EBR-II X447 Experiment

Pin Design Parameters

All the fuel pin design data of this assessment case are adopted from the FIPD database. As multiple versions of pin design data are available in FIPD, including nominal design description, as-built design specifications, and measured fabrication data. As-built design specifications are used in this assessment case due to their consistence and completeness. For each of the fifteen pins involved in this assessment case, a separate CSV file available in the FIPD-BISON Integration Data is read by BISON's FIPDRodletMeshGenerator to generate the axisymmetric 2D mesh as well as the corresponding MeshMetaData.

Operating Conditions and Irradiation History

Figure 2: Time and axial dependent power profile for pin DP11.

Calculated pin-by-pin operating conditions data from the FIPD database are used in this assessment case. For each pin, time-varying pin-averaged power and fast neutron flux information are used along with corresponding axial peaking factors to provide complete time and axial dependent irradiation condition profiles (see Figure 2 and Figure 3). Here, the power profile is used as the heat source and then to deduce fuel depletion (burnup) for other models, while the fast neutron flux profile is used to account for irradiation effects especially the irradiation creep of the cladding.

Figure 3: Time and axial dependent fast neutron flux profile for pin DP11.

In the FIPD-BISON Integration Data, both power and fast neutron flux data are provided in the form of two separate CSV files, respectively: a time-dependent average power/flux CSV file in the standard format that can be directly loaded by MOOSE's intrinsic PiecewiseLinear Function class, and a peaking profile CSV file that can be loaded by BISON's dedicated FIPDAxialProfileFunction.

Due to the existence of the dummy pins and pin reconstitution in the experiment X447, BISON's intrinsic coolant channel models (i.e., the generic CoolantChannelAction and the specific SodiumCoolantChannel) might not make best prediction, especially when the neighboring fuel pins have dissimilar power profiles. In that case, time-varying cladding outer surface temperature available in the FIPD database, which is calculated by thermal hydraulics code SuperEnergy2 (Basehore and Todreas, 1980), is used directly as the temperature boundary conditions (see Figure 4 for an example).

Figure 4: Time and axial dependent outer surface temperature profile for pin DP11.

The time-varying cladding outer surface temperature is provided as a single CSV file for each pin in the FIPD-BISON Integration Data, which can also be read by FIPDAxialProfileFunction.

Post-Irradiation Examinations

The main focus of this assessment case is the consequences of cladding degradation due to the FCCI/CCCI phenomena, which is the deformation and failure of the HT9 cladding. The damage/failure of the cladding is usually quantified by cumulative damage fraction (CDF), which is a statistical and virtual quantity that cannot be directly measured. Therefore, the major experimentally measured data that are valuable here are the deformation profiles of the HT9 cladding. The cladding deformation of the X447 fuel pins were measured by contact profilometry and sometimes also laser profilometry. The digitized data are available in FIPD and used in this assessment case for assess the cladding deformation predicted by BISON.

In the FIPD-BISON Integration Data, the cladding strain profile based on profilometry measurement is provided in a single CSV file for each pin. The data can be loaded by FIPDAxialPIEComparison to be directly compared with the BISON predictions.

Geometry and Mesh

The 2D-RZ meshes for the X447 pins are generated with the intrinsic rodlet meshing capability in BISON's FIPDRodletMeshGenerator. The mesh generator directly reads the FIPD-based pin design parameter CSV file and generates the mesh along with a series of MeshMetaData to help ensure consistent use of pin geometry data throughout the simulations. For the enhanced model set, lower-dimensional elements are then added to the fuel and cladding contact surface sidesets with LowerDBlockFromSidesetGenerator. These additional side elements serve as contact surfaces for the Lagrange multiplier variables parameterizing mortar contact.

