : 519.283 : 681 3.06
October 1980
Risø National Laboratory, DK 4000 Roskilde, Denmark
ISBN
87-550-0715-5
ISSN
0418-6435
Risø Repro 1981
CONTENTS
1.
INTRODUCTION
2.
INPUT SPECIFICATION
2.1. Heading
2.2. Control variables
2.2.1. Administrative variables
2.2.2. Model selectors
2.2.3. Numerical data
2.3. Stochastic variables in design and material data
X°
2.4. Experimental data
2.5. Power history, H(t)
2.6. Special design and material data, X s
3.
4.
page
5
7
7
7
8
10
11
11
15
16
16
OUTPUT SPECIFICATION
3.1. Detailed description of the output common for all
cases
3.2. Description of the output special for deterministic calculations (CASE 1 and 4)
3.3. Description of the output special for Monte Carlo
Calculation (CASE 2)
3.4. Description of the output special Taylor approximation (CASE 3)
3.5. Additional output for OUT=2 (Maximum output) ....
17
24
26
REFERENCES
27
18
20
23
APPENDIX A.
Specification of an example
APPENDIX B.
Complete input for a calculation
APPENDIX C.
Complete output from a deterministic calculation
(CASE 1)
APPENDIX D.
Complete output from a Monte Carlo simulaticn
(CASE 2).
- 5 1. INTRODUCTION
A computer system for the statistical evaluation of LWR fuel
performance has been developed. The computer code FRP , Fue'
Reliability Predictor, calculates the distributions for parameters characterizing the fuel performance and failure probability.
The statistical methods employed are either Monte Carlo simulations or a low-order Taylor approximation.
Included in the computer system is a deterministic fuel performance code, FFRS2), which has been verified by comparison with
data from irradiation experiments.
The distributions for all material data utilized in the fuel
simulations are estimates from the best available information
in the literature.
For the failure prediction, a stress corrosion failure criterion
has been derived. The failure criterion is based on data from
out-of-reactor stress corrosion experiments performed on unirradiated and irradiated zircaloy with iodine present.
Figure 1 illustrates the general layout of the system.
Based on the applied load, H(t), the design and material data,
X, the program calculates the fuel state, Y(t), distribution of
temperature, strain, stress, etc., in pellet and cladding as
functions of time, and the failure probability for different
failure criteria as a function of time, W(t) .
In the following chapters the detailed input specifications aregiven together with some explanation of the output. Finally,
the use of the program is illustrated by an example.
- 6 -
H(t)
o £g
o
STATISTICAL
FUEL MODEL
DETERMINISTIC
FUEL MODEL
FFRS
Hit):applied load on the
fuel (power, flux. etc.).
stochastic process or
a deterministic function
of time.
Ylt)
Ylt): fuel state Istress.
strain, etc.). stochastic
process.
STATISTICAL CLAD
FAILURE MODEL
FAILURE MODEL
CDAM
-
Wit)
Figure 1.
X design and material
data,
stochastic variables.
Wit): clad failures (stress
corrosion, overstrain,
etc.), stochastic process.
Ylt)
The Fuel Reliability Predictor.
- 7 -
2. IMPUT SPECIFICATION
The syntax of the input is illustrated in Figure 2. Each bracket
corresponds to a logical unit which is described in this chapter.
[Head (1 card text information)
1
[
Control variables:
Namelist GBOTID
Data for the whole
run
Stochastic variables in design
and Material data
I
I Experiment name and experimental
data
I
[
H(t) Power history;
each card describes 1 time step
Specific data for
an experiment.
Can be repeated for
up to 100 experiments
X ; Design and material data, spe*
cific for this experiment
['
Figure 2.
Syntax of the input to FRP.
2.1. Heading
Head:
Text information about the run (1 card)
2.2. Control variables
A namelist, GEOTID, containing administrative variables and
numerical constants.
