3. Reactor Physics

Introduction by M. A. Jessee and F. Bostelmann

SCALE supports a wide range of reactor physics analysis capabilities. SCALE reactor physics calculations couple neutron transport calculations with ORIGEN to simulate the time-dependent transmutation of various materials of interest. The two reactor physics analysis tools within SCALE are TRITON and Polaris. TRITON is SCALE’s modular reactor physics sequence for a wide variety of system types; Polaris is SCALE’s light water reactor (LWR) lattice physics sequence.

The primary function of TRITON is to simulate the time-dependent evolution of nuclide inventories of a reactor system through a series of multigroup transport calculations and depletion/decay calculations. Before each multigroup transport calculation, TRITON executes the XSProc module to calculate multigroup cross sections for each user-designated depletion material. The XSProc calculation is performed based on the time-dependent material compositions and the user-defined cross section processing definitions. TRITON provides maximum modeling flexibility, supporting the full range of cross section processing options in XSProc along with support for four different multigroup transport modules available in SCALE. These transport modules include the following:

• XSDRN: one-dimensional discrete ordinates (S_N) transport module for modeling simple slab, cylindrical, and spherical geometries,

• NEWT: two-dimensional (2D) S_N polygon-mesh deterministic transport module with arbitrary geometry model definitions, and

• KENO-V.a and KENO-VI and Shift: three-dimensional Monte Carlo transport modules with arbitrary geometry model definitions.

In addition to the multigroup-based calculation sequences, TRITON supports continuous-energy (CE) transport calculations with KENO-V.a and KENO-VI and Shift. For each depletion material, the CE Monte Carlo calculation tallies energy-integrated nuclide-dependent reaction rates to couple the transport solution to the ORIGEN depletion calculation. Both the multigroup- and CE-based depletion calculations are parallelizable and can run on an arbitrary number of processors.

TRITON provides easy-to-use input options to define the time-dependent reactor condition, including power history, material temperatures, and material compositions. TRITON also provides the option to perform lattice physics calculations, with input options to define branch calculations, homogenization edits, few-group energy structures, and assembly discontinuity factors. The homogenized few-group cross sections are archived onto auxiliary data files for subsequent in-reactor core calculations.

TRITON generates several data files for follow-on SCALE analysis. It creates the ORIGEN binary concentration file (.f71 extension) that stores all of the material inventories at each depletion/decay step. This file can be used as input to ORIGEN, ORIGAMI, and MAVRIC to support spent fuel characterization and shielding analysis. TRITON also creates the ORIGEN binary library file (.f33 extension) that stores the ORIGEN transition matrix for each depletion material at each depletion/decay step. The ORIGEN library files can be used as input to ORIGEN or ORIGAMI for rapid assessment of spent fuel inventories. Finally, TRITON also generates the aforementioned lattice physics few-group cross section archive (xfile016) for reactor core calculations.

In addition to the TRITON reactor physics sequence, SCALE supports an alternative easy-to-use LWR depletion sequence for generating lattice physics data for full-core reactor calculations. The Polaris lattice physics sequence couples 2D multigroup transport calculations with ORIGEN depletion to simulate LWR fuel assemblies. Polaris provides easy-to-use input definitions for defining the primary inputs necessary for lattice physics analysis, namely the pin and lattice geometry, the material compositions, and specifications for the power history and branch calculations. Polaris supports systematic input defaults for analysis of both fuel and reflector models for both pressurized water reactor (PWR) and boiling water reactor (BWR) geometries. It uses a novel approach for cross section processing called the Embedded Self Shielding Method (ESSM). The hallmark feature of ESSM is that the self-shielding calculation is performed on the 2D fuel assembly geometry, eliminating the need for user-defined cross section processing definitions. The ESSM calculation and the keff calculation are performed with a deterministic transport module based on the Method of Characteristics (MOC) approach. The Polaris sequence generates the lattice physics archive file (.t16 and .x16 extension), the ORIGEN binary concentration file (.f71 extension), the ORIGEN binary library file (.f33 extension), and a geometry plot file (.png extension).

