Numerical investigation of flow-induced vibrations in two tandem circular cylinders at low gap ratios with considering collisions

In this study, two tandem elastically supported cylinders with the same parameters undergo numerical simulations using the overset grid method to analyze flow-induced vibrations (FIVs) with two degrees of freedom (2DOF). This study presents a model that can consider the collision of two tandem circular cylinders with FIVs in order to systematically analyze the FIV response, hydrodynamic characteristics, and wake vortex shedding patterns of two tandem circular cylinders with varying gaps of 0.5D, 1.0D, and 1.5D. The critical collision gap was found to be 1.6D for the 2 DOF FIV of two tandem circular cylinders. ​At each initial gap ratio, the streamwise amplitude of the upstream cylinder closely matches that of the isolated cylinder at lower reduced velocities (U_r ≤8.0), but increases significantly at higher reduced velocities (U_r >8.3). Furthermore, the reduced velocity at which the downstream cylinder reaches its maximum transverse amplitude exceeds that of the isolated cylinder. For the large initial gap ratios (G = 1.0D, 1.5D), the transverse vibration frequency ratios of the upstream and downstream cylinders are close to those of the isolated cylinder. However, the reduced velocity at frequency ratio f_y/f_n equal to 1.3 is larger compared to the isolated cylinder case, and the delay effect becomes more noticeable as the initial gap ratio decreases. The upstream cylinder presents a figure 8 vibration trajectory only for small reduced velocities (U_r ≤7.0) and large gap ratios (G/D = 1.0, 1.5). However, in the range of reduced velocity and gap ratio considered in this study, the downstream cylinder exhibits chaotic vibration trajectories. For an initial gap of G = 0.5D, both the collision frequency and collision force between the upstream and downstream cylinders increase with increasing reduced velocities. As the initial gap ratio increases, the collision frequency and the collision force of the two cylinders decrease. The flow patterns of the two cylinders are mainly the shear layer reattachment flow pattern and the shear layer embedding flow pattern at small initial gap ratio. With the increase of the initial gap ratio, the synchronized gap vortex shedding flow pattern gradually occupies the dominant position. When the initial gap G = 0.5D, the wake vortex shedding patterns of the upstream and downstream cylinders are essentially 2S. When the initial gap G = 1.5D, both upstream and downstream cylinders can form super upper branches with 2T wake vortex shedding pattern, and the maximum transverse amplitude of the downstream cylinder reaches 1.73D.