This paper considers the physical processes in the structure of the material for a heat-emitting fuel element (FE) shell, caused by various damaging defects, on its outer and inner surfaces, and affecting the change in the geometric parameters of a nuclear reactor’s FE. The task to improve the model of damage to an FE shell is being solved, taking into consideration structural and phase changes in the material of the shell with damaging defects on the outer and inner surfaces, in order to establish the actual criterion for assessing the FE hermeticity degree. It is proposed to study the structure of the shell material with damaging defects (macropores and microcracks), which is a porous heterogeneous structure with fractal properties of self-similarity and scalability, to use the apparatus of fractal geometry. A physical model of the FE shell has been built and proposed, in the form of a geometric cylinder-shaped figure, which makes it possible to investigate the fractal properties of the structure of the material of the damaged shell and their influence on a change in the geometric parameters of FE An improved model of damage to the FE shell was derived, which makes it possible to take into consideration fractal increases in the geometric parameters of FE, for the established values of the fractal dimensionality. Experimental studies of the FE shell, using the skin effect, confirmed the theoretical results and showed the validity of the choice of practical use of the fractal dimensionality parameter as an effective criterion for assessing the hermeticity degree of an FE shell. It has been experimentally established that the value of the fractal dimensionality of 2.68 corresponds to the maximum degree of damage to the shell for a leaky FE.

Low carbon dioxide (CO₂) emissions make nuclear energy crucial in decarbonizing the economy. In this context, nuclear safety, and especially the operation of nuclear power plants, remains a critical issue. This article presents a new fractal cluster method of control that improves the quality of assessing fuel element cladding integrity, which is critical for nuclear and environmental safety. The proposed non-destructive testing method allows for detecting defects on the inner and outer cladding surfaces without removing the elements from the nuclear reactor, which ensures prompt response and prevention of radiation leakage. Studies have shown that the fractal dimension of the cladding surface, which varies from 2.1 to 2.5, indicates significant heterogeneity caused by mechanical damage or corrosion, which can affect its integrity. The density analysis of defect clusters allows quantifying their concentration per unit area, which is an important indicator for assessing the risks associated with the operation of nuclear facilities. The data obtained are used to assess the impact of defects on the vessel’s integrity and, in turn, on nuclear safety. The monitoring results are transmitted in real time to the operator’s automated workstation, allowing for timely decision making to prevent radioactive releases and improve environmental safety. The proposed method is a promising tool for ensuring reliable quality control of the fuel element cladding condition and improving nuclear and environmental safety. While the study is based on VVER-1000 reactor data, the flexibility of the proposed methodology suggests its potential applicability to other reactor types, opening avenues for broader implementation in diverse nuclear systems.

This study's object is the technological process that occurs at the power unit of a nuclear power plant, which is considered as a complex technical system with a multi-level hierarchical structure of functional subsystems. This paper addresses the task to improve the efficiency of modeling, monitoring, and controlling the technological process at a nuclear power plant as a complex technical system with a multi-level hierarchical structure. A new approach to modeling the modes of a nuclear power plant based on system-cluster theory has been proposed. A cluster structure with key subclusters has been built: power control, protection, heat carrier adjustment, and emergency shutdown. Mathematical models have been constructed that take into account physical processes and logical-dynamic behavior of the monitoring and control system. A feature of the devised approach is the use of the value of fractal dimensionality as a quantitative indicator of the self-similar scaled structure of functional subclusters. An algorithm for calculating fractal dimensionality has been proposed, which allows for real-time analysis of dynamic changes in the external and internal structure of the power unit process control. Threshold values of the fractal dimensionality of subclusters have been determined for comparison with current parameters under normal and emergency modes. It was established that the loss of one control level in a subcluster leads to a decrease in fractal dimensionality from 1.83 to 1.60, signaling a possible degradation of the SCADA level. A model of a digital twin of the power unit process has been built based on a system-cluster approach, which allows for the implementation of visualization, simulation, monitoring, and diagnostics functions