Vibrations of cylindrical objects obstructing a Poiseuille-type flow.

Using the lattice Boltzmann equation, we numerically studied the dynamics of a physical model system, the Poiseuille flow-induced vibrations (PFIV). At a moderate Reynolds number, for flows past a cylinder that is free to move in the cross-flow direction while being fixed in the streamwise direction, between two parallel walls, a variety of distinct vibration regimes involving symmetrical periodic vibration, deflective quasiperiodic vibration, and deflective periodic vibration with corresponding wake states were observed. The data analysis shows that the distribution of the lift coefficient depending on the blockage ratio plays an important role in such a system. A further study of the case of two side-by-side identical cylinders demonstrates the existence of two distinct cooperative vibrations of the cylinders, e.g., in-phase-synchronized vibration (IPSV) and anti-phase-synchronized vibration (APSV). The result reveals that there is a critical blockage ratio, beyond which a phase transition between IPSV and APSV occurs. For the phenomena observed here, PFIV can be considered a new type of vortex-induced vibration, and such a system is expected to find applications in fluid mixing.