Vortex-induced Vibration Research Articles

Applying PID control to 2-dof vortex induced vibration of a cylinder

Suppressing a cylinder's vortex-induced vibration (VIV) is an essential means to improve the fatigue life of risers. There is limited research on Proportional integrated derivative (PID) control in cylinder vortex-induced vibration, which has an industrial occupancy rate of over 90%. Therefore, this paper uses PID to study the cylinder's 2-DOF VIV. Firstly, the VIV model of PID control based on a wake oscillator is established and verified. Finally, the control effect of PID on VIV is studied, and some results are obtained. It is feasible to suppress the VIV of the cylinder based on the wake oscillator by PI or PID method. The control force time history curve shows the change of multi-frequency and multi amplitude period of the control force, and the cylindrical trajectory range after control is significantly reduced, which is 68.4%–97.1% lower in X direction and Y direction than that of no-control.

Energy extraction and optimization studies on vortex-induced vibration of the elastically mounted rigid cylinder using wake oscillator model

The vortex-induced vibration (VIV) response of an elastically mounted rigid cylinder from the standpoint of energy harvesting is analyzed with the aid of the wake oscillator model (WOM). A model of an elastically mounted rigid cylinder free to oscillate in the in-line (IL) and cross-flow (CF) directions subjected to different uniform flow velocities is considered and its responses under different mass ratios are predicted using the modified wake oscillator model. For modeling structure motion, the dynamic equilibrium equation, and for modeling the fluid part, the Van der Pol wake oscillator is utilized and they are coupled together to get the response in IL and CF directions. A comparative study is performed between the numerical and the experimental results and they are found to be in good agreement. The study is then probed into the scope of energy extraction from VIV which will presumably throw light into the development of VIV-based energy harvesting methods which is a potential future hope for the renewable energy sector. Parametric optimization study is carried out to determine the maximum harnessable energy from VIV. The response of the cylinder for the optimal parametric combination is analyzed in the time and frequency domain. It is observed that damping and reduced velocity play a crucial role in the energy extraction.

Adjacency-based, non-intrusive model reduction for vortex-induced vibrations

Vortex-induced Vibrations (VIV) pose computationally expensive problems of high practical interest to several engineering fields. In this work we develop a non-intrusive, reduced-order modeling methodology, applied to two-dimensional (2D), VIV cases subject to a laminar, incompressible flow. Performing a physics-informed approximation of the Arbitrary Lagrangian–Eulerian (ALE) incompressible Navier–Stokes (NS), we derive a discrete-time, quadratic-bilinear model structure for the velocity flowfield on a reference domain. This structure, along with a predefined sparsity pattern motivated by the adjacency-based sparsity of the discretized NS-ALE operators, leads to the formulation of a sparse, full-order model (sFOM) inference problem. Thus, the data-driven inference task requires solving many “local” least squares (LS) problems, isolating the contribution of geometrically “nearest neighbours” for each degree of freedom. Numerical aspects of inference such as data centering and regularization, as well as the direct enforcement of boundary conditions under the sFOM formulation are extensively discussed. The inferred, sFOM operators are then projected to a non-intrusive reduced-order model (ROM) for the velocity flowfield via the Proper Orthogonal Decomposition (POD). The resulting non-intrusive ROM (sFOM-POD) is coupled with the first-principle, 2D solid oscillation equations, resulting to a hybrid physics-informed/first-principle VIV dynamics model, simulated using an implicit time integration scheme. The mapping of the coupled solution from the ALE reference domain to the current configuration is also presented. This methodology is applied to two testcases of an elliptical, non-deformable solid mounted on springs, subject to Re=90,180 flows. Numerical results indicate a successful coupling between the data-driven flowfield and solid dynamics, with prediction errors of less than 3% for both the flowfield and the solid oscillation. A comparative study with respect to the sFOM-POD dimension indicates the robustness and potential of the approach.

