Flexible Cylinder Research Articles

Numerical Study of Vortex-Excited Vibration of Flexible Cylindrical Structures with Surface Bulge

This study conducted numerical simulations of three-dimensional vortex-induced vibrations (VIV) on cylindrical bodies with various surface protrusion coverage rates, systematically investigating the impact of coverage and protrusion height on the vibrational response of flexible cylinders. The fluid forces on the surface of the riser were resolved using the finite volume method, while the structural forces were solved with the finite element method. A strongly coupled approach was employed for iterative updates between the flow field and structural field data, achieving a bidirectional flow–structure coupling simulation of VIV in a marine environment. The study further explored the performance of surface protrusions in suppressing VIV and considered protrusion heights of 0.1 times the cylinder diameter (0.1D) under coverage rates (CR) of 0%, 10%, 20%, 30%, and 40%, as well as seven different protrusion heights of 0.05D, 0.1D, and 0.15D at a 20% coverage rate. The mechanism of VIV suppression by surface protrusions was identified as altering the separation point of the shear layer and the frequency of vortex shedding through the vortices formed between the surface protrusions. It was found that a 20% coverage rate with a protrusion height of 0.01D (CR20) effectively suppressed the VIV of the cylinder, showing the best performance in VIV suppression, with an efficiency of 30.04%. These results provide a theoretical basis for designing more efficient VIV suppression devices and contribute to enhancing the resistance of marine structures against vortex-induced vibrations.

Vortex-induced vibration experiments of flexible cylinders with floaters: effects of diameters, length, relative distance, total buoyancy and helical strakes

Vortex-induced vibration experiments of flexible cylinders with floaters: effects of diameters, length, relative distance, total buoyancy and helical strakes

Vortex-Induced Vibration of Flexible Cylinders in Cross-Flow

This review provides a comprehensive analysis of the literature on vortex-induced vibration (VIV) of flexible circular cylinders in cross-flow. It delves into the details of the underlying physics governing the VIV dynamics of cylinders characterized by low mass damping and high aspect ratio, subject to both uniform and shear flows. It compiles decades of experimental investigations, modeling efforts, and numerical simulations and describes the fundamental findings in the field. Key focal points include but are not limited to amplitude–frequency response behavior, the relationship between the distributed loading acting on the cylinder and the trajectories and the near wake structures around the cylinder, the existence of traveling waves, the identification of power-in/power-out regions, and the modal overlapping and mode competition phenomena.

Numerical investigation on the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow

Vortex-induced vibration (VIV) of flexible cylinders is an important phenomenon in ocean structures, which may cause fatigue damage and structural failure of offshore structures. Much literature has extensively explored VIV of flexible cylinders under various flow conditions, such as uniform and linearly varying shear flow. However, real scenarios in most cases involve non-uniform, non-linearly varying shear flow profiles. Hence, it is important to investigate the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow profiles. This study employs a wake oscillator model (WOM) that simulates the VIV response of the flexible cylinder under the action of non-linearly varying shear flow velocity profiles. The flexible cylinder subjected to linearly varying sheared flow velocity profiles not only overpredicts but also underpredicts the VIV responses compared to the non-linearly varying sheared flow profile, which represents the real scenario. The VIV mode number for the flexible cylinder subjected to non-linear shear flow was found to have a non-linear relationship with that of linear shear flow. The VIV response of the flexible cylinder subjected to a linearly varying shear flow profile exhibits more travelling wave behaviour compared to non-linear shear flow. The location of the maximum VIV response of the structure having the same aspect ratio (L/D) and shear parameter (β), was different for linear and non-linear flow profiles across the span. The time and frequency domain responses showed a shift in the frequency band. The results obtained from the numerical simulations give better insights into the vibrational behaviour of flexible cylinders in realistic flow environments.

Exploring Wave–Vegetation Interaction at Stem Scale: Analysis of the Coupled Flow–Structure Interactions Using the SPH-Based DualSPHysics Code and the FEA Module of Chrono

Aquatic vegetation in the littoral zone plays a crucial role in attenuating wave energy and protecting coastal communities from hazardous events. This study contributes to the development of numerical models aimed at designing nature-based coastal defense systems. Specifically, a novel numerical application for simulating wave–vegetation interactions at the stem scale is presented. The numerical model employed, DualSPHysics, couples the meshfree Smoothed Particle Hydrodynamics (SPH) fluid solver with a structural solver to accurately capture the two-way interactions between waves and flexible vegetation. The proposed numerical model is validated against experimental data involving a submerged rubber cylinder representing an individual vegetation stem, subjected to regular waves. The results demonstrate excellent agreement in hydrodynamics, force transfer, and the swaying motion of the flexible cylinder. Importantly, the approach explicitly captures energy transfer between the fluid environment and the individual stem. The numerical results indicate persistent turbulent flow along the vegetation stem, even when its swaying speed matches that of the surrounding environment. This reveals the presence of vortex shedding and energy dissipation, which challenges the concept of passive swaying in flexible aquatic vegetation.

