MODELLING ASTRID-LIKE SODIUM-COOLED FAST REACTOR WITH SERPENT-DYN3D CODE SEQUENCE

This study explores the feasibility of applying the Serpent-DYN3D sequence to the analysis of Sodium-cooled Fast Reactors (SFRs) with complex core geometries, such as the ASTRIDlike design. The core is characterised by a highly heterogeneous configuration and was likely to challenge the accuracy of the Serpent-DYN3D sequence. It includes axially heterogeneous fuel assemblies, non-uniform fuel assembly heights and large sodium plena. Consequently, the influence of generation and correction methods of various homogenised, few-group crosssections (XS) on the accuracy of the full-core nodal diffusion DYN3D calculations is presented. An attempt to compare the approximate time effort spent on models preparation against the accuracy of the result is made. Results are compared to reference full-core Serpent MC (Monte Carlo) solutions. Initially, XS data was generated in Serpent using traditional methods (2D single assemblies and 2D super-cells). Full core calculations and MC simulations o ered a moderate agreement. Therefore, XS generation with 2D fuel-reflector models and 3D single assembly models was verified. Super-homogenisation (SPH) factors for XS correction were applied. In conclusion, the performed work suggests that Serpent-DYN3D sequence could be used for the analysis of highly heterogeneous SFR designs similar to the studied ASTRID-like, with an only small penalty on the accuracy of the core reactivity and radial power distribution prediction. However, the XS generation route would need to include the correction with SPH factors and generation of XS with various MC models, for different core regions. At a certain point, there are diminishing returns to using more complex XS generation methods, as the accuracy of full-core deterministic calculations improves only slightly, while the time effort required increases significantly.


Serpent MC reference simulations
The un-rodded and fully rodded 3D ASTRID-like core simulations in Serpent were completed with the neutron population set to 500000, 1000 active runs and 200 inactive runs. A reference 3D full core solution in an un-rodded state was attained by averaging 15 simulation runs, while in the case of a fully rodded state 1 run was considered. The number of inactive runs was based on the convergence of Shannon entropy investigated during previous research on the Uranium Carbide SFR core by Fridman and Shwageraus [1].

DYN3D models' configuration
Core models in DYN3D were axially divided into 35 layers for an un-rodded core and 37 layers in a fully rodded core. The number of the layers depended on the axial layout of the inner core and outer core fuel sub-assemblies, and the axial position of control rods and safety rods. In each subsequent calculation of a distinct DYN3D ASTRID-like core model, more complex methods of few-group XS generation were applied. In both cases, 19 different models (with specific XS generated or corrected by various means) of both the rodded and the un-rodded core were tested. More complex few-group XS models required further efforts in the preparations stage. However, they were expected to more accurately capture the actual in-core conditions of a particular core zone or a sub-assembly (macroscopic cross-sections, scattering matrices and diffusion coefficients), thus positively influencing the precision of the nodal diffusion solution of the full core. Finally, each DYN3D full core model was compared against a Serpent MC reference simulation.

Results division and qualitative effort assessment
Among all of the 19 DYN3D models, for the rodded and un-rodded core respectively, there were similar ones, with XS generated at a comparable level of complexity. Therefore, to facilitate the discussion, all of the models are grouped into representative Models #1 to #6 (for both un-rodded and rodded cores respectively). In each Model, the results of the best performing approach are shown. Models are ranked by the efforts required to generate an entire set of XS (from #1, least effort, to #6, greatest effort) in Table 1.

Model #
Fuel regions or sub-assemblies Non-multiplying regions or subassemblies 2D single assemb.

2D super-cells + SPH 2D supercells 2D super cells + SPH
2D fuelreflector 1 All  The wider the variety of Serpent models for XS set generation is, and the larger these models are, the longer the calculations to create this set, on the same CPU, take. The same rules apply for SPH factors -more CPU time is needed if they are employed to correct the distinct 2D super-cell generated XS. The proposed ranking is a qualitative division. It is crucial in the context of the assessment of efforts vs. accuracy. This ranking also happens to correspond to the increasing accuracy of the results of the full-core deterministic calculations.

Un-rodded and rodded core results accuracy
The changes in the values of RMS (axial and radial power peaking factors, Serpent vs. DYN3D) and k-eff (DYN3D vs. Serpent) in the function of Model # are presented in Figure 5.
For the un-rodded core, Model #1 resulted in an RMS error of radial power peaking factor of 0.93 % ( Figure  4a) and the k-eff difference of equal to -447 pcm (Figure 4b). The power map is presented in Figure 5a. The best performing approach, Model 6#, offered the RMS error of power peaking of 0.59 % (Figure 4a) and the reactivity discrepancy of -119 pcm (Figure 4b). The power map is presented in Figure 5b.
In the case of the rodded core, Model #1 the RMS of the radial power map difference was 2.10 % (Figure  5a), while the k-eff difference was at -682 pcm (Figure 5b). Model #6 was the best performing approach, with k-eff at -249 pcm ( Figure 5b) and RMS of the radial power map of 0.90 % (Figure 5a).
In the case of the axial power distribution (and its RMS value) of both the un-rodded and rodded core, the gradual enhancements in XS generation showed varying, yet minor, improvements with regards to the reference MC solution (Figure 5c and 5d).

