The Advanced Fuel Cycle Initiative Status of Neutronics Modeling Won Sik Yang Argonne National Laboratory NEAMS Reactor Simulation Workshop May 19, 2009

NEAMS Reactor Simulation Workshop 2 Within the current knowledge of physics, theory and governing equations are well known –Boltzmann equation for neutron transport –Bateman equation for fuel composition evolution The coefficients of these equations are determined by nuclear data, geometry, and composition –Nuclear data are for the most part relatively well known for the most commonly used nuclides But still improved data are required to reduce design uncertainties –Geometry and composition have stochastic uncertainties and are affected by thermal, mechanical, irradiation, and chemical phenomena These coupled phenomena are not as well described, and they can dominate the analysis errors The challenge in neutronics analysis is to determine the solution efficiently by taking into account geometric complexity and complicated energy dependence of nuclear data Status of Neutronics Analyses

May 19, 2009NEAMS Reactor Simulation Workshop 3 Monte Carlo simulation with MCNP5 (INL) –Reaction rate tally uncertainties < 1% C/E values for U-235 fission rate distribution in CIRANO-2A (Blanket) and CIRANO-2B (Reflector) experiments Reaction Rate Traverse Example

May 19, 2009NEAMS Reactor Simulation Workshop 4 Negative Reactivity Transients of PHENIX Four unexpected scrams occurred in due to short negative reactivity transients (200 ms) with the same signal shape Several potential explanations were given, but not satisfactory Experiments are planned for PHENIX end-of-life tests for further investigation

May 19, 2009NEAMS Reactor Simulation Workshop 5 Current and Target Uncertainties for sodium cooled fast reactors Generation IV Target Uncertainties Parameter Current Uncertainty (SFR) Targeted Uncertainty Input data origin Modeling origin Multiplication factor, K eff (  k/k) 1%0.5%0.3% Power peak 1%3%2% Power distribution 1%6%3% Conversion ratio (absolute value in %) 5%2% Reactivity coefficients (component) 20% 10% Control rod worth (total)5%4%2% Burnup reactivity swing (  k/k) 0.7%0.5%0.3%

May 19, 2009NEAMS Reactor Simulation Workshop 6 The final objective is to produce an integrated, advanced neutronics code that allows the high fidelity description of a nuclear reactor and simplifies the multi-step design process –Integration with thermal-hydraulics and structural mechanics analyses to account for reactivity feedbacks due to geometry deformation accurately Required modeling capabilities –Reactivity and power distribution (coupled neutron and gamma heating) –Non-equilibrium and equilibrium fuel cycle analyses Refueling, fuel shuffling, and ex-core models –Perturbation and sensitivity analyses Uncertainty analysis and optimization –Transient analysis (coupled with T/H and T/M analyses) Reactivity coefficients and kinetics parameters –Shielding, decay heat, coolant activation and dose rate calculations, etc. Objectives and Requirements

May 19, 2009NEAMS Reactor Simulation Workshop 7 Utilize modern computing power and computational techniques –Meshing, domain decomposition strategies, parallel linear solvers, new visualization techniques, etc Allow uninterrupted applicability to core design work –Phased approach for multi-group cross section generation Simplified multi-step schemes Online cross section generation –Adaptive flux solution options from homogenized assembly geometries to fully explicit heterogeneous geometries in serial and parallel environments Allow the user to smoothly transition from the existing homogenization approaches to the explicit geometry approach Rapid turn-around time for scoping design calculations Detailed models for design refinement and benchmarking calculations Selected Approaches

May 19, 2009NEAMS Reactor Simulation Workshop 8 Adaptive Flux Solution Options Unified geometrical framework –Unstructured finite element analysis for coupling with structural mechanics and thermal-hydraulics codes Homogenized assembly Homogenized assembly internals Homogenized pin cells Fully explicit assembly