- 8 2.2.1. Administrative variables
Name
CASE
Type" Default
I
1
Selector for calculational mode
CASE = 1 Deterministic calculation using the
mean values of X
CASE = 2 Monte Carlo simulation
CASS = 3 Calculation by a second order
Taylor approximation
CASE = 4 Deterministic calculation using
*he mode values of X.
IROD
IROD = 0
IROD / 0
Selector for experiment, 0.<IROD<100
Gives the result for all experiments
specified in the input.
Gives the result for experiment
number IROD
LOOPS
I
100
Number of trials in a Monte Carlo
simulation
2<LO0PS<1000
RANDST
I
777
The starting point for the random
generator, RANDST/O
NBGR
I
Grouping of the Monte Carlo output,
see. p. 23.
POINTS
I
3
ORDER
I
1
DEL
R
0.5E-1
Describes the polynominal approximation used for the calculation of
the partial derivatives in the
Taylor approximation. A polynomial
of order "ORDER", is fitted to
"POINTS" sets of x, P(x) where the
values of x are spaced by DEL x
mean (X) for DEL>0 or by - DEL x
standard deviation (X) for DEL<0
I = integer, R » real, and L = logical
- 9 -
Name
Type
ALL
Default
TRUE
All stochastic variables are
used in the Taylor approximation.
ALL-FALSE only the variables specified by
IMPORT are used in the Taylor approximation.
IMPORT
Integer array
If IMPORT (i) = 1, variable no i
is included in the taylor app.
(ALL=TRUE overwrites IMPORT).
IMPORT is initialized to all zeros
FILEUD
I
Generation of data to plots
No plot information
The plot information is written on
permanent files with the names
FILEX, where X is FILEUD, FILEUD+1,
. .., for the experiments in the
input. 11<X<.20 are valid file names
FILEUD=0
FILEUD=X
MAXBER
I
MAXBER=1
PAR
1.00
No calculation with maximal interaction.
For MAXBER=1 the program performs
2 simulations, the normal as for
MAXRER=0, and a calculation with
maximal interaction, where the same
time step and gas release as in
the first is used, but the thermal
expansion of the fuel is ALFAF x
MALFAF and the BOL cold gap is
TGAB X MTGAB
Factor for modification of the
standard deviations. All standard
deviations are multiplied by PAR
- 10 -
OUT
OUT=0
Minimal output
0UT=1
Normal output
(XJT=2
Maximal output
Not used
0UT2
WDATA
L
FALSE
If WDATA=TRUE a file with the m
FILES is generated. The file contains the complete input for a
calculation with the WAFER code.
Should be used together with IROD/0
If IP0W=1, the stochastic variables
IPOH
in the power history are used.
If IPOW=0 the stochastic variables
in the power history are neglected
2.2.2. Model selectors
Name
Type
Default
ROSST
L
TRUE
The heat transfer model proposed
by Ross and Stoute
RELMOD
is used
Selector for the 3 possible gas-
I
release models
RELM0D=1
A model proposed by W.B. Lewis
RELM0D=2
A modified BNWHT
4)
model.
For fuel temperatures below 1000°C
a constant instead of the proposed
equation is used.
RELM0D=3
The LOOPY
model, developed at
Studsvik
The NRC correction for high burnup is
incorporated in all three models
NKPSW
L
FALSE
Swelling model from ref. 1
NKPSW=TRUE Swelling model proposed by N. KjarPetersen 7)
- 11 -
Name
Type
DefauH
EPSILO
R
O.iE-1
General accuracy used as stop-criteria in iterations.
EPSH
R
0.1E-1
Stop-criterion for iterations on
the gap-conductance
EPSK
R
O.lE-1
Stop-criterion for iterations on
the contact pressure
ANTITR
I
100
Vtaximum number of
MAXTID
R
800.0
Maximum time step for constant
power (hours)
POM0
R
2000.0
Maximum power seep during contact
<W/m)
DG0
DRBRG
MAXPST
R
R
I
0.5E-5
0.5E-1
Constants used for the determination of the time step length
NANULI
I
20
iterations
5
Number of annuli used in the calculation of gaseous swelling.
