Koopman mode analysis on discovering distributed energy transfer of post-transient flutter of a bluff body

Abstract

The flutter response of a rectangular cylinder model with an aspect ratio of 5 is investigated by direct numerical simulation for various Reynolds numbers (Re) and flow angles of attack (α). The results show that the lower α and Re, the larger the torsional amplitude at the critical reduced flow velocity (Ur) corresponding to the occurrence of flutter. High-order Koopman mode analysis method (HOKM) was developed to synchronously capture the inherent flow and structural modes. The element-mode-based energy transfer between cylinders and flow modes was used to reveal the underlying mechanism. HOKM analysis shows that only odd-order modes contribute to the occurrence of flutter, with an augmentation in Ur enhancing this phenomenon. By analyzing the work done in odd-order modes, it is found that the primary mode always occupies the main contribution to the work done. The leading-edge endpoint portion is always where the maximum work is done. An escalation in Re and α notably influences both the spatially relevant part (WΦ) and the temporally relevant part (Wc), while an increase in Ur predominantly impacts WΦ. This study offers universal guidance on the safety and protection of ocean engineering structures and flow control strategies.