Discussion on results improvements
Introduction of 3D single assembly models improved k-eff significantly (improvement, from Model #2 to Model 3#, of 207 pcm and 129 pcm, for the un-rodded and rodded cores respectively). Notable results were also attained with the application of SPH-corrected XS for non-multiplying regions of control rods, safety rods and steel diluent (an improvement from Model #3 to Model #4, by 76 pcm and 130 pcm, for the unrodded and rodded cores respectively). Finally, in the rodded core case, a similar development was noted when SPH-corrected XS were used for fuel around the still diluent (Model #4 to Model #5), as the k-eff difference was lower by 115 pcm.
In case of the radial power map, initially, 2D fuel-reflector models, as in work by Fridman and Shwageraus [1], were tested to correct the undervaluation of power in the outer core regions (Figure 4a). XS generated this way advanced only the outermost fuel assemblies peaking factors coherence, not k-eff, and only if they were used for fertile fuel regions. Moreover, it was revealed during the study that XS created with 2D fuelreflectors should not be used in connection with 3D single assembly models, unless SPH-corrected XS for non-multiplying regions of control rods (CSD), safety rods (DSD) and steel diluents (SD) are introduced in the XS set. Such a connection improved the k-eff, but worsen the coherence of the power peaking factors in the inner core region. Consequently, 2D fuel-reflector models were not applied in Models #3 -#5. The greatest advancement in terms of RMS values of power peaking factors happened with the application of SPH-corrected XS in Model #4. Further attempts to increase the coherence of the results were also successful, yet there were diminishing returns in increasing the efforts of more distinct XS generation.
In the case of axial power distribution, no specific pattern was recognised (Figure 4c and 4d).

SUMMARY AND CONCLUSIONS
The goal of this study was to test the feasibility of applying the Serpent-DYN3D sequence to the calculations of an SFR core of a non-standard design -ASTRID-like. The results were compared against the reference Serpent full-core simulations. Simultaneously, an attempt to qualitatively assess the approximate time effort spent on new XS generation or correction methods against the accuracy achieved was made.
In the case of accuracy, the application of more complex models and methods affects the reliability of the DYN3D simulations, as it, in general, improves the agreement in k-eff and radial power distribution. It has a limited impact on the axial power distribution. In general, replacing XS produced with 2D single assemblies (for fuel regions) by XS created with 3D single assemblies (for fissile and fertile regions in the inner core) or with 2D fuel-reflector models (for fertile fuel regions in the outermost fuel assemblies) is recommended. Moreover, correcting the XS generated with 2D super-cells with SPH factors, for nonmultiplying regions of the inner core, adjacent to the fuel, is highly advised. Optionally, XS corrected this way may be applied to these adjacent fuel regions inside the core. However, care should be taken when introducing XS generated or corrected with more complex methodologies, as their simultaneous application to various core regions may worsen the overall results. They may influence one another.
In the case of an attempt to assess the approximate efforts needed to prepare the calculations against the achieved accuracy, it should be noted that at a certain point the time efforts seem to outweigh benefits. In the case of Model #4 to #6, a full-core Serpent MC simulation can be programmed and processed with a similar time effort and more accurate results. However, when the XS are adequately prepared, and the reference calculations give results of acceptable accuracy, and multiple core configurations in the same conditions are to be tested, it may be stated with certainty that fewer resources are required to interchange the XS configurations and run DYN3D calculations (for example for rod insertion) than to prepare and run a new MC full-core simulation.
To sum up, Serpent-DYN3D sequence may be used for complex, heterogeneous SFR core designs deterministic calculations. However, there are diminishing returns to using the more complex XS generation methods. It is more profound if the complexity of the core's design requires reconstruction of significant regions of the core for XS generation. Therefore, applying XS generation methods as described in Model #4 would be advisable, based on the quantitative analysis of the quality of the results and qualitative analysis of the effort required to obtain these results. Finally, it should also be noted that the enhancements in the results are clearly more visible in the case of the fully rodded state.
With regards to future work, it could be viable to provide a quantitative analysis of the e൵orts required to prepare increasingly complicated models that resemble a larger percentage of parts within the advanced reactors core for the XS generations. Moreover, further research on the applicability of 2D fuel-reflector models for modelling of outermost fuel assemblies could be undertaken. It would be advisable to asses why the coupling of the radial reflector and adjacent fuel sub-assemblies in space and energy provides the most realistic XS for the fertile fuel sub-assemblies (SA), and not for fissile fuel SA.