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Modeling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The basic model includes a multidimensional set of coupled parabolic equations and ordinary differential equations. Dynamic processes are modeled by a successive change of the reactor states, which a...
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... geometric model of the VVER-1000 core consists of a set of hexagonal- shaped cassettes and is shown in Fig.2, where fuel assemblies of various types are shown. ...
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... a more complex transition to a subcritical state. The subcriti- cal stage will be characterized by a different increase in the coefficient Σ 2 for material 4 in the diffusion constants in the upper and lower half of the reac- tor cross-section (see Fig.2). Now let the reactor dynamics corresponds to the following transformation ...
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The article considers an opportunity of increasing the neutron flux by means of two subcritical nuclear reactors. These nuclear reactors have variable reactivity, and generate neutrons in the form of a narrow bright beam. To ensure that the beam of the second reactor would not fall into the first one, this second reactor must be turned at some angl...
Modelling of dynamic processes in nuclear reactors is carried out, mainly, using the multigroup neutron diffusion approximation. The basic model includes a multidimensional set of coupled parabolic equations and ordinary differential equations. Dynamic processes are modelled by a successive change of the reactor states. It is considered that the tr...
Citations
... However, the physics-based modern numerical analysis or computer simulations that simulate physical systems using mathematical concepts and language essentially began with studying sources and rounding the errors by Von Neumann and Goldstine (1947). The study of numerical modeling has significantly progressed since then and opened new ways to investigate various problems that would be extremely difficult, if not impossible, to investigate experimentally (Avvakumov et al., 2018;Galati and Iuliano, 2018;Abedini and Zhang, 2021). However, most of these models require heavy computation to produce results with acceptable accuracy, for they simulate the physics behind the problems. ...
... However, the physics-based modern numerical analysis or computer simulations that simulate physical systems using mathematical concepts and language essentially began with studying sources and rounding the errors by Von Neumann and Goldstine (1947). The study of numerical modeling has significantly progressed since then and opened new ways to investigate various problems that would be extremely difficult, if not impossible, to investigate experimentally (Avvakumov et al., 2018;Galati and Iuliano, 2018;Abedini and Zhang, 2021). However, most of these models require heavy computation to produce results with acceptable accuracy, for they simulate the physics behind the problems. ...
Industry 4.0 targets the conversion of the traditional industries into intelligent ones through technological revolution. This revolution is only possible through innovation, optimization, interconnection, and rapid decision-making capability. Numerical models are believed to be the key components of Industry 4.0, facilitating quick decision-making through simulations instead of costly experiments. However, numerical investigation of precise, high-fidelity models for optimization or decision-making is usually time-consuming and computationally expensive. In such instances, data-driven surrogate models are excellent substitutes for fast computational analysis and the probabilistic prediction of the output parameter for new input parameters. The emergence of Internet of Things (IoT) and Machine Learning (ML) has made the concept of surrogate modeling even more viable. However, these surrogate models contain intrinsic uncertainties, originate from modeling defects, or both. These uncertainties, if not quantified and minimized, can produce a skewed result. Therefore, proper implementation of uncertainty quantification techniques is crucial during optimization, cost reduction, or safety enhancement processes analysis. This chapter begins with a brief overview of the concept of surrogate modeling, transfer learning, IoT and digital twins. After that, a detailed overview of uncertainties, uncertainty quantification frameworks, and specifics of uncertainty quantification methodologies for a surrogate model linked to a digital twin is presented. Finally, the use of uncertainty quantification approaches in the nuclear industry has been addressed.
... Also note a class of methods for modelling the non-stationary neutron diffusion, which is associated with the multiplicative representation of the space-time factorization methods and the quasistatic method [6,7]. The general strategy for the approximate solution of the non-stationary problems of neutron transport, which is oriented to fast calculations using the state change modal method was formulated in [8]. ...
... Then, we choose eigenvectors corresponding to dominant M i eigenvalues from (8) and use them to construct the multiscale basis functions. As partition of unity functions, we use linear functions in each domain ω i . ...
Modelling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The neutron diffusion approximation is widely used for reactor analysis and applied in most engineering calculation codes. In this paper, we attempt to employ a model reduction technique based on the multiscale method for neutron diffusion equation. The proposed method is based on the use of a generalized multiscale finite element method. The main idea is to create multiscale basis functions that can be used to effectively solve on a coarse grid. From calculation results, we obtain that multiscale basis functions can properly take into account the small-scale characteristics of the medium and provide accurate solutions. The results calculated with the GMsFEM are compared with the reference fine-grid calculation results.
The behaviour of the neutrons inside a nuclear reactor core can be modelled by using the time dependent neutron diffusion equation. Different time schemes have been used to integrate this equation. One possibility is to use a modal method, which is based on the expansion of the neutron flux in terms of spatial modes that are the eigenfunctions associated with a given configuration of the reactor core. Several spatial modes can be defined for the neutron diffusion equation such as the λ, α and γ-modes. In this work, the λ, the α and the γ-modes have been used to develop different modal kinetics equations, using a high order finite element method for the spatial discretization of the neutron diffusion equation. The performance of the different modal kinetic equations has been tested and compared using two 3D transient benchmark problems.