Wavelength-induced shedding frequency modulation of seal whisker inspired cylinders

The spanwise undulated cylinder geometry inspired by seal whiskers has been shown to alter shedding frequency and reduce fluid forces significantly compared to smooth cylindrical geometry. Prior research has parameterized the whisker-inspired geometry and demonstrated the relevance of geometric variations on force reduction properties. Among the geometric parameters, undulation wavelength was identified as a significant contributor to forcing changes. To analyze the effect of undulation wavelength, a thorough investigation isolating changes in wavelength is performed to expand upon previous research that parameterized whisker-inspired geometry and the relevance of geometric variations on the force reduction properties. A set of five whisker-inspired models of varying wavelength are computationally simulated at a Reynolds number of 250 and compared with an equivalent aspect ratio smooth elliptical cylinder. Above a critical non-dimensional value, the undulation wavelength reduces the amplitude and frequency of vortex shedding accompanied by a reduction in oscillating lift force. Frequency shedding is tied to the creation of wavelength-dependent vortex structures which vary across the whisker span. These vortices produce distinct shedding modes in which the frequency and phase of downstream structures interact to decrease the oscillating lift forces on the whisker model with particular effectiveness around the wavelength values typically found in nature. The culmination of these location-based modes produces a complex and spanwise-dependent lift frequency spectra at those wavelengths exhibiting maximum force reduction. Understanding the mechanisms of unsteady force reduction and the relationship between undulation wavelength and frequency spectra is critical for the application of this geometry to vibration tuning and passive flow control for vortex-induced vibration (VIV) reduction.

Nonlinear State-Space Model of Self-excited forces for Bluff Body Aeroelasticity

This paper introduces a novel state-space model of nonlinear self-excited forces designed to capture amplitude dependency and unsteady effect in bluff body aeroelasticity. In the present form, this model represents a theoretical extension of the classical linear state-space model into the nonlinear regime, particularly relevant when a bluff section undergoes large amplitude oscillations. The proposed model incorporates additional state variables to approximate nonlinear convolution-based indicial functions, thereby providing a valuable tool for estimating nonlinear wind-induced instabilities, including nonlinear flutter limit cycle oscillation (LCO), vortex-induced vibration (VIV), and unsteady galloping. Furthermore, we establish the analytical foundation for identifying nonlinear parameters through the equivalent linearization of nonlinear transfer functions and the development of a numerical solving algorithm for the nonlinear governing equation. The feasibility of this model is rigorously validated through experimental results pertaining to nonlinear flutter, unsteady galloping, and VIV of typical bluff sections. Additionally, this model serves as the cornerstone for a nonlinear analytical framework in the time domain, facilitating the integration of both aerostatic and structural nonlinearities into comprehensive structural analyses.

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.

Vortex-induced vibration of a functionally graded metamaterial plate attached to a cylinder in laminar flow

Understanding the interaction between fluid and structures under various fluid conditions is critical for engineering applications, with vortex-induced vibration (VIV) being a significant area of research. This study presents a comprehensive numerical investigation on the VIV behaviors of functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) splitter plates attached to a circular cylinder by employing the finite element analysis. The splitter plate is composed of multiple GOEAM layers with the material properties possessing a gradient variation along the thickness direction. The local mesh quality is monitored and improved by Yeoh smoothing. The present work is focused on the effect of the auxetic properties of GOEAM on plate vibrations, the influence of plate length on wake patterns, and the effect of fluid loads on the cylinder–plate body and vortex pattern. The study reveals that: (1) the plate structure with HGRX-WGRX metamaterial distribution pattern with high elastic moduli in surface layers exhibits low deflection amplitudes, (2) shorter plates intensify vortices while longer plates reduce vortex prevalence, (3) the natural frequencies of both FG-GOEAM and pure metallic plates are found to be well above the vortex shedding frequency and as such, the fluid loads have a negligible effect on the cylinder–plate body and vortex patterns. These insights offer an in-depth understanding of fluid-structure interactions and valuable knowledge for the design and optimisation of graphene based metamaterial structures in engineering applications.

A Data-Driven Model for Predictive Modeling of Vortex-Induced Vibrations of a Long-Span Bridge

Vortex-induced vibration (VIV) of long-span bridges can be of large amplitude, which can influence serviceability. Therefore, it is important to predict the response of vortex-induced vibration to aid the management of long-span bridges. A novel data-driven model is proposed to predict the time history of the dynamic response of VIV events. Specifically, the proposed model consists of gated recurrent unit (GRU) neural networks and the Newmark-beta method. GRU neural networks can perform accurate sequential prediction, and the Newmark-beta method can complement the physical meaning of the middle output of the proposed model. To aid the accurate prediction of the amplitude of VIV events, the proposed model employs weighted mean square error as the loss function, which can put more emphasis on the amplitude. The proposed model is validated on measured VIV events of a long-span suspension bridge. The weighted mean absolute percentage error and Pearson correlation coefficient of the trained model indicate the effectiveness of the proposed model.

