Advanced Neutronics Modeling

1
Advanced Neutronics Modeling

• GNEP Fast Reactor Working Group Meeting
• Argonne, IL
• August 22, 2007
• M. A. Smith, C. Rabiti, D. Kaushik, C. Lee,
• and W. S. Yang
• Argonne National Laboratory

2
Current Status

• Current fast reactor physics analysis tools were
  developed during the 1985-94 time period, as part
  of the IFR/ALMR programs
• Current approach is based on cumbersome
  multi-step calculations
• Cross sections self-shielded at ultra-fine group
  (2000) level with 0D/1D spectrum calculation
• Spatial collapse to form regional broad group
  cross sections with 1D/2D flux calculation
• Broad group (33) nodal diffusion or transport 3D
  core calculations with homogenized nodes
• Number of design calculations (fuel cycle
  analysis, heating calculation, reactivity
  coefficient calculation, control rod worth and
  shutdown margin evaluation, etc.) based on broad
  group 3D core calculation
• Current tools are judged to be adequate to begin
  the design process
• Extensive critical experiment and reactor
  operation database exists
• Validation and capabilities have evolved in
  parallel

3
Improvement Needs

• However, significant improvements are needed to
  allow more accurate and economical design
  procedures
• Significant efforts are also required to utilize
  all the existing design tools on modern computer
  frameworks
• Improved accuracy is needed to meet burner design
  challenges
• Radial blanket typically replaced by reflector
• Many critical experiments (BFS-62, MUSE-4)
  exhibit problems in accurate prediction of
  reaction rates in the immediate reflector region
• Important for bowing (safety) and shielding
  considerations
• High leakage configurations also challenge design
  methods
• Transport effects are magnified
• Key reactivity coefficients (void worth)
  under-predicted
• Improved pin power and flux distributions
• Accurate pin power distributions for T/H
  calculations
• Accurate pin flux distributions for isotopic
  depletion prediction

4
Improvement Needs (Contd)

• Applicable range of problems needs to be extended
• Modeling of structure deformation (for accurate
  reactivity feedback)
• Neutron streaming in voided coolant condition
• Control assembly worth (relatively large
  heterogeneity effects)
• Shielding calculations (severe spectral
  transitions)
• A modern, integrated design tool is crucial to
  improve the current design procedure, which is
  time-consuming and inefficient
• Eliminate piecemeal nature vulnerable to
  shortcomings in human performance, organizational
  skills, and project management
• Improved automation of data transfers among
  codes/modules
• Greatly improve the turn-around time for design
  iterations
• Utilize advances in computer science and software
  engineering
• Improved modeling in the integrated design tool
  allows radical improvements
• Ability to optimize the design (e.g., reduce
  nominal peak temperatures)
• New knowledge to alter and redirect the design
  features and approach

5
Objective and Approaches

• 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 calculations
• Allow uninterrupted applicability to core design
  work
• Phased approach for multi-group cross section
  generation
• Simplified multi-step schemes to online
  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
• Unified geometrical framework
• Finite element analysis to work within the
  existing tools developed for structural mechanics
  and thermal-hydraulics
• Domain decomposition strategies for efficient
  parallelization

6
Adaptive Flux Solution Options
7
Work Scopes of FY07

• Develop an initial working version (V.0) of
  deterministic neutron transport solver in general
  geometry
• General geometry capability using unstructured
  finite elements
• First order form solution using method of
  characteristics
• Second order form solution using even-parity flux
  formulation
• Parallel capability for scaling to thousands of
  processors
• Adjoint capability for sensitivity and
  uncertainty analysis
• Targeted computational milestones
• An ABR full subassembly with fine structure
  geometrical description for coupling with
  thermal-hydraulics calculation
• A whole ABR configuration with pin-by-pin
  description
• Multi-group cross section generation
• Develop an initial capability for investigating
  important physical phenomena and identifying the
  optimum strategies for coupling with the neutron
  transport code
• ANL techniques in the fast energy range
• ORNL techniques in the resonance range

8
General Geometry Capability

• Unstructured finite element mesh capabilities
  have been implemented
• CUBIT package is the primary mesh generation tool
  (hexahedral and tetrahedral elements)
• Further research is required for reducing mesh
  generation efforts and robust merging of the
  meshes of individual geometrical components