Improvement for modeling the damping of the wake oscillator based on the Van der Pol scheme

Given the importance of risers and umbilical cables in the exploitation of deep-sea resources, the vortex induced vibration (VIV) of long flexible cylinders has been systematically studied, and it is acknowledged that the wake oscillator is a satisfactory tool in practically predicting the VIV for offshore engineering applications. Based on the conventional wake oscillator with different damping term formulations, the present study systematically explores the influences of the coefficients and the maximum order of a polynomial damping term within the Van der Pol type wake oscillator. More specifically, the coefficients of the second-order polynomial are adjusted to vary inside a reasonable range, and the polynomial order is increased from the conventional specification of 2–4, 6, and 8. The vibrations of the flexible cylinder predicted by the revised wake oscillator are compared to the measurements taken from an experiment reported in the literature. The comparison indicates that increasing polynomial coefficients generally reduce VIV dominant mode numbers. In addition, increasing the polynomial order aligns the dominant mode more closely with experimental data, although this effect diminishes when the polynomial order exceeds 4. It is argued that the gradual change in phase differences along the cylinder induced by increasing either polynomial coefficient or maximum order could be the reason. The present study sheds light into the mechanism for the damping effect observed in hydrodynamic forces observed in VIVs and lays the foundation for suggesting an optimal formulation of the damping terms as 0.45q2+0.6q−0.3 compared to the conventional formulation of 0.3q2−0.3.

In Situ Forming, Enzyme-Responsive Peptoid-Peptide Hydrogels: An Advanced Long-Acting Injectable Drug Delivery System.

Long-acting drug delivery systems are promising platforms to improve patient adherence to medication by delivering drugs over sustained periods and removing the need for patients to comply with oral regimens. This research paper provides a proof-of-concept for the development of a new optimized in situ forming injectable depot based on a tetrabenzylamine-tetraglycine-d-lysine-O-phospho-d-tyrosine peptoid-D-peptide formulation ((NPhe)4GGGGk(AZT)y(p)-OH). The chemical versatility of the peptoid-peptide motif allows low-molecular-weight drugs to be precisely and covalently conjugated. After subcutaneous injection, a hydrogel depot forms from the solubilized peptoid-peptide-drug formulation in response to phosphatase enzymes present within the skin space. This system is able to deliver clinically relevant concentrations of a model drug, the antiretroviral zidovudine (AZT), for 35 days in Sprague-Dawley rats. Oscillatory rheology demonstrated that hydrogel formation began within ∼30 s, an important characteristic of in situ systems for reducing initial drug bursts. Gel formation continued for up to ∼90 min. Small-angle neutron scattering data reveal narrow-radius fibers (∼0.78-1.8 nm) that closely fit formation via a flexible cylinder elliptical model. The inclusion of non-native peptoid monomers and D-variant amino acids confers protease resistance, enabling enhanced biostability to be demonstrated in vitro. Drug release proceeds via hydrolysis of an ester linkage under physiological conditions, releasing the drug in an unmodified form and further reducing the initial drug burst. Subcutaneous administration of (NPhe)4GGGGk(AZT)y(p)-OH to Sprague-Dawley rats resulted in zidovudine blood plasma concentrations within the 90% maximal inhibitory concentration (IC90) range (30-130 ng mL-1) for 35 days.

