An Investigation of the Stiffness Characteristics of a PWR Nuclear Fuel Spacer Grid by a 3D Shell Model

Abstract

The structural integrity of fuel assemblies hinges significantly on the effectiveness of spacer grids. In this paper, we introduce a novel approach to assess the structural robustness of the mid-spacer grid (SG) of the PLUS7 fuel assembly (FA) using 3D shell elements. Any excessive external load from seismic activity can be broken down into two perpendicular components, namely normal load and shear load. The decomposition enables easy assessment of the structural integrity of the fuel spacer grid for any external loads. From the analysis, the reaction force of normal input displacement is around 440 times greater than that for shear input displacement for the same amount of displacement. This result highlights how vulnerable the spacer grid is to shear load and this should be considered in studies of fuel assembly integrity assessment. This study also highlights the need for improved and more robust spacer grids for safer operation of NPPs.

1. Introduction

A nuclear fuel assembly consists of a fuel rod, a lower end-fitting, an upper end-fitting, spacer grids, and guide tubes. Figure 1 shows the fuel assembly and components of the APR1400 reactor. There are 12 spacer grids that are used to support and protect the fuel rod. These spacer grids are uniformly positioned along the vertical axis and securely welded to guide tubes, thus constituting integral structural elements within the fuel assembly, alongside the lower and upper end-fittings. Individual fuel rods are merely attached to or grabbed by spacer grids. Due to the long and slender shape of the fuel assembly, a horizontal motion due to seismic load or other form of dynamic load can result in interaction between neighboring fuel assemblies. The structural strength of the spacer grid becomes important for such instances.

Subhan and Namgung [1] presented a natural analysis of a single fuel assembly. As shown in Figure 1, a 3D model of the fuel assembly is almost impossible to use for modal analysis because of the large size of the model; hence, there was no analysis. Hence, they developed a simplified model of the fuel assembly by a model reduction technique based on lumped mass, beam, and shell elements. The spacer grid and guide tubes were modeled by a beam and the upper and lower end-fittings were modeled by the shell elements, while the fuel rods were modeled by lumped mass since fuel rods are not a structural element of the fuel assembly. With this simplified model, they were able to perform a modal analysis. Some of the important analysis results are shown in Figure 2 for the first three modes of natural vibration. The analysis revealed not only the expected bending mode, or beam mode, of vibration but also uncovered a torsional mode of vibration. Consequently, the dynamic motion of fuel assemblies (FAs) within the core is a blend of various vibration modes, exhibiting a complex interplay of motions. Notably, the torsional vibration mode within the reactor core prompts interactions among fuel assemblies, inducing shear deformation in both the fuel assemblies and spacer grids.

If heavy seismic activity acts on the reactor system, the core will shake and fuel assemblies will vibrate as a result. This motion will not be in unison and each fuel assembly will vibrate in a different direction. This phenomenon was discussed by analyzing the structural integrity of a fuel assembly [1]. In this study, the authors presented that fuel assemblies can come into contact with and impact each other due to torsional motion. The fuel assembly was modeled by lumped mass and beam elements in order to reduce model size and analysis complexity. They showed that the dynamic response of the fuel assembly contained a beam mode of vibration and a torsional mode of response.

Another significant source of fuel assembly deformation is the deformation of reactor internals. Jung and Namgung [2] conducted a natural vibration analysis of reactor internals, focusing on the core shroud, which forms the reactor core, houses fuel assemblies, and provides protection for them. Their study analyzed the shell model of the core shroud, showing that the vibration pattern in mode-1 aligns with the normal deformation of the fuel assembly. Furthermore, in mode-2 and mode-3, the vibration patterns demonstrated the potential to induce diagonal deformation in the fuel assembly, highlighting the necessity of studying shear deformation. These results indicated that the dynamic behavior of fuel assemblies in the core will not behavior in unison and they will interact each other in random manner over time and can damage fuel assemblies. If fuel assemblies collide with each other, it is likely to happen at spacer grids since they are the structural component of the fuel assembly and encase the fuel rods. This is the topic this study deals with, and understanding the structural behavior of the spacer grid is the first step toward understanding the more complicated phenomena of fuel collision and interaction.

