Finite element formulations of the semi-analytical time-domain model for flow-induced vibration of tube bundles in steam generators

This paper describes the finite element method (FEM) formulations for flow-induced vibration of steam generator tube bundles, based on a semi-analytical time domain (SATD) model proposed by us recently (Sun et al., Appl. Math. Modell. 132, 2024, 252-273). The SATD model is featured by explicit fluid force expressions in terms of multiple integrals with time delays. The new SATD model allows for a unified treatment of both time domain and frequency domain fluidelastic instability (FEI) analysis of a tube due subjected to crossflow. Specifically, this study adds to the body of knowledge through two contributions: (1) This paper presents the details of FEM formulations on this newly formulated SATD theory, in particular the discretization of fluid forces in both lift and drag directions, which are crucial for FEM implementation but missing in the literature; (2) This study presents the formulations based on FEM discretization for frequency domain FEI analysis of tubes, and provides very the first reference on FEI stability analysis of U-tubes. Our FEM results agree well with reported experimental data and numerical results. The numerical examples presented here, including single-span straight tubes subjected to uniform flow and multi-span U-tubes subjected to nonuniform flow , not only demonstrate the merit of the theory for academic research, but also exhibit the potential of the FEM code for realistic engineering applications . Our efforts provide useful and powerful numerical tools for flow-induced vibration analysis of tube bundles in steam generators and other heat exchangers . • The FEM formulations for time/frequency domain analysis of flexible tubes are given. • Time- and frequency-domain analysis of straight tubes and U-tubes are validated. • The nonlinear impact analysis of U-tubes is conducted using finite element method.