Dynamics and Wake Interference Mechanism of Long Flexible Circular Cylinders in Side-by-Side Arrangements

The vortex-induced vibrations of two side-by-side flexible cylinders in a uniform flow were studied using a three-dimensional direct numerical simulation at Reynolds number Re = 350 with an aspect ratio of 100, and a center-to-center spacing ratio of 2.5. A mixture of standing-traveling wave pattern was induced in the in-line (IL) vibration, while the cross-flow (CF) vibration displayed a standing-wave characteristic. The ninth vibration mode prominently occurred in both IL and CF directions, along with competition between multiple modes. Proximity effects from the neighboring cylinder caused the primary frequency to be consistent between IL and CF vibrations for each cylinder, deviating from the IL to CF ratio of 2:1 in isolated cylinder conditions. Repulsive mean lift coefficients were observed in both stationary and vibrating conditions for the two cylinders due to asymmetrical vortex shedding in this small gap. Comparatively, lift and drag coefficients were notably increased in the vibrating condition, albeit with a lower vortex shedding frequency. Positive energy transfer was predominantly excited along the span via vortex shedding from the cylinder itself and the neighboring one, leading to increasing lower-mode vibration amplitudes. The flip-flopping (FF) wake pattern was excited in the stationary and vibrating cylinders, causing spanwise vortex dislocations and wake transition over time, with the FF pattern being more regular in the stationary cylinder case.

Numerical investigation of vortex induced vibrations on cylinders

The paper addresses Vortex Induced Vibrations (VIV) caused by tower vortex shedding through LES simulations of a wind tunnel experiment. A high-fidelity (HiFi), Fluid Structure Interaction (FSI) framework for aeroelastic analysis of 3D flexible cylinders is established, based on the open-source Computational Fluid Dynamics (CFD) code OpenFOAM and the coupling library preCICE. In the present study, the FSI framework is employed with the aim to replicate a low Reynolds (Re=26000) forced vibrations wind tunnel experiment of a circular cross-section rigid cylinder. The paper compares predictions of the aerodynamic damping of the oscillating cylinder for different oscillation frequencies within the lock-in range and amplitudes against experimental results. While the model consistently predicts the lock-in range of frequencies and the trends in the variation of the aerodynamic damping with the oscillation amplitude, it falls short of accurately capturing the maximum value of the aerodynamic damping at the onset of lock-in.

Determination Of Drag And Inertia Coefficients By An Analytical Model

Hard structures like dykes or groins have been recognized for their negative environmental impact and limited durability in the face of climate change (Sutton-Grier et al., 2015). The concept of Shore Soft Engineering (SSE) has allowed ecological considerations to be embedded in the design of coastal protection (Hartig et al., 2011). Among emerging defense structures, nature-based solutions are built with natural materials and rely on physical properties and mechanisms observed in nature. They aim to protect, manage and restore ecosystems while providing some benefit to the human-being and biodiversity (Cohen-Shacham et al., 2016); they offer an interesting alternative to hard structures. However, implementing these solutions in urbanized coastal areas where ecosystems are vulnerable can be challenging. Another alternative approach is using biomimetic solutions, which can provide the functions of natural systems like seagrass, dunes, or coral through robust human-made constructions. Natural habitats exist in a variety of more or less complex forms, ranging from rigid (mangroves, coral) to flexible (seagrass) (Mullarney and Henderson, 2018); and they drive changes in the current profile, in wave dissipation or in sediment motion. Understanding how to mimic these systems, in particular their internal geometry and hydrodynamic effects, is challenging. This complexity makes the development of biomimetic solutions difficult (Perricone et al., 2023). In this context, this study strictly focuses on wave dissipation by flexible systems. Wave dissipation by natural habitats has been extensively studied through laboratory experiments (Houser et al., 2015) and in-situ measurements (Bradley and Houser, 2009). The pioneer analytical model (Dalrymple et al., 1984) depicted aquatic vegetation as rigid cylinders; however, the rigidity assumption fails to capture the inherent flexibility of plants. Alternative strategies emerged to account for this flexibility, such as using an empirical drag coefficient (Mendez and Losada, 2004) or introducing an effective length, representing the length that a rigid cylinder would have to dissipate the same wave height as flexible cylinders (Luhar and Nepf, 2016). However, to define this effective length or an empirical drag coefficient, it is necessary to carry out in-situ measurements. Numerous analytical models based on force balance (Luhar and Nepf, 2016; Leclercq and de Langre, 2018) have been developed to represent the movement of flexible vegetation like seagrass. These models depict the flexible vegetation as a series of segmented rigid stems attached to each other and subjected to oscillating flows. Some models attempt to link stem motion with wave dissipation to integrate this coupling into numerical models (Yin et al., 2022). However, these models still require unknown quantities such as drag and inertial coefficients. The present study aims to develop an analytical model for determining drag and inertial coefficients based solely on the geometry, the structure flexibility and wave forcing. At last, the method could help better represent the dissipation into numerical simulations without the need for prior parametrization.

