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In this work, we apply the Ronen method to obtain highly-accurate approximations to the solution of the neutron transport equation in simple homogeneous problems. Slab, cylindrical, and spherical g...

CAMIVVER (Codes And Methods Improvements for VVER comprehensive safety assessment) is a three years project launched under the European Union research program HORIZON 2020. The main aim of the Project is to develop and improve computer codes and methods for VVER comprehensive safety assessment. VVER reactors constitute a significant and dynamic part of the European energy market. Their safe Long Term Operation (maintenance, refuelling, safety-upgrade, revamping) relies on the industrial use of neutronics and thermal-hydraulics codes and methods that allow studying the behaviour of the plant in normal and accidental conditions. Computer codes development is strongly required for the following reasons: 1) Current codes and methods used for VVER safety assessment are subjected to growing international export controls from outside EU, threatening the EU sovereignty and security in terms of energy supply. 2) A new generation of innovative codes and methods are under development within Europe. They are improving 3D-multiphysics modelling and uncertainty quantification capabilities and are worth being transferred from lab to industry as they will substantially improve the physics comprehension of PWR and VVER. 3) European codes and methods development for VVER safety assessment will open the VVER market to the European nuclear industry. CAMIVVER will perform developments required for the new generation codes and will generalize 3D-multiphysics coupling, performing benchmark against current industrial codes used for PWR and VVER safety assessment. CAMIVVER will demonstrate CFD assets and compatibility with uncertainty propagation in the frame of a safety assessment.

In reactor core analysis, the energy deposition in the coolant is often regarded as a fixed amount. In this work we study the validity of this assumption at normal operation and under accident conditions in PWR. A fuel pin cell and other lattice elements from the VERA benchmark’s 2-D 17 × 17 fuel assemblies are used to calculate photon and neutron energy deposition in the coolant by OpenMC. The adoption of a subcooled-boiling model for the coolant with non-uniform void fraction in the sub-channel is taken into account, without revealing however significant differences on the reaction rates used to score the coolant heating. Specifically, we study the effects of void fraction, pressure and coolant temperature on deposited energy. Chemical shim operated by diluted boric acid in water is also considered. Results show that coolant heating fraction can change significantly under accident conditions. Moreover, it can be expressed as a function of pure water density and boron concentration, where water is always considered as a homogeneous mixture also in presence of two-phase flow. Specifically, we provide a correlation fitting the numerical results from OpenMC pin cell calculations by least squares regression, in order to predict energy deposition in the coolant of the subchannels present in a fuel lattice. This correlation is explicitly intended for implementation in thermal–hydraulics computer codes used for coupled full-core calculations.

M&C 2017 - International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering,Jeju, Korea, April 16-20, 2017; International audience; The alpha eigenvalue problem in multigroup neutron diffusion is studied with particular attention to the theoretical analysis of the model. Contrary to previous literature results, the existence of eigenvalue and eigenflux clustering is here investigated without the simplification of a unique fissile isotope or a single emission spectrum. A discussion about the negative decay constants of the neutron precursor concentrations as potential eigenvalues is provided. An in-hour equation is derived by a perturbation approach recurring to the steady state adjoint and direct eigenvalue problems of the effective multiplication factor and is used to suggest proper detection criteria of flux clustering. In spite of prior work, the in-hour equation results for a necessary and sufficient condition for the existence of the eigenvalue-eigenvector pair. A simplified asymptotic analysis is used to predict bands of accumulation of eigenvalues close to the negative decay constants of the precursor concentrations. The resolution of the problem in one-dimensional heterogeneous problems shows numerical evidence of the predicted clustering occurrences and also confirms previous theoretical analysis and numerical results.

Several 3D distributions of pin-by-pin data are produced in nodal core calculations. In particular, burnup distributions are used as input of thermo-mechanical computer codes in one-way coupling in order to verify the compliance to safety constraints, either at operation or in accidental transients. Their storage is required because they are computed with restart from previous calculations. Since one value is needed per fuel pin and per axial level, the amount of data to be stored for one reactor configuration is very high. Data compression techniques are very powerful to reduce the storage need. They are proposed in this work to optimise the amount of data saved and processed, without compromising the final accuracy. Specifically, we recommend the Hotelling transform to achieve higher compression performances.

In this paper, the Ronen method is developed, implemented, and applied to resolve the neutron flux and the criticality eigenvalue in simple one-dimensional homogeneous and heterogeneous problems. The Ronen method is based on iterative calculations of correction factors to use in a multigroup diffusion model, where the factors are actually given by the integral transport equation. In particular, spatially dependent diffusion constants are modified locally in order to reproduce new estimates of the surface currents obtained by the integral transport operator. The diffusion solver employed in this study uses finite differences, and the transport-corrected currents are introduced into the numerical scheme as drift terms. The corrected solutions are compared against reference results from a discrete ordinate code. The results match well with the reference solutions, especially in the limit of fine meshes, but slow convergence of the scalar flux is reported.

International audience; Several types of nuclear reactors rely on lattices of fuel rods, where the fuel cells constitute the basic units of energy production by the nuclear reactions and of energy removal by the flowing coolant. The coolant channel is physically identified by the volume within adjacent fuel cells, being the fundamental purview of design and safety studies resolving coupled thermo-hydraulic and neutron problems. Although channels are generally opened for optimal heat transfer, its closed version is often in use to describe representative channels in boxed fuel assemblies, or simply faster predictive modelling. This work aims to find a solution to the coupled closed channel problem without solving separately for the different physics in an iterative scheme. The new methodology developed hereafter is demonstrated on a realistic PWR channel with UO$_2$ fuel, and compared against the traditional one based on operator-splitting. The simple model presented in this work serves both research and educational purposes.

