A MOC-based neutron kinetics model for noise analysis

A 2-D noise model is implemented in the deterministic reactor code APOLLO3® to simulate a periodic oscillation of a structural component. The Two/Three Dimensional Transport (TDT) solver, using the Method of Characteristics, is adopted for the calculation of the case studies, constituted by a moving detector and control-rod bundle. The periodic movement is built by properly linking the geometries corresponding to the temporal positions. The calculation is entirely performed in the real time domain, without resorting to the traditional frequency approach. A specifically defined dynamic eigenvalue is used to renormalize in average the reactivity over a period. The algorithm is accelerated by the DPN synthetic method. For each cell of the domain, the time values of fission rates are analysed to determine the noise extent. Moreover we propose a systematic approach to the definition of the macroscopic cross sections to be used in dynamical calculations starting from library data. As an aside of our work we have found that even in static calculation this approach can produce significant changes

Modeling noise experiments performed at AKR-2 and CROCUS zero-power reactors

CORTEX is a EU H2020 project (2017-2021) devoted to the analysis of ’reactor neutron noise’ in nuclear reactors, i.e. the small fluctuations occurring around the stationary state due to external or internal disturbances in the core. One important aspect of CORTEX is the development of neutron noise simulation codes capable of modeling the spatial variations of the noise distribution in a reactor. In this paper we illustrate the validation activities concerning the comparison of the simulation results obtained by several noise simulation codes with respect to experimental data produced at the zero-power reactors AKR-2 (operated at TUD, Germany) and CROCUS (operated at EPFL, Switzerland). Both research reactors are modeled in the time and frequency domains, using transport or diffusion theory. Overall, the noise simulators managed to capture the main features of the neutron noise behavior observed in the experimental campaigns carried out in CROCUS and AKR-2, even though computational biases exist close to the region where the noise-inducing mechanical vibration was located (the so-called ”noise source”). In some of the experiments, it was possible to observe the spatial variation of the relative neutron noise, even relatively far from the noise source. This was achieved through reduced uncertainties using long measurements, the installation of numerous, robust and efficient detectors at a variety of positions in the near vicinity or inside the core, as well as new post-processing methods. For the numerical simulation tools, modeling the spatial variations of the neutron noise behavior in zero-power research reactors is an extremely challenging problem, because of the small magnitude of the noise field; and because deviations from a point-kinetics behavior are most visible in portions of the core that are especially difficult to be precisely represented by simulation codes, such as experimental channels. Nonetheless the limitations of the simulation tools reported in the paper were not an issue for the CORTEX project, as most of the computational biases are found close to the noise source

A New Tone'S Method In Apollo3 And Its Application To ZPPR Benchmarks

International audienceThis paper presents a newly developed resonance self-shielding method based on Tone's method in APOLLO3 for fast reactor calculations. The new method is based on the simplified models, the narrow resonance approximation for the slowing down source and Tone's approximation for group collision probability matrix. It utilizes the mathematical probability tables as quadrature formulas in calculating the effective cross sections. Numerical results for the ZPPR drawer calculations show that, in case of the double column fuel drawer, Tone's method gives equivalent precision to the subgroup method while reducing largely the total number of the collision probability matrix calculations hence the CPU time. In case of the single column fuel drawer with presence of a uranium metal material, Tone's method obtains less precise results than those of the subgroup method due to less precise heterogeneous-homogeneous equivalence

a simple multiphysics coupling for high-fidelity neutronic modelling in fuel performance codes

International audienc

2D core calculation based on the method of dynamic homogenization

International audienceThree-dimensional core deterministic calculations are typically based on the two-steps approach,where the homogenized cross-sections of an assembly type are pre-calculated for different physicalparameters and then interpolated to the actual state in the reactor. On the other hand, direct transportcalculations, mostly based on the method of characteristics, have recently been applied, showinga prohibitive computational time for routine design purposes, due to current machine capabilities.Because of this, a simplified transport solution, the so called 2D/1D Fusion method [1], has been developedachieving very precise results but remaining still expensive in the context of multiphysics andcore depletion calculations. In the present work, we propose a method of Dynamic Homogenization(DH) as an alternative technique for three-dimensional core calculations which can lie between thetwo approaches, the classical and the direct one, in terms of precision and performance. The aim ofthe present work is to present preliminary analysis and tests of the DH technique for two-dimensionalconfigurations

