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The study of the eigenvalues of the neutron transport operator yields an important insight into the physical features of the neutronic phenomena taking place in a nuclear reactor. Although the mult...

International audience; The knowledge of higher-order harmonics beyond the fundamental mode is important and useful in the prediction of the spatial behaviour of nuclear reactors. Previous works have evidenced that the information on higher-order modes is of great relevance in the interpretation, by means of perturbation techniques (Gandini, 1978), of flux tilts in large cores. In order to assess the performance of the methods that are available to evaluate such modes in nuclear systems, simple configurations that allow for an analytical solution are analysed, and the iteration processes of filtered power, of sub-space iteration and of implicitly restarted Arnoldi methods are compared and discussed. The drawbacks of the filtered power method are highlighted. The implicitly restarted Arnoldi and the sub-space iteration methods are then applied to two benchmarks, the C5G7 and the more realistic UAM configurations, in order to draw some practical indications on their performances. The analysis of the results for all the different configurations considered allow highlighting the better computational performance of the implicitly restarted Arnoldi method as compared to the sub-space iteration method. © 2019 Elsevier Ltd

The study of the steady-state solutions of neutron transport equation requires the introduction of appropriate eigenvalues: this can be done in various different ways by changing each of the operators in the transport equation; such modifications can be physically viewed as a variation of the corresponding macroscopic cross sections only, so making the different (generalized) eigenvalue problems non-equivalent. In this paper the eigenvalue problem associated to the time-dependent problem (α eigenvalue), also in the presence of delayed emissions is evaluated. The properties of associated spectra can give different insight into the physics of the problem.

In this work some characteristics of the eigenvalue problem for the neutron transport equations are considered. Various formulations are examined, discussing some theoretical and practical aspects. The standard multiplication eigenvalue that is particularly relevant for nuclear reactor physics applications is analysed, together with the time eigenvalue, including also the contribution of delayed neutrons. In addition, the less common collision and density eigenvalues are also discussed, highlighting interesting physical features. A semianalytical approach is developed allowing to evidence some interesting structures of the eigenvalue spectra. The study is carried out within the spherical harmonics approach. For the plane one dimensional geometry, the mathematical relationship between even and odd-order approximations for the homogeneous form of the equations for the eigenvalue formulation is investigated. It is shown that the even-order system of equations can be re-cast in the form of the contiguous lower odd-order one. Numerical results are obtained in the two-group energy model for various configurations for which a reference is available, providing also results for high-order approximations. The study includes a presentation and discussion of the spectra patterns for the various eigenvalue formulations.

The FRENETIC code is being developed at Politecnico di Torino in the frame of the international effort for the deployment of lead fast reactors technology. FRENETIC is a multiphysics computational tool solving the neutronics and thermal-hydraulics equation at the full-core level, aiming at performing steady-state and time-dependent simulations in different conditions. In the present work, the validation activity of FRENETIC is carried forward by performing a benchmark against a reference computational model for the ALFRED design implemented in Serpent. Different core configurations in FRENETIC and different temperature distributions are considered, performing consistent comparisons between the two codes. All the results obtained show an extremely good agreement between the two models, implying that the ALFRED core can be well characterized by the FRENETIC code. The present study sets the basis for the future application of the code to simulate safety-relevant transients with FRENETIC.

The Fast REactor NEutronics/Thermal-hydraulICs (FRENETIC) code has been developed during the last years at Politecnico di Torino, implementing a full-core coupled neutronic/thermal-hydraulics model for steady-state and transient analysis of liquid-metal cooled fast breeder reactor (LMFBR). In the framework of the validation activities for the code, an analysis of the sodium-cooled reactor EBR-II, previously carried out in the frame of a IAEA Coordinated Research Project, is performed with FRENETIC including the most recent physics models. In particular, photon transport and heat deposition are taken into account, a feature which has been proved in previous studies to be relevant to the correct study of the EBR-II core. To this purpose, a set of nuclear data for photons has been generated by means of the Monte Carlo code Serpent-2, and it is demonstrated that the code is able to take into account the photon heat deposition in the EBR-II.

The paper shows the application of the most recent sensitivity techniques implemented in Serpent-2 in order to propagate the uncertainty from the nuclear data to the macroscopic, homogenised cross sections of the ALFRED reactor, which is then simulated with the multi-physics code FRENETIC. The main results are encouraging and define a possible methodology to propagate the nuclear data uncertainties to the main macroscopic parameters computed with FRENETIC, in order to perform thorough safety analyses for the ALFRED reactor.

The paper studies the effect of the distribution of the fissile material in a nuclear system on its multiplication properties. Some general results and specific examples on the dependence of the value of the effective multiplication constant on the fuel distribution are presented. The approach to the problem is established on a rather general mathematical ground, referring to a variational approach which leaves room to add constraints, when needed. Examples in one-and two-group diffusion are illustrated. It is well known that the effective multiplication factor of a homogeneous system can be increased by the addition of a reflector but it is not obvious that it is possible to obtain an effective multiplication factor larger than the value of the infinite medium multiplication factor of the material constituting the core region. This can never happen in a one group model, as can be easily demonstrated, for instance, in diffusion theory. However, when taking into account spectral effects related to slowing down phenomena, it is shown in this work that such a situation can be realized by a proper choice of the reflector material. Some analyses are carried out in the frame of two-group diffusion theory and comparisons are performed with Monte Carlo evaluations.