Vortex Induced Vibration Analysis Research Articles

Coupling of the immersed boundary and Fourier pseudo-spectral methods applied to solve fluid–structure interaction problems

The current manuscript addresses fluid–structure interaction (FSI) problems to the analysis of vortex-induced vibration (VIV), employing the methodology designated as IMERSPEC2D. The approach seamlessly integrates the Fourier pseudo-spectral method (FPSM) and the immersed boundary method (IBM) to solve the Navier–Stokes (NS) and continuity equations. Simultaneously, the effects of cylindrical structure, involving 1 and 2 degrees of freedom (d.o.f.) are simulated, by incorporating structural motion equations into NS via the IBM source term and implementing a two-way FSI algorithm. In the paper are presented the comparison of low and high-order temporal integration methods applied to solve the dynamic behavior of the structure and the dimensionless of the cylinder’s structural motion equations, resulting in an increase in computational time step from 1E(-9\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-9$$\\end{document}) to 1E(-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-3$$\\end{document}). Validation results to refined mesh simulations include the accurate representation of the lock-in phenomenon to simulations of 1 d.o.f. obtaining the range between reduced velocity 5.456 and 5.568 and the maximal amplitude is 0.352. Notably, the eight-shape pattern of the 2 d.o.f. cylinder displacement is obtained and the formation of C2S wake patterns is achieved, as presented by other authors. In conclusion, the dimensionless approach reduces computational time, while the high-order both of IMERSPEC methodology and time advancement integration to FSI improve the results of the cylinder’s motion and alters distinct vortex shedding patterns in fluid dynamics.

Spanwise layout optimization of aerodynamic countermeasures for multi-mode vortex-induced vibration control on long-span bridges

Aerodynamic countermeasures are widely used to control vortex-induced vibration (VIV) on long-span bridges. However, due to the lack of appropriate three-dimensional (3-D) VIV analysis approach, these countermeasures are usually installed along the entire span of the bridge deck, leading to excessive costs. This study proposes an optimization method for the spanwise layout of aerodynamic countermeasures, aiming to achieve an economical control scheme for multi-mode VIV. An improved mode-by-mode 3-D VIV analysis approach is developed based on the generalized polynomial model to predict the VIV responses of the bridge with different spanwise layouts of aerodynamic countermeasures. The genetic algorithm (GA) is then employed to search for the most economical layout scheme with constraints of limited multi-mode VIV responses. Two alternative types of search spaces for the optimization are presented. The effectiveness of this optimization method is demonstrated on a long-span suspension bridge in conjunction with finite element simulation and wind tunnel tests. The results show a noteworthy reduction in the use of aerodynamic countermeasures, thus highlighting the necessity of countermeasure layout optimization.

Flow field characteristics analysis of vortex-induced vibration of bridge tower based on dynamic mode decomposition method

As a high-rise structure, the tower of a suspension bridge has low stiffness due to the lack of cable system constraints when it is self-supporting. Wind-induced vibration is one of the key factors in design and construction. In this paper, the wind tunnel test of the bridge tower aeroelastic model is carried out in two different flow fields, and the wind vibration response under a self-supporting state is systematically studied. Meanwhile, numerical simulation of the unsteady flow field around the tower section is carried out, and the dynamic modal decomposition (DMD) method is used to study the modal frequency of the flow field, the surface pressure of the section, flow field reconstruction error, and the stability of the flow field around tower section is discussed. The results show that in the self-supporting state, the displacement of the tower top presents a quadratic curve relationship with the wind speed, and no galloping phenomenon occurs under the test wind speed. However, in the uniform flow, when the wind attack angle is 90°, the bridge tower has an obvious vortex-induced vibration (VIV) phenomenon. After decomposing the flow field by the DMD method, it is found that there is strong aerodynamic interference between the double rectangular column sections, the first seven orders of modal energy play a major role in the flow field, and when the main modal energy accounts for more than 90%, the reconstruction can realize the accurate restoration of the information such as the surface pressure. For the complex flow field structure, it shows that the method can more accurately identify the coherent structure and background part in the unsteady flow field. This paper provides an idea for future research on the characteristics of the flow field around complex sections and helps to further improve the understanding of the VIV mechanism.