May 19, 2009NEAMS Reactor Simulation Workshop 9 PN2ND –Second-order, even-parity transport equation (CG solve) –1-D, 2-D, 3-D Cartesian with general reflected and vacuum b.c.s –Spherical harmonics combined with Serendipity and Lagrangian FE SN2ND –Second-order even-parity transport equation (CG solve) –2-D & 3-D Cartesian with general reflected and vacuum b.c.s –Discrete ordinates combined with Serendipity and Lagrangian FE MOCFE –First-order transport equation (long characteristics) –3-D Cartesian with general reflected and vacuum b.c.s –Discrete ordinates combined with Serendipity and Lagrangian FE NODAL: hybrid finite element method for structured geometries –Will replace nodal diffusion and VARIANT options in DIF3D –Use as an multi-grid preconditioner for other solvers Flux Solvers Available in UNIC

May 19, 2009NEAMS Reactor Simulation Workshop 10 Takeda Benchmark 4 Control Rod InControl Rod HalfControl Rod Out Reference ± ± ± PN2ND SN2ND MOCFE

May 19, 2009NEAMS Reactor Simulation Workshop 11 ABTR Whole-Core Calculations Angular Directions Spatial Mesh Approximation

May 19, 2009NEAMS Reactor Simulation Workshop 12 ZPPR-15 Critical Experiments Computational Mesh and Example Flux Solutions of ZPPR-15 Critical Experiment Flux expansion orderScattering orderEigenvalue P1P1 P1P P3P3 P3P P5P5 P3P Monte Carlo (VIM) ±

May 19, 2009NEAMS Reactor Simulation Workshop 13 2D OECD/NEA C5G7 Benchmark Thermal Group Flux in Core Thermal Group Flux in Pin Cell Reference ± MOCFE

May 19, 2009NEAMS Reactor Simulation Workshop 14 Parallel Implementation The scalability to peta-scale computing resources has been demonstrated –163,840 cores of BlueGene/P (Argonne) –131,072 cores of XT5 (ORNL) –Over 75% weak scalability Cores 4π Angles k eff Fission Iters. / Time Total Time (sec) Source Update (sec) Weak Scaling 32, / % 49, / % 65, / % 73, / % 131, / % * 163, / % * Weak Scaling Study by Angle on BlueGene/P (PHENIX EOL test)

May 19, 2009NEAMS Reactor Simulation Workshop 15 Parallel Implementation Weak Scaling Study by Angle on XT5 (PHENIX EOL test) Cores 4π Angles k eff Fission Iters. / Time Total Time (sec) Source Update (sec) Effective Weak Scaling 32, / % 49, / % 65, / % 98, / % 114, / % 131, / %

May 19, 2009NEAMS Reactor Simulation Workshop 16 PHENIX End-of-Life Experiments Participating in the PHENIX end-of-life experiments Whole-core geometry is required (no symmetry) using homogenized fuel and explicit control rods Space/angle convergence study completed using over 4 billion DOF on up to 163,840 cores of Blue Gene/P Energy discretization study is ongoing 0.4 MeV Max/Min= eV Max/Min= eV Max/Min= eV Flux and Radial Mesh

May 19, 2009NEAMS Reactor Simulation Workshop 17 ZPR-6 Critical Experiments Two ZPR-6 critical experiments are targeted for V&V in 2009 (Assemblies 6A and 7) Explicit fuel plate representation allows direct comparison to legacy homogenization methods Spatial mesh requirements are large; U-235 plates are 1/16 th in thick Preliminary studies performed on BG/P and Jaguar up to 130,000 processors indicate that over 10 billion DOF will be required to resolve the space-angle-energy mesh

May 19, 2009NEAMS Reactor Simulation Workshop 18 ZPR-6 Critical Experiments 14 MeV Flux / Mesh U-235 Plate Power

May 19, 2009NEAMS Reactor Simulation Workshop 19 A modular version has been integrated into UNIC for on-line generation of multi-group cross sections of each spatial region with given material and temperature distribution –Standalone code to generate ISOTXS datasets for legacy tools Ultrafine group (2082 groups) transport calculations –Homogeneous mixture, and 1-D slab and cylindrical geometries –Resolved resonance self-shielding with numerical integration of point-wise cross sections using the narrow resonance (NR) approximation –Unresolved resonance self-shielding with the generalized resonance integral method –Elastic scattering transfer matrices obtained with numerical integration of isotopic scattering kernel in ENDF/B data Advanced Multi-group Cross Section Generation Code MC 2 -3

