• Accuracy
• Adjoint
• Adjustment
• ASAP
• Best Estimate
• Calibration
• CIAU
• FSAP
• ITF
• NPP
• Nuclear
• Sensitivity
• Thermal-hydraulics
• Uncertainty

Sensitivity and uncertainty analyses can provide quantitatively in a mathematically and physically well-founded way answers to typical scientific and engineering questions such as: how much the model under consideration represents the physical phenomena, how far the calculated results can be extrapolated and etc…

Nuclear Power Plant (NPP) technology has been developed based on the traditional defense in depth philosophy supported by deterministic and overly conservative methods for safety analysis. In the 1970s, conservative hypotheses were introduced for safety analyses to address existing uncertainties. Since then, intensive thermal-hydraulic experimental research has resulted in a considerable increase in knowledge and consequently in the development of best-estimate codes able to provide more realistic information about the physical behaviour and to identify the most relevant safety issues allowing the evaluation of the existing actual margins between the results of the calculations and the acceptance criteria.

However, the best-estimate calculation results from complex thermal-hydraulic system codes (like Relap5, Cathare, Athlet, Trace, etc..) are affected by unavoidable approximations that are un-predictable without the use of computational tools that account for the various sources of uncertainty. Therefore the use of best-estimate codes within the reactor technology, either for design or safety purposes, implies understanding and accepting the limitations and the deficiencies of those codes.

Uncertainties may have different origins ranging from the approximation of the models, to the approximation of the numerical solution, and to the lack of precision of the values adopted for boundary and initial conditions. The amount of uncertainty that affects a calculation may strongly depend upon the codes and the modeling techniques (i.e. the code’s users). A consistent and robust uncertainty methodology must be developed taking into consideration all the above aspects.

Three main independent ways to perform the sensitivity and uncertainty analysis of thermal-hydraulic system code calculations have been identified in the present effort with approaches based on: a) propagation of code input errors and statistical treatment of the resulting uncertainty, b) propagation of code output errors and ‘deterministic’ treatment of the resulting uncertainty and c) experimental validation and calibration methodology of complex time-dependent numerical simulation models able to consistently incorporate both computational and experimental uncertainties making extensive use of the concepts of the sensitivity analysis.

Taking into consideration the above framework, the main objective of the thesis is to contribute to the further development and qualification of the sensitivity and uncertainty tools for performing deterministic nuclear reactor safety analyses. To this aim, the PhD activity has been subdivided in two main parts mostly related with the different state of advancement and maturity of the involved methodologies.

From one side, the goal is to consolidate and strengthen the Code with the capability of Internal Assessment of Uncertainty (CIAU) proposed by University of Pisa and to demonstrate its robustness and achieved maturity level through the application of the methodology in the framework of the BEMUSE (Best Estimate Methods Uncertainty and Sensitivity Evaluation) project promoted by OECD. From the other side, the aim is to develop a fully deterministic method, named CASUALIDAD (Code with the capability of Adjoint Sensitivity and Uncertainty AnaLysis by Internal Data ADjustment and assimilation) based on advanced mathematical tools for performing the sensitivity and the uncertainty analyses internally to the thermal-hydraulic system code.

In relation with CIAU, the contributions of the thesis’s work are 1) the extension of the uncertainty database with the addition of twelve new tests and 2) the development of a procedure for the ‘internal’ qualification of the method. Both aspects result in a more accurate CIAU uncertainty evaluation as they contribute respectively to improve the statistical performance and to perform a systematic qualitative and quantitative analysis of the data constituting the CIAU database.

In relation with the second goal of the thesis’s work, a comprehensive approach for utilizing quantified uncertainties arising from Integral Test Facilities (ITFs) and Separate Effect Test Facilities (SETFs) in the process of calibrating complex computer models for the application to NPP transient scenarios has been developed. The methodology proposed is capable of accommodating multiple SETFs and ITFs to learn as much as possible about uncertain parameters, allowing for the improvement of the computer model predictions based on the available experimental evidences. The pioneering CASUALIDAD approach can be considered also as an attempt to substitute the empiricism of the CIAU approach in relation with the statistical treatment of the accuracy for deriving the uncertainty values with rigorous mathematical deterministic methods like the advanced sensitivity tools for performing the local (the Adjoint Sensitivity Analysis Procedure, ASAP, or the Forward Sensitivity Analysis Procedure, FSAP) and global (Global Adjoint Sensitivity Analysis Procedure, GASAP) sensitivity analyses and the methodology (the Data Adjustment and Assimilation, DAA) for consistently incorporating observed available information into a predicting model to obtain an improved uncertainty estimation.
As a main conclusion from the present effort, it is clear the industrial relevance of the best-estimate plus uncertainty approach compared with the conservative approach. More in detail, in relation with the CIAU uncertainty method, the attained results demonstrate, within the framework of an international initiative, the level of robustness and adequacy of the proposed uncertainty methodology. At the same time, both the achieved advancements and the performed applications, constitute fundamental supports for the use of the CIAU method in the NPP licensing process, like for Angra-2 NPP (Brazil) in the recent past (2000) and for
Atucha-2 NPP (Argentina) currently under application.

In relation with the CASUALIDAD, for which a demonstrative application (i.e. the blowdown of a gas from a pressurized vessel taking into account the heat transfer through the vessel wall) is presented, the proposed methodology constitutes a major step forward with respect to the generally used expert judgement and statistical methods as it permits a) to establish the uncertainties of any parameter characterizing the system, based on a fully mathematical approach where the experimental evidences play the major role and b) to calculate an improved estimate of the computed response and relative improved (i.e. reduced) uncertainty.