Nonlinear vortex-induced vibration of wind turbine towers: Theory and experimental validation

Vortex-induced vibration (VIV) of wind turbine tower is a common occurrence in practical engineering, significantly impacting the safety and reliability of structure. An effective method is developed to investigate the VIV characteristics of a wind turbine tower with an elastic foundation and a lumped mass. To simulate the fluid–structure interaction, the van der Pol equation is utilized. The equations of motion of wind turbine tower, accounting for aerodynamic force, are established using Hamilton’s principle and the assumed mode method, and they are solved by the method of multiple scales. Modal functions of the wind turbine tower are obtained through the finite element method (FEM). The analysis further explores the influences of various parameters on the VIV characteristics of wind turbine tower. The results show that the VIV occurs within the frequency lock-in and multi-value ranges, and the critical wind speeds are mainly determined by the diameters of the segments near the tower top. Moreover, as the lumped mass increases or the foundation stiffness decreases, the occurrence of VIV shifts to lower wind speeds. A wind tunnel experiment of a scaled wind turbine tower model validates the frequency lock-in range of the VIV analysis results.

Eigenwave analysis of vortex-induced vibrations on long cylinders in sheared flows

The vortex-induced vibration of long cylinders in sheared flows is usually a mixture of standing and traveling waves. Understanding how the waveform is developed is of significant scientific and engineering interest. However, the interference between the traveling wave components makes the response patterns hard to interpret. Therefore, a spatial–temporal domain decomposition may offer a new perspective for the problem. This paper presents an eigenwave analysis method based on two-dimensional singular value decomposition, aiming to discover the hidden spatial–temporal modes. The application to experimental data shows its capability to separate the traveling and standing wave components, revealing the alternating dominance of these two waveforms along the span. It can also decompose the motion into two intrinsic traveling waves propagating in opposite directions, evolving and interacting in space and time. Based on the amplitude profiles of these waves, we locate the power-in/out regions and evaluate the lock-in range of reduced velocity as 4.73 to 7.68. It also reveals that the varying phase difference between multi-frequency modes, instead of the mode transition, is the main reason for the envelope fluctuation. The findings suggest that the proposed method is a useful data-driven technique extending the current toolkit for research on related topics.

Nonlinear Vortex Induced Vibration Analysis of Electrostatic Actuated Microbeam Based on Modified Strain Gradient Theory

Nonlinear Vortex Induced Vibration Analysis of Electrostatic Actuated Microbeam Based on Modified Strain Gradient Theory

Numerical Analysis on Spanwise Correlation of Vortex-Induced Force of Split Double-Box Beam

The vortex-induced force of bridges is not synchronized along the span direction. The spatial correlation of vortex-induced force becomes obvious when the span of the bridge structure gradually increases, and the mass gradually decreases. Therefore, it is important to study the spanwise correlation of vortex-induced forces of long-span bridges to ensure the accuracy of the prediction of vortex-induced vibration response of bridges. The study established and improved the theory and experimental research methods for vortex-induced vibration analysis of large-span bridges by discussing the spanwise correlation during vortex-induced vibration of the split double-box beam. Taking Xihoumen Bridge as the object, two-dimensional (2D) and three-dimensional (3D) numerical models of the scaled-down sections were designed and established based on the ANSYS Fluent platform and the RANS SST turbulence model. Based on the Newmark-β algorithm, a User Defined Function (UDF) was written for vortex vibration calculation, the three-dimensional bypass of the split double-box beam in static conditions and vortex-induced vibration of the split double-box beam of which were calculated, and the spanwise correlations of the aerodynamic coefficients, the surface pressure coefficients, and the wake wind velocity of the main girder section were analyzed for the static and vibration states of the bridge. The results show that the self-excited force of the split double-box beam in vortex-induced vibration improved its spanwise correlation. Compared with those in a static state, the spanwise correlation of the lift coefficient and torque coefficient increased by 55% and 87%, respectively, and the resistance coefficient increased by more than 10 times. The correlation of the pressure coefficients increased by 153%. The correlation of wake wind velocity increased by 37% in the along-wind direction and that in the across-wind and vertical-wind direction increased by more than 10 times. The accuracy of the numerical simulation results was verified by comparing the pressure distribution and pressure spanwise correlation of the main beam with field-measured data.

