ETD

• ANSYS
• finite element method
• fuel assembly
• modal analysis
• seismic analysis
• structural dynamics

This thesis presents a preliminary numerical study focused on the development and implementation of a finite element model of a generic VVER-1000 nuclear reactor fuel assembly, with the objective of performing a modal analysis aimed at determining its natural frequencies and corresponding mode shapes. The work is framed within the field of structural dynamics and is specifically oriented toward the preliminary characterization of the dynamic properties required for the study of dynamic transients, for example seismic events, affecting nuclear reactor core components. Given the safety relevance of fuel assemblies, the identification of their modal characteristics represents an essential preliminary step for subsequent dynamic analyses. All numerical simulations and analyses presented in this work are carried out using the commercial finite element software ANSYS.
The fuel assembly is a slender and highly flexible structure composed of multiple fuel rods mechanically constrained by spacer grids distributed along the axial direction. The global dynamic behavior of the assembly is strongly influenced by the mechanical action of the spacer grids, which provide lateral support to the fuel rods and contribute significantly to the overall stiffness of the system. A detailed geometric and contact-based representation of the spacer grid–fuel rod interaction would require a complex nonlinear modeling approach and would result in a high computational cost. For this reason, the present work adopts a simplified modeling strategy suitable for preliminary analyses and sensitivity studies.
Within the proposed approach, the spacer grid cell is represented by an equivalent simplified model, while the restraining effect exerted by the spacer grid on the fuel rods is introduced in the global fuel assembly model through elastic connections. These connections are intended to reproduce, in first approximation, the lateral stiffness contribution of the spacer grid bulges without explicitly modeling contact interactions. The stiffness values associated with these elastic connections are not assumed arbitrarily but are derived from a dedicated finite element submodel.
The submodel is exclusively focused on the structural analysis of a single spacer grid cell. In this context, the cell geometry is modeled in detail and its mechanical response is analyzed in order to evaluate its equivalent stiffness characteristics. The purpose of this submodel is to characterize the intrinsic stiffness behavior of the spacer grid cell bulges, which is subsequently used to define the properties of the elastic connections implemented in the global fuel assembly model. No explicit modeling of the fuel rod or of contact interactions between the fuel rod and the spacer grid is included at this stage, in accordance with the preliminary and methodological nature of the study.
A first validation of the adopted modeling strategy is carried out on a simplified configuration consisting of a single fuel rod segment constrained by one equivalent spacer grid cell. In this configuration, the spacer grid cell geometry is simplified by removing the bulges, whose mechanical effect is instead represented through equivalent elastic connections. The elastic connection between the spacer grid cell and the fuel rod is modeled by means of a set of three spring elements, circumferentially distributed around the rod and angularly spaced by 120 degrees. The spring elements are connected at the central points of each face of the equivalent spacer grid cell. Each spring element is assigned an elastic constant equal to the stiffness value previously derived from the spacer grid cell submodel. Modal analyses are performed on this reduced model to extract natural frequencies and mode shapes. The results are compared with those obtained by modeling the same fuel rod segment using idealized boundary conditions, defined to reproduce in a simplified manner the restraining action of the spacer grids. This comparison allows the influence of the elastic connection representation on the modal response to be assessed and provides an initial validation of the equivalence-based modeling approach.
Following this preliminary investigation, a further comparative study is conducted to analyze the influence of the finite element formulation adopted for the elastic connections. In particular, spring-type elements are replaced by beam-type elements characterized by equivalent stiffness properties. The equivalence between the two representations is established by matching the stiffness contribution derived from the spacer grid cell submodel. Modal analyses performed using both spring and beam connections are compared in terms of natural frequencies and mode shapes, allowing the sensitivity of the results to the chosen connection modeling strategy to be evaluated.
Once the modeling approach is assessed at the level of a single fuel rod segment, the analysis is extended to the complete fuel assembly. A three-dimensional finite element model of the entire assembly is developed in ANSYS, including all fuel rods and spacer grids, with the latter represented through equivalent elastic connections. The modal analysis of the full assembly allows the identification of global vibration modes and the evaluation of the overall dynamic behavior of the structure, which are of primary interest for preliminary dynamic investigations.
The influence of thermal conditions on the modal characteristics of the fuel assembly is also investigated. Modal analyses are performed considering two different temperature sets, namely room temperature and a uniform reference temperature intended to approximate the fuel assembly temperature under operating conditions, given that a detailed temperature field is not considered in the present work. The effect of temperature-dependent material properties and the resulting variations in structural stiffness on the natural frequencies and mode shapes is analyzed within the adopted modeling framework.
Finally, the results obtained under the different modeling assumptions are systematically compared. The influence of the elastic connection representation, the finite element type adopted and the thermal conditions on the modal properties of the fuel assembly is discussed. The outcomes of this preliminary study provide a quantitative assessment of the sensitivity of the dynamic response to the adopted modeling choices and contribute to the definition of a consistent and computationally efficient finite element modeling strategy for future, more comprehensive dynamic analyses of nuclear fuel assemblies.