9
Accomplishments for Second Order Form Solutions

• PN2ND and SN2ND solvers have been developed to
  solve the steady-state, second-order, even-parity
  neutron transport equation
• PN2ND Spherical harmonic method in 1D, 2D and 3D
  geometries with FE mixed mesh capabilities
• SN2ND Discrete ordinates in 2D and 3D geometries
  with FE mixed mesh capabilities
• These second order methods have been implemented
  on large scale parallel machines
• Linear tetrahedral and quadratic hexahedral
  elements
• Fixed source and eigenvalue problems
• Arbitrarily oriented reflective and vacuum
  boundary conditions
• PETSc solvers are utilized to solve within-group
  equations
• Conjugate gradient method with SSOR and ICC
  preconditioners
• Other solution methods and preconditioners will
  be investigated
• Synthetic diffusion acceleration for within-group
  scattering iteration
• Power iteration method for eigenvalue problem
• Various acceleration schemes will be investigated

10
Initial Benchmarking Based Upon Takeda Benchmarks

• More spatial refinement is necessary for VARIANT
• Serial computational performance is comparable to
  other codes
• VARIANT P5 was 2 minutes
• PN2ND P5 was 4 hours
• SN2ND S3 was 10 minutes
• DFEM S4 54 minutes (LANL 2001 )
• Improper preconditioner is an issue
• SSOR for PN2ND

11
ABTR Whole-Core Calculations

• Four benchmark problems are being analyzed
• All require P7 or S8 angular order
• 33, 100, and 230 groups are planned
• 30º symmetry core with homogenized assemblies
• 40,000 spatial DOF
• 100 processors
• 120º periodic core with homogenized assemblies
• 400,000 spatial DOF
• 500 processors
• 30º symmetry core with homogenized pin cells
• 1.7 million spatial DOF
• 1000 processors
• Single assembly with explicit geometry
• 2.2 million spatial DOF
• 5000 processors

12
30º Symmetry Core with Homogenized Assemblies

• VARIANT result is 12 pcm off with P9 angular flux
  approximation
• CPU time was 12 hours
• SN2ND was ran on Janus
• S10 solution took 8 hours on 1 processor
• PN2ND was ran with different XS
• P7 solution with SSOR took 1 hour on 132
  processors

13
120º Periodic Core with Homogenized Assemblies

• P11 solution of PN2ND on 512 processors was 2.1
  hour (total 1093 hours)
• MeTiS domain decomposition for 512 processors and
  14th of 33 group flux solution

14
Scalability Test of PN2ND

• Parallel performance (strong scaling) from 512 to
  4096 Cray XT4 processors
• 120º periodic ABTR core with homogenized
  assemblies
• 33 group P5 calculation
• Mesh contains 587,458 quadratic tetrahedral
  elements and 793,668 vertices
• About 12 million space-angle degrees of freedom
  per energy group

15
30º Symmetry Core with Homogenized Pin Cells

• MCNP 24 hours on 40 processors (or 40 days)
• SN2ND and PN2ND calculations under progress
• PN2ND P3 was completed

16
Accomplishments for First Order Form Solution

• MOCFE solver has been developed to solve the
  steady-state, first-order neutron transport
  equation
• Method of characteristic in space and discrete
  ordinates in angle
• Linear tetrahedral and quadratic hexahedral
  elements
• Utilizes the very efficient Moller-Trumbore
  algorithm to find intersection with triangle
• Surface of quadratic hexahedral element is meshed
  with 48 triangles
• Synthetic diffusion acceleration with the use of
  PETSc parallel matrices and vectors
• Have performed ray tracing for meshes containing
  1 million elements
• Ray tracing accounts for a minor component of the
  total time
• Fully scalable process
• Algorithm analysis for parallelization is ongoing
• Single assembly T/H coupling calculation is ready
  to go given computational time
• Estimated time for the initial flux solution is 5
  hours on 128 proc.

