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RELAP5-3D Uncertainty Analysis

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:

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RELAP5-3D Uncertainty Analysis

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  1. RELAP5-3D Uncertainty Analysis A.J. Pawel and Dr. George L. Mesina International RELAP Users’ Seminar 2011 July 25-28, 2011

  2. Overview • Methodology • Test Cases • Required programs and scripts • Results • Conclusions

  3. 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.

  4. 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%

  5. 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?

  6. 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.

  7. 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.

  8. 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

  9. 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

  10. 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

  11. 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

  12. A Different Hypercube

  13. FLECHT-SEASET Results *LHC and SS numbers are averages over ten trials.

  14. Marviken Critical Flow Test 22 Facility Description Marviken Model Diagram • 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%

  15. Marviken Results *LHC and SS numbers are averages over ten trials.

  16. 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.

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