Research On Vortex-induced Vibrations In The Flow Around Circular Cylinders

Flow past cylinders and vortex-induced vibrations (VIV) exist ubiquitously in nature and have been classical problems in fluid mechanics. To comprehend the mechanism well can not only be helpful in understanding the nature, but also find applications in engineering. This thesis numerically studied vortex-induced vibrations (VIV) of elastically mounted cylinders and Poiseuille flow-induced vibrations (PFIV) of cylinders via a lattice Boltzmann method.We first studied the dynamics of VIV of one and two elastically mounted rigid cylinders in tandem with one degree of freedom. VIV at subcritical Reynolds number occurs in both the one-and two-cylinder systems. An anomalous biased vibration regime has been observed, which is the first time that the existence of such an asymmetric vibration regime has been confirmed. The biased oscillation regime mainly exists at the subcritical Reynolds number region. A further data analysis demonstrates that in the biased vibration regime, the relative biased degree increases as reduced velocity increases, separation decreases and mass ratio decreases, respectively. The mechanism of the appearance of such a biased vibration regime is that there is a competition between the structural restoring force and the repulision force induced by the gap flow between the two cylinders.A novel physical model system, the Poiseuille flow-induced vibrations, was introduced in this thesis. In such a model system, one or more cylinders are immersed into a viscous incompressible fluid between two parallel channel walls. Each cylinder is free to move in the cross-flow direction under the hydrodynamic force on the cylinder surface, while is fixed in the streamwise direction. Vibrations of one cylinder, two side-by-side cylinders and two tandem cylinders were studied separately.For the case of an isolated cylinder, results demonstrate that Reynolds number, blockage ratio and mass ratio play significant roles. Based on the cylinder motions and the corresponding flow patterns, four distinct oscillation regimes were observed: rest-in-centerline state, symmetrical periodic vibration, deflective periodic vibration and small-amplitude vibration. The effect of mass ratio at different Reynolds numbers and blockage ratios has also been systematically investigated with special attention to the phenomenon of critical mass ratio. An analysis of the lift coefficient of a stationary cylinder placed at different transverse displacements of a plane channel shows that the distribution of lift force plays an important role in such a system.For the case of two side-by-side cylinders, results show that as the blockage ratio decreases, the coupled motions of cylinders which have low mass ratios behave as: flip-flopping vibration, in-phase-synchronized vibration, bistable vibration and antiphase-synchronized vibration, respectively. The tendencies of vibration amplitude, frequency and relative equilibrium position versus blockage ratio of two side-by-side sylinders are all similar with that of an isolated cylinder. Results also demonstrate that the coupled vibration regime is mainly dependent on the blockage ratio, while not Reynolds number and mass ratio. For the similar fluid conditions, the critical mass ratio of two side-by-side cylinders is a little larger than that of a single cylinder.For the case of two tandem cylinders, results show that the separation between the two cylinders plays an important role. As the separation is small, the two cylinders have strong interference to each other and as the separation becomes large, the interaction of two cylinders decouples gradually. Based on the Reynolds number, blockage ratio, mass ratio and separation, two rest regimes and six oscillation regimes were observed. When the blockage ratio is large, the final vibration state of cylinders is exclusive, and while the blockage ratio is small, the final vibration state is bistable. Results indicate that the critical mass ratio of two tandem cylinders with small separation is about an order of magnitude larger than that of an isolated cylinder.Based on the current observations, the PFIV introduced in this thesis can be considered as a novel model system of flow-induced vibrations, and is expected to find applications in fluid mixing and heat transfer.