1,721,032 research outputs found
A re-visitation of space asymptotic theory in neutron transport
No full textThe space asymptotic theory has constituted a powerful tool for the determination of neutron energy spectra in nuclear reactors, which are the basis of the generation of group constants for the neutronic core design. The method can provide a deep physical insight into the basics of reactor physics and may still give new ideas for modern computational methods. This contribution presents a re-visitation of the method, illustrating its most important general results, some of which may not be well known. In particular, the criticality theory and the space–energy separability theorem are presented. The validity of such theorem is extended also to the net neutron current. The procedure allows to generalize the Fick’s law with a consistent definition of the energy-dependent diffusion coefficient. Some numerical examples are given in simple multigroup models to illustrate the relevant features of the theory
Generalized perturbation techniques for uncertainty quantification in lead-cooled fast reactors
Full text linkThe design of innovative nuclear fission systems requires a careful evaluation of the uncertainties affecting the basic input data. Among them, nuclear data are particularly relevant, due to their dramatic energy dependence. Because of this feature and of the strong spatial heterogeneity of nuclear reactors arrangement, full-core calculations are carried out using energy collapsed and spatially homogenised constants. Nowadays, collapsing is often performed with Monte Carlo codes, which allow a discretisation-free treatment of the neutron transport equation. The most popular method to propagate the uncertainty in the nuclear data libraries throughout the Monte Carlo transport calculation is the Generalised Perturbation Theory (GPT). However, due to its multi-group nature, GPT often blurs the continuous-energy feature of the Monte Carlo method. Therefore, in order to fully exploit its advantages, the XGPT method has been recently proposed. After discussing the main differences between these two approaches, the paper presents the application to an uncertainty quantification study on the lead-cooled fast reactor ALFRED design, performed with GPT and focused on the multi-group cross sections. Afterwards, the two nuclides that most contribute to the overall uncertainties, i.e. Pu-239 and U-238, are considered to compare the GPT results to some XGPT calculations carried out with different multi-group energy structures. This analysis suggests that XGPT is a consistent method for uncertainty quantification in the continuous-energy Monte Carlo framework. Moreover, it can be concluded that an adequate number of low-energy groups is necessary for an accurate uncertainty evaluation in the case of a fast system
A non-intrusive reduced order model for light water reactor core stability analysis
Full text linkA non-intrusive reduced order model for studying the nuclear reactor core stability in presence of localised perturbations due to operational uncertainties is analysed. Following the standard neutronics calculation chain, a two-step model based on a combination of POD and RBF approaches is proposed in order to reduce the computational time of both the cell calculation, devoted to produce homogenised data for the full-core diffusion calculation, and the diffusion calculation itself. The results presented suggest that, while the cell model seems adequate to reproduce untrained operating conditions, the diffusion model still needs to be properly tuned, improving the training set quality
Early warning in Molten Salt Fast Reactors based on a data-driven method for the online incident detection and diagnosis
Full text linkThis paper presents an innovative online incident detection and classification method, which aims at improving the safety, reliability and availability of Molten Salt Fast Reactor (MSFR) power plant, focusing on scenarios characterized by deviations from normal operational conditions. The first part of the paper is devoted to describing and discussing the proposed online data-driven incident detection and classification methodology (based on adaptive Singular Value Decomposition-SVD and kNN algorithm), which aims at identifying abnormal plant conditions thanks to a continuous monitoring of some measurable parameters and variables (e.g., the molten salt temperatures in the secondary circuit). The developed incident detection algorithm is trained on a set of simulated scenarios featured by deviations of the main MSFR plant parameters from their nominal values. The data-driven model is then assessed considering increasingly complex incident classification rules and tasks, showing satisfactory performances in detecting and classifying plant anomalies (with an accuracy ranging between 89 % and 99 %). Finally, a fault diagnosis framework is proposed to carry out probabilistic inference on the most likely root causes (or precursors) - e.g., combinations of physical parameter values and component failures - that lead the system to the detected abnormal states
Development of a new Thermal-Hydraulic Module for FRENETIC, a Code for the Multiphysics Analysis of Liquid Metal-Cooled Reactors
No full textThe present paper describes the development of a new thermal-hydraulic (TH) module for FRENETIC, a multi-physics
code for the full-core simulation of liquid metal-cooled fast reactors, developed at Politecnico di Torino. The code
performs steady state and transient neutronic (NE) and TH coupled calculations, while maintaining a relatively low
computational cost thanks to the adoption of simplified physical models. The NE module implements the nodal formulation
of the multigroup neutron diffusion equations with delayed neutron precursors, whereas the TH module treats
the reactor hexagonal assemblies as separate channels, which are individually modelled as 1D in the axial direction,
accounting for the thermal coupling in the horizontal direction. The new TH module is more robust and portable while
providing improved performance with respect to the previous implementation, also thanks to the adopted OpenMP
parallelization. Some physics aspects that were previously neglected, such as the thermal inertia of non-fuel rods,
have also been included. The development was carried out in accordance with current best practices for code design,
implementation and testing, thus rendering the code easier to be maintained and possibly extended in the future. The
code usability has also been improved by means of a set of Python classes purposely developed to simplify the input
generation and post-processing phases. This can potentially widen the usage of FRENETIC within the fast reactor
community for the simulation of full-core coupled NE-TH transients and/or as a platform to test new solution methods.
