Advanced Couplings and Multiphysics Sensitivity Analysis Supporting the Operation and the Design of Existing and Innovative Reactors

Codes and methods are subjected to a continuous update process for answering the regulatory requirements concerning the long-term operation of existing reactors and new concept deployment. In this continuous improvement process, new generation codes are developed for supporting industrial applications and the long-term strategy. In this paper, attention is devoted to selecting codes under development in France for lattice and core steady-state and transient calculations. These codes, APOLLO3® and CATHARE3, have been selected for carrying out the activities of the H2020 CAMIVVER Project oriented to the 3D-multiphysics couplings improvements. Multiscale and multiphysics solutions are key topics to keep competitiveness and answer to newer industrial needs in plant operations, licensing, and safe operating envelope requirements. The paper presents an overview of the activities performed by Framatome to support the definition of benchmarks exercises proposed in the CAMIVVER Project. Small core configurations subjected to a Reactivity Insertion Accident (RIA) are presented with associated preliminary results. To open the discussions toward the development of Best-Estimate Plus Uncertainties (BEPU) solutions, the URANIE statistical platform was used for sensitivity analysis over different configurations. These preliminary results are also presented.

Overview of SERMA’s Graphical User Interfaces for Lattice Transport Calculations

This article presents an overview of the graphical user interfaces (GUIs) developed at CEA/SERMA (Service d’Études des Réacteurs et de Mathématiques Appliquées) in Saclay, France, which have been used for over forty years by engineers and scientists to build geometries and meshes for general-purpose lattice transport calculations (neutrons and photons). Several applications make use of these calculations, from fuel assembly to full core design, criticality and safety, needing consistency check of the geometry and input properties before starting any lattice calculation. The software pattern design of the GUIs is briefly discussed, showing also the rationale behind the two interfaces for the construction of the geometries for simple fuel assemblies and complex motifs including the reflector (colorsets). The new GUI, ALAMOS, specifically developed for APOLLO3® with a Python Application Programming Interface (API), is here presented as the successor of Silène, which was the first GUI released in the 1990s to serve APOLLO2 calculations. The considerable experience gained by Silène over the years with plenty of various applications has provided a crucial support for the development of ALAMOS.

A SUBGROUP METHOD BASED ON THE EQUIVALENT DANCOFF-FACTOR CELL TECHNIQUE COMPARED WITH THE FINE-STRUCTURE METHOD IN APOLLO3®

We compare a newly implemented subgroup method, which is based on the equivalent Dancoff-factor cell technique, with the fine structure method in APOLLO3®. The new method obtains precise reaction rates and consequently is precise in predicting multipli-cation factor. It can reduce the time in the self-shielding calculation by a factor of 38 compared with the subgroup method based on the multi-cell approximation in a PWR Gd-UOX assembly calculation. The fine structure method obtains larger errors in reac-tion rates than the subgroup method, but the error compensation sometimes leads to small errors in multiplication factors. This work demonstrates the precision and the efficiency of the new method.

3D CORE CALCULATION BASED ON THE METHOD OF DYNAMIC HOMOGENIZATION

The classical two-step calculation scheme has been extensively used to perform three-dimensional deterministic core calculations thanks to its fast results. On the other hand, direct 3D transport calculations and 2D/1D Fusion methods, mostly based on the method of characteristics, have recently been applied showing a prohibitive computational time for routine design purposes as well as in the context of multiphysics and core depletion calculations, due to current machine capabilities.

The Dynamic Homogenization method is here proposed as an alternative technique that may lie between the classical and the direct approaches in terms of precision and performance. In this work, the method is applied to the NEA ”PWR MOX/UO2 Core Benchmark” for a 3D configuration. Comparison of pin power relative errors and computational cost against the two-step and direct approaches are presented.

FEW-GROUP CROSS SECTIONS MODELING BY ARTIFICIAL NEURAL NETWORKS

This work deals with the modeling of homogenized few-group cross sections by Artificial Neural Networks (ANN). A comprehensive sensitivity study on data normalization, network architectures and training hyper-parameters specifically for Deep and Shallow Feed Forward ANN is presented. The optimal models in terms of reduction in the library size and training time are compared to multi-linear interpolation on a Cartesian grid. The use case is provided by the OECD-NEA Burn-up Credit Criticality Benchmark [1]. The Pytorch [2] machine learning framework is used.