Vortex-induced vibration analysis of submerged floating tunnel tension legs

Considering the influence of axial and transverse vibration of tension legs of submerged floating tunnel, the non-linear vibration equation of the tension leg under the action of vortex-induced excitation is derived and solved numerically by Galerkin and Runge–Kutta methods. The results show that the vibration amplitude and frequency of tension legs under the action of vortex-induced excitation are related to the natural frequency of tension legs. Due to water damping, the vortex-induced vibration response of tension legs in submerged floating tunnel is lower than that of the tension leg in air; the shorter the length of the tension leg, the higher will be the current velocity needed to produce vortex-induced resonance; the larger the initial tension of the tension leg, the faster will be the current velocity needed to generate vortex-induced resonance; the transverse pulse force increases with an increase of the initial tension and the outside diameter of the tension leg, and decreases with an increase of the length of the tension leg.

Numerical analysis of vortex-induced vibration on a flexible cantilever riser for deep-sea mining system

The flexible cantilever riser, as a special form of the marine riser, can be encountered in a deep-sea mining system, where the bottom of the long vertical lifting pipeline is connected with the intermediate warehouse. The main objective of this paper is to investigate the effects of the bottom weight caused by the intermediate warehouse and the flow speed on the dynamic responses of the cantilever pipeline. A quasi-3D coupling algorithm based on the discrete vortex method and finite element method is employed to calculate the unsteady hydrodynamic forces and vortex-induced vibrations of this pipeline in the time domain, respectively. We first simulate the VIV of a long flexible riser with two fixed ends in a stepped flow to validate the feasibility of the present method. Then, systematic simulations of cross-flow VIV of the cantilever riser are carried out under a wide range of bottom weights and different current speeds. The number of the vibration mode shows the decreasing tendency with the increase of the bottom weight. In a certain range of the weight, the number of the dominant mode remains unchanged, while the vibration amplitude declines with increasing weight. An amplitude jump phenomenon can be observed when the transition of the dominant mode in two contiguous mode clusters occurs. Moreover, the higher-order modes are excited with the increase of the current speed.

A transfer learning-physics informed neural network (TL-PINN) for vortex-induced vibration

Vortex-induced vibration (VIV) is a typical nonlinear fluid-structure interaction (FSI) phenomenon, which widely exists in practical engineering (such as flexible risers, bridges and aircraft wings). Conventional numerical simulation and data-driven approaches for VIV analysis often suffer from the challenges of computational cost and dataset acquisition. This paper proposed a physics-informed neural network (PINN) enhanced by transfer learning (TL) to study a VIV system (2D). The TL-PINN only used 1/2, 1/4 and 1/8 of the training set (for PINN model) to reconstruct the information of flow field and structure, but with the same prediction accuracy as PINN model. In addition, a stepwise iterative training strategy was proposed to train PINN model. The strategy can effectively reduce the dependence of neural networks on data sets, so as to reduce the training cost of PINN model. The results show that PINN with the stepwise iterative training strategy and TL-PINN can enhance learning efficiency and keep predictability without requiring a huge quantity of datasets. Based on the proposed method, limited and scattered label data from monitoring, numerical and experimental can be fused to realize the reconstruction and prediction of flow field and structure information. It can break the limitation of monitoring equipment and methods in practical projects, and promote the in-depth study of VIV.

