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The full neutron spectrum code for advanced reactor simulation named FSAR has recently been developed at Nuclear Power Institute of China in order to meet the requirements of advanced reactor with large neutron energy range. Based on the two-step calculation scheme, FSAR consists of two-dimensional lattice calculation code and core calculation code. In two-dimensional lattice calculation, the subgroup method with ultrafine energy groups was implemented in the two-dimensional resonance self-shielding by incorporating the MOC to get the accurate self-shielded cross-section. For better consideration of the strong space coupling in different geometric sizes due to different mean free path of neutrons, the super-homogenization method and the leakage model were applied. In the core calculation, the discrete-ordinate method and micro burnup calculation method were used to simulate the core neutron transport and depletion. Preliminary calculation results showed that for the problems with wide spectrum, the self-shielded cross-sections have a good agreement with the Monte Carlo solution. The results shown in this paper indicate that FSAR has good performances of the cross-section generation in full neutron spectrum problem simulation.
The research and development of advanced reactors has been pushed globally in recent decade (
At present, there are two main kinds of calculation methods for the reactor core simulation. First is the one-step calculation method (
In the two-step scheme, deterministic procedures are currently the most widely used simulation methods. Compared to the traditional PWR codes, the fast reactor codes are easier to be extended for more complicated reactor design benefiting from their features of ultrafine group cross-sections, full core transport calculation, etc. However, there are several limits of the current fast reactor codes when they are applied in the full neutron spectrum cases. The first one is the accurate heterogeneity effect estimation in complex geometries coming with wider spectral range. The long mean free path of neutrons makes the local heterogeneity effect of typical fast reactors less important, thus the equivalent homogeneous models and one-dimensional models are accurate enough for the conventional fast reactor subassemblies (
The resonance self-shielding effect is another important element. In reactor lattice analysis, the aim of resonance self-shielding calculation is to estimate the group-averaged cross-sections for solution of the core multi-group transport equation. The accuracy of the group parameters determines the precision of the core calculation. In the fast reactor analysis code, the method proposed by T. Tone (
In this paper, an overview of the Full neutron Spectrum code for Advanced Reactor simulation named FSAR is provided which is developed by Nuclear Power Institute of China (NPIC), China National Nuclear Corporation (CNNC). The important modules and their models contained in FSAR are introduced in
The deterministic two-step calculation strategy based on the homogenization theory is utilized in FSAR to perform the reactor core neutronics analysis. Firstly, the two-dimensional lattice calculation is performed. The two-dimensional method of characteristics (
The second step is the core simulation, which is to simulate core neutron behaviors based on the neutron transport solvers and micro burnup calculation. The discrete-ordinate method is utilized to carry out the neutron transport calculation, and the Chebyshev rational approximation method is used to compute the exponential of the burnup matrix.
In two-dimensional lattice calculation, the subgroup method with ultrafine groups was implemented in the two-dimensional resonance self-shielding by incorporating MOC to get the accurate self-shielded cross-sections. In FSAR, the number of the ultrafine energy group is 2164 and that of subgroups is determined according to the change amplitude of the cross section (maximum is three groups). For the heterogeneous system, the neutron source term is assumed to be isotropic and the steady Boltzmann transport equation shows as follows:
In the statistical model, the probability that the neutron source in group
In the fixed source model, the narrow resonance approximation is implemented, the corresponding subgroup transport is simplified as below:
Compared to the statistical model, the fixed source model has better parallel performance. The subgroup flux of different subgroups in the entire energy range is coupled with each other, and can be calculated together. The self-shielding cross section is collapsed as:
Comparing the above two models, it can be noticed that the statistical model needs iterations, while the fixed source model does not. It means that the latter requires fewer fixed source iterations. In the lattice calculation, the bondarenko iteration (
The subgroup flux is then calculated by Eq.
Resonance calculation flow chart.
The single assembly problems with reflective boundary condition are used to determine the homogenized cross-sections of fuel material. For better consideration of the strong space coupling in different geometric sizes due to different mean free path of neutrons, the super homogenization method (
Based on the multi-group cross-sections generated by the lattice calculation, the three-dimensional whole core calculation is carried out by the core simulator. The
For the reactor system without outer neutron source, the source
The micro-depletion scheme is applied to simulate the core burn up and the Chebyshev Rational Approximation Method is used to solve the depletion equation. In FSAR, the depletion chains containing 21 heavy isotopes and 49 fission products is provided for the advanced reactor core system.