• 3.1. TRITON: A Multipurpose Transport, Depletion, And Sensitivity and Uncertainty Analysis Module
  • 3.1.1. Introduction
  • 3.1.2. Overview of TRITON Sequences
    • 3.1.2.1. Cross section processing sequence (T-XSEC)
    • 3.1.2.2. Transport sequences (T-XSDRN, T-NEWT)
    • 3.1.2.3. Depletion sequences (T-DEPL, T-DEPL-1D, T5-DEPL, T6-DEPL, T5-DEPL-SHIFT, T6-DEPL-SHIFT)
      • 3.1.2.3.1. Predictor-corrector depletion process
      • 3.1.2.3.2. Lattice physics analysis
  • 3.1.3. Input Description
    • 3.1.3.1. Cross section processing
      • 3.1.3.1.1. Combined two-region and S_N cross section processing
      • 3.1.3.1.2. User-defined Dancoff factors
    • 3.1.3.2. Transport sequences
    • 3.1.3.3. Depletion sequences input
      • 3.1.3.3.1. BURNDATA block
      • 3.1.3.3.2. BRANCH block
      • 3.1.3.3.3. BRANCH block with user-defined Dancoff factors
      • 3.1.3.3.4. DEPLETION block
        • 3.1.3.3.4.1. Basic DEPLETION block format
        • 3.1.3.3.4.2. ORIGEN depletion options
        • 3.1.3.3.4.3. Cross section processing simplification using ASSIGN
      • 3.1.3.3.5. TIMETABLE block
        • 3.1.3.3.5.1. Temperature and density
        • 3.1.3.3.5.2. Material swap
        • 3.1.3.3.5.3. Material flow
      • 3.1.3.3.6. OPUS block
        • 3.1.3.3.6.1. Selection of materials for OPUS processing
        • 3.1.3.3.6.2. Specification of stacked OPUS cases
      • 3.1.3.3.7. FGXS block
      • 3.1.3.3.8. TALLIES and DEFINITIONS block
    • 3.1.3.4. ALIAS block
      • 3.1.3.4.1. COMPOSITION block aliases
      • 3.1.3.4.2. CELLDATA block aliases
      • 3.1.3.4.3. DEPLETION block aliases
      • 3.1.3.4.4. TIMETABLE block aliases
      • 3.1.3.4.5. BRANCH block aliases
      • 3.1.3.4.6. NEWT MATERIAL block aliases
      • 3.1.3.4.7. KEEP_OUTPUT block
    • 3.1.3.5. TRITON control parameters
      • 3.1.3.5.1. Check mode: parm=check
      • 3.1.3.5.2. Multigroup cross section processing options
      • 3.1.3.5.3. Creating a broad group library: parm=weight, parm=(weight=N)
      • 3.1.3.5.4. Inclusion of additional nuclides for depletion: parm=(addnux=N)
      • 3.1.3.5.5. Few-group reaction cross section calculation control for continuous energy depletion: parm=(cxm=N)
      • 3.1.3.5.6. Infinite dilution cutoff control: parm=(infdcutoff=X)
      • 3.1.3.5.7. Override of the maximum number of days per depletion subinterval: PARM=(MAXDAYS=N)
  • 3.1.4. Output Files Created by TRITON
    • 3.1.4.1. Standard composition restart files
    • 3.1.4.2. Lattice physics parameters
    • 3.1.4.3. ORIGEN binary library files (.f33)
    • 3.1.4.4. ORIGEN binary concentration file (.f71)
    • 3.1.4.5. Binary mesh response files (.3dmap)
    • 3.1.4.6. Binary Shift output file (.h5)
  • 3.1.5. Output Description
    • 3.1.5.1. Control parameter edit
    • 3.1.5.2. T-XSEC output
    • 3.1.5.3. T-NEWT and T-XSDRN output
    • 3.1.5.4. Depletion sequence output
      • 3.1.5.4.1. Burnup history summary (all depletion sequences)
      • 3.1.5.4.2. Embedded transport model output
      • 3.1.5.4.3. System mass balance table
      • 3.1.5.4.4. Power balance tables
        • 3.1.5.4.4.1. ORIGEN binary concentration file listing
  • 3.1.6. TRITON Sample Cases
    • 3.1.6.1. TRITON sample problem 1: triton1.inp
    • 3.1.6.2. TRITON sample problem 2: triton2.inp
    • 3.1.6.3. TRITON sample problem 3: triton3.inp
      • 3.1.6.3.1. TRITON sample problem 4: triton4.inp
    • 3.1.6.4. TRITON sample problem 5: triton5.inp
    • 3.1.6.5. TRITON sample problem 6: triton6.inp
    • 3.1.6.6. TRITON sample problem 7: triton7.inp
    • 3.1.6.7. TRITON sample problem 8: triton8.inp
    • 3.1.6.8. TRITON sample problem 10: triton10.inp
    • 3.1.6.9. TRITON sample problem 11: triton11.inp
    • 3.1.6.10. TRITON sample problem 12: triton12.inp
    • 3.1.6.11. TRITON6 sample problem 1: triton6-1.inp
  • 3.1.7. Appendices
    • 3.1.7.1. XSDRN Model Block Description
      • 3.1.7.1.1. XSDRN PARAMETER block
      • 3.1.7.1.2. XSDRN MATERIAL block
      • 3.1.7.1.3. XSDRN COLLAPSE block
