Fluid–structure-coupled Koopman mode analysis of free oscillating twin-cylinders

Abstract

Flow-induced vibration (FIV) of twin square cylinders in a tandem arrangement was numerically investigated at Reynolds numbers 200 and gap L/D = 2.0, 4.0, and 6.0 ( D is the side length of the cylinders). Fluid-structure-coupled Koopman mode analysis method was developed to synchronously identify the coherence flow and structural modes. Then, the energy transfer between cylinders and Koopman modes was analyzed to uncover the underlying mechanism of FIV. The results showed that at L/D = 2.0 and 4.0, only soft lock-in vortex-induced vibration (VIV) was observed. The oscillating amplitude for L/D = 4.0 was much higher than that of L/D = 2.0, due to the interference effects induced by fully developed gap vortices. As L/D = 6.0, VIV and galloping coexisted. For the coherence mode, the primary flow mode induced by the vortex shedding dominated the flow field at L/D = 2.0 and 4.0. The direct mode energy dominated the energy transfer process. The upstream cylinder (UC) contributed to the negative work done and thus tended to stabilize the vibration; in contrast, the downstream cylinder (DC) exhibited the opposite behavior. In the galloping branch at L/D = 6.0, both the flow field and structural response contained three main modes: one vortex-shedding-induced mode and two vibration-induced modes. For the direct mode energy, owing to the interference effects, DC contributed to more positive work done than UC by the vibration-induced modes. The vortex-induced mode was governed by DC and afforded negative work done. Moreover, all the coupled mode energy was almost equal to zero.