NANULI<50
2.3. Stochastic variables in design and material data, J^*
Each card in X° contains the following data:
Variable no
Distribution
1 card
The mean value
The coefficient of variation
col 1
col 11
col 21
col 31 -
Defined as, the standard deviation divided by the mean value.
If the mean value is 0.0, the standard deviation is giver
directly.
- 12 -
The remaining columns are not used.
Valid distributions are:
1
2
3
4
=
=
=
=
normal distribution
lognormal distribution
uniform distribution
deterministic value
The integers in cols. 1-10 and 11-21 must be placed correctly
and justified without any decimal point. The variables need not
follow in ascending order. X° is terminated by a "variable no">
80.
DESIGN DATA
NO Name
Unit
1
2
3
4
5
L
RCI
TCLAD
TGAB
TDEN
m
m
m
m
*TD
6
7
8
9
LEQ
VP
RF
RR
m
m3
m3
m3
10
SIGMAF
N/ia'
11
KAPPA
m -1
12 YF
13 YH
14 YG
15 GRAIN
16 RH1
17 RH2
The pellet length, not used
Inner radius of the cladding
Thickness of the cladding
The radial gap
The pellet density in per cent of the
theoretical density
The equivalent stack length
Volume of plenum
Volume of the fill gas, helium
Additional gas volume, fission gas
mixture
Uniaxial yield strength at 300°C for
unirradiated material
The inverse diffusion length for
thermal neutrons in the fuel
Anisotropic factors for the cladding
material
urn
cm
cm
Grain size in the pellets
Surface roughness of the cladding
Surface roughness of the pellet
- 13 -
Unit
No
Name
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
P0RR1
P0RR2
PORR3
P0R1
POR2
POR3
WEFF
DUMMY
CO
CI
ALFAF
ALFAC
EC
HOHE
HOFISG
HMEYER
KM
m
m
35
CRS
W/m
36
37
AO
EO
W/m
38
39
40
41
42
43
44
45
46
47
48
49
50
51
El
E2
E3
E4
EFIS
KMAX
DELK
NPL
BFL
FCLAD
FU02
KSW
KHTSW
MHTSWL
The porosity in the fuel is assumed
to have three typical radii: P0RR1,
PORR2, and PORR3; the porosity in
each group is POR1, POR2, and POR3
hi
m
W/m
W/m
K-1
K-1
N/m2
W/cm°C
W/cm°C
2
Kg/mm
W/m
}
Densification parameter
Dummy variable
1st- and 2nd-order terms in the thermal
Conductivity of zircaloy
Thermal expansion of the fuel (U02)
Thermal expansion of zircaloy
Young's modulus for zircaloy
Contact conductivity with helium gas
Contact conductivity with fission gas
The Meyer hardness of zircaloy
Mean thermal conductivity of U0and zircaloy
Constant in the gap conductions
equation.
Not used
Factor in the porosity correction to
the U0 2 thermal conductivity
Constants in the U0 2 thermal conductivity equation
MeV
MP
MP/K
Fission energy
Constants in relation to plastic
deformation of zircaloy
cm/n
Coefficient in the fluence hardening
Zircaloy creep
UO« creep
Solid swelling rate
FIMA"1
FIMA^K" 1
Constant in the hot (gaseous) swelling rate
Maximum gaseous swelling fraction
- 14 -
£o Name
52
53
54
55
56
57
KBU
LAM
NY
QREF
QBURN
PO
58
TSC
59
SIGN
60
FSC
61
62
SIGFAC
ECCBNT
63
64
MALFAF
MTGAB
65
66
67
68
RAMPST
PFAC1
PFAC2
PFAC3
69
TFAC
70
FFAC
71
TAUREL
Unit
N/m2
}
Not used
Not used
Poisson's ratio for zircaloy
Parameters in FFRS
Saturation pressure of fission gas
with respect to stress corrosion
Temperature difference, corresponding
to one decade shift in time to
failure for stress corrosion
Normalization stress for stress
corrosion
Factor containing the uncertainty
for the stress corrosion failure
criterion
Stress concentration in the cladding
Eccentricity of the pellet's location
in the cladding
Factors used in determining the maximum interaction. See definition of
MAXBER
The first time step in the ramp
Scaling factors in the power history
The power from step 0 to step 1X1 is
multiplied by PFAC1.
