2. Criticality Safety

Introduction by B. T. Rearden ¹ and K. B. Bekar

SCALE provides a suite of computational tools for criticality safety analysis primarily based on the Monte Carlo codes KENO and Shift for eigenvalue neutronics calculations. [CritSafetyGPJD+11], [CritSafetyPJE+16].

Two variants of KENO provide identical solution capabilities with different geometry packages. KENO V.a uses a simple and efficient geometry package sufficient for modeling many systems of interest to criticality safety and reactor physics analysts. KENO-VI uses the SCALE Generalized Geometry Package, which provides a quadratic-based geometry system with much greater flexibility in problem modeling but with slower runtimes. Both versions of KENO perform eigenvalue calculations for neutron transport primarily to calculate multiplication factors (keff) and flux distributions of fissile systems in both continuous-energy and multigroup modes. KENO’s grid geometry capability extends region-based features for accumulating data for source or biasing parameter specifications, as well as for tallying results from a calculation for visualization or communication of data into or out of a calculation.

Shift, an advanced Monte Carlo code specifically designed for efficient parallel and GPU executions for high-performance computers, provides both eigenvalue and fixed-source Monte Carlo transport capabilities as well as hybrid capabilities for variance reduction methods with the Denovo deterministic transport solver. [CritSafetyPJE+16], [CritSafetyESSC10]. Shift supports different geometry engines including the Oak Ridge Adaptable Nested Geometry Engine (ORANGE) designed to provide particle transport capabilities on both KENO V.a and KENO-VI geometries as well as geometry visualization capabilities in the Fulcrum user interface. Shift with both versions of KENO geometries performs eigenvalue calculations in both continuous-energy and multigroup modes. Shift supports most widely used primary capabilities available with KENO codes.

Capabilities with both KENO codes and Shift code are typically accessed through the integrated SCALE sequences described below. Criticality safety analysts may also be interested in the sensitivity and uncertainty analysis techniques that can be applied for code and data validation as described elsewhere in this document.

¹ Formerly with Oak Ridge National Laboratory.

Criticality Safety Analysis Sequences

The Criticality Safety Analysis Sequences (CSAS) with KENO V.a (CSAS5), KENO-VI (CSAS6), and Shift (CSAS5-Shift, CSAS6-Shift) provide a reliable, efficient means of performing keff calculations for systems routinely encountered in engineering practice. The CSAS sequences implement XSProc to process material input and provide a temperature and resonance-corrected cross section library based on the physical characteristics of the problem being analyzed. If a continuous energy cross section library is specified, no resonance processing is needed, and the continuous energy cross sections are used directly in KENO, with temperature corrections provided as the cross sections are loaded.

CSAS sequences with 3D Monte Carlo transport capabilities currently available in SCALE 6.3 are listed in Table 2.1. The transport module run by each sequence, and the geometry engine used by each transport module, are also provided in this table. Note that the sequence names CSAS25 and CSAS26—similarly, CSAS25-Shift and CSAS26-Shift—are only the alias names of the CSAS sequences, and they were added to the SCALE repository for backward compatibility purposes.

Table 2.1 Valid CSAS sequences available in SCALE 6.3

Sequence Name	Transport Module	Geometry Engine
CSAS5, CSAS25	KENO V.a	KENO V.a
CSAS6, CSAS26	KENO-VI	SGGP 1
CSAS5-Shift, CSAS25-Shift	Shift with KENO V.a geometry	ORANGE 2
CSAS6-Shift, CSAS26-Shift	Shift with KENO-VI geometry	ORANGE
1 SGGP is SCALE General Geometry Package 2 ORANGE is a new C++ geometry package, the Oak Ridge Adaptable Nested Geometry Engine, has been designed to provide particle transport capabilities on both KENO V.a and KENO-VI geometries in SCALE sequences as well as geometry visualization capabilities in the Fulcrum user interface.

For continuous energy calculations, reaction rate tallies can be requested within the CSAS input, and for multigroup calculations, reaction rate calculations are performed using the KENO Module for Activity-Reaction Rate Tabulation (KMART) post-processing tools. A conversion tool is provided to up-convert KENO V.a input to KENO-VI either as a direct KENO input (K5toK6) or, more commonly, as a CSAS sequence (C5toC6). Note that these capabilities are only available with CSAS5 and CSAS6 sequences.