CONTRIBUTION OF THERMAL-HYDRAULICS SIMULATION TO CRITICALITY ANALYSIS OF A DEBRIS BED NUMERICAL MOCK-UP

In this work, we evaluate the impact of simulating the thermal-hydraulics feedback in criticality risk assessment in a benchmark configuration corresponding to a simplified debris bed. We have recently discussed the coupling of the multi-phase thermal-hydraulics code MC3D with a reactivity evaluation scheme based on multi-point kinetics, which paves the way towards the assessment of the system behavior in terms of energy release. In this work, we analyze the system reactivity as a function of the thermal-hydraulics state of the system. For our investigation, we have considered a simplified cylindrical region and assumed that the fuel particles in the mixture consist of spheres of small diameter. The power has been adjusted to be representative of nuclear decay heat. For most of the examined configurations, the maximum reactivity lies below zero, which shows that the occurrence of a criticality event is likely to be excluded, thanks to the contribution of the decay heat of the fuel.

How to obtain an enhanced extended uncertainty associated with decay heat calculations of industrial PWRs using the DARWIN2.3 package

Decay heat is a crucial issue for in-core safety after reactor shutdown and the back-end cycle. An accurate computation of its value has been carried out at the CEA within the framework of the DARWIN2.3 package. The DARWIN2.3 package benefits from a Verification, Validation and Uncertainty Quantification (VVUQ) process. The VVUQ ensures that the parameters of interest computed with the DARWIN2.3 package have been validated over measurements and that biases and uncertainties have been quantified for a particular domain. For the parameter “decay heat”, there are few integral experiments available to ensure the experimental validation over the whole range of parameters needed to cover the French reactor infrastructure (fissile content, burnup, fuel, cooling time). The experimental validation currently covers PWR UOX fuels for cooling times only between 45 minutes and 42 days, and between 13 and 23 years. Therefore, the uncertainty quantification step is of paramount importance in order to increase the reliability and accuracy of decay heat calculations. This paper focuses on the strategy that could be used to resolve this issue with the complement and the exploitation of the DARWIN2.3 experimental validation.

Simulation of a hypothetical MSLB core transient in VVER-1000 with several stuck rods

A hypothetical main steam line break transient in a VVER-1000 core with multiple equipment faults was simulated with the coupled COBAYA4/CTF and COBAYA3/FLICA4 nodal core models. The objective was to test recent versions of the models developed in the EU NURISP and NURESAFE projects and to analyze the thermal-hydraulic conditions in the hot assembly at the pin-cell level. The accident scenario was specified as an aggravated variant of the OECD/NEA VVER-1000 MSLB benchmark with eight peripheral control rod clusters stuck out of the core after scram, all of them in the overcooled sector. Coarse-mesh models and a realistic cross-section library were used to compute the full-core behavior with pre-calculated MSLB boundary conditions and to identify the hot assembly. Then a sub-channel thermal-hydraulic analysis of the hot assembly was performed with the CTF code, using time-dependent assembly boundary conditions from the coarse-mesh vessel and core simulation. The results show that the predicted values of the safety parameters do not exceed the safety limits.

Parallel Analysis of Linear Systems in CORTH and KYLIN2

Subchannel thermal-hydraulics program named CORe thermal-hydraulics (CORTH) and assembly lattice calculation program named KYLIN2 have been developed in Nuclear Power Institute of China (NPIC). For the sake of promoting the efficiencies of these programs and achieving the better description on fined parameters of reactor, programs' linear systems and details are interpreted and parallelized. Test results show that the calculation efficiencies of linear systems occupy a large proportion of according serial computation. Based on the analysis, both programs' efficiencies are improved greatly through the proposed distributed-memory parallel strategy.

Application of the EGPT methodology in the analysis of small-sample reactivity worth experiments

In the current paper, we investigate the application of the Equivalent Generalized Perturbation Theory (EGPT) to derive trends and associated covariances on the neutron capture cross section of one major fission product for both light water reactors and sodium-cooled fast reactors which is Rhodium-103. To do so, we have considered the ERMINE-V/ZONA1 & ZONA3 fast spectrum experiment and the MAESTRO thermal-spectrum experiment, where samples of these materials were oscillated in the MINERVE facility. In the paper, the theoretical formulation of EPGT is described and its derivation in the special case of the close loop oscillation technique where the reactivity worth is determined thanks to a power control system. A numerical benchmark is presented to assess the relevance of sensitivity coefficients provided by EGPT against direct perturbations where the microscopic cross sections are manually changed before calculating the adjoint and forward flux. The breakdown between direct and indirect contributions in the sensitivity analysis of the sample reactivity worth is presented and discussed, with the impact of using a calibration reference sample to normalize the measured reactivity worth. Finally, the assimilation of integral trends is done with the CONRAD code, using C/E comparisons between TRIPOLI4/JEFF3.2 calculations and experimental results and the sensitivity coefficients provided by the EGPT. Preliminary results of this study are showing that the JEFF3.2 evaluation of 103Rh gives satisfactory agreements in both thermal and fast spectrum experiments and that the combination of them can lead to a significant uncertainty reduction on the capture cross section, from ±5% to ±3% in the resolved resonance range (1 eV–10 keV) and from ±8% to ±5% in the unresolved resonance range (10 keV–1 MeV).