A vortex-induced vibration device based on MG-TENG and research of its application in ocean current energy harvesting

In recent years, with the extensive research on the application of triboelectric nanogenerators (TENGs) by scholars all over the world, the development of TENGs in harvesting and utilization of ocean energy has attracted more and more attention according to the advantages of TENGs in low-frequency energy harvesting. As a kind of ocean energy, the development and utilization of ocean current energy is of great significance to the diversification of energy sources, the promotion of sustainable energy development, the protection of ecological environment and the response to climate change. In this work, a novel device based on the combination of vortex-induced vibration (VIV) and multi-grating TENG (MG-TENG) is proposed for energy harvesting in low-speed ocean currents. The device consists of an up and down moving float driving the TENG to convert kinetic energy into electrical energy. The result shows that the system has a maximum average output power of nearly 20 μW under the condition of 8 grating TENG. This work demonstrates the ability of devices based on the combination of VIV and MG-TENG to drive low-power electronic components, demonstrating future applications for sensing, positioning, and more.

Analysis of the vortex-induced vibration response characteristics of riser under the soft suspension evacuation condition

This paper establishes a nonlinear dynamic model for a suspended riser under the condition of considering realistic configurations, based on the principles of virtual work and Hamilton's variational principle. The nonlinearity of the model is manifested by considering vortex-induced vibration in the cross flow (CF) and in-line (IL) directions, as well as large deformations, taking into account the variable diameter of the riser in the compliant riser system. The model is discretized using the finite element method and solved using the Newmark-β method. Experimental validation is conducted to verify the effectiveness of the model. Utilizing the parameters of a riser in a well in the South China Sea, the paper explores the influence of different environmental and structural parameters on the VIV response characteristics of a compliant riser. Results show that the vibration frequency is controlled by both the bare tube and buoyant block when the buoyant block coverage rate is 25%, which can significantly inhibit VIV. With the increase of flow velocity, the VIV energy jumps from low order to high order, and the riser mode also transitions from low order to high order. The increase in suspension length transfers the vibration energy from high to low frequency, thus realizing energy transition and mode shape transformation. With the increase in LMRP weight, the vibration and natural frequencies of the riser increase synchronously, the vibration amplitude decreases, and the mode shape remains unchanged.

Study on the mechanism of vibration signal generation in water supply pipeline leaks

This study addresses water supply network leakage by employing numerical simulations to overcome challenges related to too small orifice hindering sensor deployment. Utilizing computational fluid dynamics and finite element methods, coupled with large eddy simulation, flow field distribution within pipes and at leakage orifice is investigated. The formation of leakage flow fields is categorized into three stages: leakage formation, unstable leakage, and stable leakage. During the leakage stage, the flow field is analyzed, and four regions—bottom central, bottom vortex, upper central, and upper vortex—are identified based on spatial characteristics. Detailed variable distribution patterns (velocity, pressure, vorticity) are provided in various planes. Understanding these distribution characteristics, six excitation sources responsible for generating leakage vibration signals are identified: pulsating velocity, pulsating pressure, bubble rupture, cavity pulsation, vortex-induced vibration, and gas expansion. The relationships among these excitation sources and their intensities concerning pipeline pressure and leak orifice radius are analyzed. Notably, a positive correlation between pressure and the intensity of all excitation sources is observed, while the impact of leak orifice size on these sources is found to be intricate. This research significantly contributes to an enhanced understanding of the physical processes associated with pipeline leakage.

Numerical investigation on the effect of bionic fish swimming on the vortex-induced vibration of a tandemly arranged circular cylinder

The effect of bionic fish swimming on the vortex-induced vibration (VIV) of a circular cylinder arranged in tandem at a low Reynolds number of 150 is numerically investigated in this work. The bionic fish placed upstream of the cylinder with gap ratios of 1, 3, and 5 and that located downstream of the cylinder with gap ratios of 3 and 5 are examined in the simulations that were carried out in the reduced velocity range of Ur = 2–15. It is found that both the gap ratio and the reduced velocity have a significant influence on the VIV response and wake flow structure. When the bionic fish is placed upstream, the maximum response amplitude of the downstream cylinder is much greater than that of an isolated one. Two flow regimes are identified in terms of the shear layer reattachment, i.e., the continuous reattachment and the alternate reattachment. Comparing the vortex shedding frequencies of the cylinder and the swimming fish, it is found that the frequency of the cylinder is always locked in the fish swimming frequency, and multiple frequencies occur at Ur = 5. When the bionic fish is arranged downstream, four flow regimes are observed, including the extended-body, continuous reattachment, alternate attachment, and co-shedding regimes. Furthermore, the time-mean energy transfer coefficient of the cylinder is considerably higher at Ur = 5 than that when the fish is placed upstream of the cylinder.

