Reduced-order modeling of nonlinear flow-induced vibration of a loosely supported elastic tube via proper orthogonal decomposition

Numerical simulations of complex flow-induced vibration (FIV) systems play a crucial role in predicting nonlinear dynamics and potential wear in heat exchangers and steam generators. However these simulations pose a challenge due to their excessive demand for computational resources. In this study, the tube bundle impacting on the generally loose baffle plated under numerous cross-flow velocities are numerically investigated by high fidelity reduced order models (ROMs). Combined with Proper Orthogonal Decomposition (POD) and fluid-elastic instability quasi-static model containing delay differential equations (DDE), a ROM equations of FIV motion was established. Various types of flexible tube behaviors, such as limit cycle oscillations, quasi-periodic vibrations, and chaotic motions, are observed and analyzed by ROM method. Results demonstrate that the POD-FDM method accurately and efficiently captures chaotic motions, surpassing Galerkin methods for nonlinear systems while reducing dimensionality compared to full-order modeling. There is a substantial reduction in computation time, saving over 70%. Additionally, criteria for selecting POD modes are presented across periodic, quasi-periodic, and chaotic FIV systems. Our efforts represent the first attempt to utilize POD for nonlinear DDE calculations to predict the chaotic response of tube bundles subjected to cross-flow-induced vibration. The proposed strategy is readily applicable to other nonlinear FIV simulations and has practical importance for users either in industry or academia.