Resumen de Towards a bepu methodology for containment safety analyses
Containment safety analyses are usually performed applying conservative assumptions. These conservatisms are taken to ensure the safety margins overcoming the lack of knowledge in physical phenomena involved. With these assumptions, the results are unrealistically conservative, but also satisfy the regulatory authority requirements. However, in order to obtain an optimal design and reactor operation, conservatism may be limited from the safety analyses. Consequently, in 1989, the U.S. NRC modified the licensing requirements allowing the use of realistic methods if uncertainties are identified and quantified.
Nevertheless, the containment building, and the in-containment equipment are still licensed based on the pressure and temperature obtained with conservative containment calculations under the lumped parameters framework. The average containment pressure calculated with the lumped parameters approach is fairly representative of the containment pressure, as the pressurization develops quite homogeneous. On contrary, the containment temperature calculated by the lumped parameters approach is an averaged temperature and does not necessarily represent its heterogeneous nature.
Therefore, realistic containment analyses accounting for local conditions are needed, and consequently, a modeling guideline for high-detailed evaluation models with the GOTHIC code is proposed. It is based in three main steps: Development of a 3D detailed Computer-Aided Design (CAD) model; Adapting the detailed CAD model to obtain a simplified version of the geometry; Making use of the geometric data from the simplified CAD model, a three-dimensional thermal-hydraulic evaluation model is conformed.
In addition, when a complex system (e.g. a containment building) is modeled with a CFD code like GOTHIC, it is important to assure that results are not dependent on the mesh chosen. That means that results will not change substantially even if the mesh is subsequently refined. This process is clear when the employed code separates the fluid region from the solids (as traditional CFD codes do) but becomes more complicated when the computational cells includes fluid and solids, as the case of the porous media approach.
According to that, a mesh sensitivity study using 12 different meshes was performed to analyze the mesh independence in the 3D GOTHIC containment evaluation model under the porous media framework. When the traditional CFD method of mesh refinement is applied, results become not conclusive. There are no big discrepancies when key parameters are compared (averaged temperature and pressure peaks). Nevertheless, it was found that cell aspect ratio influences negatively in the results of highly blocked cells generating numerical instabilities during the calculation. In addition, size differences also influence the fluid velocity field modifying the flow patterns, and therefore, the local temperature profiles. Considering the lessons learned from this study, different recommendations are suggested to be applied in case of performing a mesh independence studies using porous CFDs codes like GOTHIC.
To test the developed 3D containment evaluation model, an application case was performed for assessing the generic equipment qualification criteria when local data for pressure and temperature is obtained. The transient simulated was a DEGB-LOCA located at the cold leg. Results shown how the temperature heterogeneity in the containment compartments makes inadequate averaged values like those obtained with evaluation models under the lumped parameters framework.
Since a single Best-Estimate (BE) calculation brings results with unknown accuracy, an uncertainty analysis is required to estimate the solution accuracy. Nonetheless, BEPU analyses has been historically applied to RCS transient analysis, but it starts to be also applied to containment analysis with limited scope. Consequently, accounting for the experiences that many analyst and researchers have gathered along the last three decades, a BEPU methodology, with the containment safety analysis in mind, is proposed. Conservative assumptions are avoided by developing best estimate containment evaluation models. Uncertainties are quantified and propagated through the code in order to obtain the results accuracy. The proposed methodology is defined in a hierarchical structure, similar to the U.S. NRC Regulatory Guide 1203. It is divided in two main blocks; the first is related to the best estimate model setting; and the second to the uncertainty treatment.
The BEPU-CSA methodology was applied for the same analysis performed for the equipment qualification criteria above named. It was started with a “traditional” BEPU analysis based on the non-parametric tolerance interval calculation applying the famous Wilks approach with no segregation between epistemic and random uncertainties. Two series were calculated, one with a sample set of 59 elements for a one-sided tolerance region (Wilks-OS), and other with a sample set of 93 elements for a two-sided region (Wilks-TS).
Then, a method based on the LHS for obtaining similar bounds as in the case of applying the Wilks formula is also discussed, but with a reduced number of cases. Two series were also calculated, one with a sample set of 20 elements for a one-sided tolerance region (LHS-20), and other with a sample set of 40 elements for a two-sided region (LHS-40).
For both, Wilks and LHS series, maximum values obtained for pressure and temperature are quite similar, resulting more conservative the LHS sampling even having a smaller sample size.
In addition, a second order uncertainty analysis, where the epistemic uncertainties were treated based on the Dempster-Shafer theory with LHS sampling and the random uncertainties by applying the Wilks method, was compared against these obtained with the Wilks and LHS methods. A set of 30 Wilks series were obtained, being this the result of the LHS sample with size 30 for the outer loop, and 59 runs for every of the 30 LHS sample elements, which led to a 1770 code runs.
Analogously, another second order uncertainty analysis was also performed based entirely on the LHS sampling method (denominated 2nd Order LHS-20), were the epistemic uncertainty sample size was set to 20, and the random uncertainty sample size also to 20 based on the results obtained in the comparison between the Wilks and LHS series above commented.
Both methods, the LHS-Wilks and the 2nd order LHS-20, showed similar results between them, but it was observed that, when the uncertainties are segregated between random and epistemic, pressure and temperature bounds become larger than that obtained in the “traditional” BEPU analyses. This is caused by the underestimation when uniformity is assumed over imprecise uncertainties that are in fact governed by a random nature, as is the case of the initial conditions. When uncertainties are purely epistemic, and it is mean with purely epistemic as a property of the analyst and not over the parameter itself, uniformity resulted adequate.
At the end, a sensitivity analysis was performed over the LHS-Wilks calculation showing that for short-term analysis, only a few of the parameters analyzed resulted correlated with the maximum pressure and temperature obtained. In addition, it was observed that uncertainties affecting the averaged values differs from that affecting local values, indicating that dominant phenomena may differs at different scales, something to be accounted in scaling analyses.