The power from step 1X1+1 to step 1X2
is multiplied by PFAC2. The power from
step 1X2+1 to step 1X3 is multiplied
by PFAC3. The power from step 1X3+1
is unchanged
Temperature factor, the cladding surface temperature is multiplied by TFAC
Flux factor, the fast flux is multiplied, by-FFAC
Time constant in the transient fission
gas release
- 15 -
No
72
73
74
75
76
77
78
79
80
Name
Unit
The release in a time step is
(l-exp(-TAUREL x AT)) multiplied by
the steady-state release
Separating points in the power
history- (See PFAC1)
1X1
1X2
1X3
RELOPT
KPOR
RINNER
DUMMY3
DUMMY2
DUMMY1
Parameters in the WAFER swelling
model.
Inner fuel radius in the LOWI design
Dummy variables
The end of the material data list is indicated by a No > largest
valid number (80).
2.4. Experimental data
It is possible to specify the most important PIE data in connection with the experiment name, these data are then printed in a
table together with the corresponding calculated values.
2 cards <
Experimental name
Midpellet ramp strain, EPSMAX
Interface ramp strain, MEPSM
Max centre temperature, MTCENT
Midpellet EOL strain, EPSSL
Interface EOL strain, MEPSSL
Released fission gas, RELFG
Failure (l=failure, 0=No-failure)
col
col
col
col
col
col
col
col
1
11
21
61
71
1
11
31
-
6
20
30
70
80
10
20
40
- 16 -
2.5. Power history, H(t)
Each card contains the following data in format (7G10.0)
step end time (hours)
i card
step power (W/m)
step outer cladding temperature ( C)
step coolant pressure (Pa)
step inverse neutron diffusion length (KAPPA), m-'
2
step fast flux (n/cm • s)
The number of subdivisions of the step
If for any step ^ step 1, the power, the outer cladding temperature, the coolant pressure, KAPPA or the fast flux are 0.0
(= blank columns), the value from the previous time step is
used in the time step. If KAPPA = 0.0 in time step 1, KAPPA is
assumed to be constant, given by KAPPA in the design data.
The power history is terminated by a "step-end-time" = 0.0.
2.6. Special design and material data, X s
The specific design and material data for each experiment are
in the same format as X°- Even if no specific design and material
data are present, the logical unit (specific ...) must be terminated by a card with no>80.
- 17 -
3. OUTPUT SPECIFICATION
The general form of the output from FRP is illustrated in Fig. 3.
Each bracket corresponds to a logical item which is further
described in the following. The parameter "OUT" determines the
amount of output, on the Figure is specified for which values of
"OUT" the individual logical items are printed.
[Head]
[Control variables]
[X°]
[Experiment name]
[H(t)]
[xs]
X; Stochastic variables used for th is
experiment. (X° with the changes
specified by Xs)
For each
> experiment
OUT > 1
y(t) and w(t); Fuel state and clad
failures
CASE 1 and 4
Z; Distribution of EOL and extreme
values
CASE 2 and 3
z; EOL and extreme values compared
with experimental values
CASE 1 and 4
Z} EOL, extreme values and failure
probability compared with
experimental values.
CASE 2 and 3
Figure 3. Output from FPP
- 18 3.1. Detailed description of
; output common for all Cases
Head
Always printed
Control variables:
Always printed
Printout of the present variables
General input design
Data, X°:
Always printed
NO
The number of the variable
VARIABLE
The name of the variable
DISTRIBUTION
The distribution ustJ for the
variable
MEAN VALUE
The mean value of the variable
COEF. OF VAR.