The paper also includes the application of this new FRENETIC version to a representative configuration of the
Advanced Lead-cooled Fast Reactor European Demonstrator (ALFRED) reactor core
Verification and validation of the modular ray tracing MOC using the coupled forward-adjoint approach and application to C5G7 benchmark
No full textNeutron transport adjoint calculations are useful in many reactor physics applications. Among various applications, the adjoint flux can be used in perturbation theory to prevent large calculations and computational costs when estimating a small reactivity insertion into the system. Furthermore, they can serve as validation tests for numerical schemes, since both direct and adjoint calculations for a given system should lead to the same eigenvalue, although using two different physicomathematical formulations of the transport model. The synchronized implementation of the method of characteristic (MOC) for neutron transport in forward and adjoint approaches is accomplished in this work. The result is validated using the C5G7 benchmark with comparisons of the multiplication factor and pin power values. Differences between forward and adjoint multiplication factors in the results are achieved in the order of 1.0E-6. Meanwhile, the difference between the multiplication factor and the C5G7 benchmark is in order of 1.0E-5, using an S16 level symmetric angular discretization and a track spacing of 0.01 cm
On the boundary conditions for the neutron transport equation
No full textThe solution of the linear transport equation used for the study of neutral particle fields requires the imposition of appropriate boundary conditions. The choice of the conditions to impose for an infinite medium is not straightforward. The question has been given different formulations in the literature with various justifications based on some physical reasoning. Some aspects of the question are here analysed, from both the mathematical and the physical point of view. It is concluded that the inspiring golden rule should be the establishment of conditions that do not require any reference to the properties of the specific medium being considered for their justification
Neutron kinetics equations in Apollo3® code for application to noise problems
No full textA 2-D noise model is implemented in the deterministic reactor code APOLLO3®R 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 period is constructed 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 dynamic eigenvalue is defined that takes into account the system average 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
On some features of the eigenvalue problem for the PN approximation of the neutron transport equation
Full text linkIn 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
A Data-driven Incident Detection Method for the Safe Operation of Molten Salt Fast Reactors
Full text linkThis paper presents an innovative incident detection method aiming at improving the safety and reliability of the Molten Salt Fast Reactor power plant, focusing on operational scenarios involving some deviations from normal operational conditions. The first part of the paper is devoted to presenting and discussing a data-driven incident detection and classification methodology (based on the kNN algorithm), which aims at identifying abnormal plant conditions thanks to a continuous monitoring of some measurable system parameters and variables (e.g., the molten salt temperatures in the secondary circuit). Then, the incident detection algorithm proposed is trained with a set of
simulated scenarios featured by deviations of the main plant parameters from their nominal values.
The data-driven model is then assessed considering increasingly complex incident classification rules, showing good performances of the model in detecting plant anomalies (with a classification accuracy ranging between 89% and 99%). Finally, for a certain abnormal state of the system, a fault detection method is sketched to estimate the probability that certain combinations of physical parameters could lead the system in that abnormal state
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