The new 3-D multigroup diffusion neutron noise solver of APOLLO3 and a theoretical discussion of fission-modesnoise

International audienceTraditional neutron noise analysis addresses the description of time-dependent flux fluctuations induced by small global or local perturbations of the macroscopic cross-sections, which may occur in nuclear reactors due to stochastic density fluctuations of the coolant, to vibrations of fuel elements, control rods or any other structures in the core. Neutron noise equations are obtained by assuming small perturbations of macroscopic cross-sections around a steady-state neutron field and by subsequently taking the Fourier transform in the frequency domain. In this work, we present the new 3-D multigroup diffusion neutron noise solver implemented in APOLLO3, the new multi-purpose deterministic nuclear code under development in CEA. We illustrate the capacities of this new 3-D diffusion neutron noise solver by performing two neutron noise simulations in a large pressurized water reactor with heavy baffle in three dimensions a cross-sections oscillation and a traveling perturbation. Moreover, we give a separate analysis of the neutron noise anomaly recently observed in KWU PWRs while proving the existence of steady-state like global noise modes in the low frequency spectrum

Polynomial Characteristics Method for Neutron Transport in 3D extruded geometries

International audience- A polynomial expansion in the axial direction has been implemented in the Method Of Characteristics framework, for the solution of the mono-group, steady state neutron transport equation for 3D extruded geometries. This work has been realized in the context of the APOLLO3$^R$ project and, in particular, in the Two & three Dimensional Transport (TDT) module. In this paper we weigh up benefits and disadvantages of this approach, when comparing to the classical Step Characteristics (SC) approximation, already available in APOLLO3$^R$

Considering the up-scattering in resonance interference treatment in APOLLO3

TRIPOLI-4 $^R$ is a registered trademark of CEAInternational audienceThe use of the exact elastic scattering in resonance domain introduces the neutron up-scattering which must be taken into account in the deterministic transport code. The existing resonance interference treatment method in APOLLO3 is not able to take into account the resonance up-scattering phenomenon, since this method employs the asymptotic scattering kernel in the calculation of the infinite homogeneous medium reaction rates of mixture. It is known that the use of the asymptotic kernel instead of the realistic free-gas model has non-negligible impact on the calculated results. In order to consider both the resonance interference phenomenon and the resonant up-scattering, the resonance interference factor method was implemented in APOLLO3. The numerical results showed that this method gived good results in both k-eff values and reaction rates.An improved method was also proposed for the solution of the mixture heterogeneous equation by the fine-structure self-shielding method. Compared to the existing method, it requires less storage memory and less solution time, but it gives the same numerical results as those of the existing method

Application of the SPH method to account for the angular dependence of multigroup resonant cross sections in thermal reactor calculations

International audienceThe issue of the angular dependence of the multigroup total cross sections in the multigroup transport equation solution was recognized a long time ago. Only recently has its impacts on resonant self-shielding been identified. A viable solution for this problem is the superhomogenization (SPH) corrections. In the present work, two applications of the SPH method are presented, one applying to the APOLLO3 deterministic calculations with the multigroup cross sections condensed from the TRIPOLI-4 Monte Carlo simulation results and the other applying to a subgroup method based on the fine-structure equation. The numerical results show the effectiveness of the SPH method in dealing with this difficulty in both situations. This work also demonstrates that the subgroup method based on the fine-structure equation plus the SPH corrections is a practical, effective and accurate resonant self-shielding solution for the PWR fuel pin-cell and fuel assembly calculations

Analysis of Alpha Modes in Multigroup Diffusion

M&C 2017 - International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering,Jeju, Korea, April 16-20, 2017International audienceThe 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