International audience; The cross section preparation for reactor calculations produces few-group data libraries, whose storage needs in memory increase severelywhen more physical output is requested. As a matter of fact, depletion chains with many isotopes are suggested for a more accurate isotopic inventory all along the fuel cycle, and coarse meshes are not suitable to compute finer distributions of reaction rates in highly heterogeneous systems. This work investigates the use of compression techniques on the power form factors to evaluate the potential storage reduction for homogenized pin-by-pin data. The form factors are analyzed in several physical conditions of normal operation for a Gd-poisonedUO2 and a MOX fuel assemblies, whose specications come from a benchmark problem. Two numerical transforms are studied on two different applications, providing recommendations for general use in core calculations.

International audience; We present a review of the methodologies for history effect modelling with few-group cross sections for PWR fuel assemblies. Different depletion conditions with varying moderator density, fuel temperature and protracted control rod insertion are considered where the exposure history can show significant changes in the local isotopic inventory and in the neutron spectra.Cross sections are homogenized over a classical PWR-type $\text{UO}_2$ fuel assembly provided by the Burn-up Credit Criticality Benchmark NEA-6227 and condensed in two energy groups by the lattice code APOLLO2.8. The methodologies are analyzed in view of their capability to improve the error in microscopic and macroscopic cross sections, and the associated multiplication factor and the spectral index in the infinite homogeneous medium.

Realistic simulations of nuclear reactors by computer codes are complex multi-physics problems, coupled through different physical feedbacks on nuclear cross sections. Within these calculations, heat conduction in fuel rods has a crucial importance, especially in thermal reactors, providing the fuel temperature necessary to reproduce the Doppler broadening effect. In this work, the Kirchhoff transformation is applied to solve the non-linear heat conduction problem in the classical fuel rod model. Comparisons with the common numerical scheme based on successive substitutions are presented in a simple case, also discussing the higher computational performances achieved by this integral transformation. Moreover, polynomial approximations are introduced to obtain further computational gain. This technique yields almost analytical fuel temperature distributions, thus ensuring high accuracy in the evaluation of the neutron reactivity from the Doppler effect of nuclear fuel.

Nowadays, the application of nodal methods and cross section homogenization is a standard practice in reactor core design and safety studies. Specifically, nodal cross sections are prepared with the planned physical operating conditions in the single fuel assemblies, thus assuming different approximations like for instance a constant exposure at nominal power. Concerning the light water reactors, this scheme was especially suitable for the first PWR units operating on base load, and much less for BWRs due to the strong core heterogeneities and strong axial water density variation which required ad hoc corrections. The new generation of PWRs and yet the current units in Europe show frequent use of control rod elements in order to operate on load-following. In general, the current few group cross section models of core simulators are not designed to cover very long periods of control bank insertions, thus arising the problem of the physical representation. In this work, we quantify the errors on nodal cross sections in presence of strong insertion of control rods, using the classical approach for the cross sections preparation based on a single PWR assembly homogenization. The framework of the Burn-up Credit Criticality Benchmark NEA-6227 (Phase II-D) is used to model different rodded configurations of a UO2 fuel assembly by the lattice code APOLLO2.8, providing also additional validation elements for the code. Different insertion patterns along the multiple core cycles are investigated and differences against the standard cross section generation, which considers the control rods insertion only as a perturbation along the exposure in the nominal depletion sequence, are studied. Still using the framework of this benchmark, other test cases are formulated to investigate the influence of varying boron concentration along the fuel cycles, different water densities and the aging of control elements. In particular, the latter is marked as potential issue when staging a very long insertion as with the main cases of the benchmark. We also discuss mesh refinement to model “the skin effect” when depleting the absorption materials of control rods. The suggestions for the improved modelling are given in the conclusion.

Integral parameters can give useful information on the physical properties of a multiplying system. However, various theoretical problems are encountered when trying to introduce them in a consistent way for source-driven systems. Many questions also arise for their experimental estimation. After some general considerations, the paper presents comparisons of numerical results obtained in different approaches and by the application of inverse methods to localized neutron flux signal detections. Results presented refer to the Yalina Booster experimental facility, which constitutes an excellent challenging test for the models and methods, being a neutronically, spatially and spectrally decoupled system. Some considerations on the usefulness of such parameters for kinetic analyses and to qualify the system characteristics are also included in the paper, analyzing both highly and loosely coupled configurations.

AREVA has developed a new coupled neutronics/thermal-hydraulics code system, ARCADIA®. It makes use of modern computing resources to enable more realistic reactor analysis as improved understanding of nuclear reactor behavior is the basis for efficient margin management, i.e. optimization of safety and performance. One of the principal components of this new system is the core simulator, ARTEMIS™. The purpose of this paper is to recall its features, present the latest developments and give a summary of the validation tests.

Several alternative approximations of neutron transport have been proposed in years to move around the known limitations imposed by neutron diffusion in the modeling of nuclear cores. However, only a few complied with the industrial requirements of fast numerical computation, concentrating more on physical accuracy. In this work, the AN transport methodology is discussed with particular interest in core performance calculations. The implementation of the methodology in full core codes is discussed with particular attention to numerical issues and to the integration within the entire simulation process. Finally, first results from core studies in AN transport are analyzed in detail and compared to standard results of neutron diffusion.