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.
The main objective of this benchmark is to specify a series of space-time neutron kinetics test problems with heterogeneous domain description for solving the time-dependent group neutron transport equation without feedback. Physical materials in these benchmarks are described by transport macroscopic cross-sections. Such benchmarks would allow carrying out verification of developed deterministic codes and rigorously revealing methodical errors. Moreover, such benchmarks would allow studying possible inaccuracy of spatial homogenisation and diffusion approximation in time-dependent cases. After the completion of the proposed kinetics benchmark, it will be extended to more realistic dynamics benchmark, which will take into account the thermal-hydraulic feedback mechanisms.
This benchmark has been approved by the Organisation for Economic Co-operation and Development Nuclear Energy Agency (OECD/NEA) Nuclear Science Committee (NSC) Working Party on Scientific Issues in Reactor Systems (WPRS) in the meeting in February 2015.
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. It is a miniature light water reactor (LWR) with sixteen fuel assemblies (mini-core): eight uranium oxide (UO2) assemblies and eight mixed oxide (MOX) assemblies, surrounded by a water reflector. It features a quarter-core radial symmetry in the 2-dimensional (2-D) configuration.
There are two sets of exercises considered in this problem. The first set, including three exercises, is focused on the 2-D configuration of the C5G7 core. The second set, including two exercises, is about the 3-D C5G7 configuration.
The draft specification document entitled Deterministic Time-Dependent Neutron Transport Benchmark without Spatial Homogenisation (C5G7-TD) had been prepared and distributed for comments and corrections. The detailed perturbation law of each exercise is described in the specification. Accurate multi-group Monte Carlo reference solutions will be obtained for all configurations.
After the completion of the proposed kinetics benchmark, it would be extended to a more realistic dynamics benchmark, which will take into account the thermal-hydraulic feedback mechanisms.
There are two sets of exercises considered in this problem. The first set, which consists of 3 exercises, is focused on the 2-D configuration of the C5G7 core. The second set, including 2 exercises, is about the 3-D C5G7 configuration. Accurate multi-group Monte Carlo reference solutions will be obtained for all configurations.
The 2-D time-dependent benchmark, including four transient exercises featured with control rod cluster movement and moderator density change with various rate and magnitude, is based on the 2-D configuration of the C5G7 core.
Exercise 0 of this time-dependent benchmark problem (TD0) is focused on the simulation of a postulated control rod insertion and withdrawal event. It is assumed that all control rods are fully removed from the core initially, and the transient is initiated by an abrupt control rod insertion (one rod bank per fuel assembly) for a depth equivalent to 10% of the active core height at time 0. The control rod stays still until the end of 1 s when it extracted by half of the inserted length and maintains the position for another second. All the inserted rod banks are withdrawn to their initial positions at the end of 2 s. It is assumed that all rod bank movements take place instantaneously.
Exercise 1 (TD1) is also concerned with control rod insertion and extraction transient, starting from the unrodded core condition, while the difference from TD0 is that all rod banks move at a constant speed. To start the transient, one or more control rod banks (one rod bank per fuel assembly) are inserted to a depth equal to 1% of the total core height within 1 s. During the next 1 s, all the inserted rod banks are withdrawn to their initial positions.
Exercise 2 of the current benchmark problem (TD2) is designed to simulate a control rod transient that is very similar to TD1, but with a different depth (or magnitude) of the control rod insertion. In TD2, the maximum depth that the control rods can reach 1 second after the transient starts is 10% of the total core height. All control rods are at a fully withdrawn position at the end of the transient (2 seconds). Again, the control rod insertion/withdraw happens linearly.
The third exercise (TD3) is intended as a simulation of a transient event of the change of core moderator density. It is assumed that the moderator density in all fuel assemblies is at its nominal value as the starting point, and starts to decrease linearly before reaching its minima after 1 s into the transient. This minimum value is represented as a fraction, denoted as ω (0 ≤ ω ≤ 1), of its initial value. The moderator density then linearly returns to its initial value within next 1 s. It should be noted that this change mechanism affects all cells in the core uniformly but the water density in the reflector is not affected.
The simulation of TD3 transient can be achieved by the linear perturbation of the moderator cross-sections of all cells across the core. At the end of 1 s, all cross-sections are equal to a certain fraction of their initial values. The perturbation continues by the linearly increasing these cross-sections to their initial values during another 1 s.
The 3-D time-dependent benchmark adopts the 3-D configuration of the C5G7 core. Two exercises are defined to simulate transient events including control rod insertion/withdrawal and moderator density change with various rate and magnitude.
The TD4 exercise is driven by the control rod insertion/withdrawal transient in the 3-D core configuration. An initial core condition, referred to as the Unrodded case, is first defined, where the control rod banks (one bank for each assembly) are inserted into the upper axial water reflector. It is suggested that the fission chambers and control rods present in the axial reflector region should be modelled.
It is assumed that the rod bank moves at a constant speed, which allows it to be fully inserted into the assembly from the fully withdrawn position within 6 s. Note that this is a hypothetic value proposed only to reduce the computational effort in the transient calculation.
The exercise 5 (TD5) models a series of moderator density change transient events. It is assumed that all control rods are positioned in the fully withdrawn position (Unrodded configuration) throughout the transient and the moderator density is at the nominal level at the starting point. Totally 4 test problems have been defined for various transient mechanisms by varying the rate and location of moderator density change.
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