The design of the fuel assembly must adhere to Level D service limits, which are crucial for maintaining the pressure boundary’s integrity during a loss-of-coolant accident (LOCA), as specified in ASME Boiler and Pressure Vessel Code, Section III, Non-mandatory Appendix F [3]. The load transmitted by a spacer grid to a fuel rod should not exceed loads for a LOCA event. Hence, the spacer grid should protect the fuel rod under design condition load, normal operation load, and LOCA for acceptance of the fuel assembly in the evaluation process.

Below is a review of some of the research related to the structural integrity of spacer grids. Namgung [4] presented an FEM analysis of a spacer grid with a fuel rod [1,4,5]. In their study, to overcome the complexity of a full spacer grid FEM model, they reduced the problem to a typical unit of a spacer grid and a fuel rod. This model facilitated the assessment of thermal gradients across the fuel pellet, fuel rod, and fill gas. The single unit cell model of the spacer grid was used to calculate thermal and mechanical stress for normal and shear displacement. From the analysis, they obtained the stiffness of the spacer grid in normal and shear direction displacement and discovered that shear stiffness is around 2500 times lower than normal stiffness. This study was about a single cell of a spacer grid; it is necessary to extend to a full spacer grid model in a structural analysis. Adli [5] extended these results to a full spacer grid, and they obtained a stiffness ratio result of 260, which is much lower than previously calculated.

Song et al. [6] investigated and published a spacer grid structural and mechanical performance experiment. From the research, they concluded that laser welding techniques will produce greater stiffness than spot welding of spacer grid plates. They conducted a comparative analysis between Finite Element Analysis (FEA) and experimental assessment to determine the compression strength of the spacer grid under different welding processes. Their findings illustrated the superior performance of laser welding techniques over conventional methods. In their experiment and analysis, the loading on the spacer was aligned in the normal direction, and did not cover shear direction loadings.

Areva [7] studied the dynamic response of a PWR fuel assembly to external excitations. In this study, a mathematical model was formulated to represent the fuel assembly using lumped mass and beam elements, which were divided into vertical and horizontal models. As a result, it was not a true 3D model, and was merely a mathematical model for horizontal and vertical excitation.

An impact test of a spacer grid of 5 × 5 cells was performed by Koo and Yoon [8]. For the identical 5 × 5 spacer grid cell, they conducted an impact analysis of the grid structure under lateral impact loads, employing multipoint constraint (MPC) equations. Additionally, they devised a Finite Element Method (FEM) model designed to replicate real-world behavior by utilizing equivalent stiffness values for the grid model. They introduced an analytical model capable of accurately predicting the dynamic buckling load of the spacer grid.

Schettino et al. [9] created compression strength test apparatus of a spacer grid, performed compression of a 3D model of a 16 × 16 spacer grid under normal loading, and obtained the structural behavior of fuel assemblies, thereby extracting insights into the structural behavior of fuel assemblies.

It is noted that not many studies have been performed to investigate the structural behavior of spacer grids in fuel assemblies. It is imperative to assess the strength of spacer grids under diverse operating conditions to prevent significant deformation and damage to the nuclear fuel rods. A damaged fuel rod will release radioactive materials to the coolant; it is important to understand the deformation pattern of spacer grids for all loading conditions for the safety of the fuel rods. Since spacer grids are very complicated in geometry, we need to simplify the analysis model and analysis methodology. If we decompose loading into two components, i.e., one is in the normal direction and the other is in the shear direction, then we can combine the two cases to represent the loading cases.

