Estimation of Dynamic Stiffness and Analysis of Error Source of Spacer Grid for Pressurized Water Reactor Fuel Assembly

Fuel assemblies are core components in pressurized water reactor (PWR), in which spacer grids serve as essential structural elements to support fuel rods, maintain fuel rod spacing, mix coolant, and resist external loads. The mechanical reliability of spacer grids is of great significance to ensure the integrity and safety of nuclear fuels, particularly under low-speed impact loads that may occur during transportation, handling, or accident scenarios. The dynamic stiffness of spacer grids is a key parameter that characterizes their ability to withstand dynamic forces and deformations, and a critical input for the safety analysis of fuel assemblies under accident conditions like seismic events or loss of coolant accident (LOCA). Currently, the estimation of dynamic stiffness for spacer grids primarily relies on dynamic stiffness testing, which involves measuring impact force, impact velocity, and the period of impact pulse. These measurements are used to derive the dynamic stiffness through various analytical methods. However, there is a lack of comprehensive discussions on the differences and error sources between different estimation methods. The gap in understanding has led to the absence of a standardized estimation procedure, which could potentially introduce uncertainties in the safety assessments of fuel assemblies. Addressing these uncertainties is crucial for improving the accuracy and reliability of dynamic stiffness estimations. In this paper, the dynamic stiffness testing of a specific type of spacer grid was conducted, aiming to obtain impact loads, impact velocity, and the period of impact pulse. Two primary approaches were employed to estimate the dynamic stiffness, i.e., the energy-based method (including both direct and iterative calculations) and the periodic-based methods. The energy-based method estimates the dynamic stiffness of a spacer grid relying on the principle of energy conservation, while the periodic-based method relies on the period of an impact pulse. The error sources associated with each estimation method were discussed, respectively. A more stable estimation could be obtained by the energy-based method based on the current vehicle-impact testing system, where the relative error by direct or iterative calculations is around 12% or 16%. Additionally, the error transfer characteristics were thoroughly examined, which describe how errors in measured parameters affecting the calculations of other parameters in the model. A profound amplification effect could be expected when the error of external dynamic stiffness (the dynamic stiffness of a spacer grid obtained by the current testing) being transferred to internal dynamic stiffness. But the error would regress to around 5% when it further transfers to the estimation of impact loads of a fuel assembly. By identifying and quantifying these errors, the paper provides valuable insights into the improvement of the accuracy of dynamic stiffness estimations. This could further support more reliable safety assessments of fuel assemblies under accident conditions.