Experimental study of the vortex-induced vibration of a circular cylinder considering coupling effect in along- and across-wind direction

Tower-like structures with circular section are prone to unexpected across-wind vortex-induced vibration (VIV), and the along-wind response is usually neglected due to its amplitude being much smaller than that of VIV. Recent research pertaining to tall buildings has revealed, nevertheless, that the structural responses in the along-wind and across-wind directions are coupled in a way that results in a decrease in the across-wind response at the wind speed of VIV along with an increased along-wind response. However, the impact of coupling on tower-like structures has not yet been examined. Moreover, tower-like structures with a circular cross section undergo tip-induced vibration at the wind speed higher than vortex-resonance wind speed. However, the impact of this coupling effect on the tip-induced vibration remains uncertain. In this paper, a two-degree-of-freedom rocking model wind tunnel test is carried out under low turbulence and turbulent flow to investigate the coupling effect of tower-like structures. Experiment results show that the coupling effect exists at both the vortex-resonance vibration wind speed and the tip-induced vibration wind speed. Besides, when the along-wind response is coupled with the across-wind responses, it illustrates a steady harmonic vibration with a hardened non-Gaussian characteristic, and its kurtosis decreases to 1.5. Finally, the measured tip-associated vortex shedding frequency suggests that there is a “lock-in” phenomenon of the tip-induced vibration, this new finding improves the understanding of the wind-induced response at high wind speeds.

Experimental investigation on the vortex-induced vibration response of a lazy-wave flexible riser filled with different fluid media

This paper reports the experimental results of the vortex-induced vibration (VIV) of a lazy-wave flexible riser filled with different fluid media, including the water and helium as typical liquid and light gas examples. The lazy-wave configuration was produced by mounting a buoyancy module of approximately triple the riser diameter on the one-third of the riser length measured from the riser base. The VIV tests were carried out in the depth-averaged reduced velocity (U¯r) range of 9.32–23.19 using the non-intrusive optical measurement with a couple of high-speed cameras. The experimental results indicate that not only the excited mode of in-plane response but also the response amplitude is significantly adjusted when the internal fluid changes, while the excited mode of the out-of-plane response has no obvious modification. Both the water- and helium-filled risers experience the space-varying dominant frequency. However, the helium-filled riser segment possessing a higher dominant frequency is significantly shortened as compared to the water-filled one. When the internal fluid shifts from water to helium, the in-plane mode transition from the first to second becomes incomplete, and the mode transition becomes smoother as U¯r grows. It is found that the starting position of the mode transition is related to the dominant mode as well as the response direction. Then, the influenced length of the riser response from the buoyancy module and the affecting length of the riser on the buoyancy module response are quantified in terms of the spatial distribution of the dominant frequency in comparison with the natural frequencies. The in-plane response of the helium-filled riser is more vulnerable to the oscillation of the buoyancy module, and hence, the coupling between the in-plane and out-of-plane responses is weaker than the water-filled riser. When the impact of buoyancy module on the riser response is enhanced, the reverse effect is weakened.

Hybrid Method for Large Diameter Spool Vortex-Induced and Flow-Induced Vibration Analysis

Hybrid Method for Large Diameter Spool Vortex-Induced and Flow-Induced Vibration Analysis

Fluid–structure interaction simulation and optical fibre stress analysis of submarine cables in vortex‐induced vibration

AbstractUnder the current scouring, submarine cables are prone to be exposed, suspended, and even vortex‐induced vibration (VIV), threatening their mechanical and electrical properties. In this contribution, a finite element simulation model of 110‐kV single‐core optical fibre composite submarine cable is established. The natural frequency and resonant frequency of the model are obtained through wet mode analysis and harmonic response analysis. Then the VIV is simulated by the fluid–structure coupling method. Moreover, the stress extraction method of the torsional optical fibre position under the VIV is proposed. The results show that when the reduced speed is 2.57, the submarine cable appears beating vibration, which is composed of two vibrations with similar frequencies. When the reduced speed is 7.08, the vibration frequency is about 7.813 Hz, causing a rapid increase in vibration amplitude. The stress distribution of the torsional optical fibre presents a mirror image relationship at two moments separated by half a vibration cycle. Also, the frequency of stress change is the same as the frequency of VIV, which can judge whether the VIV occurs. The VIV range and position can be determined by the location where the stress changes the most.

