MONK Under-sampling bias calculations for benchmark S2 - Initial results. Presented by PAUL SMITH EGAMCT Meeting, Paris 6 th July 2016

Transcription

1 MONK Under-sampling bias calculations for benchmark S2 - Initial results Presented by PAUL SMITH EGAMCT Meeting, Paris 6 th July 2016

2 Acknowledgement Team work the work was performed by the following ANSWERS staff: Nigel Davies Simon Richards Geoff Dobson Max Shepherd Chris Baker 2

3 Contents of presentation Model basics S2 Specification a reminder MONK Status & useful features for the benchmark calculations K eff results from MONK Flux tally results Fission densities Conclusions 3

4 Model basics Number of settling stages = 500. Should be more than sufficient for settling under normal circumstances MONK used superhistories per stage (i.e. sps ) of 100, 200, 500, 1k, 2k, 5k, 10k, 20k, 50k Used MONK default of 10 generations per superhistory The runs aimed to preserve the total number of samples at 1x10 9 (although due to computing resource management issues a small number were run for fewer). Therefore 100 sps was run for 1 million stages, 1k sps was run for 100k stages, 50k sps was run for 2k stages, etc. Initially runs were submitted to single nodes using 16 cores on the Poundbury HPC. 4

5 S2 Specification a reminder 3D infinite lattice (radial boundaries reflective, vertical boundaries black) 17x17 bundle in the infinite lattice All assemblies are modelled with an assembly average burnup of 40 GWD/MTU with 5 year cooling time Uniform storage temperature 293K 18 axial zones Fission density results in axial locations Flux is tallied over the fuel volume only in the desired locations Reaction Tally top, midplane & bottom 5

6 MONK Current Status The current version of MONK is MONK10A_RU0 Released in May 2014 Supported platforms Linux 32-bit Linux 64-bit (parallel processing using MPI) Windows 32-bit Visual Workshop Version 3A (released with MONK10A) Version 3B (current version released October 2014) New nuclear data libraries (BINGO and WIMS format) JEFF 3.1, and ENDF-B/VII.0 CENDL

7 New Features in MONK10A The new features in MONK10A included: additional input, control, parameter and looping features; new FG options; new Hole geometries; CAD import (for evaluation); new action tallies; unified tally scoring; action tallies in UT meshes; new sensitivity options; data assimilation (ADJUST option); Shannon entropy; fixed source option; run-time Doppler broadening; new energy group schemes; material and energy dependent fission spectrum (WIMS); mesh-based burn-up option (for evaluation); and parallel processing. 7

8 The Next Release The next release of MONK will be MONK10B_RU0. Improvements to the mesh-based burn-up option, with a focus on burn-up credit applications. Improved user image New COWL options for transferring irradiated materials between models (e.g. from a reactor core burn-up calculation to a storage or transport criticality model) Includes the ability to include/exclude specific fission products and actinides e.g. For actinide-only burnup credit Improvements to sensitivity/covariance calculations Nuclides specified by name rather than DFN Sensitivity to fission spectrum Sensitivity/covariance now supported in parallel calculations Fission matrix Eigenvalues and eigenvectors of fundamental and higher order modes Dominance ratio estimator Unified Tally Interim results Run to target standard deviation on UT results 8

9 The Next Release - continued Fractal geometry improvements EROD body (elliptical cross-section cylinder) FG Body reflection capability Hole geometry improvements Improved support for CAD (IGES format) import Better support for long calculations Wider output formats LONG PRINT option for displaying greater precision Loop selection Allow individual loops to run concurrently Based on modularised Fortran code. Improved error trapping at compile time Better code base for future developments New BINGO nuclear data libraries JEFF3.2 and ENDF/B-VII.1 All reported errors will be fixed Expected to be released in later half of

10 k k eff results - from the 16-core runs The plot below shows the results taken from a mean of all the 16-core runs Approximately 22 k eff results per sps values above 500 sps and approximately 10 at 500 sps and below. Plus 3 runs at 20k sps. Undersampling bias at large is clear K(THREE) k sps k sps 500sps k, 10k, 20k, 50k sps 200sps 100sps E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03 1.E-03 10

11 k(3) k eff results additional calculations Additional runs with fewer total samples or fewer cores used were added to assess the fine structure behaviour at small The 4 core jobs were run in batches of 3 and only used 1k sps and above Plot below including these shows the results from 5k sps and greater values ALL K eff Regardless of total samples or HPC cores 5k sps k sps 20k sps 10k sps E E E E E E-05 11

12 Comparison of 4 Core and 16 Core Results Blue =16 core result, Amber = 4 core result 12

13 Flux Tally Results (16 core results) Flux Tally 1 to 10 are small regions in zslice 1 and zslice 2. As sps INCREASES Tally values DECREASE: Tally E E E-05 Tally 5 Tally E E E-05 Tally E E E-05 Tally 3 Tally 7 Tally E E E E E E E E E E E E E E E E-04 Tally E E E-04 Tally E E E E-04 Tally E E E E-04 13

14 Flux Tally Results (16 core results) Tally 11 to 15 are at zslice 10 and show the same behaviour as 1 to 10. Tally E E E E E E E E-02 Tally E E E E E E E E-02 Tally E E E E E E E E-02 Tally 14 Tally E E E E E E E E E E E E E E E E E E E E-02 14

15 Flux Tally Results (16-core results) The remaining Tally values show the opposite behaviour i.e. convergence from below. These are at zslices 16, 17 and 18 Tally 16 Tally 17 Tally 18 Tally 19 Tally E E E E E E E+00 Tally E E E E E E E+00 Tally E E E E E E E+00 Tally E E E E E E E E+00 Tally E E E E E E E E+00 Tally E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+01 Tally 26 Tally 27 Tally 28 Tally 29 Tally E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 15

16 Fission densities Note how the varies as we increase z-slice: 1.400E E E E E E E In terms of k eff the most important fission densities are the last 3 (i.e. 16 to18). In all other regions we see a POSITIVE bias with fewer sps However in the last 3 we see the negative bias that is reflected in the k eff graph. The steep gradient in axial is under-estimated in calculations suffering from under-sampling bias. 16

17 Fission densities First 15 z-slice regions: Fission density 1 Fission density 2 Fission density 3 Fission density 4 Fission density E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-02 Fission density 6 Fission density 7 Fission density 8 Fission density 9 Fission density E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 Fission density 11 Fission density 12 Fission density 13 Fission density 14 Fission density E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+02 17

18 Fission densities The last 3 z-slice regions (where the most important fission densities are) Fission density 16 Fission density E E E E E E E E+02 0.E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03 1.E E E E E E E E E E+03 0.E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03 1.E-03 Fission density E E E E E E E+02 0.E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03 1.E-03 18

19 Conclusions Undersampling bias in k eff is evident when less than 1000 superhistories (~ 10,000 samples) is used per stage. The steep axial gradient in the tallies and fission densities is under-estimated in calculations suffering from under-sampling bias. 19