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Abstract Two-degree-of-freedom (2-DOF) vortex-induced vibration (VIV) of an elliptic cylinder is numerically investigated at a Reynolds number R e = 150. The incompressible Navier–Stokes equations in arbitrary Lagrangian–Eulerian formulation are solved by a four-step fractional finite element method. The elliptic cylinder, with a variety of aspect ratios (AR = 1.0–2.5), is free to vibrate in both transverse and azimuthal directions. At each AR , the computations are conducted within a wide range of reduced velocities (2 ≤ U r ≤ 15). For comparison, the one-degree-of-freedom (1-DOF) responses of the cylinder vibrating only transversely are also provided. The results show that significant rotations occur under a condition of frequency synchronization similar to the lock-in condition of VIV in the transverse direction. Under the rotation effect, the transverse peak amplitude at AR = 1.0 reaches a higher value about 20% larger than its counterpart of 1-DOF VIV, whereas it fells by more than half at AR = 2.0 and 2.5, and the corresponding wake patterns present distinct characteristics. The typical phenomenon of phase switch can be captured successfully between the torque and rotation response, which occurs at the same reduced velocity to the phasing between the transverse force and motion. Our simulation results also elucidate that the free rotation may significantly affect the statistics of the drag, lift and moment coefficients. The most striking observation is that all of the force responses at AR = 2.0 and 2.5 collapse onto a very low level compared to those of the transverse-only VIV. This is consistent with the dramatic drop in the transverse vibration amplitude at the same AR. [ABSTRACT FROM AUTHOR]

Abstract: A numerical study is performed on the flow-induced vibrations of isolated and tandem elastically mounted cylinders having two degrees of freedom and a variety of the in-line to the transverse natural frequency ratio, f nx /f ny . The characteristic-based-split finite element method is utilized to obtain the solution of the incompressible flow equations in primitive variables. The Reynolds number, based on the upstream flow velocity U ∞ and the diameter of the cylinder D, is fixed at Re=150, and for a tandem arrangement, the centre-to-centre distance between the cylinders is 5.0D. The computation is carried out at a lower reduced mass ratio of M r =2.0 and for a wide range of reduced velocities (U r =3.0–12.0). The structural damping ratio is set to zero to maximize the vortex-induced response of the bodies. In this study, we mainly focused on the effect of the natural frequency ratio on the characteristics of vortex-induced vibration (VIV) responses, including wake frequencies, orbital trajectories, response amplitudes, hydrodynamic forces and wake mode patterns. The natural frequency ratio is varied in the range of f nx /f ny =1.0–2.0 with an increment of 0.25. We found that the condition of the occurrence of a dual-resonant response exists over a broad range of tested natural frequency ratios. A third harmonic frequency component appears in the lift fluctuation, along with additional multi-harmonics, which also interact with the drag frequency. Instead of double response peaks, multiple small peaks occur in the amplitude response of the cylinder. These peaks are distributed over a narrow range of U r from 4.45 to 5.15, and their magnitudes increase with the increase in U r . For a tandem arrangement, the response characteristic of the upstream cylinder is similar to that of a single cylinder, whereas that of the downstream cylinder is greatly affected by the upstream wake. For a downstream cylinder, the in-line dynamic response is more sensitive to the natural frequency ratio than the response in the transverse direction. As the dual-resonance is excited, the isolated cylinder and the upstream cylinder of the tandem arrangement may show a P+S wake pattern, which strongly suppresses the vortex shedding of the downstream cylinder. [Copyright &y& Elsevier]

The vortex-induced vibration (VIV) of circular cylinder in uniform flow with two-degree-of-freedom (2DOF) and geometrical nonlinear system is investigated numerically using the combined sliding and layering dynamic meshes. The characteristics of vibration amplitude, fluid force coefficients, branching behaviour, vibration trajectory, energy transfer and flow pattern of circular cylinder in VIV are studied with two-dimensional shear stress transfer (SST) k - ω turbulence model and three-dimensional large eddy simulation (LES). It is found that in the simulation with LES model the predicted vibration amplitude and fluid force coefficients show good agreement with the experimental data, while in the simulation with SST k - ω model these parameters are significantly underestimated. The two triplets (2T) vortex shedding mode happens in the super upper branch of circular cylinder with 2DOF linear system and leads the large-magnitude positive energy transferring from fluid to cylinder, which causes the maximum vibration amplitude. For the circular cylinder with 2DOF nonlinear system, the vibration simulated by LES model shows a galloping-like phenomenon that the amplitude keeps increasing with the reduced velocity U r. The crescent-shaped trajectory and the 2T vortex shedding mode happen upon the critical U r , which is similar to that in the super upper branch of circular cylinder with 2DOF linear system. This phenomenon is caused by the amplitude-dependent stiffness of nonlinear system and the modified reduced velocity U ∗ reveals the universality of vibration amplitude for the circular cylinders with linear and nonlinear systems. • The VIV of circular cylinder with 2DOF linear system is accurately simulated. • The machanism of super upper branch of 2DOF VIV of circular cylinder is illustrated. • The galloping-like vibration of circular cylinder with nonlinear system is explained. [ABSTRACT FROM AUTHOR]

Although flow past cylinders has a vast spectrum of applications in various fields of engineering, the existence of flow-induced vibrations (FIVs) add a need for a more precise and thorough approach when studying such flows. In this context, this work investigates the FIVs' mechanism due to two square cylinders placed in tandem arrangement through a characteristics-based-split (CBS) finite element method. Both cylinders, with a low mass ratio (m r = 2), are free to oscillate in in-line and transverse directions. The center-to-center distance of 5 D (D being the cylinder side width) is kept fixed between the cylinders. The Reynolds number (R e) is ranged from 40 to 200 with an increment of 40, and computations are carried out for the reduced velocity (U r) ranging from 3 to 13 under each R e value. Results show that the effects of Re and U r on the dynamic responses are qualitatively similar for both cylinders. However, effects on the downstream cylinder are stronger due to the upstream wake. For R e equal to or beyond 120, the in-line low-frequency characteristic becomes obvious at some higher values of U r for the upstream cylinder, whereas it exists over a wide range of U r for the downstream cylinder. For lower R e (up to 120), cylinders show steady behavior at U r = 5. However, for higher R e , they vibrate with the maximum amplitudes (especially the in-line amplitude of the downstream cylinder), and show complex wake flow at the same U r. Compared to higher R e , the maximum vibration amplitudes in the transverse direction of lower R e are relatively higher, while the opposite trend is observed for in-line vibration amplitudes. Several unstable trajectories are also identified other than the typical figure-eight trajectories. In context of vortex shedding, different permutation of steady state, 2S, P+S, and complex modes are observed for different values of R e. It is also noted that the vortex shedding pattern keeps changing in the far wake for higher R e. [ABSTRACT FROM AUTHOR]