The coefficient of variation for
the variable
Input power history, H(t):
Printed for OUT > 1
STEPNR
Step no. in the power history
SLUTTID
The accumulated time (hours)
at the end of the time step.
EFFEKT
The pin power at the end of the
time step (W/m)
TCY
The outer cladding temperature
<°C)
PY
The outer pin pressure (Pa)
- 19 KAPPA
The inverse diffusion length
On-1)
FIFAST
The fast flux (energy > 1 MeV)
Printed for OUT _> 1
Outprint of the design data,
including the default values
Design data, X:
Printed for OUT _> 1
Outprint of the material data,
including the default values
Material data, X:
CASE X:
X = 1
X - 2
X = 3
X = 4
Deterministic calculation using
the mean values
Monte Carlo simulation
Taylor approximation
Deterministic calculation
using the mode values
At last there is a comparison of some important calculated data
and PIE data, for each of the specified pins. Where no PIE data
is specified a question mark is printed.
Exp. no.
Experiment numbers in the input
Name
Experimental name
EPSMAX
Midpellet ramp strain. Calculated from the time step given
by RAMPST. If RAMPST » 0, the
deformation between the EOL
strain and the minimum strain
during the life is used
MEPSM
As for EPSMAX with stress
concentration
20 -
SIGNAX
Maximum stress without stress
concentrat * ••>.-.
PKSTRS
Maximum stress with stress
concentration
MAXSCD
Stress corrosion damage index
with stress concentration
MTCENT
Maximum center temperature
EPSSL
Midpellet EOL strain
MEPSSL
Interface EOL strain
RELFG
Released fission gas
SIGDAM
Eqvivalent SCC damage stress
without stress concentration
PKDAM
Eqvivalent SCC damage stress
with stress concentration
P OF F
Probability of failure. Calculated based on the assumption
that PKDAM is normally distributed. The failure criteria is
(225, 15) MPa.
P Of F = P(PKDAM > (225, 15) MPa)
3.2. Descrlpticn of the output special for CASE 1 and 4
Fuel state, Y(t):
Printed for OUT > 1
1. Page
STEPNO
The actual step number
- 21 -
END-TIME
The accumulated time froat
the starting point (hours)
DURATION
The duration of the present
step (hours)
TYPE
1 of 3 possible power states.
RAMP, STEADY, or FALL
which mean increasing-, steadyor decreasing power
POWER
The power of the end of the
time step (W/cm)
BURNUP
The fuel burnup measured in
parts per million
PRATE MIDDEL
The mean fission rate in the
fuel during the time step
(PPM/hour)
TCY
Outer temperature of the
cladding (°C)
TCI
Inner temperature of the
cladding (°c)
TSURF
Surface temperature of the
fuel (°C)
TCENT
Centre temperature of the
fuel (°C)
TBRIDGE
The bridge temperature ( C)
RBRIDGE
The radius of the bridge (mm)
2. Page
STEPHO
The present step number
EPSEL
Elastic strain (0/00)
EPSTH
Permanent tangential strain (0/00)
PLAST
Yield and primary creep deformation in the present step (0/00)
TOTPLAST
Plastic deformation giving the
position in the yield diagram
(strain hardening) (0/00)
DVS
Relative U0 2 volume increases
by swelling, densification, and
relocation (0/00)
RELFG
Fission gas release (0/0)
HG
Thermal conductivity between
fuel and cladding
CA
The contact area between fuel
and cladding. (Fraction of total
area)
SIGTH
Tangential stress (MPa)
SGEN
The generalized stress (MPa)
KONPRE
The contact pressure between
fuel and cladding (MPa)
GAB
The gab between fuel and
cladding (urn)
- 23 3. Page. Calculation with maximum interaction
STEPNO
The actual step number
MSIGTH
Maximal tangential stress (MPa)
MAXSCD
Maximal stress corrosion
damage index
MAXEPS
Maximal permanent tangential
strain (0/00)
TCENT
Centre temperature ( C)
TBRIDGE
Bridge radius (mm)
KONPRE
Contact pressure between fuel
and cladding (MPa)
GAB
The gab between fuel and cladding
(um)
'Exp. No.' Gas data
HELIUM
The amount of helium in the
3
pin (m )
FISGAS
The amount of released fission
3
gas in the pin (m )
3.3. Description of the output special for CASE 2
For all of the variables ?.. (explained for CASE 1), the following
are calculated:
MEAN
The mean value
STDEV
Standard deviation
- 24 MY2
2nd order laoment around mean,
the variance
MY3
3rd order moment around mean,
skewness of the distribution
MY4
4th order moment around mean,
the kurtosis
COEFV
Coefficient of variation
SQBl
The skewness relative to the
degree of spread
B?.