Exploring Wave-Vegetation Interaction At Blade Scale: A Comprehensive Analysis Of A Flexible Cylinder Through Experimental Data And A Direct Numerical Simulation

Aquatic vegetation in the littoral zone, particularly seagrass, is gaining increasing recognition for its net positive impact on the hosting environment. This recognition is rooted in its capacity to absorb wave energy, regulate water flow, and manage nutrient levels, sedimentation and accretion. Thus, there is a growing interest in integrating seagrass as a key component of a comprehensive climate-conscious strategy (Ondiviela et al., 2014). An effective approach to quantify the positive potential of seagrasses in altering coastal wave dynamics is by using numerical models. These numerical models operate at various spatio- temporal scales, ranging from large domains and multiple years to just a few regular waves in high resolution CFD numerical simulations. Zeller et al. (2014) classified these models, operating at different scales into three categories, each addressing the wave-vegetation interaction at a distinct scale: (1) blade scale, (2) meadow scale, and (3) ecosystem scale. The aim of the present study is to investigate the interaction between waves and vegetation at the blade scale. The primary objectives are two: first, to introduce a direct numerical technique that involves a two-way coupling between a fluid solver and a structural solver, and second, to present novel experimental data for a single flexible cylinder (Reis, 2022) serving as validation for the present (and future) numerical model(s).

Numerical study of a synergistic hybrid energy harvesting system for bladeless wind turbines

Using energy of the fluid flow over an oscillating vertically-mounted flexible cylinder, as a representative configuration of bladeless wind turbines (BWTs), has recently attracted wide attention in the fluid mechanics community. In this paper, the fluid–structure interactions of a novel BWT-based hybrid piezo-electromagnetic energy harvesting system have been numerically studied in the vortex-induced-vibration (VIV) lock-in region by using the Reynolds Averaged Navier-Stokes (RANS) equations with the SST k-ω turbulence model. It is found that by implementing the electromagnetic (EMT) and/or piezoelectric (PVDF) transducers, the lock-in region becomes wider (up to 33% for the hybrid system) while being shifted to the higher Reynolds number (Re) range. Also, the dimensionless BWT cross-flow tip displacement amplitude (Yamp∗) is seen to reduce about 20%, 70%, and 70% by using the single-alone EMT-based, single-along piezo-based, and the hybrid harvester, respectively, which can potentially lead to substantial improvements in the fatigue life of the system Furthermore, the synergetic action of the hybrid system is observed to cause an overall increase in the harvested energy levels besides broadening of the associated range, as each of energy harvesting components appears to produce higher output power as compared to the respective single-alone system. In other words, up to 260% increase (100% increase) in the overall harvested energy level and up to 300% increase (60% increase) in the harvestable Re range with respect to the single-alone piezo-based (EMT-based) system are obtained, in which about 50% (about 10%) synergetic effects can be associated with the EMT- and piezo-based transducers, respectively.

Effect of slug characteristics on the nonlinear dynamic response of a long flexible fluid-conveying cylinder

Hydrocarbon flows in a marine riser may appear in multiple phases with varying flow patterns, among which, slug flows are known to exhibit complex flow characteristics due to fluctuations in multiphase mass, velocities, and pressure changes. Bulk of the literature concerning internal single and two-phase flow induced vibrations have largely focused on the use of a linearized tension beam model. In this study, the fluid-structure interaction phenomena of a submerged long flexible cylinder conveying two-phase slug flows is investigated taking into account the geometric and hydrodynamic nonlinearities. A semi-empirical theoretical model which consists of nonlinear structural equations of coupled out-of-plane, in-plane and axial structural motions is presented for the analysis and prediction of two-phase slug flow induced vibrations (SIV). The model includes equations involving centrifugal and Coriolis forces to capture mass variations in the slug flow regime. A numerical space-time finite difference approach combined with a frequency domain analysis is used for analyzing the highly nonlinear three-dimensional responses. The model assumes constant geometric properties across the span of the cylinder and utilizes an idealized slug unit concept, wherein slug properties are considered to be fully developed and undisturbed by pipe oscillations. Model validations are performed through comparisons with published experimental internal flow-induced vibration results. Parametric study captures the effects of several key slug characteristics on the vibration responses of a fluid-conveying cylinder. The results demonstrate amplitude-modulation response, mean displacements, three-dimensional cylinder displacements due to geometric nonlinear couplings and the influence of internal flow velocities. Higher dominant modes and oscillation frequencies were observed when the cylinder experiences large amplitude motions at specific slug formations. A new dimensionless parameter is introduced to predict scenarios of high amplitude oscillations for long flexible cylinders carrying two-phase slug flows.

