عدم قطعیت و تجزیه و تحلیل حساسیت به عنوان یک ابزار اعتبارسنجی برای پیش بینی های هیدروترمال بسته نرم افزاری BWR

In recent years, more realistic safety analyses of nuclear reactors have been based on best estimate (BE) computer codes. The need to validate and refine BE codes that are used in the predictions of relevant reactor safety parameters, led to the organization of international benchmarks based on high quality experimental data. The OECD/NRC BWR full-size fine-mesh bundle test (BFBT) benchmark offers a good opportunity to assess the accuracy of thermal–hydraulic codes in predicting, among other parameters, single and two phase bundle pressure drop, cross-sectional averaged void fraction distributions and critical powers under a wide range of system conditions. The BFBT is based on a multi-rod assembly integral test facility which is able to simulate the high pressure, high temperature fluid conditions found in BWRs through electrically heated rod bundles. Since code accuracy is unavoidably affected by models and experimental uncertainties, an uncertainty analysis is fundamental in order to have a complete validation study. In this paper, statistical uncertainty and sensitivity analyses are used to validate the thermal–hydraulic features of the POLCA-T code, based on a one dimensional model of the following macroscopic BFBT exercises: (1) single and two phase bundle pressure drop, (2) steady-state cross-sectional averaged void fraction, (3) transient cross-sectional averaged void fraction and (4) steady-state critical power tests. The Latin hypercube sampling (LHS) strategy was chosen since it densely stratifies across the range of each uncertain input probability distribution, allowing a much better coverage of the input uncertainties than simple random sampling (SRS). The results show that POLCA-T predictions on pressure drop and void fractions under a wide range of conditions are within the validation limits imposed by the uncertainty analysis, while the accuracy of critical power predictions depends much on the boundary and input conditions.

At the end of the year 2009, nuclear energy provided about 15% of the world's electricity as a continuous and reliable based-load power. Nowadays, nuclear energy is experiencing a renaissance because it represents a very good option to fulfill the growing demand for electricity around the globe. Concerns over climate change and dependence on overseas supplies of fossil fuels are the main reasons for such a renaissance. Therefore, with an increased number of light water reactors (LWRs) in the world, there is a huge interest on improving deterministic safety analysis as an essential tool for demonstrating the safety of nuclear power plants. BE computer codes constitute one of the actual acceptable options for demonstrating that safety is ensured with an adequate margin. Nowadays, they are employed to calculate postulated accidents and transient scenarios in a realistic way, replacing the conservative approach used in the past in computational reactor safety analysis. However, code predictions are uncertain due to several sources of uncertainty, like code models as well as uncertainties of plant and fuel parameters. Therefore, BE calculations should be supplemented by a quantitative uncertainty analysis. On the other hand, the study of how output uncertainty can be apportioned to the different input sources, known as sensitivity analysis, is an important complement to uncertainty quantification since it identifies the most dominant model parameters. The need to validate and refine BE codes that are used in the predictions of relevant reactor safety parameters, led to the organization of international benchmarks based on high quality experimental data. The OECD/NRC BFBT benchmark was established in 2002 based on available data from the Nuclear Power Engineering Corporation (NUPEC), and offers a good opportunity to assess the accuracy of thermal–hydraulic codes in predicting, among other parameters, single and two phase bundle pressure drop, cross-sectional averaged void fraction distributions and critical powers under a wide range of system conditions. With respect to the void distribution inside a fuel assembly, which has been regarded as an important factor in the determination of boiling transition in boiling water reactors (BWRs), NUPEC performed from 1987 to 1990 a series of radial void measurements at four axial locations in a full-size mock-up test facility able to simulate the high pressure, high temperature fluid conditions found in BWRs through electrically heated rod bundles. Therefore, since other important parameters such as system pressure, inlet sub-cooling and power input conditions were also supplied, these test series form a substantial database for the assessment of the accuracy of thermal hydraulic codes in predicting radial and axial assembly void distributions, under both steady-state and transient conditions. Nevertheless, due to uncertainties coming, for example, from approximations in the physical and mathematical models, variation and imprecise knowledge of initial and boundary conditions, scatter of measured experimental data, etc., it has been recognized in the last years that uncertainty analysis would not only be necessary if useful conclusions are to be obtained from BE calculations, but would also complete the validation process of BE models (Mehta, 1998 and Glaeser, 1995). Among the different approaches to perform uncertainty analysis, the one based on statistical techniques begins with the treatment of the code input uncertain parameters as random variables. Thereafter, values of these parameters are selected according to a random or quasi-random sampling strategy and then propagated through the code in order to assess the output uncertainty in the corresponding calculations. This framework has been highly accepted by many scientific disciplines not only because of its solid statistical foundations, but also because it is affordable in practice and relatively easy to implement thanks to the tremendous advances in computing capabilities. In this paper, statistical uncertainty and sensitivity analyses using the POLCA-T code and based on the following BFBT benchmark exercises are presented: 1. Ex. 0, Phase II. Steady-state single and two phase pressure drop 2. Ex. 2, Phase I. Steady-state cross-sectional averaged void fraction 3. Ex. 3, Phase I. Transient cross-sectional averaged void fraction 4. Ex. 1, Phase II. Steady-state critical power benchmark The chosen sampling strategy for the current studies is Latin hypercube sampling. The quasi-random LHS allows a much better coverage of the input uncertainties than SRS because it densely stratifies across the range of each input probability distribution. A comparison of both sampling methodologies applied to uncertainty analysis of cross-sectional averaged void fraction predictions based on the BFBT benchmark, can be found in (Hernandez-Solis et al., 2010), where the advantages of LHS over SRS are clearly shown. Other work comparing such advantages on uncertainty propagation in analysis of complex systems can be found in (Helton and Davis, 2003). In the following sections, a description of the NUPEC integral test facility (ITF) and the systems employed for the different test measurements is given, along with a brief explanation of the thermal–hydraulic models used in the Westinghouse POLCA-T code. Thereafter, a deeper review on how to perform a statistical uncertainty analysis is presented, with emphasis on how it can be applied as a code validation process. Finally, quantitative and qualitative uncertainty and sensitivity analyses are shown for the different BFBT exercises.

In this paper, uncertainty analysis was used to enhance the validation process of a code employed for safety analysis of nuclear reactors. In order to obtain a quantitative validation limit, the estimation of both experimental and code statistical uncertainty was taken into account. Based on the different exercises of the BFBT benchmark, it can be said that the code is very accurate on predicting steady-state pressure drops and cross-sectional averaged void fractions under a wide range of conditions, where the absolute error of all test cases was below the validation uncertainty. Regarding the transient analyses, the qualitative behavior of the code tracked very well the measured void fraction, and only three comparison errors were found to be slightly higher than the validation limit on the turbine trip scenario. Regarding the critical power exercise, four different tests with very different nominal conditions were analyzed. This fact has a big impact on the code accuracy since the CPR model is designed to work with nominal BWR pressure conditions, therefore explaining why the absolute errors of the two low pressure test cases were higher than the validation uncertainty. Finally, it can be said that the present study is based on solid statistical principles, making the computation of the uncertainty limits a reliable validation tool. However, due to the fact that many code runs are necessary to obtain a statistical significant sample size, the analysis may become computationally time consuming.