Effect of spacing ratios on coupling mechanism of three tandem cylinders in planar shear flow

Using four-step semi-implicit characteristic-based split method, flow-induced vibrations of three tandem cylinders in planar shear flow are numerically simulated at Re = 100. The vibration responses are more complicated than that of a single cylinder due to the gap development and mutual interference with each other. The spacing ratio (L/D) between three tandem cylinders of equal size ranges from 2.5 to 5.5, with a mass ratio (m(r)) of 2.0 attributed to each one. The reduced velocity (U-r) spans from 3 to 30, and the shear ratio (k) varies as 0, 0.05 and 0.1 respectively. The numerical results show that spacing ratio and shear ratio have an influence on the dynamic responses, performances of frequency, phase and energy for three tandem cylinders. The vibration responses of each cylinder can be clearly divided in three major branches, which first increase then decrease with increasing U-r. The gap flow inside cylinders at small L/D heightens the probability of vortex merging, intensifying mutual interference and consequently amplifying the amplitude. It is worth noting that as k increases to 0.1, downstream cylinders exhibit different vibration responses at L/D >= 4.0. Specifically, a secondary increase occurs after U-r > 18 at L/D = 4.0, and the amplitude is completely suppressed after U-r > 25 at L/D = 5.5. With the help of other performances, the differences in vibration responses of three tandem cylinders at different k and L/D are revealed.