FFTF FO-2 fuel pin L09

Rod Design Specifications

The fuel specifications from (Gilpin et al., 1989) and (Teague et al., 2014) for the L09 fuel pin are summarized in Table 1.

Operating Conditions and Irradiation History

The base irradiation power history is shown in Figure 1. The coolant inlet temperature and pressure for the base irradiation is shown in Table 2.

Figure 1: Base irradiation average power history for the fuel pin L09 of the FO-2 experiment (Teague et al., 2014).

Geometry and Mesh

The fuel rod L09 was modeled as a smeared fuel pellet stack for the 2D RZ simulations. The geometric parameters specified in Table 1 were used to create the meshes for these simulations. The smeared fuel was meshed as a single smeared fuel column with 10 radial elements and 500 axial elements except for the calculation of the central void size. For the central void simulation was used a finer mesh with 30 radial elements and 500 axial elements. For the 1D simulations meshes of 1000 elements were used. Figure 2 shows a section of the mesh in 2D RZ with a temperature contour plot. This contour plot was made near the end of the run. Actual numbers are irrelevant in this case as this plot is only meant to show the discretization.

Figure 2: A section of the L09 fuel rod mesh with a temperature contour plot.

Material and Behavioral Models

The following material and behavioral models for MOX fuel were used:

FissionRateMOX: model that takes into account of the pore migration for the fission rate calculations

MOXPoreContinuity: pore migration, or restructuring, is modeled by applying the concept of pore conservation (Novascone et al., 2018).

MOXPoreDiffusion: pore migration, or restructuring, is modeled by applying the concept of pore conservation (Novascone et al., 2018).

MOXPoreVelocity: calculates pore speed according to (Sens, 1972) and (Novascone et al., 2018).

MAMOXThermal: model for temperature and porosity dependent thermal properties

ComputeFiniteStrainElasticStress: elastic mechanical behavior

MAMOXElasticityTensor: constant values from JAEA are used for the two elastic constants Young's modulus ( Pa) and Poisson ratio ()

MAMOXThermalExpansionEigenstrain: isotropic thermal expansion's eigenstrain from (Kato et al., 2011) and (Kato et al., 2016)

UO2VolumetricSwellingEigenstrain: volumetric expansion due to solid and gaseous swelling

UO2Sifgrs: fission gas release model used with the gaseous swelling model UO2VolumetricSwellingEigenstrain (Pastore et al., 2015)

The following material and thermal behavior models were used for the cladding:

HT9Thermal: computes thermal properties of HT-9 martensitic steel

ComputeIsotropicElasticityTensor: constant values are used for the two elastic constants Young's modulus ( Pa) and Poisson ratio ()

ComputeThermalExpansionEigenstrain: constant values are used for the thermal expansion coefficient ( )

HT9CreepUpdate: steady state creep as sum of thermal and irradiation creep

Details and references for all of these models listed above can be found on the linked BISON documentation pages.

Central void

The calculated central void size , (Novascone et al., 2018),for the fuel rod L09 is compared to the measured data in Figure 3, Figure 5 and Figure 7. There is also a comparison between 1D, 2D coarse mesh with just 3 positions for the Multi-App Interpolation and 2D fine mesh with 30 positions for the Multi-App Interpolation simulations. The Multi-app was used in order to have a better numerical solution in a point of view of convergences respect to a fully-coupled system. Since with a 2D coarse mesh and just 3 positions Multi-App simulation (yellow line Figure 3 and Figure 5) there is a negative value of porosity, we decided to refine the mesh and add more positions to the Multi-App Interpolation in order to fix that not physical porosity value (purple line Figure 3 and Figure 5). We assumed a value of 50% of porosity as threshold to consider a void and we delimited the end of the equiaxed region where the porosity equals the as-fabricated value.

Figure 3: Comparison between the three simulations taken into account and the data for the sample H (43.2 cm from the fuel bottom). The Experimental dotted black line refers to the radius of the central void and the gray one refers to the restructured region size (Gilpin et al., 1989). Every curve begins from the inner radius of the annular fuel.

Figure 4: Temperature calculated with the 2D fine mesh Multi-App Interpolation simulation for the sample H (43.2 cm from the fuel bottom). The Experimental dotted black line refers to the radius of the central void and the gray one refers to the restructured region size (Gilpin et al., 1989). The curve begins from the inner radius of the annular fuel.

Figure 5: Comparison between the three simulations taken into account and the data for the sample J (68.6 cm from the fuel bottom). The Experimental dotted black line refers to the radius of the central void and the gray one refers to the restructured region size (Gilpin et al., 1989). Every curve begins from the inner radius of the annular fuel.

Figure 6: Temperature calculated with the 2D fine mesh Multi-App Interpolation simulation for the sample J (68.6 cm from the fuel bottom). The Experimental dotted black line refers to the radius of the central void and the gray one refers to the restructured region size (Gilpin et al., 1989). The curve begins from the inner radius of the annular fuel.

Figure 7: Comparison between the three simulations taken into account and the data for the sample L (91.3 cm from the fuel bottom). The Experimental dotted black line refers to the radius of the central void and the gray one refers to the restructured region size (Gilpin et al., 1989). Every curve begins from the inner radius of the annular fuel.

Figure 8: Temperature calculated with the 2D fine mesh Multi-App Interpolation simulation for the sample L (91.3 cm from the fuel bottom). The Experimental dotted black line refers to the radius of the central void and the gray one refers to the restructured region size (Gilpin et al., 1989). The curve begins from the inner radius of the annular fuel.

Fission Gas Release

The calculated integral fuel rod FGR is compared to the measured data in Figure 9 . BISON results with the recommended lower limit for the number density of grain boundary bubbles (10 bubbles/m) for FBR MOX fuels show a good agreement with the experimental data, in line with the intrinsic modeling uncertainties (Pastore et al., 2014).

Figure 9: Fission gas release comparison. The purple line refers to the basic case with the current lower limit for the bubble number density at the grain boundary of 10 bubbles/m; the red one refers to the new basic case with the new lower limit for the bubble number density at the grain boundary of 10 bubbles/m; the green line corresponds to the new basic case that uses the diffusion coefficient for fission gasses proposed in (Turnbull et al., 1988); the yellow one corresponds to the new basic case with the grain growth model turned on (Ainscough et al., 1973); the blue curve refers to the new basic case with the diffusion coefficient for fission gasses proposed in (Turnbull et al., 1988) and with the grain growth model turned on.

Discussion

The use of a Multi-App system with a fine mesh and many positions for the interpolation is recommended for the simulation of the central void.

For fast MOX fuels, higher temperatures are reached compared to LWR fuels. The associated pronounced bubble growth and coalescence can lead to the attainment of the lower limit for the number density of grain boundary bubbles systematically. Preliminary simulations of FBR MOX irradiations have indicated that a value of leads to a more accurate result in terms of both FGR and swelling compared to the default LWR UO value. A value of is compatible with experimental observations, e.g., (White, 2004).