May 19, 2009NEAMS Reactor Simulation Workshop 20 1-D hyperfine group (~100,000) transport capability –Consistent P 1 transport calculation for entire resolved resonance energy range (< ~1 MeV) with anisotropic scattering sources –Optionally used for accurate resolved resonance self-shielding and scattering transfer matrix generation Efficient strategy to generate accurate multi-group cross sections for heterogeneous assembly or full-core calculations is being developed by combining various solution options –1-D hyperfine group cell calculation –1-D ultrafine group whole-core calculation (with homogenized regions) –2-D MOCFE calculation in several hundred groups Advanced Multi-group Cross Section Generation Code MC 2 -3

May 19, 2009NEAMS Reactor Simulation Workshop 21 MC and Coupling with UNIC

May 19, 2009NEAMS Reactor Simulation Workshop 22 Reconstructed Pointwise Cross Sections (ENDF/B-VII.0)

May 19, 2009NEAMS Reactor Simulation Workshop 23 Hyper-Fine-Group Spectrum Calculation Inner core composition of ZPR-6/6A

May 19, 2009NEAMS Reactor Simulation Workshop 24 Hyper-Fine-Group vs. Ultra-Fine- Group Spectra

May 19, 2009NEAMS Reactor Simulation Workshop 25 LANL Criticality Assembly Benchmarks (UFG Calculation) Multiplication factors are in an excellent agreement within 0.15% ∆ρ by taking into account the anisotropy of inelastic scattering

May 19, 2009NEAMS Reactor Simulation Workshop 26 MC 2 -3 vs. VIM for ZPR-6/7 (Standalone UFG Calculation) RegionVIM MC 2 -3 (  k pcm) Inner Core ± Outer Core ± Radial Blanket ± Axial Blanket ±

May 19, 2009NEAMS Reactor Simulation Workshop 27 ZPPR-15 Critical Experiments Reflector Blanket Outer core Inner core

May 19, 2009NEAMS Reactor Simulation Workshop 28 A Realistic View of ZPPR-15 Double Fuel Column Drawer STAINLESS STEEL PU-U-MO FUEL DEPLETED URANIUM STAINLESS STEEL DEPLETED URANIUM SODIUM DEPLETED URANIUM SODIUM STEEL BLOCK SODIUM STAINLESS STEEL SODIUM PU-U-MO FUEL STAINLESS STEEL DEPLETED URANIUM STAINLESS STEEL Matrix tube Drawer SODIUM Void Z X

May 19, 2009NEAMS Reactor Simulation Workshop 29 ZPPR-15 Critical Experiments Three loading configurations of ZPPR-15 Phase A were analyzed –Loading 15: initial criticality –Loading 16: reference configuration for sodium void worth measurement –Loading 20: configuration with an 18” sodium void in part of inner core VIM - ExpDIF3D - Exp DataConfigurationExperimentVIM∆k, pcmDIF3D Sn∆k, pcm ENDF/B-V.2 L L L Void Worth (pcm) ENDF/B-VII.0 L L L Void Worth (pcm) * Standard deviations of Experiment and VIM ≤

May 19, 2009NEAMS Reactor Simulation Workshop 30 Summary An initial version of new multi-group cross section generation code MC 2 -3 has been developed –Preliminary tests showed significantly improved performance relative to MC 2 -2 –Integrated with UNIC for online cross section generation Consistent thermal feedbacks Account for spectral transition effects Second order solvers PN2ND and SN2ND have been improved –SN2ND demonstrated good scalability to >100,000 processors –Working on enhancing the anisotropic scattering iteration –Fixing the load imbalance for reflected boundary conditions –Starting next phase of pre-conditioner development p-refinement multi-grid and Algebraic multi-grid beyond that or possibly h-refinement