The relative measure of kurtosis
For all Z. the calculated values of z. are written in ascending
order. If NBGR > 1 the values are grouped with NBGR in each
group, and the group avarage value is written. LOOPS/NBGR must
be an integer. Below each value (or group) the corresponding
fractile is given.
3.4. Description of the output special for CASE 3
For all the variables Z. (explained for CASE 1) the following
are calculated:
VAR*(DF/DX)KX2
Lowest-order contribution to
the variance. The variance multiplied by the 1st derivative
of the state variable
VAR*(D2F/DX2)
The second-order term in the
mean value. The variance multiplied by the 2nd derivative of
the state variable
- 2!
VAR-2.LED
The second-order contribution
to the variance
KY3
3rd order moment around w a n ,
skewness of the distribution
MY4
4th order »ment around mean,
the kurtosis
DFCX
The 1st derivative of the state
variable
D2FDX2
The 2nd derivative of the state
variable
MEAN
Mean value
STDEV
Standard deviation
F(MEAN(X)>
The lowest-order approximation
to the mean value. The deterministic value calculated using
the mean value of all stochastic variables
3.0RD-VAR
3rd order term in the approximation of the variance
COEFV
Coefficient of variation
SQB1
The skewness relative to the
degree of spread
The relative measure of kurtosis.
- 26 3.5. Additional output for 0UT«2 (Maximum output)
For 0UT=2 there is an output of the namelist GEOTID. After the
material data, there is a complete outprint of the initialized
data, so it is possible to check the values in case of trouble.
In CASE 1 there is an outprint of a name list TESTUD containing
global variables for FFRS.
In CASE 2 there is an outprint of the values of Z\ for each
Monte Carlo trial.
- 27 -
4. REFERENCES
1.
2.
3.
4.
5.
6.
7.
MISFELDT, IB. Probabilistic Assessment of Light Water
Reactor Fuel Performance. Risø Report No. 390, October 1978.
(63 p ) .
MISFELDT, IB. FFRS: A Computer Program for the Thermal and
Mechanical Analysis of Fuel Rods. Risø Reports No. 373,
February 1978. (53 p ) .
ROSS, A.M., STOUTE, R.L. Heat Transfer Coefficient between
U02and Zircaloy-2. AECL-1552 (1962) (67 p ) .
LEWIS, V.B. Engineering for the Fission Gas in U0 2 Fuel.
Nucl. Appl., Vol. 2, April 1966. (171 p ) .
BEYER, C.E. CAPCON-THERMAL-2: A Computer Program for
Calculating the Thermal Behaviour of an Oxide Fuel Rod.
BNWL-1898 (1976).
JOON, K. et.al. Private communication.
KJÆR-PEDERSEN, N. A New Version of the LWR Fuel Performance
Model WAFER. In: Transactions of the 4th International
Conference on Structural Mechanics in Reactor Technology,
San Francisco, Calif., 15-19 August 1977. Edited by T.A.
Jaeger and B.A. Boley. Vol. D. (Commission of the European
Communities, Luxembourg). Paper no. D 1/3.
