IFA-562 Rods 15-17

Rod Design Specifications

The IFA-562.2 rods were short rods of annular fuel and were enriched to 13% U-235. The fuel and cladding specifications are tabulated in Table 1.

Operating Conditions and Irradiation History

The HBWR operating conditions are tabulated in Table 2. The reactor power history is shown in Figure 1. The measured reactor coolant temperature was used as the boundary temperature on the cladding outer surface.

Figure 1: Through life power profile for IFA-562.2 rod 15. Note: Rods 15-17 power histories were very similar.

Geometry and Mesh

The assumed geometry and mesh are shown in Figure 2 and Figure 3. The fuel pellet stack was modeled as a smeared column with merged insulator pellets. The insulator pellets were modeled as UO, meaning they the same mechanical and thermal properties of the rest of the column. The expansion thermometer was modeled as a void in the pellet/insulator stack; this was done to ease the simulation. The BISON fuel centerline temperature was calculated as an average of the pellet interior (BISON sideset 13). The plenum length for the mesh was adjusted from the experiment length to account for the difference in volume caused by the voided expansion thermometer. The initial gas volumes for the simulations were as listed in (P. Lösönen, 1989). A 2-dimensional axisymmetric quadratic mesh was used. The fuel column was meshed with 177 axial and 11 radial elements (aspect ratio 14) and the insulator pellets with 3 axial and 11 radial elements (aspect ratio 14). The cladding was meshed with 183 axial and 4 radial elements (aspect ratio 23.3).

Figure 2: Close-up view of the IFA-562.2 rod 15. Note: This is only a cut from the bottom of the fuel rod meant to show the fuel and insulator pellet. The volume where the expansion thermometer would be in the experiment can also be seen.

Figure 3: Close-up view of the IFA-562.2 rod 15. Note: This is only a cut from the bottom of the fuel rod meant to show the fuel and insulator pellet. The volume where the expansion thermometer would be in the experiment can also be seen.

Material and Behavioral Models

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

• UO2Thermal - NFIR: For temperature and burnup dependent thermal properties.

• ComputeFiniteStrainElasticStress and UO2ElasticityTensor: elastic mechanical behavior

• UO2VolumetricSwellingEigenstrain: volumetric expansion due to solid and gaseous swelling

• UO2RelocationEigenstrain: relocation strains, relocation activation threshold power set to 5 kW/m

• ComputeThermalExpansionEigenstrain:thermal expansion with a constant instanteous thermal expansion coefficient

• UO2Sifgrs: fission gas release model used with the gaseous swelling model UO2VolumetricSwellingEigenstrain

For the clad material, a constant thermal conductivity of 16 W/m-K was used and both thermal (primary and secondary) and irradiation creep were considered using the Limback creep model (Limbäck and Andersson, 1996). The following material and thermal behavior models were used for the cladding:

• HeatConductionMaterial: Thermophysical material properties

• ZryCreepLimbackHoppeUpdate and ZryElasticityTensor: mechanical creep and elastic deformation behavior for Zircaloy-2

• ZryIrradiationGrowthEigenstrain: ESCORE model for volumetric swelling due to irradiation exposure

• ZryThermalExpansionMATPROEigenstrain: thermal expansion of Zircaloy with the MATPRO model

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

Simulation Parameters and Assumptions

As mentioned in the Geometry & Mesh section, the mesh used is not an exact representation of the experiment. The insulator pellets were not included in the heat source term. The expansion thermometer was physically neglected in this mesh. This was done to alleviate troubles with thermal and mechanical properties between the thermometer and the fuel/insulator stack. The plenum length of the fuel rod was adjusted to account for the extra gas volume made from the voided thermometer. The simulation initial gas volumes were as listed in (P. Lösönen, 1989). The initial fuel grain size and the fuel roughness were not given in (P. Lösönen, 1989). The value of 7.75e-6 m was used for the initial grain size. This value was taken from IFA-515A1. The BISON default value of 2e-6 was used for the fuel roughness. Peaking factors were not given for this experiment. It is assumed that the rod were short enough that they did not experience much power tilting.

Temperature

BISON's temperature predictions are compared to the experimental measurements for each rod in the following sections. Differences between the measurements and the BISON predictions are quantified in terms of the validation metrics to understand how well the code predictions statistically behave against the experimental measurements.

Rod 15

Figure 4: Fuel centerline temperature histories for IFA-562.2 rod 15.

Figure 4 shows the fuel centerline temperature history for IFA-562.2 Rod 15. The measured fuel centerline temperatures are compared against the BISON predictions in Figure 5 at three different burnup ranges (in MWd/kgUO): [0,20), [20,40), and [40,60). Differences between the measurements and the BISON predictions are quantified in terms of the validation metrics. These are tabulated in Table 3. BISON slightly overpredicts the fuel centerline temperatures at higher temperatures and higher burnup ranges. However, this overprediction occurs with an average relative error of 3.0%. Overall, the computed -scores are very close to the ideal score of 1.0, meaning that the code predictions are in near optimal agreement with the measurements.

Figure 5: Measured fuel centerline temperatures against the BISON predictions for IFA-562.2 Rod 15 at three different burnup ranges ( for measured; for predicted).

Table 3: The validation metrics for the fuel centerline temperature predictions.

Experiment	(-)	II (K)	RMSE (K)	rRMSE (%)
0Bu20	0.991	47.1	23.7	2.2
20Bu40	0.983	65.3	31.5	3.0
40Bu60	0.984	56.9	27.7	3.0

Rod 16

Figure 6: Fuel centerline temperature histories for IFA-562.2 rod 16.

Figure 6 shows the fuel centerline temperature history for IFA-562.2 Rod 16. The measured fuel centerline temperatures are compared against the BISON predictions in Figure 7 at three different burnup ranges (in MWd/kgUO): [0,20), [20,40), and [40,60). Differences between the measurements and the BISON predictions are quantified in terms of the validation metrics. These are tabulated in Table 4. BISON's predictions are in near optimal agreement with the measurements (-score 1.0), with less than 2% average relative error.

Figure 7: Measured fuel centerline temperatures against the BISON predictions for IFA-562.2 Rod 16 at three different burnup ranges ( for measured; for predicted).

Table 4: The validation metrics for the fuel centerline temperature predictions.

Experiment	(-)	II (K)	RMSE (K)	rRMSE (%)
0Bu20	0.997	33.0	13.8	1.5
20Bu40	0.998	49.6	10.4	1.2
40Bu60	0.996	31.6	13.7	1.6

Rod 17

Figure 8: Fuel centerline temperature histories for IFA-562.2 rod 17.

Figure 8 shows the fuel centerline temperature history for IFA-562.2 Rod 17. The measured fuel centerline temperatures are compared against the BISON predictions in Figure 9 at three different burnup ranges (in MWd/kgUO): [0,20), [20,40), and [40,60). Differences between the measurements and the BISON predictions are quantified in terms of the validation metrics. These are tabulated in Table 5. BISON's predictions are in near optimal agreement with the measurements (-score 1.0), within an average relative error of 1.5%.

Figure 9: Measured fuel centerline temperatures against the BISON predictions for IFA-562.2 Rod 17 at three different burnup ranges ( for measured; for predicted).

Table 5: The validation metrics for the fuel centerline temperature predictions.

Experiment	(-)	II (K)	RMSE (K)	rRMSE (%)
0Bu20	0.997	34.8	14.5	1.5
20Bu40	0.996	53.0	14.1	1.5
40Bu60	0.996	31.0	12.9	1.5