The CSAS5 search capability available in previous SCALE versions is no longer supported by the CSAS sequences in SCALE 6.3. Research is being conducted to support the equivalent search capabilities in a more robust modernized code framework for the next SCALE release.

CSAS sequences support parallel execution of KENO V.a, KENO-VI, and Shift transport modules. When running on multiple cores, Shift performance is always better than KENO codes since its design was targeted for high-performance computers.

Criticality Accident Alarm System Analysis with KENO and MAVRIC

Criticality accident alarm systems (CAAS) safety analyses modeling presents challenges because the analysis consists of a criticality problem and a deep-penetration shielding problem [CritSafetyPPJ09]. Modern codes are typically optimized to handle one of these types of problems, but not both. The two problems also differ in size-the criticality problem depends on materials relatively close to the fissionable materials, whereas the shielding problem can cover a much larger range.

CAAS analysis can be performed using the CSAS6 criticality sequence and the MAVRIC shielding sequence. First, the fission distribution (in space and energy) is determined via CSAS6. This information is collected on a grid geometry that overlies the physical geometry model and is saved as a Monaco mesh source file. The mesh source is then used as the source term in MAVRIC. The absolute source strength is set by the user to the total number of fissions (based on the total power released) during the criticality excursion. MAVRIC can be optimized to calculate a specific detector response at one location or to calculate multiple responses/locations with roughly the same relative uncertainty. See Sect. 4.2 for further details.

Note

The Sourcerer sequence is no longer supported in SCALE 6.3 because it depends on several legacy components not supported in SCALE 6.3. The equivalent capability will be designed as another start data type in CSAS sequences for the next SCALE release.

Note

DEVC sequence is a deprecated capability in SCALE 6.3.

