Flow-induced vibration of a cylinder in the wake of another of smaller diameter

This paper presents cross-flow induced response of a both-end-spring-mounted circular cylinder (diameter D) placed in the wake of a rigid circular cylinder of smaller diameter d. The cylinder vibration is constrained to the transverse direction. The cylinder diameter ratio d/D and spacing ratio L/d are varied from 0.2 to 1.0 and 1.0 to 5.5, respectively, where L is the distance between the center of the upstream cylinder to the forward stagnation point of the downstream cylinder. A violent vibration of the cylinder is observed for d/D = 0.2 ∼ 0.8 at L/d = 1.0, for d/D = 0.24 ∼ 0.6 at 1.0 < L/d ≤ 2.5, for d/D = 0.2 ∼ 0.4 at 2.5 < L/d ≤ 3.5, and for d/D = 0.2 at 3.5 < L/d ≤ 5.5, but not for d/D = 1.0. A smaller d/D generates vibration for a longer range of L/d. The violent vibration occurs at a reduced velocity U_r (=U_∞/f_nD, where U_∞ is the free-stream velocity and f_n the natural frequency of the cylinder system) beyond the vortex excitation regime (U_r ≥ 8) depending on d/D and L/d. Once the vibration starts to occur, the vibration amplitude increases rapidly with increasing U_r. It is further noted that the flow behind the downstream cylinder is characterized by two predominant frequencies, corresponding to the cylinder vibration frequency and the natural vortex shedding frequency of the cylinder, respectively. While the former persists downstream, the latter vanishes rapidly.