Flow induced vibration of two rigidly connected circular cylinders in different arrangements at a low Reynolds number

The flow induced vibration (FIV) responses of two rigidly connected cylinders in various arrangements have been studied numerically using the two-dimensional incompressible Navier-Stokes equations coupling with a fourth-order Runge-Kutta method. Four different values of the angle of incidence (α) and two different values of center-to-center pitch (P) between the two cylinders have been selected for the study. The FIV response amplitudes, lock-in regions, hydrodynamic force coefficients, phase portraits, and flow fields have been systematically compared. The numerical results demonstrate that for P = 4D and increasing α, the maximum value of the total mean drag coefficient tentatively increases, however, the maximum response amplitude shows a decreasing tendency. Furthermore, the maximum amplitude for P = 4D occurs when α = 0° at V_r = 7. For P = 4D and α = 0°, the response amplitude remains a certain value during the large V_r range, which is caused by the participation of the wake-induced vibration. For P = 2D, the maximum amplitude happens when α = 30° at V_r = 12. For P = 2D when α = 90°, owing to the proximity-induced galloping, during the large V_r range, the response amplitude increases slightly with increased V_r, displaying no desynchronization characteristics.