• 2.1. CSAS: Control Module For Enhanced Criticality Safety Analysis Sequences With KENO
  • 2.1.1. Acknowledgments
  • 2.1.2. Introduction
  • 2.1.3. Sequence Capabilities
    • 2.1.3.1. Multigroup limitations
    • 2.1.3.2. Continuous energy limitations
  • 2.1.4. Input Data Guide
    • 2.1.4.1. XSProc data
    • 2.1.4.2. CSAS input data
      • 2.1.4.2.1. Definitions data
      • 2.1.4.2.2. Tallies data
      • 2.1.4.2.3. Mesh tally output files
    • 2.1.4.3. KENO data
  • 2.1.5. Description of Output
    • 2.1.5.1. Program verification information
    • 2.1.5.2. Mixture table
    • 2.1.5.3. Cross section processing summary
  • 2.1.6. Warning and error messages
  • 2.1.7. Sample problems
    • 2.1.7.1. CSAS5 sample problems
      • 2.1.7.1.1. CSAS5 sample problem 1: k_eff calculation
      • 2.1.7.1.2. CSAS5 Sample problem 8: k\(_{\infty}\) for a pebble bed fuel
    • 2.1.7.2. CSAS6 sample problems
      • 2.1.7.2.1. CSAS6 Sample problem 1: Aluminum 30 Degree Pipe Angle Intersection
      • 2.1.7.2.2. CSAS6 Sample problem 2: Plexiglas Cross
      • 2.1.7.2.3. CSAS6 Sample problem 3: Sphere
      • 2.1.7.2.4. CSAS6 Sample problem 4: Sphere Models Using Chords and Mirror Albedos
      • 2.1.7.2.5. CSAS6 Sample problem 5: Sphere Models Using Chords and Mirror Albedos
      • 2.1.7.2.6. CSAS6 Sample problem 6: Sphere Models Using Chords and Mirror Albedos (Eighth Sphere)
      • 2.1.7.2.7. CSAS6 Sample problem 7: Grotesque without the Diaphragm
      • 2.1.7.2.8. CSAS6 Sample problem 8 Infinite Array of MOX and UO2 Assemblies
• 2.2. CSAS-Shift: Criticality Safety Analysis Sequence with Shift
  • 2.2.1. Introduction
  • 2.2.2. CSAS-Shift Input Requirements
  • 2.2.3. Sequence Capabilities
    • 2.2.3.1. Multigroup limitations
    • 2.2.3.2. Continuous-energy limitations
    • 2.2.3.3. Unsupported Capabilities
  • 2.2.4. Input Data Guide
    • 2.2.4.1. KENO input data in CSAS-Shift
      • 2.2.4.1.1. Parameter data
      • 2.2.4.1.2. Geometry data
        • 2.2.4.1.2.1. Random geometry
      • 2.2.4.1.3. Start data
  • 2.2.5. Notes to CSAS-Shift Users
  • 2.2.6. CSAS-Shift Output
    • 2.2.6.1. Shift output
      • 2.2.6.1.1. Program verification information
      • 2.2.6.1.2. General problem information
      • 2.2.6.1.3. Input Warnings
      • 2.2.6.1.4. Tables of parameter data
      • 2.2.6.1.5. Energy boundaries data
      • 2.2.6.1.6. Mixing table data edits
      • 2.2.6.1.7. Geometry data edits
      • 2.2.6.1.8. Volume information
      • 2.2.6.1.9. Initial source edits
      • 2.2.6.1.10. K-effectives by generation
      • 2.2.6.1.11. Final k-effective edit
      • 2.2.6.1.12. Plot of average k-effective by generations run and by generations skipped
      • 2.2.6.1.13. Shannon Entropy Diagnostics
      • 2.2.6.1.14. Fission densities
      • 2.2.6.1.15. Flux Edit
      • 2.2.6.1.16. Final results table
      • 2.2.6.1.17. Final timing report table
• 2.3. Example Applications of CSAS6
  • 2.3.1. Run KENO-VI using CSAS6
  • 2.3.2. Run KENO-VI containing cell-weighted mixtures
  • 2.3.3. Run KENO-VI containing multiple unit cells
• 2.4. DEVC: Denovo EigenValue Calculation
  • 2.4.1. Introduction
  • 2.4.2. Sequence input
    • 2.4.2.1. Parameters block
    • 2.4.2.2. Grid geometry block
    • 2.4.2.3. Macromaterial block
      • 2.4.2.3.1. Ray tracing
      • 2.4.2.3.2. Point testing
      • 2.4.2.3.3. Example
    • 2.4.2.4. Starting sources block
  • 2.4.3. Sequence Output
    • 2.4.3.1. Using the mesh file viewer
    • 2.4.3.2. Viewing the starting source
  • 2.4.4. Sample Problems
• 2.5. KMART5 and KMART6: Postprocessors for KENO V.A and KENO-VI
  • 2.5.1. Introduction
  • 2.5.2. KMART Input Data
  • 2.5.3. KMART Sample Input
• 2.6. C5toC6: Input File Conversion Programs for CSAS
  • 2.6.1. Introduction
  • 2.6.2. Description and Input Guide

References

CritSafetyESSC10

Thomas M. Evans, Alissa S. Stafford, Rachel N. Slaybaugh, and Kevin T. Clarno. Denovo: A new three-dimensional parallel discrete ordinates code in SCALE. Nuclear technology, 171(2):171–200, 2010.

CritSafetyGPJD+11

Sedat Goluoglu, Lester M. Petrie Jr, Michael E. Dunn, Daniel F. Hollenbach, and Bradley T. Rearden. Monte Carlo criticality methods and analysis capabilities in SCALE. Nuclear Technology, 174(2):214–235, 2011.

CritSafetyPJE+16(1,2)

T. M. Pandya, S. R. Johnson, Evans, T.M., G. G. Davidson, S. P. Hamilton, and A. T. Godfrey. Implementation, capabilities, and benchmarking of shift, a massively parallel monte carlo radiation transport code. Journal of Computational Physics, 308:239–272, 2016. Publisher: Elsevier.

CritSafetyPPJ09

Douglas E. Peplow and Lester M. Petrie Jr. Criticality Accident Alarm System Modeling with SCALE. In Proceedings of the 2009 International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics. 5 2009. URL: http://inis.iaea.org/Search/search.aspx?orig_q=RN:40080894 (visited on 2020-08-10).

CritSafetyUMN97

Taro Ueki, Takamasa Mori, and Masayuki Nakagawa. Error estimations and their biases in Monte Carlo eigenvalue calculations. Nuclear science and engineering, 125(1):1–11, 1997. Publisher: Taylor & Francis.