Numerical investigation on flow-induced vibrations of two tandem cylinders localized selective roughness with different natural frequencies

The characteristics of flow-induced vibrations (FIVs) of two tandem rough cylinders with different natural frequencies transversely to the flow direction are computationally investigated using two-dimensional Unsteady Reynolds-Averaged Navier-Stokes (2-D URANS) equations. Seven different sets of natural frequency ratios f_n* between upstream and downstream cylinders (f_n*= f_n,u/f_n,d =0.5, 0.707, 0.866, 1.0, 1.155, 1.414, and 2.0) are performed in the range of 30,000≤Re≤120,000, where f_n,u and f_n,d are the natural frequencies of the upstream and downstream cylinders, respectively. The spacing ratio is d/D=2.57 (where d is the center-to-center longitudinal spacing between two cylinders and D is the diameter). The mass ratio is m*=1.343. The characteristics of amplitude response and frequency response are analyzed in detail. According to the frequency response of the two cylinders with different natural frequency ratios, three main interactive oscillating patterns of the downstream cylinder are observed: (1) Forced oscillating pattern: the downstream cylinder oscillates forcedly with the upstream cylinder, and the dominant oscillating frequency of the downstream cylinder is equal to that of the upstream cylinder. (2) Independent oscillating pattern: the downstream cylinder oscillates independently with its own natural frequency. (3) Beat oscillating pattern: the downstream cylinder oscillates with two dominant frequencies, one is equal to the oscillating frequency of the upstream cylinder, and the other one is equal to its own natural frequency. The different natural frequencies of the cylinders suppress the vibration of the downstream cylinder at different reduced velocity ranges. The displacement time history, frequency spectrum, and vortex structures of each oscillating pattern case are also analyzed for elucidation.