17
Mesh Refinement Study of MOCFE on Takeda 1
Benchmark

• Max 0.01 cm2 ray area and 80 angular directions

18
Scalability Test of MOCFE on Takeda 4 Benchmark

• 85538 elements without synthetic diffusion
  acceleration

19
Algebraic Collapsing Synthetic Acceleration of
MOCFE
20
Single Assembly Geometry

• One group, fixed source scoping study for T/H
  coupling calculation

21
Multi-group Cross Section Generation

• Phased approach was adopted to allow
  uninterrupted applicability to core design
• Tens of thousands groups are required for
  accurate representation of self-shielding effects
• Near term goal is to use 50-500 energy groups
• Simplifies the existing multi-step cross section
  generation schemes
• Improvements to resolved and unresolved
  resonances are underway
• Provide the user the option to choose the level
  of approximation

• Online cross section generation
• Libraries of ultra-fine group smooth cross
  sections and resonance parameters (or point-wise
  XS)
• Utilize fine group MOCFE solutions
• Fine group cross section libraries
• Functionalized XS data
• Subgroup method is being considered

22
Multi-group Cross Section Generation (Contd)

• Starting set of methodologies
• Above resolved resonance energy range
• Ultra-fine group methodologies of MC2-2
• Resolved resonance energy range
• Ultra-fine group calculation of MC2-2 with
  analytic resonance integrals using a narrow
  resonance approximation
• Hyper-fine group (almost point-wise) calculation
  of MC2-2 with RABANL integral transport method
• Point-wise resonance calculation using CENTRM
  (ORNL)
• Thermal energy range
• CENTRM methodologies (ORNL)
• ENDF/B data processing
• ETOE-2 create MC2-2 libraries
• NJOY point-wise resonance cross sections

23
Multi-group Cross Section Generation (Contd)

• Update and testing of the ETOE-2/MC2-2 system
• The MC2-2 code is currently being revised for
  eventual coupling with UNIC and use in a parallel
  computing environment
• FORTRAN 90
• Current focus is on off-line cross section
  generation
• Use of ENDF/B-VII.0 data
• Required coding changes to ETOE-2
• Completed processing major actinides and
  structural material nuclides
• Preliminary tests of the ENDF/B-VII.0 libraries
  of MC2-2
• MC2-2/TWODANT R-Z modeling is compared with Monte
  Carlo R-Z
• Good agreement within 0.25 ?? for bigger systems
  with relatively soft spectrum (Big-10, ZPR-6, and
  ZPPR-21)
• Overestimated multiplication factors by 0.22
  0.35 ?? for small systems (Flattop, Jezebel, and
  Godiva)
• Good agreement of C/E ratios of spectral indices
  within 2.7 (Godiva and Jezebel)

24
Preliminary Results of ENDF/B-VII.0 Data
C/E calculated / experimental values
25
Conclusions

• Code development is progressing well
• ETOE-2 and MC2-2 are being revised
• Second order solvers PN2ND and SN2ND have been
  developed
• Demonstrated good scalability to 4000 processors
• First order solver MOCFE has been developed
  including synthetic acceleration scheme and
  quadratic hexahedral meshes
• Adjoint solver has not been completed
• Preconditioner study has yet to be completed
• Milestone calculations are primary area to be
  completed
• Jaguar (Cray XT4 at ORNL) is being expanded and
  job queue is typically saturated
• We are very grateful of ORNL for the cpu time
• BlueGene and JAZZ (ANL) are typically saturated
• Production machines are not effective for code
  development
• Average 4-8 hour wait in the queue for scoping is
  problematic
• Purchase request for a small cluster is under
  progress
• INCITE proposal was submitted in collaboration
  with ORNL for computer time on big leadership
  computers (XT4 and BlueGene/P)

26
Plans for FY08

• Further development of high fidelity neutronics
  solvers
• Implement acceleration for steady state
  eigenvalue calculations
• Optimize acceleration schemes based upon geometry
  and cross section data
• Investigate strategy utilizing parallelization by
  group and space
• Formalize user interface and cross section
  management
• Develop a time dependent solution capability
  (kinetics)
• Develop a multi-group cross section generation
  code based on the ETOE-2/MC2-2 methodologies for
  use in a parallel computing environment
• Interface the new cross section code with the
  neutronics solvers
• Develop platform independent library interface of
  all key cross section data
• Investigate online cross section generation
• Complete the process of ENDF/B-VII.0 for fast
  reactor analysis work
• Verification and validation
• Systematic verification of multi-group cross
  section generation scheme
• Benchmark using ZPR critical experiments for fast
  reactors
• ZPR 6-6a or ZPR 6-7