The purpose of this study is to evaluate the structural integrity of spacer grids under diverse loading conditions to ensure the safety of nuclear fuel assemblies, as required by regulatory standards such as the ASME Boiler and Pressure Vessel Code, Section III [3]. While previous studies have primarily focused on normal loading conditions, research on shear and combined loading conditions is limited, posing risks to fuel rod integrity during extreme events. To address this gap, we developed a simplified 3D shell model of the spacer grid, enabling efficient analysis of normal and shear loads across three operational temperatures (21 °C, 290 °C, and 325 °C). This approach not only provides a comprehensive understanding of spacer grid behavior but also serves as a foundation for improving spacer grid design and enhancing structural safety.

2. Model Development

A detailed 3D model of the mid-spacer grid of the PLUS7 nuclear fuel assembly for the APR1400 reactor is presented in Figure 3. The mid-spacer grid model of PLUS7 nuclear fuel assembly was chosen for this study, specifically designed for the APR1400 and OPR1000 reactors. This design represents an enhancement aimed at improving fuel efficiency and overall performance [10]. As explained above, there are five large holes for guide tube installation. From Figure 1, there are nine mid-spacer grids used in a single fuel assembly. Constructing a Finite Element Analysis (FEA) model using a full spacer grid design entails a significant number of elements and nodes, demanding substantial computational resources and time to solve the system equations. A typical coarse mesh will produce an FEA model that can exceed 1 million nodes and half a million elements.

The complete spacer grid includes mixing vanes, among other elements, in its design, which serve no role in its structural strength. To streamline the model, we can eliminate extraneous features unrelated to structural strength. Additionally, exploiting geometric and load symmetry can further simplify the reduced model.

2.1. Development of FEA Model

To streamline the model and reduce computational complexity—i.e., reducing the number of nodes and elements compared to the original geometry—the design of the spacer grid was reduced or made less complex. The complex curved structures of the springs and dimples in the spacer grid were simplified to straight structures, reducing the mesh size and the time required for element analysis. This does not directly affect the study of the stiffness characteristics of the spacer grid in this research. After simplifying complex corners and eliminating unnecessary features, such as mixing vanes, the simulation difference between the original spacer grid and the simplified one was only 0.02%. Figure 4 depicts the simplified model under symmetry conditions.

For this research, we used CATIA V5 6R2021 and SpaceClaim R2024, 3D CAD software, to create a surface model of the mid-spacer grid of a PLUS7 fuel assembly. This surface model was used to develop an FEM model in which a shell element is utilized as the base element. The meshed models were subsequently employed to conduct static structural analysis using ANSYS Mechanical. The simplified and meshed models were employed to evaluate the structural response under both normal and shear displacement input across core inlet, core outlet, and room temperatures. The modeling and analysis flow is depicted in Figure 5.

2.2. Meshing

The default shell model was meshed using default settings, producing a default element size of 0.76194 mm, comprising 259,893 nodes and 231,138 elements. Figure 6 illustrates the resulting mesh.

2.3. Boundary Conditions

Figure 7 displays the assigned boundary conditions. The outer wall surfaces facing the +X direction of each model were set to a fixed boundary condition, as indicated by the green arrows in the figure. On the surfaces facing the −X direction, displacement loads were applied. Normal displacement input ranging from 0.2 mm to 10 mm was applied in the positive X direction. Conversely, shear input displacement ranging from 0.5 mm to 20 mm was applied on the same surface, but towards the positive Y direction.

2.4. Zircaloy Material Data

The mid-spacer grid of the PLUS7 fuel assembly is constructed using a zirconium alloy. To ensure accurate results in structural analysis, the material properties of Zr-4 were gathered and put into a database. We utilized MATPRO data, which are widely recognized and well-known primary sources for addressing nuclear material properties Siefken [9]. Below are the equations and parameters applicable for temperatures below 816.85 $°\mathrm{C}$.