To verify the effectiveness of the method used in this paper, we test different spectrum and different scale problems. The ultrafine group library used in this section is made by the NJOY program (
In this section, the serval pin cell problems with different spectrum characteristics are selected as the verification problems. The results for the eigenvalue
UO_{2} and MOX pin cell problems from JAEA benchmark (
Geometry of thermal spectrum problem.
For the thermal spectrum problems, the results of eigenvalue are presented in
JAEA pin cell eigenvalue.
Pin cell type | Open MC | FSAR | Error/pcm |
---|---|---|---|
UO_{2} | 1.53270 ± 9pcm | 1.52928 | −342 |
MOX | 1.28279 ± 8pcm | 1.28234 | −45 |
^{238}U absorption cross section results
^{238}U absorption cross section results
^{239}Pu absorption cross section results
In the figures, the errors of cross section are calculated as follows:
It can be found that the cross-sections have high accuracy for most groups. However, in the UO_{2} problem, the absorption cross section of ^{238}U has a large deviation at 20 eV energy. While the absorption cross section error of ^{238}U at 20 eV energy of the MOX problem is smaller. This is because the MOX fuel including serval Pu isotopes hardens the neutron flux spectrum, as shown in
Flux comparison in fuel region.
In order to determine the error source of the eigenvalue, the cross-sections tallied from OpenMC are used to get the macroscopic cross-sections. The multi-group model in OpenMC is used to perform the transport calculation. The results are shown in
UO_{2} pin cell eigenvalue error.
OpenMC | Multi-group OpenMC | FSAR | |
---|---|---|---|
Eigenvalue | 1.53270 ± 9pcm | 1.52975 ± 6pcm | 1.52928 |
Error | −295 | −342 |
The hexagonal UO_{2} cell with high enrichment (
Geometry of intermediate spectrum problem (unit: mm).
For the intermediate spectrum problem, the reference eigenvalue obtained by OpenMC is 1.28829 ± 8 pcm and the value of FSAR is 1.28465. The results of cross-sections are shown in
^{238}U absorption cross section results
In order to test the performance of FSAR in the fast reactor, the calculations of UO_{2} cell with high enrichment and MOX cell are carried out. The same hexagonal geometry of the two problems is shown in
Geometry of fast spectrum problem (unit: mm).
The eigenvalue results are shown in
Fast spectrum problem eigenvalue.
Pin cell type | OpenMC | FSAR | Error/pcm |
---|---|---|---|
MOX-SS316-Na | 1.53697 ± 7pcm | 1.53679 | −18 |
UO2-SS316-K | 1.39732 ± 7pcm | 1.39648 | −84 |
^{238}U absorption cross section results
^{239}Pu absorption cross section results
^{238}U absorption cross section results
The full neutron spectrum code for advanced reactor simulation named FSAR developed by NPIC, CNNC is introduced in this paper. The deterministic two-step calculation strategy based on the homogenization theory is utilized in FSAR. In the lattice calculation, the MOC method is used to determine the neutron flux, and the subgroup method with ultrafine energy groups was implemented to get the accurate self-shielded cross-section. In the core calculation, the discrete-ordinate method and micro burnup calculation method were used to simulate the core neutron transport and depletion. The preliminary verifications have been carried out, and the results indicated that FSAR has good performances in dealing with the resonance self-shielding effect of the full-range spectrum problems. In the near future, the verification of each module and the whole code system will be carried out. What’s more, other calculation functions such as thermal feedback module are being developed.
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
LW: Methodology, Software, Investigation, Numerical Analysis, Writing—Original Draft; BZ: Methodology, Numerical Analysis; DL: Numerical Analysis; CZ: Methodology; JL: Writing—Original Draft.
This research is supported by the National Natural Science Foundation of China (Approved number Nos.12075228 and Nos.12205283). All the authors would like to thank Zhejiang University for the help with resonance self-shielding treatment model.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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