- 28 -
APPENDIX A
A numerical example
The use of the program is illustrated by an example which simulates a control rod sequencing in a BWR, where the power is
returned to full power immediately after the control rod movements. A fuel rod in a high power position, close to a control
rod which was inserted a short period and then withdrawn is
analysed. For the design data values are chosen that are typical
for BWR.
The power history, design data, and stochastic variables in the
material data are described in the following.
The power as a function of time is shown in Fig. A.l.
The uncertainty of the individual pin powers, as calculated by
a reactor physics calculation, is at least -5% (-1 standard
deviation). The three power levels (P., P 2 , and P,) can be considered as independent. The uncertainties of the fast flux and
the outer cladding temperature are assumed to be -5% (-1 standard deviation) and -2% (-1 standard deviation), respectively.
The power levels, the outer cladding temperature and the fast
flux are assumed to follow a normal distribution.
The irradiation conditions (power history) are summarized in
Table A.l.
The used design data are shown in Table A. 2. The nominal values
are used as mean values, the standard deviations are based on
typical tolerances for BWR fuel. All design variables are assumed to be normally distributed.
For the material data the default values in FRP are used. The
mean value, standard deviation, and distribution type is shown
in Table A.3 for the stochastic variables in the material
equations.
- 29 -
p3
-J
LU
->
Pi
111
cc
LU
£
O
0.
p2
IRRADIATION
TIME
Fig. A.l. Power history for the example.
Table A.l. Power history for the example
period
h
power*
w/ca
0-24
24-1S400
15400-15401
15401-17630
17630-1700. 01
17630.01-17654
0-360
mmmn value«
360
360-136
(ait flux* outer cladding
10 14 n/c* 2 »«c temperature*
0-1.0
1.0
1.0-0.4
136
0.4
136-410
0.4-1.15
1.15
410
29S
295
295
295
295
295
- 30 -
Table A.2. Design data for the example
Malo.fi parameter
Inner cladding radius
Cladding thlcknass
Radial gap
SvnSiLy
Equivalent length
Pieman voluae
Pill jas volume
Cladding yield
strength at 300°
Inverse neutron
diffusion length
Average grain aire
Cladding surface
roughness
Short
naiae
Mean
value
RCI
5.33
TCLAO
O.SO
TGAB
0.11
TDEM
»6
3.6
37.
37.
LR,"
VP
RF
Standard
deviation
0.0075
0.021
0.011
0.«7
0.72
7.«
7.4
SIGHAF
300.
15.
KAPPA
GRAIN
80.
25.
16.
5.
RH1
Fuel surface roughness RH2
130
90
•m
•a
m>
1 TO
*
o»i
«J
MP
26.
IS.
2)
Denslficatlon parasieter WEFF" 0.1x10 * 0.035x10,-«
Anlsotropy factors
YF • .5j YH
.75, »G
Unit
UM
.25
Porosity distribution: 0.16% porosity with r - 0.1 vm
1.6* porosity with r » 0.6 u*
2.2t porosity with r • 6 urn
- 31 -
Table A.3.
Stochastic variables In the material equations
Short
Haterlal property
Distribution*
Mean
Standard
value
deviation
Zlrcaloy thermal conductivity
CO
M
UOj thermal expansion
ALFAF
M
13.5
-5
1x10
Zlrcaloy thermal expansion
ALFAC
H
0.53x10
Youngs modulus• zlrcaloy
EC
N
1.01
0.1x10""
-5
7.S.10
Unit
10
--1
-5
0.05x10
O.SxlO
10
M/.'