Density:

$$\rho =6.55\times {10}^3 \mathrm{k}\mathrm{g} {\mathrm{m}}^{-3}$$

(1)

Thermal expansion:

$$\epsilon =4.95\times {10}^{-6}(T+273.15)-1.485\times {10}^{-3}$$

(2)

Young’s modulus:

$$E={\displaystyle \raisebox{1ex}{$\left(1.088\times {10}^{11}-5.475\times {10}^7·(T+273.15)+K_1+K_2\right)$}\!\left/ \!\raisebox{-1ex}{$K_3$}\right.}\mathrm{P}\mathrm{a}$$

(3)

Shear modulus:

$$G={\displaystyle \raisebox{1ex}{$\left(4.04\times {10}^4-2.168\times {10}^7·(T+273.15)+K_1+K_2\right)$}\!\left/ \!\raisebox{-1ex}{$K_3$}\right.}\mathrm{P}\mathrm{a}$$

(4)

where

$$T=temperature, °C$$

$$K_1=\left(6.61\times {10}^{11}+5.912\times {10}^8·(T+273.15)\right)∆$$

$$∆=oxygen content\left({\displaystyle \frac{\mathrm{k}\mathrm{g} oxygen}{\mathrm{k}\mathrm{g} Zircaloy}}\right)$$

$$K_2=-2.6\times {10}^{10}·CW$$

$$CW=cold work,unitless ratio of area$$

$$K_3=0.88+0.12e^{\left({\displaystyle \raisebox{1ex}{$-\Phi $}\!\left/ \!\raisebox{-1ex}{${10}^{25}$}\right.}\right)}$$

$$\Phi =fast neutron fluence\left({\displaystyle \raisebox{1ex}{$\mathrm{n}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^{-2}$}\right.}\right)$$

Zircaloy, like all materials, exhibits varying behavior with changes in temperature. To cover the shut-down condition and normal operation condition, three different temperature conditions were used for the analysis: core inlet temperature (290 °C), core outlet temperature (325 °C), and room temperature (21 °C).

Oh [11] presented data for the thermal expansion coefficient of zirconium, while IAEA-TECDOC-949 [12] offers comprehensive material properties used in water-cooled reactors. In determining elastic constant and shear modulus, we took into account factors such as the fast neutron influence, oxygen content, and cold work constant based on the formulas given by Siefken [9] and Geelhood [13].

$$∆=352 \mathrm{p}\mathrm{p}\mathrm{m}$$

$$CW=4.17\times {10}^{-5}$$

$$\Phi =11.4\times {10}^{26} {\displaystyle \raisebox{1ex}{$\mathrm{n}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^2$}\right.}$$

Using these parameters, the shear and elastic moduli along with Poisson’s ratio were calculated. The results are outlined in

Table 1. Zircaloy-4’s mechanical properties.

Temp. (°C)	Young’s Modulus (GPa)	Shear Modulus (GPa)	Poisson’s Ratio
21	105.678	38.999	0.355
290	89.005	32.436	0.372
325	86.836	31.577	0.375

.

3. Analysis Results and Discussions

Korea Nuclear Fuel Co. (KNF) invested in improving the performance of nuclear fuel specifically in spacer grids and developed a mixing vane for spacer grids. Their investigations ranged from ensuring mechanical integrity to refining core neutronics and thermal hydraulics.

Building upon this foundation, our study advances the field by undertaking a comprehensive examination of structural integrity. We employ sophisticated shell models subjected to normal and shear loads across different temperature conditions, encompassing room temperature, core inlet, and core outlet scenarios. Through this investigation, we aim to provide a comprehensive understanding of generalized structural integrity assessment of the spacer grid, contributing to the robustness and safety of nuclear fuel systems.

