ML20031A139
| ML20031A139 | |
| Person / Time | |
|---|---|
| Site: | Calvert Cliffs  |
| Issue date: | 09/30/1981 |
| From: | ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY |
| To: | |
| Shared Package | |
| ML19268A437 | List: |
| References | |
| CEN-182(B), NUDOCS 8109210037 | |
| Download: ML20031A139 (9) | |
Text
.
.. 5 t
)
i i.r-I
! \\
v y.:
ia t
STATISTICAL APPROACH TO ANALYZING CREEP COLLAPSE OF OVAL FL'C' R0D CLADDING USING CEPAN l
CEN-182(B) i I
I I
l September,1981
.o l
Combustion Engineering, Inc.
Windsor, Ct.
i t
6
..f i LEGAL NOTICE.
THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY COMBUSTION ENGINEERING, INC. NEITHER COMBUSTION ENGINEERING NOR ANY PERSON ACTING ON ITS DEHALF:
,e A.
MAKES ANY WARRANTY OR f.EPRESENTATION, EXPRESS OR IMPLIED INCLUDING THE WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE OR MERCHANT ABILITY, WITH RESPECT.TO THE ACCURACY, COMP: ETENESS, OR USEFULNESS OF THE INFORMATION CONTAINED IN THIS REPORT, OR THAT THE USE OF ANY INFOP.MATION, APPARATUS, METHOD, OR PROCESS DISCLOSED IN THIS REPORT MAY NOT INFRINGE PRIVATELY.
OWNED RIGHTS;OR B. ASSUMES ANY LIABILITIES WITH RESPECT TO THE USE OF, OR FOR DAMACFS RESULTING FROM THE USE OF. 4NY INFORMATION, APPALATUS, METHOl' OR PROCESS DISCLOSED IN THIS REPORT.
Y u
h 4
+
I i
. i j
STATISTICAL APPP0ACH TO ANALYZIftG CREEP COLLAPSE OF OVAL CLADDING USING'CEPAN
1.0 INTRODUCTION
Topical Report CENPD-187, "CEPAN-Method of Analyzing Creep Collapse of Oval Cladding",
was submitted in March 1976.
It describes a method which utilizes the CEPAN computar code to predict creep deformation and collapse of-Zircaloy fuel cladding containing initial ovality. The NRC has concluded that this report provides an acceptable analytical procedure for determining the minimum time to collapse for Combustion Engineering (C-E) Zircaloy clad fuel. The purposes of this document are to (a) describe an improvement to the existing procedure which provides a method for statistically determining the effects of the uncertainties on some of the input parameters used in the analysis and, (b) to document an acceptance criterion for collapse times predicted by the improved procedure. The CEPAN computer model is not changed technically by the statistical treatme -t of the input.
The current method of selecting and combining input parameters results in combinations of dimensions and operating conditions that are extremely improbable. For example, 95% probability (at 95% confidence) levels are used in the selection of each cladding dimension which is input to the CEPAN code. Though individually evaluated statistically, each of these values is input to CEPAN in a deterministic manner. Therefore, a number of adverse dimensional values are applied simultaneously in each CEPAN case.
This is equivalent to assuming that all adverse cladding dimensional deviations occur simultaneously in the limiting fuel rod.
In addition to these dimensional values, the most unfavorable combination of operating conditions is assumed in licensing calculations using CEPAN.
The probability of all adverse cladding dimensions and operating conditions occuring simultaneously in any given fuel rod is extremely remote. The improved methodology described in this document results in a more reasonable degree of conservatism by statistically determining the effects of uncertainties in cladding dimensions. The conservatism resulting from the most unfavorable combination of operating conoitions is not reduced by this improved methodology, since they continue to be assumed.
I
I
. i 2.0 CURRENT METHOD FOR CALCULATING MINIMUM CLADDING COLLAPSE TIME CENPD-187 details the mechanics of the CEPAN Computer Code and the selection method for input data in cladding collapse calculations. The seven case-specific inputs to the CEPAN Code fall into two general categories:
cladding dimensions and operating conditions. The operating conditions are external pressure, rod internal pr'ssure, e
cladding temperature and fast neutron flux.
f In the current deterministic method for calculating minimum cladding collapse time, 60 most unfavorable value for each of the input parameters is attributed to the same fuel rod, and this hypothetical limiting rod is analyzed by CEPAN to determine collapse time. The current methods for selecting values for the input parameters are described i
below:
4 (a) Cladding Dimensions _ - in the hypothetical limiting fuel rod, cladding outside diameter and initial ovality are assigned upper 95/95 probability / confidence interval limits, and cladding wall thickness is assigned a lower 95/95 probability / confidence interval limit, based on actual measurements of the cladding being analyzed.
(b) Operating Conditions - For calculating long term creep effects, external pressure is assumed to remain constant at the nominal primary system coolant pressure. Mininum internal pressure is generated based on a deterministic combination of adverse initial pellet and clad dimensions and the minimum initial fuel rod fill pressure allowed by manufacturing tolerances.
In addition, the combination of operating conditions most l
unfavorable to collapse time is assumed in the calculation of minimum internal pressure, and no credit is taken for the beneficial effect of released fission gas. Cladding temperatures and neutron fluxes are calculated at an elevation equal to 80% of the active core height for a fuel rod under these operating conditions.
Inherent in this calculation is the assumption that the cladding is entirely unsupported by the pellet column.
i i
The seven parameters discussed above are used by CEPAN to calculate a collapse time.
L The ' result represents an extremely conservative minimum based on the described method of selecting and deterministically combining the input values.
3
,l
. s -.
3.0 STATISTICAL METHOD FOR CALCULATING MINIMUM CLAPDING COLLAPSE TIME I
Because the cladding dimensions are independent variables, the probability of the limiting fuel rod simultaneously having the combination of dimensions currently assumed is very remote.