Nonlinear Numerical Analysis of Vortex-Induced Vibration of A Three-Dimensional Deepwater Steep Wave Riser with Large Deformation Features

Nonlinear Numerical Analysis of Vortex-Induced Vibration of A Three-Dimensional Deepwater Steep Wave Riser with Large Deformation Features

Stability analysis of vortex-induced vibrations on wind turbines

A parked wind turbine can be subjected to large yaw angles, which causes vortex shedding. Under some particular inflow conditions, the interaction between the shed vorticity and the blade structure could lead to Vortex-Induced Vibrations (VIV). VIV are an instability where the response grows until it reaches a limit cycle oscillation. In this paper, we will focus on this last part of the response. We will see that the shedding makes the aeroelastic system linear time-periodic, and study its stability with Floquet theory. We will use high-fidelity simulations of different inflow conditions, and quantify the stability of the system using a model-free approach.

Three-dimensional vortex-induced vibration analysis of catenary-type risers under flow with different incident angles

This paper proposes a three-dimensional (3D) numerical model for the analysis of vortex-induced vibration (VIV) on catenary-type risers (CTRs). Fully considering the geometrical nonlinearities and large deformation behavior of CTR, this model is established based on the vector form intrinsic finite element (VFIFE) theory and the independence principle (i.e., consider only the flow component perpendicular to the riser axis). The riser is discretized into a finite number of particles, the motion of these particles only has to satisfy Newton's second law and the structure is in perpetual dynamic equilibrium under the combined excitation of internal and external forces on the particles. Moreover, the unsteady hydrodynamic force associated with cross-flow (CF) vibration is modeled as distributed Van der Pol wake oscillators. The model is used to predict the VIV response of the CTRs under various flow conditions (i.e., in-plane uniform flow, shear flow, and diverse angled flow), and the results show well agreement with the corresponding experimental results. Then, the CTR's VIV characteristics under diverse angled flow are further analyzed. The obtained results highlight that the incident angle of the flow has a great influence on the mode transition, frequency locking position, energy transfer, and internal forces.

Incorporation of subcritical Reynolds number into an aerodynamic damping model for vortex-induced vibration of a smooth circular cylinder

Vortex-induced vibration (VIV) of a circular cylinder is known to be affected by the Reynolds number, while this effect has rarely been considered in VIV modeling. This paper attempts to incorporate the Reynolds number into an aerodynamic damping model for simulating the VIV of a circular cylinder with a smooth surface immersed in a smooth flow. Aerodynamic damping parameters within the Reynolds number range of 500 ∼ 33000 (i.e., the TrSL1 and TrSL2 regimes) are identified according to the griffin plots and existing forced vibration experimental data. The model can simulate the peak VIV amplitudes of an elastically supported rigid circular cylinder at different mass-damping parameters in the TrSL1 and TrSL2 regimes. Both experimental results and numerical simulations demonstrate that the peak VIV amplitude of a low-damping cylinder is highly dependent on the Reynolds number, while the dependency is decreased by increasing the mass-damping parameter. The results suggest that the Reynolds number effect is significant in the VIV analysis of a lightly damped cylindrical structure, while the role of Reynolds number seems insignificant for a moderate-damping or high-damping cylindrical structure. For a flexible circular cylinder, the proposed model is expected to predict slightly higher peak VIV amplitudes because the aerodynamic damping effects are overestimated at some segments along its length.