Material and Behavioral Models

The following material and behavioral models for the UPuZr fuel (note that in the case of X447, all the pins use U-10Zr fuels) were used in these cases. The "AD" prefix denotes that the material properties are computed with Automatic differentiation:

The following material and behavioral models for the HT9 cladding were used in these cases:

Automatic Differentiation

Recently adopted into the MOOSE framework is the automatic differentiation (AD) method for calculating the Jacobian (Lindsay et al., 2021). An alternative to error-prone numerical differentiation methods, or rigorous symbolic differentiation methods, AD applies the chain rule to elementary operations at every step of the simulation. This method for computing the Jacobian incurs a small additional computational cost, due to requiring a larger number of arithmetic operations, but ensures the formation of an accurate Jacobian, which can ultimately reduce the overall simulation time requirement (Lindsay et al., 2021). The use of AD in the X447/A assessment case, and the corresponding increased accuracy of the computed Jacobian, ensures appropriate convergence of the highly nonlinear, strongly coupled differential equations that describe the multiphysics of the system and its complex material properties (Matthews et al., 2023).

Mortar Contact

Another recent implementation into the MOOSE framework is mortar-based contact. Previously, fuel-clad mechanical and thermal contact in BISON was enforced with a node-on-face approach through which node locations on a secondary surface (the cladding) was matched to its closest counterpart on the primary surface (the fuel) (Recuero et al., 2022). This approach is relatively straightforward to implement but suffers from a lack of both smoothness and robustness, which can diminish the overall efficiency of solution convergence, or even prevent convergence altogether (Recuero et al., 2022). Mortar contact, on the other hand, alleviates these smoothness and robustness concerns. This advanced contact method uses Lagrange multipliers to enforce mechanical and thermal contact constraints. These Lagrange multipliers comprise an additional set of variables, whose solutions are determined on lower-dimensional domains of the contact surfaces (Recuero et al., 2022). Mortar contact methods enable tighter problem convergence and more reliable contact enforcement, including frictional interactions.

The mortar contact method was implemented for contact between the inner radial surface of the cladding and outer radial surfaces of the fuel, cap, and stand. Both normal and tangential mechanical contact are modeled, with tangential contact including considerations of friction between the contact surfaces, parameterized by a friction coefficient, . A value of =0.1 was determined to result in fuel axial elongation in DP04 consistent with PIE measurements. For uniformity, this value is applied to all 15 pins in the subassembly.

FCCI and CCCI Wastage Thickness

Figure 5: Comparison of the FCCI wastage thickness of four pins irradiated in X447/A between legacy BISON prediction and micrograph measurement.

Figure 6: Comparison of the FCCI wastage thickness of four pins irradiated in X447/A between enhanced BISON prediction and micrograph measurement.

The FCCI wastage thickness profiles predicted by BISON are compared with the experimental measurement on micrograph photos of the sectioned irradiated fuel pins. As shown in Figure 5 and Figure 6, BISON prediction with the legacy assessment case is quite consistent with the measurement data, providing a foundation for reliable prediction of cladding deformation due to FCCI thinning. For the enhanced assessment case, these predictions changed a little bit, leading to slightly lower predictions. Although the overall FCCI prediction is still consistent with the measured data, the slight underestimation could result in a slight underestimation in consequent cladding deformation. It is worth mentioning here that the parameters of the FCCI correlation were optimized using the legacy model set. On the other hand, the CCCI wastage formation was found to be 20 microns near the cladding outer surface elevation corresponding to the top of the fuel, which is also consistent with the BISON prediction.

Cladding Hoop Strain

In X447, a major consequence of cladding thinning, mainly due to FCCI, is the degradation in cladding's mechanical strength and thus enhancement in cladding deformation caused by accumulated fission gas within the cladding. As the FCCI is only severe near the cladding inner surface corresponding to the top section of the fuel slug, the cladding deformation is also prominent in this region. As shown by the blue curves in Figure 7 and Figure 8, the majority of the cladding only experienced minor deformation after the 10% burnup. On the other hand, near the top of the fuel slug, prominent cladding deformation up to 2.0% strain was observed. Unlike other fuel irradiation experiments, where the cladding stayed far away from the the creep rupture domain, the cladding in X447 was observed to be subjected to breaching due to creep rupture. In that case, tertiary creep was expected to make significant contributions to the cladding deformation. In Figure 7 and Figure 8, using the enhanced model, it is prominent that taking into account the tertiary creep, the predicted cladding deformation is more consistent with the profilometry measurement. Additionally, it is worth mentioning that the measured cladding deformation values shown in Figure 7 and Figure 8 are the circumferentially maximum values, the corresponding minimum peak values are 2.956 mm and 2.963 mm (compared to 2.967 mm and 2.977 mm) for DP04 and DP11, respectively.

