Gamma-radiation field

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Serpent Ants - Serpent

3.00 3.25 3.50 3.75 4.00

Sourceratedensity1 cm3s

×10¹⁰

−20

−10 0 10

Relativedifference(%)

Figure 4.13: Fuel average gamma source-rate densities in rim and central regions separately.

Dimensions are otherwise in scale, but the thickness of rim regions is exaggerated for better visualization. The lattice pitch is 1.25984 cm.

gamma source-rate densities are underestimated by almost 25 % and central regions are overestimated at most 10 %.

The gamma radiation field within a one-meter radius from the fuel assembly is visualized by a two-dimensional dose-rate distribution in figure4.14. The distribution is shown for the Ants-based fuel composition and it is compared to the reference calculation sequence. The dose rate distribution calculated with the low-fidelity sequence agrees within few percent with the reference solution. The dose rate inside the assembly is underestimated and the dose rate outside the assembly is overestimated. The largest differences are obtained in fuel assembly corners.

A comparison of the dose rate one meter away from the assembly center is shown in figure4.15. The intensity of radiation changes depending on the assembly rotation.

0 50 100

x (cm) 0

50 100

y(cm)

Ants

0 50 100

x (cm) 0

50

100 Ants - Serpent

10¹ 10²

Doserate(Gy/h)

−3

−2

−1 0 1 2 3

Relativedifference(%)

Figure 4.14: Gamma radiation dose-rate distribution calculated using fuel compositions from the two-step depletion calculation and comparison to the full Serpent calculation sequence. Like the fuel assembly itself, the geometry has a 1/8 rotational symmetry and the distribution is shown for one quarter of the whole geometry.

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Distance to the closest pin, self-shielding effects, and source rate distribution have an impact on measured dose rates. The lowest dose rate is obtained when the fuel assembly side is perpendicular to the tally point and the highest source rate is obtained when the assembly is rotated by 45 degrees.

Generally, both calculation sequences give similar results, but the low-fidelity sequence yields higher dose rates compared to the reference solution. The relative difference is highest between 25 and 30 degrees and it is slightly greater than 1.5 %.

The dose rate is underestimated by 0.5 % when the assembly lies perpendicular to the measurement point and it smoothly increases as the assembly is rotated. The mean dose rate was 9.01 Gy/h for the reference and 9.10 Gy/h for Ants yielding a 1.1 % relative difference.

0 10 20 30 40 50 60 70 80 90 Rotation (degrees)

7.5 8.0 8.5 9.0 9.5 10.0

Doserate(Gy/h)

Ants Serpent Difference

−0.5 0.0 0.5 1.0 1.5 2.0

Relativedifference(%)

Figure 4.15: Comparison of gamma-radiation dose rate in air one meter away from the spent nuclear fuel assembly center. The rotation angle refers to the rotation with respect tox-axis. Results are periodic and the length of the period is 90 degrees. The average 1σ relative statistical uncertainty for both results was 0.017 %.

In summary, the low-fidelity sequence predicts spent nuclear fuel properties well for the 2D infinite lattice depletion calculation. Properties on the assembly level are predicted accurately, but the sub-assembly level detail can only be approximated. In this case, assuming equal distribution of nuclides yielded good results in the gamma transport problem. However, the reference solution had only modest differences in the pin-by-pin source rate distribution. Therefore, the gamma dose-rate distribution from the low-fidelity sequence deviated only slightly from the reference. Even though the net gamma source rate was underestimated by 0.16 %, the mean dose rate one meter away from the assembly was overestimated by 1.1 %. Thus the distribution of nuclides in the fuel may also have an important role in secondary safety analyses.

4.2 3D SMR core depletion

The two-dimensional depletion problem results show that the micro-depletion method does not contain any major flaws. However, the simplified problem does not itself have any significant practical use. The 3D SMR depletion problem represents the actual target application of the two-step calculation sequence.

The homogeneous full-core model can be expected to have larger differences in reaction rates compared to the simple two-dimensional model. These differences will further impact the accumulation of new nuclides. In addition, the full core model will have larger gradients in burnup, especially near the core periphery. These two factors can be expected to cause challenges for the two-step calculation sequence.

Otherwise, the structure of the following sections is similar to 2D results. First, the success of the homogenization process is assessed by comparing the critical boron concentration and the average neutron flux. Second, nuclide inventories are compared between the two-step sequence and the reference. Third, assembly-level properties are calculated based on the fuel composition. Finally, the gamma radiation field is compared in a two-dimensional geometry similar to the 2D depletion results.

Restart files were created only for two different fuel assemblies. Selected assemblies were assemblies two and seven in the loading map presented in figure 4.16. The former is near the core center, and the latter is at the core periphery. Both assemblies were without burnable absorber rods.

FA 1 3.1 %

FA 2 1.6 %

FA 3 2.4 %

FA 4 3.2 % FA 5

3.1 % FA 6 2.4 %

FA 7 3.4 % FA 8 3.4 % FA #

w.t. %

Figure 4.16: Loading map of the SMR core utilizing 1/8 rotational symmetry. Each assembly has two labels: an upper label for the assembly number and a lower label for uranium enrichment. Assembly number one is at the core center and assemblies four, seven, and eight are at the core periphery.

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