Likelihood and depth-based criteria for validation of numerical simulators, from comparison with experimental data

Within the framework of Best-Estimate-Plus-Uncertainty approaches, the assessment of model parameter uncertainties, associated with numerical simulators, is a key element in safety analysis. The results (or outputs) of the simulation should be compared and validated against experimental values, when such data is available. This validation step is required to ensure a reliable use of the simulator for modeling and prediction. In addition, it must take into account both model and experimental uncertainties (measurement uncertainties). This work aims to define quantitative criteria to carry out this validation for multivariate outputs, while taking into account the different sources of uncertainty. For this purpose, different statistical indicators, based on likelihood or statistical depths, are investigated and extended to the multidimensional case. First, the properties of the criteria are studied, either analytically or by simulation, for some specific cases (Gaussian distribution for experimental uncertainties, identical distributions of experiments and simulations, particular discrepancies). Then, some natural extensions to multivariate outputs are proposed, with guidelines for practical use depending on the objectives of the validation (strict/hard or average validation). From this, transformed criteria are proposed to make them more comparable and less sensitive to the dimension of the output. It is shown that these transformations allow for a fairer and more relevant comparison and interpretation of the different criteria. Finally, these criteria are applied to a code dedicated to nuclear material behaviour simulation. The need to reduce the uncertainty of the model parameters is thus highlighted, as well as the outputs on which to focus

Nonparametric Bayesian approach for quantifying the conditional uncertainty of input parameters in chained numerical models

Nowadays, numerical models are widely used in most of engineering fields to simulate the behaviour of complex systems, such as for example power plants or wind turbine in the energy sector. Those models are nevertheless affected by uncertainty of different nature (numerical, epistemic) which can affect the reliability of their predictions. We develop here a new method for quantifying conditional parameter uncertainty within a chain of two numerical models in the context of multiphysics simulation. More precisely, we aim to calibrate the parameters $θ$ of the second model of the chain conditionally on the value of parameters $λ$ of the first model, while assuming the probability distribution of $λ$ is known. This conditional calibration is carried out from the available experimental data of the second model. In doing so, we aim to quantify as well as possible the impact of the uncertainty of $λ$ on the uncertainty of $θ$. To perform this conditional calibration, we set out a nonparametric Bayesian formalism to estimate the functional dependence between $θ$ and $λ$, denoted by $θ(λ)$. First, each component of $θ(λ)$ is assumed to be the realization of a Gaussian process prior. Then, if the second model is written as a linear function of $θ(λ)$, the Bayesian machinery allows us to compute analytically the posterior predictive distribution of $θ(λ)$ for any set of realizations $λ$. The effectiveness of the proposed method is illustrated on several analytical examples

Modelling the fuel failure behavior with a micromechanical approach in the HBS area

International audienceThe aim of this study is to define a macroscopic fragmentation model based on a micro mechanical approach to have a better understanding of the fuel mechanical behaviour at lower scale: size and volume fraction of fragments. This talk introduces a stepwise micromechanical method: firstly, we detail how to model the HBS microstructure including pressurized porosities, based on experimental or numerical data and define a Representative Volume Element (RVE). Then we use 3D full field computations in order to determine crack snapshot. Elastic computations are performed to find the bubbles pressure level which is required to reach the cracks initiation threshold. Then nonlinear computations, using a failure local behavior law, are conducted to identify the failure snpashot. The latters will be used as an input data of the homogenization (“macroscopic”) model. This model is exposed in the last section

Studying fuel failure behavior with a micromechanical approach

International audienceUnder Loss Of Coolant Accident (LOCA) conditions, the temperature evolution within the fuel pellets combined with a reduction of the cladding confinement can lead to fuel fragmentation. This phenomenon provides additional fission gas release, inducing a higher rod internal pressure and possibly an additional driving force to disperse the smallest fuel fragments out of the cladding when the cladding balloons and bursts. Experiments show that the pellets are fractured in many fragments, with size ranges varying from a few millimetres to a few microns. Usually the hypothesis used to explain fuel pellet fragmentation during transient, is grain cleavage induced by over pressurized fission gas bubbles, located at the grain boundary. This work focuses on the pellet rim, where bubbles density increases owing to a higher irradiation level. This area, called “High Burn-up Structure” (HBS), has a specific behaviour due to a microstructure reorganization composed of small grains about 100 nm compared to 10 μm for initial UO2 fuel. The aim of this study is to define a macroscopic fragmentation model based on a micro mechanical approach to have a better understanding of the fuel mechanical behaviour at lower scale: size and volume fraction of fragments. This paper introduces a stepwise micromechanical method: firstly, we detail how to model the HBS microstructure including pressurized porosities, based on experimental or numerical data and define a Representative Volume Element (RVE). Then we use 3D full field computations in order to determine crack snapshot. Elastic computations are performed to find the bubbles pressure level which is required to reach the cracks initiation threshold. Then nonlinear computations, using a failure local behavior law, are conducted to identify the failure snpashot. The latters will be used as an input data of the homogenization (“macroscopic”) model. This model is exposed in the last section

Use of a micromechanical approach to investigate transient fuel fragmentation mechanisms