Mean thermal conductivity
KM
of 00, and tlrcaloy
t.5
0.9S
1.2
0.42
2.5
0.5
8.056
0.3
20
«/•
A constant in the gap
CMS
conductance equation
LM
Factor in the porosity correction
EO
to the UOj thermal conductivity
Constant in the U 0 2 thermal
KSH
M
H
H
N
N
N
LM
LM
N
KHTSM
n
4.75xl0"3
MMTSWL
N
N
II
N
II
LM
0.1
0.3
conductivity
EI
Fission energy
EFIS
UMAX
DELK
Zlrcaloy plastic deformation
(
HPL
BFL
Zlrcaloy creep
FCLAD
(X>2 creep
Solid swelling
FU02
Hot (gaseous) swelling
4
Poisson*s ratio, slrcaloy
MY
Parameters in FPUS
0REF
OBum
Stress concentration in the cladding
Eccentricity of the pellet
N
- normal distribution
LM - lognormal distribution
SIGFAC
ECCEMT
200
1.2xlo'
-1.4xl0
6
0.1
0.12X109
MeV
MP
0.22x10*
M»/R
0.012
-
0.4xl0~ 21
O.OSxlO" 21
cm/n
1.2
1.7
0.5
2.5
-
o.a
O.OS
20.X10 3
0.5x10"'
1.25
0.5
riMA - 1
lxlO*3
PIMA
0.02
0.07
-
4.X10 1
0.1x10"'
0.2
0.2
- 32 -
APPENDIX B
Complete input for the example described in Appendix A.
With this input a deterministic calculation is performed, the
mean value is used for all stochastic variables (CASE 1 ) .
If one of the other 3 cases are wanted the only necessary change
is to insert a specification of the case in the namelist GEOTID.
-
33
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- 34 -
APPENDIX C
Complete output from a deterministic calculation with FRP. The
output corresponds exactly to the job given in Appendix B.
- 35 t*»nH.C 1
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- 44 -
APPENDIX D
Complete output from a Monte Carlo simulation. Only "CASE" is
changed relative to the input given in Appendix B.
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- . 3 0 1 1 - 0 3 - . 1 * 7 1 - 0 3 -.149E-03 -.«57£*04 - . 6 6 0 E - 0 * -.603E-04 - . 7 0 0 1 - 0 4 - . 2 »71-0«
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0.0444
0.01*9
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0.1J46
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0.1544
0.11*5
0.0966
0.1769
0.13*}
0.3667
.UOE-03 .I21E-J3 .123E-03 .134E-01 .146E-03 •1671-01 .1*41-03
0.20*2
0.2161
0.1*42
0.2241
0.2341
0.1663
0.1743
0.1143
.2*11-03 .258E-03 •2401-01 .2421-03
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0.2759
0.285*
0.3056
0.2560
0.265*
0.2»5 U
0.3157
0.2440
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0.3755
0.325?
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0.3456
0.3556
0.3*54
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0.4094
0.4153
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0.4552
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0.4345
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0.5747
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0.6444
0.4743
0.4641
0.7042
0.7141
0.6544
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0.6643
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0.7440
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0.7*39
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0.14*3
0.2062
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0.1663
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0.2241
0.1763
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0.2759
0.25*0
0.2459
0.265«
0.3»57
0.3098
0.24«0
0.293«
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0.3635
0.3556
0.345*
0.3655
0.3257
0.3725
0.3357
0.3*54
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0.4054
0.4353
0.4253
0.4492
0.4451
0.4153
0.4552
0.4751
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0.51*9
0.9249
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Rise-M-l2257
Risø National Laboratory
T i t l e and a u t h o r ( s )
Date O c t o b e r
USER MANUAL
1980
Department or group
For the probabilistic fuel performance code FRP
Department of Reacbor
by
John F r i i s
lb
Technology
Group's own r e g i s t r a t i o n
number(s)
Jensen
Misfeldt
pages +
tables +
illustrations
Abstract
This report describes the use of the probabilistic fuel performance code FRP. Detailed descriptions of both input to and output from the
program are given. The use of the program is
illustrated by an example.
Available on request from Risø Library, Risø National
Laboratory (Risø Bibliotek), Forsøgsanlæg Risø),
DK-4000 Roskilde, Denmark
Telephone: (02) 37 12 12, ext. 2262. Telex: 43116
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