Figure 7: BISON predicted cladding deformation for legacy and enhanced (with and without tertiary cladding creep) models compared with profilometry measurement (DP04).

Figure 8: BISON predicted cladding deformation for legacy and enhanced (with and without tertiary cladding creep) models compared with profilometry measurement (DP11).

Leveraging the FIPD-BISON integration framework, BISON is capable of predicting such cladding deformation behavior that is comparable to the profilometry measurement results. Furthermore, modeling changes introduced in the enhanced assessment case only change these radial deformation predictions by approximately 0.01 mm. It is noticeable that the current BISON model predicts lower cladding strain compared to the PIE measurement, which will be discussed later.

Fuel Axial Elongation

An improvement of the enhanced X447 case over the legacy model is the calculation of non-recoverable axial fuel elongation, which is the final fuel elongation minus thermal expansion. As shown in Figure 9 and Figure 10, the legacy penalty formulation overpredicts fuel elongation, whereas the enhanced model, whose elongation estimate is tightly controlled by the combined effects of the fuel anisotropic swelling factor and the fuel-clad tangential contact coefficient of friction, more closely matches the PIE measurement, which is plotted with dashed black lines. It is also worth mentioning that tertiary creep of cladding has marginal effects on fuel axial elongation.

Figure 9: BISON predicted fuel elongation compared with profilometry measurement (DP04).

Figure 10: BISON predicted fuel elongation compared with profilometry measurement (DP11).

Statistics of Pin Failure

Under the legacy Integrated Fast Reactor (IFR) program, two pin failure criteria were developed for normal operation condition based on HT9 cladding damage Briggs et al. (1995):

1. Thermal component of plastic hoop strain during normal operation is less than 1%.

2. CDF during normal operation is less than 0.05.

Figure 11: The maximum cladding hoop strain values (percentage) predicted for the X447/A subassembly. The red line indicates the fuel safety criterion defined for the EBR-II Mark V driver fuel during the IFR program (Briggs et al., 1995).

For the first criterion, the maximum predicted cladding hoop strain values are illustrated in Figure 11. Under the high cladding temperature conditions involved in the experiment X447, the cladding hoop strain is dominated by thermal creep. It is noticeable that the two failed pins (i.e., DP70 and DP75) and their sibling pins (i.e., DP04 and DP11) have highest predicted cladding hoop strain values, showing the consistence with experimental observation. Additionally, three out of these four pins have maximum cladding hoop strain approaching or exceeding the failure criterion of 1%. While BISON prediction provides correct trends and consistence, it is worth noting that the 1% criterion is conservative because the actual observed failure starts at ~2%. As shown in Figure 7 and Figure 8, current models still slightly underestimate hoop strain, as the PIE measured circumferential peak strain values of some pins do exceed 2%.

On the other hand, the maximum predicted CDF values are listed in Figure 12. Based on the enhanced model, the two failed pins and their sibling pins are the only four pins with CDF values exceeding the failure criterion of 0.05, which is again consistent with the experimental observation. When the CDF based criterion was established, a statistical relation between CDF and cladding failure probability was developed based on the long-term thermal creep rupture experiment results of unirradiated HT9 specimens, as shown in Figure 13. Based on this correlation, the BISON predicted CDF values, especially the enhanced model, correspond to a failure probability that is much lower than the observed 2 out of 15 pins. Similar underestimation in CDF was also reported in the original IFR documentation (Briggs et al., 1995) when using LIFE-METAL, which is potentially related to the limitations of the experimental data used for developing the correlation (e.g., unirradiated specimens).

Figure 12: Cumulative Damage Factors values for the X447/A subassembly. The red line indicates the fuel safety criterion defined for the EBR-II Mark V driver fuel during the IFR program (Briggs et al., 1995).

Figure 13: The correlation between CDF and failure probability with CDF ranges predicted for X447/A pins included. The red line indicates the fuel safety criterion defined for the EBR-II Mark V driver fuel during the IFR program (Briggs et al., 1995).