Study for the cross-flow coupling mechanism of tandem cylinder groups at low Reynolds number

A numerical analysis of flow-induced vibrations for tandem cylinder groups which include two and three tandem cylinders with a spacing ratio of L/D = 5.5 (where L is the distance between the circular cylinders and D is the circular diameter) in planar shear flow is carried out. The cylinders can only vibrate freely in the cross-flow direction. A finite element method called four-step semi-implicit characteristic-based split (4-SICBS) is used to solve the Navier-Stokes equation. On the other hand, in order to maximize the oscillation response of the dynamic system, the damping ratio of it is xi = 0. And the mass ratio of structure is set to m(r) = 2.0. The four main parameters, such as the number of cylinders (Num = 2, 3), Reynolds number (Re = 100, 160), the shear ratio (k = 0.0, 0.05, 0.1) as well as the reduced velocity (U-r = 3-30) are mainly studied the dynamic behaviors, frequency and spectrum characteristics, phase characteristics as well as energy characteristics of tandem cylinder groups. The results show that vibration responses of the upstream cylinders in tandem cylinder groups are similar to that of a single cylinder, while the parameters play a key role in flow-induced vibrations of the midstream and downstream cylinders. As Re = 100, the downstream cylinder of two tandem cylinders and the midstream cylinder of three tandem cylinders are in the state of increasing and then decreasing, and the downstream cylinder of three tandem cylinders has a larger vibration response with the change of k. As k = 0.1, the amplitude drops to zero with the increase of U-r. In addition, the situation becomes more complicated with the increase of Re. For the downstream cylinder of three tandem cylinders at Re = 160, there are two peaks of the cross-flow amplitude. The oscillation remains strong at larger U(r )for the case of k = 0.1. Finally, the interactions between cylinders are revealed, together with the vortex dynamic mechanism underlying the oscillation characteristics of tandem cylinders exposed to planar shear flow.