Oscillation regimes and mechanisms in the vortex-induced vibrations of three circular cylinders with equilateral-triangular arrangements

Abstract

This paper presents the oscillation regimes and underlying mechanisms of the vortex-induced vibrations (VIVs) of three separated and elastically mounted circular cylinders aligned in equilateral-triangular arrangements with the Reynolds number Re = 100, the mass ratio m* = 2.0, the spacing ratio L* = 2.0–5.0, and the reduced velocity Ur = 0.0–15.0. Three cylinders, with one placed upstream and the other two placed side-by-side downstream, are constrained to vibrate only in the transverse direction. In the examined L* range, the responses of the three cylinders can be divided into five regimes. The features of the vibration amplitudes, vibration frequencies, displacement phase lags, and mean position shifts in each regime are explored in detail. The mechanisms of several important issues regarding the VIV are elucidated. We found that (1) the roles of the separation, reattachment, detachment, merging, and rolling-up of the shear layer in sustaining the cylinder vibrations differ in each regime. (2) The significant increase in the amplitudes of the two downstream cylinders in regime II stems from the vorticity supply from the upstream cylinder. (3) The low vibration frequency of the upstream cylinder in an anti-phase flow is closely related to the presence of a slightly asymmetric wake of the downstream cylinders. (4) The large-amplitude vibrations of the two downstream cylinders in regime V at L* = 2.0 is maintained by the shear layer reattachment of the upstream cylinder and the pushing effects between the two downstream cylinders. (5) Finally, the different incoming flow velocities for the upstream and downstream cylinders may cause different vibration frequencies.