The probability of any one fuel rod having these dimensions, in addition to having the most unfavorable operating conditions, is even more remote.
The statistical method for determining minimum collapse time reduces the portion of this extreme conservatism which is associated with deterministically combining adverse,
^
cladding dimensions.
l The statistical method combines the SIGIM stochastic simulation computer code (Reference 1) and the CEPAN code. Similar applications of the SIGl% code have been documented in Reference 2.
The relationship between the SIGMA and CEPAN computer codes is illustrated in Figure 1.
The function of the SIGIM code is to generate a specified number of randon combinations of cladding dimensions,- based on the actual known probability distributions of each of the dimensions, and to input each random combination into a separate CEPAN case.
For each CEPAN case, the unfavorahic combination of operating conditions remains the same. The result from each CEPA.i case is a unique value for collapse tirne. After the collapse time has been calculated for each random combination of cladding dimensions, SIGMA organizes all of the collapse times into a probabil'ty histogram.
Since each individual collapse time in the histogram represents the minimum collapse time for a realistic combination of cladding dimensions, the histogram shows the overall statistical distribution of collapse times that can be attributed to the variations in cladding dimensions.
If the probability histogram generated by SIG!M indicates that 95% of the calculated collapse times are greater than or equal to 30,000 hours0 days <br />0 hours <br />0 weeks <br />0 months <br />, this means that a fuel rod randomly selected from the batch of fuO rods being analyzed and subjected to the most unfavorable combination of operating conditions will have 95% probability of h1ving a collapse tirre greater than or equal to 30,000 hours0 days <br />0 hours <br />0 weeks <br />0 months <br />.
4.0 ADDITIONAL DESCRIPTION OF THE SIGMA COMPUTER CODE The function of the SIGtM code is to generate a dependent variable probability histogram for a number of independent variables.
Each of the independent variables has a specifice probability distribution.
This is illustrated in Figure 1 for the specific application described in this document.
For this case, the independent variables are the cladding dimensions (outside diameter, wall thickness, and ovality).
The dependent variable is cladding collapse time.
3
I The theoretical bases upon which this code depends are those involving the 11onte-Carlo 1
and Stratified Sampling Techniques. The SIGMA data sau1pling module performs data selection using Latin-flypercube Sampling (LilS) (Reference 3).
LilS is a stratified sampling scheme that covers the range of the independent variables with a minimum of simulation data points.
Distributional characteristics of the independent variables are input to SIGMA (either in the 6 "n of the defining parameters of a standard probability distribution (normal, unifonn) or in the form of a nomalized frequency histogram).
In LHS the range of parameter variation is divided into equal probability,- j i
intervals.
In each interval a point is selected at random from the distribution. TheI sampled values from each interval are stored in an array.
To generate sets of input 4
i values, SIGMA selects intervals at random for each variable using each interval only once in a simulation.
I The functional relationship between the dependent variable and the independent variabic:
is defined by some algorithm, which in this case is the CEPAN computer code.
Ccabining each set of independent variables generated by SIGMA in accordance witn the appropr.ste functional relationship results in a calculated va~ue of the dependent variable.
This process is continued until all data in each set have been used and the resulta.it dependent variable probability histogram has been generated.
The functional characteristics of the CEPAN Code used in combination with SIGMA are identical to those in the CEPAN Code described in CENPD-187.
}
5.0 COLLAPSE CRITERION Resistance to collapse is demonstrated if the one-sided lower 95% probability interval limit for collapse time shown on the histogram exceeds the operating time of the fuel.
In reality, the actual probability of collapse would be significantly lower than 5%
at this time since the overall probability of collapse depends heavily on the effects
]
of uncertainties 'n the remaining input parameters, which continue to be accounted for conservatively.
4 6.0
SUMMARY
A method has been pr;esented which determines the effects of variations in cladding i
dimensions on collapse time. The result of using this method for licensing calculations l 1s a probability histogram of collapse times, with each individual time based on the
,tj approved CEPAN model.
. s.
A collapse criterion based on the probability histogram has been stated. The criterion is conservative in its use of a 95% probability value, and the underlying calculations remain extremely conservative in tl.eir use of biased values for all input parameters except cladding dimensions.
O I
l t
9 n
eA
l s-
\\
\\
D.EFERENCES:
(1)
F. J. Berte, "The Application of Monte-Carlo and Bayesion Probability Techniques to Flow Prediction and Detennination", TIS-6122, February 1977 (2) CEN-124(B)-P, " Statistical Combination of Uncertainties", Part 1 (December 1979)
Part 2 (January 1980), and Part 3 (March 1980)
(3) McKay, M. D., et., al., " Report on the Application of Statistical Techniques to the Analysis of Computer Codes", LA-NVREG-6526-MS, Los Alamos Scientific Laboratory, October 1976 t
'a
o PROBABILITY DISTRIBUTION OF DEPENDENT VARIABLE (COLLAPSE TIME)
A ADDITIONAL INDEPENDENT VARIABLES WITH NO PROBABILITY DISTRIBUTION (EXTERNAL PRESSURE, R0D INTERNAL PRESSURE, CLAD TEMPERATURE, FAST NEUTRON FLUX)
,e PROBABILITY DISTRIBUTIONS SETS OF SAMPLED FUNCTIONAL RELATIONSHIP DEPENDENT VARIABLE FOR THE INDEPENDENT VALUES OF SIGMA Bf D P(,jp (COLLAPSE TIME)
Ef EPEND
^
VARIABLES (CLADDING OUTSIDE--er
-- INDEPENDENT IB (CEPAN)
DIAMETER, CLADDING UALL VARIABLES THICKNESS, AND CLADDING A
l OVALITY) j FIGURE 1