May 19, 2009NEAMS Reactor Simulation Workshop 31 Summary First order solver MOCFE –Improving parallel performance with Krylov Method –Added more elements to ray tracing capabilities –Adding back projection for parallel Started NODAL –Implement Krylov solution technique to fix some convergence problems –Eliminate memory problems and 1970s architecture –Will investigate energy parallelization on multi-core machines (8-32 cores)

May 19, 2009NEAMS Reactor Simulation Workshop 32 Backup Slides

May 19, 2009NEAMS Reactor Simulation Workshop 33 The MCNP perturbation option was used to determine the difference in net neutron production in every fuel assembly as a resulting of reducing –Fuel density by 2%, cladding density by 5%, and coolant density by 50% While the fuel density reduction showed reasonable results, the clad and coolant density effects still showed significant statistical variations –Observed statistical errors are less than 2% for the fuel density perturbation –However, as large as 41% for the cladding density perturbation and 100% for the coolant density perturbation Direct perturbation calculations showed even worse results –Relative statistical uncertainties of the re-converged production rates are often above 50%, and in some cases reach 100% –The re-converged calculation ran 50,000 histories per cycle for 160 active cycles, each of which took 1000 minutes on a 2.7-GHz Opteron processor Perturbation Evaluation with MCNP (LANL)

May 19, 2009NEAMS Reactor Simulation Workshop 34 NGNP with 60-degree periodic symmetry Core multiplication factor converges relatively quickly Power distribution converges very slowly Number of neutron histories 100M20M5M Eigenvalue    CPU time, hr Variation, % RMS Max –Asymmetric assembly power distribution is observed –Extremely large number of histories would be required for converged pin power distribution Convergence of Assembly Power Distribution

May 19, 2009NEAMS Reactor Simulation Workshop 35 Comparison of whole core depletions performed by GA, BNL, and ANL –MONTEBURNS (MCNP5+ORIGEN2) –Simple cubic lattice model –CPU time: ~40 hours for 50K and ~100 hours for 100K histories Much larger number of histories are required for converged flux solutions DB-MHR benchmark –Cycle length = 540 EFPD –Total 7 cycles –6 burn steps per cycle (90 days interval) –50K and 100K neutron histories per burn step Note that there are ~3 billion fuel particles Depletion with Monte Carlo Method

May 19, 2009NEAMS Reactor Simulation Workshop 36 APPLO2:172-group CP and 28-group MOC calculation CRONOS2: 8-group diffusion calculation (finite element method) % difference in fission rate distributions from MCNP4C (3D core) Control Rod Position Control Rod Worth TRIPOLI4 ±38 pcm NEPHTIS, % Diff. HomogeneousHeterogeneous ARI18, ORI7, SRI5, Homogenous Element Heterogeneous Element CEA: NEPHTIS Verification Results

May 19, 2009NEAMS Reactor Simulation Workshop 37 Power Distribution of Fuel Block (CR Inserted)

May 19, 2009NEAMS Reactor Simulation Workshop 38 Effective Multiplication Factors for 2D and 3D VHTRs with Heterogeneous Fuel Compact GeometryControl Rod Position MCNP5 ±20 pcm DeCART, ∆  pcm 190 Group47 Groups 2D ARO- Standard block ARI D ARO- Standard block ARO All Rods Out (ARO) All Rods In (ARI) Operating Rods In (ORI)

May 19, 2009NEAMS Reactor Simulation Workshop 39 2D Power Distributions AROARI ORI

May 19, 2009NEAMS Reactor Simulation Workshop 40 2D Block Power Comparison with MCNP5 AROARI ORI

May 19, 2009NEAMS Reactor Simulation Workshop 41 3D Flux Distribution for All Rods Out (ARO) Case 0.13 eV1 eV 7 eV 1 MeV

May 19, 2009NEAMS Reactor Simulation Workshop 42 3D Flux Distribution for Operating Control Rods In (ORI) 0.13 eV1 eV 7 eV 1 MeV