Characterizing vibrations and associated wake structures of tandem square cylinders at different angles of incidence

Abstract

Finite element computations were conducted to investigate the transverse vibrations of three identical tandem square cylinders and the associated wake patterns at a Reynolds number Re = 150. The reduced velocities ranged from U*=3 to 20, and the angles of incidence were set at α=0°, 22.5°, and 45°. The streamwise gaps for these three α were Lx=5H, 3.8H, and 3.5H, respectively, where H represents the projected dimension of the cylinder normal to the freestream. The mass ratio of the cylinders was fixed at m*=2, and damping was neglected to allow the cylinders to attain maximum amplitudes. In the presence of primary vortices being shed from all three cylinders, the upstream cylinder at α=22.5° and 45° exhibits three distinct vibration regimes: initial excitation and upper and lower response regions. On the other hand, due to interaction with the upstream vortices, the two downstream cylinders display four response regions. In the case of α=0°, the dynamic response of the upstream cylinder appears in only two regimes, but with a higher peak amplitude compared to α=22.5° and 45°. Vibration and shedding frequencies closely synchronize with the natural frequency of the spring-mass system in the second regime, leading to high amplitude oscillations for the most upstream cylinder with α=22.5° and 45°. The third response regime for the two downstream cylinders is associated with the lock-in phenomenon. In α=0° and 22.5° configurations, the shedding mode is 2S in all response regimes, while at α=45°, the shedding mode shifts to P + S during the second regime. Up to the second regime, lift and vortex forces are in-phase with the cylinder's oscillation for α=0° and 22.5°, but they go out of phase beyond that. In the case of α=45°, although lift remains in-phase with the displacement in the second regime, the vortex force is found to be out of phase. This study is expected to enhance the understanding of fluid–structure interaction phenomena involved in multiple structures and can aid in the design of stable structures in civil engineering, offshore engineering, and development of energy harvesting devices.