Experimental Study on the Dynamics of Four Flexible Cylinders in Square Arrangement Subjected to Uniform Cross-Flow

Groups of cylinders can be found in many engineering fields such as marine and civil applications. The behaviors of the group cylinders can be very complex because it undergoes the mutual effects of adjacent cylinders arranged in different positions. In this paper, we present the results of a study on the dynamics of a group of flexible cylinders in square arrangements along with a single (isolated) cylinder subjected to uniform cross-flow (CF). Four cylinders of the same size, properties, and pretensions were tested in two configurations with different centre-to-centre separations. Horizontal and vertical separations were 2.75D & 2.75D and 5.50D & 2.75D for the first and second configurations, respectively. The tandem (horizontal) separations between the downstream and upstream cylinders, i.e., 2.75D and 5.5D, correspond to the reattachment and co-shedding regimes, respectively. Vertical separation, i.e., 2.75 was chosen in a range where the side-by-side cylinders can have proximity interference. Reynolds number ranged from 1400 to 20000 (subcritical regime). The parameter of reduced velocity reached up to 19. The aspect ratio of all the cylinders was 162 (length/diameter). Mass ratio (cylinders mass/displaced water) is 1.17, a low mass ratio. The amplitude ratio of the CF vibration of the downstream cylinders, hydrodynamic force coefficients including mean and fluctuating components of the drag and lift forces, and frequency responses for both CF and inline (IL) directions were analyzed. All the cylinders excited up to the second and fourth mode of vibrations for CF and IL directions, respectively. Mean drag coefficient of the upstream cylinders are almost twice those of the downstream cylinders at high reduced velocities. The mean lift coefficient is much higher for the upstream cylinders than the downstream cylinders with a negative value. Obvious IL and CF lock-in regions exist for all four cylinders at low reduced velocities. Among the four cylinders, the upper downstream cylinder shows the least and the most fluctuating lift and drag forces, respectively. The IL and CF frequencies of the downstream cylinders are much lower than those of the upstream ones and the single cylinder.