Bifurcation analysis of vortex-induced vibration of low-dimensional models of marine risers

A low-dimensional model of a top-tensioned riser under excitations from vortices and time-varying tension is proposed, where the van der Pol wake oscillator is used to simulate the loading caused by the vortex shedding. The governing partial differential equations describing the fluid–structure interactions are formulated and multi-mode approximations are obtained using the Galerkin projection method. The one mode approximation is applied in this study and two different resonances are investigated by employing the method of multiple scales. They are the 1:1 internal resonance between the structure and wake oscillator (also known as ‘lock-in’ phenomenon) and the combined 1:1 internal and 1:2 parametric resonances. Bifurcations under the varying nondimensional shedding frequency for different mass–damping parameters are investigated and the results of multiple-scale analysis are compared with direct numerical simulations. Analytical responses are calculated using the continuation method and their stability is determined by examining the eigenvalues of the corresponding characteristic equations. Effects of the system parameters including the amplitude of the tension variation, vortex shedding frequency and mass–damping parameter on the system bifurcations have been investigated. The analytical approach has allowed to probe bifurcations occurring in the system and to identify stable and unstable responses. It is shown that the combined resonances can induce large-amplitude vibration of the structure. Counter-intuitively, the amplitude of such responses increases rapidly as the amplitude of the tension variation grows. Comparisons between the analytical and numerical results confirm that the span of the system vibration can be accurately predicted analytically with respect to the obtained response amplitudes of responses. The proposed multi-mode approximation and presented findings of this study can be used to enhance design process of top tension risers.

Nonlinear vibration analysis of vortex-induced vibrations in overhead power lines with nonlinear vibration absorbers

Vortex-induced vibrations are one of the major factors in fatigue failure of power transmission lines and can be mitigated using vibration absorbers in the form of Stockbridge dampers. Since power transmission lines play an important role in modern infrastructure, a thorough understanding of the nonlinear dynamical interactions between conductors, dampers, and wind forces is crucial. Although different nonlinear models exist for conductor vibration with attached dampers or under wind force, no work combines all these nonlinearities in a single model and examines the dynamics of the conductor along with dampers. In an attempt to fill this gap, this work combines the nonlinearities from the mid-plane stretching of the conductor, equivalent cubic stiffness of the Stockbridge damper, and fluctuating lift force modeled as a Van der Pol oscillator in a single model to investigate the nonlinear vortex-induced vibrations. In this work, the conductor is modeled as a simply supported beam and the Stockbridge damper as a mass–spring–damper–mass system with a combination of cubic and linear stiffness. The governing equations of motion are solved analytically using the method of multiple scales for the case of primary resonance between the fluctuating lift-force and conductor. Analytical findings are further validated by comparing against the numerical integration of a reduced-order system, and the results show an excellent match. The analysis is extended by conducting a parametric study to investigate the effect of different system parameters on the frequency response curves. These findings are promising and further provide a direction to design an optimal vibration absorber.

Time-domain analysis of vortex-induced vibration of a flexible mining riser transporting flow with various velocities and densities

Vortex-induced vibration (VIV) can be inevitably encountered in deep ocean mining. As the internal flow is transported axially in the flexible riser, complicated VIV dynamics occurs undergoing both the internal and external flows. Therefore, the object here is to explore the effect of the internal flow with different velocities and densities on VIV response under various uniform current. In this study, a semi-empirical time domain prediction method for VIV dynamics of flexible risers considering both internal and external flows is introduced and adopted. The governing equations are discretized and solved by using finite element method. Firstly, validations are made for VIV without internal flow based on the numerical results and experimental data. Comparisons prove that the simulation could reproduce the VIV dynamics of a flexible riser. Then with the increase of the internal flow velocities and densities, the effect of the internal flow on VIV response is examined. It is found that the dominating frequency and the root mean square (RMS) displacement in both in-line (IL) and cross-flow (CF) directions are notably influenced by the internal flow velocity and density. Besides, the drag coefficient and IL mean deflection are detected magnified while the internal flow velocity and density are increased under different external flow velocities. It should be noted that the change of the internal flow velocity and density could trigger new mode response of the flexible riser, leading to mode transition for the IL and CF dominating modes. In addition, VIV dynamics shows a similar changing trend with the increase of the internal flow velocity and density when the flexible fluid-conveying riser is subjected to different external flow velocities.

