Coherence mode and Floquet analysis on flow past a rectangular cylinder with small angle of attack

Abstract

This paper focuses on a typical bluff body, a rectangular cylinder with an aspect ratio of 5, and quantitatively analyzes the fluid force coefficients and Strouhal number (St) under different angles of attack (α) and Reynolds numbers (Re) through numerical simulations. The higher-order dynamic mode decomposition method is used for coherence mode analysis, and Floquet instability analysis is used to identify the 3D transitional angle of attack (α3D) at different Re as well as the Floquet modes at various α. The results show that increasing the angle of attack significantly raises the mean drag coefficient ( C¯D ) and fluctuating lift coefficient (C′L), while the St number gradually decreases. This leads to the emergence of vortices and complex flow structures of different scales and frequencies at the rear edge of the rectangular cylinder and its lower cavity region, accompanied by increased downstream turbulence intensity. Furthermore, the 3D transitional angle of attack (α3D) decreases with increasing Re. Two types of Floquet modes are identified within the range of Re and α, namely, Mode A and Quasi-Periodic Mode QP. This study provides important insights and theoretical support for a deeper understanding of flow evolution problems.