International audienceUnder LOCA conditions, the temperature gradient evolution within the fuel pellets combined with a reduction of the cladding confinement can lead to fuel fragmentation. This phenomenon provides additional fission gas releases, inducing a higher rod internal pressure and possibly an additional driving force to disperse the smallest fuel fragments out of the cladding when the cladding balloons and bursts. Experiments show the pellets are fractured in many fragments, with size ranges varying from few millimetres to few microns. Experimental fuel fragmentation thresholds have been defined as a function of pellet Burnup and temperature. Nevertheless, despite of a good agreement between these empirical thresholds and integral LOCA tests results, these thresholds do not included neither fracture mechanical theories nor microstructure considerations. The aim of this study is to define a fragmentation threshold based on a micro mechanical approach to complement the former experimental observations. Usually the hypothesis used to explain fuel pellet fragmentation during transient, is grain cleavage induced by over pressurized fission gas bubbles, located at the grain boundary. In this paper we will then present the first steps of the fuel microstructure modelling including pressurized bubbles in order to have a better understanding of the fuel micro mechanical behaviour and establish a fragmentation threshold: (1) model the fuel micro structure at the beginning of the transient, (2) simulate its micro mechanical behaviour using a 3D Finite Elements approach, (3) develop a macroscopic criterion based on the 3D local results. To characterize the fission gases bubbles, the initial conditions of the Studsvik LOCA test specimens have been calculated with the fuel performance code ALCYONE V1.4 of the PLEIADES software environment co-developed by CEA, EDF. These results are useful to set up a Representative Volume Element (RVE) for each type of microstructure considered in the pellet. Then a LOCA transient is applied to the 3D finite element model of the RVE, considering a local behaviour, based on a damage law developed by CEA. Simulation results will be then be used to better understand fuel behaviour under LOCA conditions with a view to predict fuel pellet fragments size distribution

Modelling the fuel failure behavior with a micromechanical approach in the HBS area

International audienceThe aim of this study is to define a macroscopic fragmentation model based on a micro mechanical approach to have a better understanding of the fuel mechanical behaviour at lower scale: size and volume fraction of fragments. This talk introduces a stepwise micromechanical method: firstly, we detail how to model the HBS microstructure including pressurized porosities, based on experimental or numerical data and define a Representative Volume Element (RVE). Then we use 3D full field computations in order to determine crack snapshot. Elastic computations are performed to find the bubbles pressure level which is required to reach the cracks initiation threshold. Then nonlinear computations, using a failure local behavior law, are conducted to identify the failure snpashot. The latters will be used as an input data of the homogenization (“macroscopic”) model. This model is exposed in the last section

Génération de microstructures de combustible nucléaire hétérogène et homogénéisation mécanique

National audienc

Génération de milieux aléatoires continus périodiques et calculs mécaniques par FFT

National audienceLe matériau étudié est un combustible nucléaire à base de plutonium (Pu) et d'uranium, sa microstructure est caractérisée par la répartition spatiale de la teneur en Pu. L'objectif de ce travail est de générer un milieu représentatif de sa microstructure (VER), et d'effectuer les premiers calculs nécessaires à la détermination de son comportement mécanique effectif. La texture du matériau est connue par des cartographies de teneur en Pu, obtenues par microsonde électronique. Le formalisme des fonctions aléatoires, et les outils associés, permettent de caractériser statistiquement cette texture (histogramme, covariance spatiale), de s'affranchir du bruit de mesure, et enfin de générer des microstructures 3D périodiques, représentatives du combustible. Du point de vue mécanique, le combustible est un matériau à comportement viscoélastique vieillissant avec des gonflements libres, qui dépend de la teneur locale en plutonium. Les calculs sur la microstructure périodique sont effectués en utilisant une méthode de résolution par transformée de Fourier rapide (FFT)

The OSCAR code package : A unique tool for simulating PWR contamination

International audienceUnderstanding the PWR primary circuit contamination by corrosion products, fission productsand actinides is a crucial issue for reactor operation and design. The main challenges aredecreasing the impact on personnel exposure to radiation, optimizing the plant operation,limiting the activity of the wastes produced during the reactor lifetime and preparingdecommissioning.In cooperation with EDF and AREVA NP, CEA has developed the OSCAR code package, aunique tool for simulating PWR contamination. The OSCAR package results from the mergingof two codes, which simulate PWR contamination by fission products and actinides (PROFIPcode) and by activated corrosion products (PACTOLE code).These two codes have been validated separately against an extensive set of data obtained over 40years from in-situ gamma spectrometry measurements, sampling and analysing campaigns ofprimary coolant, as well as experiments in test loops or experimental reactors, which arerepresentative of PWR conditions.In this paper, a new step is presented with the OSCAR code package, combining the features ofthe two codes and motivated by the fact that, wherever they originate from, the contaminationproducts are subject to the same severe conditions (300 °C, 150 bar, neutron flux, water velocityup to 15 m.s-1) and follow the same transport mechanisms in the primary circuit. The main processes involved are erosion/deposition, dissolution/precipitation, adsorption/desorption,convection, purification, neutron activation, radioactive decrease.The V1.1 version of the OSCAR package is qualified for fission products (Xe, Kr, I, Sr),actinides (U, Np, Pu, Am, Cm) and corrosion products (Ni, Fe, Co, Cr).This paper presents the different release modes (defective fuel rod release, fissile materialdissemination, material corrosion and release), then the processes which govern contaminationtransfer, and finally, we give examples of the comparison of the OSCAR package results withmeasurements in French PWR primary circuit obtained for representative radioisotopes : $^{133}$Xe,$^{90}$Sr, $^{58}$Co, $^{60}$Co. In particular, we focus on the main upgrades in the OSCAR simulations compared to thePROFIP and PACTOLE codes : adaptation of the MARGARET module to assess fission productrelease out of fuel pellets in a defective rod, adsorption/desorption model development forstrontium behaviour, multi-criteria calibration of input data which are not well known forcorrosion product simulation