Figure 8 illustrates the result of deformation of the 3D shell model following displacement loads under normal loading conditions, while Figure 9 depicts the corresponding patterns under shear loading conditions. Additionally, the force reactions elicited by normal and shear displacement loads across all temperature scenarios are detailed in Figure 10 and Figure 11, respectively. At 21 °C, the reaction force induced by normal loading is approximately 442 times greater than that induced by shear loading. At 325 °C, this difference is around 438 times, demonstrating the relative weakness of shear loading. While the difference slightly decreases as the temperature rises, it remains significantly large. This indicates that the primary influence of normal loading on the structural strength of the spacer grid is maintained even as the temperature increases. These results suggest that the influence of normal loading should be considered the most critical factor in the design and evaluation of spacer grids.

Furthermore, our buckling analyses have yielded insightful results, revealing six distinct buckling loads corresponding to six calculated modes. These findings are visually represented in Figure 12, with further elaboration provided in

Table 2. Buckling load of the spacer grid shell model for shut-down and normal operating conditions.

Mode	Force (N)
	21 °C	290 °C	325 °C
1	14,538	12,363	12,083
2	14,595	12,412	12,131
3	15,186	12,914	12,621
4	15,305	13,015	12,719
5	18,314	15,566	15,212
6	18,507	15,733	15,375

, highlighting the specific buckling loads identified. Mode 1, representing fundamental axial buckling, showed a clear decrease in structural strength with rising temperature. The shell model consistently demonstrated a reduction in buckling load as temperature increased, with a decrease of approximately 15–20% between 21 °C and 325 °C. This reflects the degradation of Zircaloy-4’s material properties under high-temperature conditions. Higher modes (Modes 2–6) exhibited increasingly complex deformation patterns, including diagonal and torsional components. This trend emphasizes the importance of considering material property degradation in design evaluations.

4. Conclusions

The structural integrity of nuclear fuel assemblies is paramount to ensure reliability under various operational conditions. This study delves into assessing the structural strength of a nuclear fuel spacer grid against both normal and shear loads. By breaking down external loads into a canonical form, we can thoroughly evaluate spacer grid integrity, especially under scenarios such as seismic events where loads are unpredictably directed towards nuclear reactor components.

Utilizing a simplified and reduced 3D shell model of the spacer grid, we conducted comprehensive analyses to obtain load–deflection results. These analyses included room temperature and core inlet and outlet temperature conditions. Our study revealed a significant discrepancy in the structural response of the spacer grid. As shown in Figure 10 and Figure 11, the spacer grid demonstrates strong resistance to normal loads but weak resistance to shear loads, with a difference of approximately 440 times. This confirms the heightened vulnerability of the spacer grid to deformation in the shear direction. The reason for this deformation lies in the structural characteristic of the spacer grid, where intersecting plates are welded together, resulting in varying degrees of deformation depending on the direction of the applied load.

These findings suggest that the impact of shear loads must be considered in the design and evaluation of spacer grids. In particular, off-normal loading conditions, such as those caused by seismic or dynamic forces, can significantly affect the overall stability of the system. Therefore, this study underscores the critical importance of structural evaluation under shear loads and highlights the need to include assessments for both normal and shear directions when testing fuel assemblies.

This study aimed to investigate the structural behavior of spacer grids, and it was conducted without including fuel cladding and pellets. Through this simplified model, it was confirmed that spacer grids are more prone to deformation in the shear direction. In future research, cladding and pellets will be incorporated into the model to analyze their influence on deformation and reaction forces. This will enable us to evaluate the differences compared to the current findings and make more precise predictions of the structural integrity of the fuel assembly, strengthening the robustness of future designs.

This study provides critical insights into the structural behavior of spacer grids under dynamic conditions and highlights the necessity of improved design strategies to mitigate shear deformation. For instance, future designs could optimize welding points or modify material properties to enhance shear strength.

Additionally, the findings of this study serve as an important foundation for developing advanced guidelines for the safety assessment of nuclear fuel systems, particularly under seismic or dynamic loading scenarios. Addressing these vulnerabilities will ensure the long-term stability and reliability of reactor operations.