EdgeCFD: a parallel residual-based variational multiscale code for multiphysics

High fidelity multiphysics simulations are ubiquitous in science and engineering but still face many challenges to run efficiently in today's supercomputers. This work reports advanced technologies present in EdgeCFD, a hybrid parallel variational multiscale multiphysics finite element software capable of running industrial problems involving turbulent incompressible, compressible, free-surface flows, advection-diffusion of multiple scalar fields, fluid-object interaction using an Arbitrary Lagrangian-Eulerian formulation, and, more recently, used to supporting uncertainty quantification. We also show the strategies to support the solution of large scale problems, including in-situ visualisation and how EdgeCFD handles computational steering. Industrial applications in the oil and gas industry are shown to demonstrate EdgeCFD capabilities. We present the analysis of vortex-induced vibration in cylindrical risers with appendages to reduce drag and lift, and the simulation of successive discharges of turbidity currents, a critical process for understanding the formation of oil reservoirs.

Experimental Study and Fatigue Analysis of Vortex-Induced Vibration of Umbilical Cable Considering Internal Friction

In order to investigate the effect of internal friction of umbilical cable on its vortex-induced vibration (VIV) responses, the experimental study on VIV of bond umbilical cable (BUC) and un-bond umbilical cable (UBUC) was carried out in an experimental tank. A current generator in the laboratory simulated the uniform current, and the current velocities were observed in real time by using a Doppler Velocimeter. In addition, different sizes of top tension were applied to the umbilical cable model. The VIV responses of the umbilical cable model were measured by using Fiber Bragg grating (FBG) strain sensors. The displacement responses of umbilical cable model were reconstructed based on the experimental strain data processed by modal superposition method. In this paper, the traveling wave characteristics, the spatial-temporal distribution characteristics of frequency and fatigue damage of the BUC and UBUC under VIV are studied. The experimental results show that there are obvious differences between BUC and UBUC in the response characteristics of VIV. The UBUC appears the traveling wave sooner than BUC, but its standing wave characteristics are more obvious than those of BUC at high velocities. Compared with BUC, the spatial-temporal distribution of UBUC frequencies appears wide-band distribution sooner, but has narrower bandwidth in the “lock-in” state. The level of fatigue damage of BUC was approximately the same as that of UBUC.

Triangular Separation Distance Effects on Wave Electrical Energy Harvester Performance

Energy scavenging has become a topic of interest toward green and environmentally friendly. Vortex generated in the wake region behind a bluff body is potential to be harvested and transform the mechanical vortices into electrical energy. Therefore, the study of the fluid flow and piezoelectric material is highly potent and a promising research area. Thus, the vortex-induced vibration (VIV) energy harvesting of two bluff bodies in a tandem arrangement is investigated using the 3D simulation. There are four sets of bluff bodies with various distance ratio, x/D from 3 to 6, were analyzed in this simulation. The coupling analysis was analyzed using ANSYS Transient Structural and computational fluid dynamic Fluent module. The triangular width, to 100 mm and the fluid average flow velocity is 1.46 ms−1, which corresponds to Reynold number (Re) of 10k. Four types of analysis have, out; velocity vector, turbulence kinetic energy, piezoelectric tip deformation, and generated output voltage. The results show the bluff shape with spacing ratio 6 has better vortex shedding formation and turbulence kinetic energy formed on both upstream and downstream triangular bluff body. The tips mesh displacement for piezoelectric is highest at space ratio 6 with 7.0 x 10−5 essential, and after 10s the beam deflection is continuing at around 1 x 10−5 m. While the voltage generated is, at spacing ratio 6 with 0.2 v produced. The obtained results are essential to VIV analysis of the dual triangular cylinder with piezoelectric film, which is vital in energy scavenging knowledge.