VIV array for wind energy harvesting

Harvesting energy from flow using vortex-induced vibration (VIV) piezoelectric transducers has gained significant attention in recent decades due to their advantages, such as simple structure, blade-less layout, and low maintenance costs. However, most existing studies have focused on designing and analyzing a single piezoelectric energy harvester (PEH), without investigating the fluid-structure interaction and coupling of multiple PEH arrays. Here, we conducted an experimental study using a 2 × 2 PEH array to investigate its dynamic response under different wind speeds and spacings. Results show that the output voltage of the PEH array increases as the vertical spacing decreases, and the maximum average output voltage of 20.6 V per PEH is obtained when the minimum vertical spacing, maximum horizontal spacing, and resonance wind speed conditions are met. Compared to a single PEH, the 2 × 2 array arrangement increases the average output voltage by up to 168%. Additionally, the average output power under the resistance of 1 MΩ increases by 629% to 4.3×10−4 W per PEH, and the maximum output power increases by 792% to 5.3×10−4. Experiments indicate that the vortex shedding coupling can induce higher vibration in a well-defined array, which paves a new way for developing bladeless wind farms.

Revisiting the Serviceability of Long-Span Bridges under Vortex-Induced Vibrations Based on Human Body Vibration

Vortex-induced vibrations (VIVs) have been frequently observed on long-span bridges (LSBs) in recent years. Unlike other destructive aerodynamic phenomena of LSBs, VIVs are self-limited in amplitude, primarily affecting the serviceability of LSBs through unpleasant users’ feelings characterized by human body vibration. Most existing studies discussed this issue based on a popular human body vibration measure, the human comfort index (HCI) in ISO 2631-1. However, the HCI is primarily concerned with vibration above 0.5 Hz, which might be unsuitable for disclosing the influence of VIV because of the low-frequency features of LSBs’ VIVs. To address this limitation, this study advocates using the motion sickness index (MSI) to revisit the serviceability of LSBs experiencing VIVs based on an innovative wind-traffic-bridge simulation platform. Different from current studies exclusively focusing on vehicle riders, this paper additionally incorporates a vibration model for standing persons to understand the feelings of the pedestrians on the bridge. On this basis, the influence of VIV and traffic load is comprehensively examined. The results indicate that the HCI is inappropriate for exploring the serviceability of LSBs under VIVs regarding users’ feelings, but the MSI is a good alternative. Moreover, the increasing traffic load can obviously mitigate the adverse effect of VIVs on the bridge’s serviceability, which may be utilized to control VIVs of LSBs in real-world engineering practice.

Topology optimization of stationary fluid–structure interaction problems considering a natural frequency constraint for vortex-induced vibrations attenuation

Topology optimization applied to fluid–structure interaction problems is challenging because the physical phenomenon in real engineering applications is usually transient and strongly coupled. This leads to costly solutions for the forward and adjoint problems, the computational bottleneck of the topology optimization method. Thus, this paper proposes a topology optimization problem formulated in the steady state with post-processing and verification in the transient state. The objective is to design a stiff structure with lower effects of vibrations induced by the transient fluid vortices. For that, the compliance minimization problem is solved subject to a natural frequency constraint (without any volume constraint). The TOBS-GT (Topology Optimization of Binary Structures with geometry trimming) method is used to solve the problem. To observe the vortex-shedding around the structure, a transient simulation is performed considering an incompressible fluid flow under a laminar regime and the structure subject to large displacements. For topology optimization, the fluid flow is at a steady state and the structure is modeled considering small displacements, i.e., a one-way coupled analysis. The finite element method is used to solve the governing equations and obtain the direct/adjoint sensitivities for the compliance and natural frequency functions. In this approach, the natural frequency of the structure is shifted away from the fluid flow vortex-shedding frequency, avoiding resonance. Numerical examples show that the proposed method can be effectively applied to design 2D structures in FSI problems with lower effects of Flow-Induced Vibration, attenuating the levels of displacement at the analyzed points of the structure.

Experimental investigation on L-beam vortex-induced vibration piezoelectric energy harvester with interference step

In this study, an L-beam vortex-induced vibration piezoelectric energy harvester with interference step is proposed. The experimental results show that the interference step can broaden the effective wind speed bandwidth in the second resonance region of the energy harvester and increase its energy output amplitude significantly. When the load resistance is 90 kΩ, the effective wind speed bandwidth in the second resonance region of the energy harvester can be expanded by a maximum of more than 200%, and the peak output power can be increased by a maximum of 291% by adjusting the position, width and height of the step.