    • 3.1.7.2. Data Structure for Cross Section Database File xfile016
    • 3.1.7.3. The Flexible Branch Block
• 3.2. POLARIS - 2D Light Water Reactor Lattice Physics Module
  • 3.2.1. Introduction
  • 3.2.2. SCALE 6.3 Polaris Input Updates
  • 3.2.3. Setup
    • 3.2.3.1. title - case title lines
    • 3.2.3.2. library - nuclear data libraries
  • 3.2.4. Geometry
    • 3.2.4.1. geometry<ASSM> – assembly
    • 3.2.4.2. geometry<REFL> - reflector
    • 3.2.4.3. channel - coolant channel
    • 3.2.4.4. hgap - half distance between assemblies
    • 3.2.4.5. box - channel box geometry
    • 3.2.4.6. pin - pincell comprised of nested geometry zones of variable shape
    • 3.2.4.7. pinmap - pin layout
    • 3.2.4.8. control<RODLET> - RCCA-type layout
    • 3.2.4.9. control<BLADE> - BWR control blade
    • 3.2.4.10. insert - insert layout
    • 3.2.4.11. slab - slab geometry
    • 3.2.4.12. cross - cross geometry
    • 3.2.4.13. dxmap and dymap - pin-by-pin displacement maps
    • 3.2.4.14. mesh - advanced material dependent meshing options
    • 3.2.4.15. detector - insert a detector geometry
  • 3.2.5. Materials
    • 3.2.5.1. material - material initialization
    • 3.2.5.2. composition<NUM|WT> – general atom/wt fraction
    • 3.2.5.3. composition<FORM> - general chemical formula
    • 3.2.5.4. composition<CONC> - general number density
    • 3.2.5.5. composition<LW> - borated light water
    • 3.2.5.6. composition<UOX> -UO₂ fuel
    • 3.2.5.7. composition<UN> - UN fuel
    • 3.2.5.8. composition<ENRU> – enriched uranium
    • 3.2.5.9. composition library (pre-defined)
    • 3.2.5.10. property<SOLP> - soluble poison by weight
    • 3.2.5.11. property<DOPANT> - fuel dopant by weight
    • 3.2.5.12. property<TWOPHASE> - density property used to control two phase mixtures
    • 3.2.5.13. deplete - material depletion and decay
    • 3.2.5.14. basis - power basis materials
    • 3.2.5.15. shield - cross section self-shielding expansion specification
  • 3.2.6. State
    • 3.2.6.1. power - total power
    • 3.2.6.2. bu - initiate calculation with cumulative burnups
    • 3.2.6.3. bui - initiate calculation with cumulative burnups (with restart)
    • 3.2.6.4. dbu - initiate calculation with incremental burnups
    • 3.2.6.5. t - initiate calculation by cumulative time
    • 3.2.6.6. ti - initiate calculation by cumulative time (with restart)
      • 3.2.6.6.1. dt - initiate calculation by incremental time
    • 3.2.6.7. branch - instantaneous change
    • 3.2.6.8. history - time-dependent history
    • 3.2.6.9. add<MNAME> - material branch
    • 3.2.6.10. add<INAME> - insert/control branch
    • 3.2.6.11. add<GNAME> - geometry branch
  • 3.2.7. Options
    • 3.2.7.1. option<KEFF> - eigenvalue
    • 3.2.7.2. option<ESSM> - embedded self-shielding
    • 3.2.7.3. option<BOND> - Bondarenko search
    • 3.2.7.4. option<DEPL> - depletion
    • 3.2.7.5. option<CRITSPEC> - critical spectrum
    • 3.2.7.6. option<PRINT> - printing
    • 3.2.7.7. option<FG> - few-group cross section generation
    • 3.2.7.8. option<RUN> - run time
    • 3.2.7.9. option<GEOM> - geometry options
    • 3.2.7.10. option<GAMMA> - gamma transport calculation
    • 3.2.7.11. option<DATA> – data libraries
  • 3.2.8. System
    • 3.2.8.1. system<PWR> - pressurized water reactor
    • 3.2.8.2. system<BWR> - boiling water reactor
  • 3.2.9. Sample Problems
  • 3.2.10. Appendices
    • 3.2.10.1. SCALE 6.2 Polaris Input Format
      • 3.2.10.1.1. box – channel box
      • 3.2.10.1.2. pin – pin or pincell
      • 3.2.10.1.3. bu – initiate calculation with cumulative burnups
      • 3.2.10.1.4. dbu – initiate calculation with incremental burnups
      • 3.2.10.1.5. t – initiate calculation by cumulative time
      • 3.2.10.1.6. dt – initiate calculation by incremental time
      • 3.2.10.1.7. option<ESSM> - embedded self-shielding
      • 3.2.10.1.8. option<FG> – few-group cross section generation
      • 3.2.10.1.9. state<MNAME> – material state
      • 3.2.10.1.10. state<INAME> – insert/control state
      • 3.2.10.1.11. state<GNAME> – geometry state