An investigation of the mode transformation and interaction underlying the behavior of vortex-induced vibration (VIV) of a flow past a circular cylinder elastically mounted on a linear spring is conducted using a high-fidelity full-order model (FOM) based on computational fluid dynamics (CFD), a reduced-order model (ROM), and a dynamic mode decomposition (DMD) of the velocity. A reduced-order model for the fluid dynamics is obtained using the eigensystem realization algorithm (ERA), which is subsequently coupled to a linear structural equation to provide a state space model for the coupled VIV system, in order to provide a simplified computationally inexpensive mathematical representation of the system. This methodology is used to study the dynamics of laminar flows past an elastically mounted circular cylinder with Reynolds number Re ranging from 20 to 180, inclusive. The results of the simulations conducted using FOM/CFD and ROM/ERA, in conjunction with the power spectral analysis and DMD, are used to identify the characteristic natural frequencies and the growth/decay of various modes (including the complex interactions between the myriad wake modes and the structural mode) of the VIV system as a function of the Reynolds number and the reduced natural frequency Fs (or, equivalently, the reduced velocity Ur). A detailed analysis of the distribution of the eigenvalues of the transfer (or, system) matrix of the reduced VIV system shows that the frequency range of the lock-in can be partitioned into resonance and flutter lock-in regimes. The resonance lock-in (lower branch of the VIV response) dominates the fluid-structure interaction. Furthermore, it is shown that when the structural natural frequency is close to one of the eigenfrequencies associated with the wake modes, resonance lock-in (rather than flutter lock-in) will be the primary mechanism governing the VIV response even though the real part of the eigenvalues associated with structural mode is positive. With increasing Reynolds number, the instability of each wake mode is enhanced resulting in a transformation of the wake modes interacting with the structural mode. It is suggested herein that the weakened interaction between the wake modes and the structural mode at Re =  180 (associated with the greater separation between the root loci of the modes) results in the premature termination of the resonance lock-in at [Formula: see text] with increasing Ur. The DMD and power spectral analysis of the time series of the transverse displacement and lift coefficient are used to support the results obtained from ROM/ERA and, more specifically, to provide a clear demonstration of the balanced interaction between the wake modes and the structural mode. This result is used to explain the beating phenomenon, which occurs in the initial branch and the significant lag time that arises between the initial branch and the occurrence of a fully developed response in the lower branch.

A two-node cable element which the axial torsion and geometrical nonlinear were considered was developed based on the update Lagrange formulation, and a model of multi-span transmission line for galloping analysis was established. A nonlinear numerical simulation of single iced conductor galloping was proposed. Using computational fluid dynamic, the aerodynamic coefficient of iced conductor with different wind attack angle was simulated. According to the finite element model of multi-span transmission line and aerodynamic coefficient curve, the galloping of iced conductor through the method of fourth-ordered Runge-Kutta method was presented. By the comparison with the classical examples, the results indicated that the presented method are efficient and reliable.

A comprehensive review of modelling techniques for the flow-induced vibration (FIV) of bluff bodies is presented. This phenomenology involves bidirectional fluid–structure interaction (FSI) coupled with non-linear dynamics. In addition to experimental investigations of this phenomenon in wind tunnels and water channels, a number of modelling methodologies have become important in the study of various aspects of the FIV response of bluff bodies. This paper reviews three different approaches for the modelling of FIV phenomenology. Firstly, we consider the mathematical (semi-analytical) modelling of various types of FIV responses: namely, vortex-induced vibration (VIV), galloping, and combined VIV-galloping. Secondly, the conventional numerical modelling of FIV phenomenology involving various computational fluid dynamics (CFD) methodologies is described, namely: direct numerical simulation (DNS), large-eddy simulation (LES), detached-eddy simulation (DES), and Reynolds-averaged Navier–Stokes (RANS) modelling. Emergent machine learning (ML) approaches based on the data-driven methods to model FIV phenomenology are also reviewed (e.g., reduced-order modelling and application of deep neural networks). Following on from this survey of different modelling approaches to address the FIV problem, the application of these approaches to a fluid energy harvesting problem is described in order to highlight these various modelling techniques for the prediction of FIV phenomenon for this problem. Finally, the critical challenges and future directions for conventional and data-driven approaches are discussed. So, in summary, we review the key prevailing trends in the modelling and prediction of the full spectrum of FIV phenomena (e.g., VIV, galloping, VIV-galloping), provide a discussion of the current state of the field, present the current capabilities and limitations and recommend future work to address these limitations (knowledge gaps).

The general expression of Lagrange nonlinear cable element is established firstly by using virtual work principle. On the basis of the theory, the specific expression of a two-node cable element having rotational degree of freedom is derived and the non-linear finite element model of multi-span transmission line for galloping analysis was established. In addition, the aerodynamic coefficient of iced conductor under different wind attack angle was obtained through computational fluid dynamics method. Based on the finite element model and aerodynamic characteristics of the iced conductor, the Runge-Kutta method was applied to carried out non-linear numerical simulation of iced conductor galloping and the Matlab program was compiled. The galloping of the multi-span transmission line crossing Hanjiang River was analyzed. The results indicate that the presented method can simulate the galloping process effectively and it can provide the basic references for further research of preventing galloping.

The effect of free-stream turbulence intensity level on the wake dynamics of square-back Ahmed body is modelled using the Improved Delayed Detached Eddy Simulation (IDDES) at Re=9.6*10^4. The center of pressure, pressure gradient on the base surface and the barycenter of the momentum deficit on the wake plane are analyzed to characterize the wake bi-modality dynamics. Given that different flow dynamics have different dominant frequencies, the spectral proper orthogonal decomposition (SPOD) is utilized to separate the wake bi-stability, pumping motion of the whole recirculation region, the Von Kármán vortex shedding and the shear layer instability. The results show that entrainment of oncoming flow into the wake is enhanced, the vorticity thickness is thickened and the length of the wake recirculation region is decreased with the increasing free-stream turbulence, resulting in a lower base suction pressure and a higher level of shear stress. The frequency of the pumping motion is increased with the increase of oncoming turbulence intensity, while the frequency of Von Kármán vortex shedding is irrespective of the level of the background turbulence. Though the correlation between the switching rate and oncoming turbulence intensity cannot be put forward due to the relative short numerical simulation time compared with the wind tunnel experiment, it is still known that the turbulence intensity has a positive effect on the wake bi-stability switching.