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RELAP5-3D Uncertainty Analysis. A.J. Pawel and Dr. George L. Mesina. International RELAP Users’ Seminar 2011 July 25-28, 2011. Overview. Methodology Test Cases Required programs and scripts Results Conclusions. Methodology. Identify qualified test cases For each case, identify: - PowerPoint PPT Presentation
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RELAP5-3D Uncertainty Analysis
A.J. Pawel and Dr. George L. Mesina
International RELAP Users’ Seminar 2011July 25-28, 2011
Overview
• Methodology
• Test Cases
• Required programs and scripts
• Results
• Conclusions
Methodology
• Identify qualified test cases
• For each case, identify:
– Figure of Merit (FOM)
– Parameters that have heavy influence on the Figure of Merit (expert judgment required)
– Realistic ranges for the values of these parameters
• Run each test case with input decks modified for every feasible combination of input parameters
• Collect the FOMs and perform relevant statistical calculations, such as the production of means, variances, order statistics, and 95/95 tolerance intervals.
FLECHT-SEASET Test 31701• Flecht-Seaset Model Diagram• Forced Reflood Exp’t
• FOM: Peak Clad Temp (PCT)
• PCT depends on:
• System Pressure
• 40 ± 10 psi
• Temperature of the Inlet Water
• 127 ± 4 ºF
• Reflood Flow Rate
• 6.1 in/s ± 10%
• Peak Power
• 2.3 kW/m ± 10%
Scripting
• Selecting which values of the parameters to be varied on each run should be automated.
• Matrix of values given to C-script with instructions to run RELAP5-3D in nested loops.
– # parameters varied = # nested loops
– Execute RELAP5-3D
• With the same input deck?
• Sift through the output by hand?
Input Modification
• FORTRAN 90/95 program to modify an existing input deck.
• Place comment cards in the input deck before lines that are to be modified with instructions on how the modification should occur.
• Input modification program recognizes the strings and calls the relevant modification subroutine.
• Writes the modified input deck to a new file with a new (distinct) name
– Name based on command line arguments.
– This is very useful, as will be shown later.
Output Collection
• FORTRAN 95 program to collect input parameters and FOM from RELAP5-3D input and output files.
• Input modification program takes input parameters from file of pre-selected values.
• Figure of merit in a special control variable added to the input deck prior to processing.
• Writes the five values to a new file with a unique name based on the indices of the parameter values used.
– Again, this is useful.
Supercomputing
• Even small jobs (e.g. 9 values/parameter) are time-consuming.
– 4 input parameters => 94 = 6,561 runs @ ~10 sec. per run. 65610s(hour/3600s) ~ 18.2 hours.
• Apply INL Massively Parallel Computer: Fission
– Appro distributed memory cluster
– 12,512 cores on 391 nodes
• Runs are independent; “embarrassingly parallel”
– Run time reduced to ~20 minutes
Statistics
• Mean – expected value of the FOM
• Variance – roughly, how much the FOM varies
• Standard Deviation – square root of the variance
• nth Percentile (Pn) – value above n% of the FOM values
• Tolerance Interval – expected range of values
– One-sided: gives only an upper/lower bound
– Two-sided: gives both upper and lower bounds
– A γ/β Tolerance Interval is such that a fraction of the population, γ, is in the tolerance interval with probability β
Sample Reduction Techniques
• Latin Hypercube
– Each value of each parameter used exactly once (E.G. in 2D, diagonal of times table)
– Same number of values per axis.
– Values generally randomized, not on diagonal
• Stratified Sampling
– Break input parameter domain into small groups (strata) of values for each parameter
– Select value from each stratum, form 4-tuples
• Create at least two 4-tuples per stratum
Use 59 samples for 95-95 Tolerance Interval• For either approach, number of 4-tuples needed to
create a 95-95 one-sided tolerance interval is 59.
• User preselects (randomly generates) 59 4-tuples and runs RELAP5-3D 59 times
• Statistical results are reasonably close to 6561 runs
– 59 runs can be repeated with different random sample.
– Statistical results reasonably close each time
• Maximum of a sample of 59 is an estimator of the 95th percentile of the population
A Different Hypercube
FLECHT-SEASET Results
*LHC and SS numbers are averages over ten trials.
Population Latin Hypercube*
Stratified Sample*
µ (K) 1159.44 1159.97 1159.96
σ2 (K2) 8.58 8.20 8.13
σ (K) 2.93 2.86 2.85
σ (% of µ) 0.25 0.25 0.25
P95 (K) 1164.40 1164.59 1164.51
Maximum (K) 1168.82 1166.33 1166.51
1-Sided T.I. (K) 1164.26 1164.69 1164.66
Marviken Critical Flow Test 22• Facility Description• Critical Flow Test
• Figure of Merit: mass flow rate
• Flow rate depends on:• Temperature in Pressure Vessel
• 484 ± 0.6 K
• Temperature in Outlet Nozzle• 441 ± 0.6 K
• Steam Pressure• 4,930 ± 9 kPa
• Nozzle Diameter• 0.5 m ± 1%
Marviken Model Diagram
Marviken Results
*LHC and SS numbers are averages over ten trials.
Population Latin Hypercube* Stratified Sample*
µ (kg/s) 15066.59 15092.66 15092.56
σ2 (kg2/s2) 26712.34 24975.40 23610.21
σ (kg/s) 163.44 157.99 153.63
σ (% of µ) 1.08 1.05 1.02
P95 (kg/s) 15357.80 15356.16 15352.49
Maximum (kg/s) 15417.00 15398.80 15405.29
1-Sided T.I. (kg/s) 15335.45 15353.57 15346.06
Conclusions
• The Developmental Assessment manual of RELAP5-3D has demonstrated that the program models these facilities acceptably well.
• The small standard deviations in all cases suggest that for reasonable variations in key parameters, the code is sure of its answer.
• One-sided tolerance limits testify that the facilities would remain within regulatory specifications with better than 95/95 confidence.
• In the applications investigated here, RELAP5-3D is a reliable reactor systems modeling software.