Increasing efforts have been made to the development of codes for transient calculations of nuclear reactors in recent years. To ensure reliable modelling of neutron physics within a state-of-the-art transient code, the neutron kinetics part of such a code should be based on the full-scale calculation of the space-time neutron kinetics equations without use of the diffusion approximation and spatial homogenisation. Such advanced approaches require the verification of neutron kinetics program modules through the cross-verification of codes, which are used to calculate thoroughly defined test cases or the benchmarks.

However, existing benchmark problems are not able to satisfy the demand for verifying codes/methods for performing the homogenisation-free time-dependent transport calculations. On one hand, some of them are simplified diffusion benchmarks in which the computational domain is composed of several homogeneous regions. On the other hand, some of them have a broad range of sources of uncertainties involved in the calculation, such as the nuclear data, group cross-section preparation procedure, and potentially other computational simplifications, making it difficult to reveal methodical errors of space-time neutron kinetics codes.

Background and purpose of the benchmark

The primary objective of this benchmark is to define a series of space-time neutron kinetics test problems featuring heterogeneous domain descriptions. The physical materials in these benchmarks are characterised by transport macroscopic cross-sections. These benchmarks facilitate the verification of deterministic computational codes and the identification of methodological errors. Additionally, they provide a framework for analysing the potential inaccuracies introduced by spatial homogenisation and diffusion approximations in time-dependent scenarios. Upon completion of the proposed kinetics benchmark phase, it will be extended during the following phases into a more realistic dynamics benchmark that incorporates thermal-hydraulic feedback effects.

The current benchmark model is based on the well-studied steady-state C5G7 benchmark problems, which were developed to test the capabilities of radiation transport codes that do not use spatial homogenisation above the fuel pin level. The benchmark has three Phases:

• Phase I (Kinetics Phase) for the verification of methods and codes for heterogeneous time-dependent neutron transport calculations without feedback:
  • Part A: Cartesian geometry exercises,   
  • Part B: Neutron noise analysis,
  • Part C: Hexagonal geometry exercises.
• Phase II (Dynamics Phase) for the verification of methods and codes for heterogeneous time dependent neutron transport calculations with feedback:
  • Part II-1: Prompt feedback,
  • Part II-2: Complete feedback.
• Phase III (High-fidelity Phase): Uncertainty propagation in high-fidelity multi-physics calculations.

Status of the benchmark

The C5G7-TD benchmark has been approved by the Working Party on Scientific Issues and Uncertainty Analysis of Reactor Systems (WPRS)  during its annual meeting in February 2015. Currently, the benchmark is in Phase 1C, and Phase II and III draf specifications are in finalisation phase.