On the galloping cross-flow vibration responses of three in-line square cylinders

Abstract

Galloping cross-flow vibration responses of three in-line identical square cylinders are numerically studied for the mass ratio m*=2, streamwise gaps Lx=3B and 5B, reduced velocity U*=3−50, and Reynolds numbers Re = 150 in two dimensions (2-D) and 2000, where the flow is three-dimensional (3-D). Here, B is the side of the cylinder. An isolated cylinder does not gallop since the mass ratio m*=2 is less than the critical value in the Re = 150 flow, whereas for the three in-line bodies, galloping instability is triggered at the upstream cylinder due to the interference effect caused by the presence of downstream bodies. The interaction with the wake of galloping upstream cylinder promotes galloping instability for the two downstream cylinders almost immediately at Re = 150. In the three-dimensional wake at Re = 2000, downstream cylinders interact with less coherent Karman vortices shed by the galloping upstream cylinder, compared to the 2-D case. This phenomenon leads to the delayed on-set of galloping response for the first downstream cylinder, while the second one never gallops.