A Two-Temperature Fractional DPL Thermoelasticity Model with an Exponential Rabotnov Kernel for a Flexible Cylinder with Changeable Properties

This article presents a new thermoelastic model that incorporates fractional-order derivatives of two-phase heat transfer as well as a two-temperature concept. The objective of this model is to improve comprehension and forecasting of heat transport processes in two-phase-lag systems by employing fractional calculus. This model suggests a new generalized fractional derivative that can make different kinds of singular and non-singular fractional derivatives, depending on the kernels that are used. The non-singular kernels of the normalized sinc function and the Rabotnov fractional–exponential function are used to create the two new fractional derivatives. The thermoelastic responses of a solid cylinder with a restricted surface and exposed to a moving heat flux were examined in order to assess the correctness of the suggested model. It was considered that the cylinder’s thermal characteristics are dependent on the linear temperature change and that it is submerged in a continuous magnetic field. To solve the set of equations controlling the suggested issue, Laplace transforms were used. In addition to the reliance of thermal characteristics on temperature change, the influence of derivatives and fractional order was also studied by providing numerical values for the temperature, displacement, and stress components. This study found that the speed of the heat source and variable properties significantly impact the behavior of the variables under investigation. Meanwhile, the fractional parameter has a slight effect on non-dimensional temperature changes but plays a crucial role in altering the peak value of non-dimensional displacement and pressure.

Multieffect bioconvective transport of oxytactic microorganisms with thermal radiation, Lorentz force, heat source, and chemical reaction over a flexible cylinder

AbstractThe multieffect bioconvective heat transfer in porous media is essential for many technological applications. However, the literature governing practical applications is very scarce. The bioconvective transport of magnetohydrodynamic cross nanofluid carrying oxytactic microorganisms across a flexible cylinder with velocity slip, viscous dissipation, thermal radiation, and chemical reaction with a heat source in Darcy–Forchheimer porous medium is predicted in this piece of work. The random movement and thermophoresis processes are revealed by the Buongiorno model. Using a suitable similarity transformation and boundary layer approximation, the simplified model equations are converted into coupled highly nonlinear ordinary differential equations (ODEs). The resulting ODEs are dealt with numerically utilizing the BVP4C and the shooting method with predetermined thermal radiation, heat source, chemical reaction, and so forth parameters. The velocity field is inversely influenced by the Forchheimer number and porosity parameter. The Sherwood number is significantly influenced by chemical reactions. For heat source parameter (S) and increasing radiation parameter (Rd), the Nusselt number increases and convection is shown for the value of Rd near about 3. Overall, this study will help researchers in science and engineering to understand the intricate and multieffective dynamic system and industrial applications like microbiology, and biodynamical systems, biological tissues, biofilms, soil, or filter media.

Direct Measurements of Vortex-Induced Vibrations on a Horizontal Flexible Cylinder in Water

Abstract This work presents experimental results on vortex-induced vibration (VIV) of a horizontal cylinder with 2.69 m in length, 21 mm in diameter, and a mass ratio equal to 3.9. The experiments were carried out in a towing tank, where the flexible cylinder was towed under constant current profiles. Twenty reduced velocities were tested in a range of 1.75 < Vr < 15.79, corresponding to Reynolds numbers from 1000 to 10,000. The displacements were measured directly through a submerged optical system that simultaneously acquired the in-line and cross-flow movements of 18 reflective targets along the length. The extensive monitored section of the model enabled the application of a modal decomposition technique, which is a methodology that is still relatively unexplored through direct measurements. A comprehensive analysis was applied and the VIV responses related to amplitudes, frequencies, phase angles, and trajectories are shown and discussed in depth. The overall dynamics exhibits a multimodal response behavior, and the modal decomposition procedure has conclusively confirmed that the total amplitude comprises several modes vibrating at the dominant mode frequency. Root mean square values of response amplitude were up to 0.77D and 0.23D in the cross-flow and in-line directions, respectively. The cross-flow synchronization had a significant impact on the in-line excitation modes, and the trajectories showed coherence between motions.

Modeling vortex-induced vibrations of branched structures by coupling a 3D-corotational frame finite element formulation with wake-oscillators

Branched structures are present in a diverse set of problems, from modeling branch pipe connections to simulating tree dynamics. Soft corals like the Bipinnate sea plume, have a branched geometry and are soft enough to bend under the waves. Due to their circular cross section, a vortex street forms in the coral’s wake inducing vibrations of its branches. Despite extensive studies on VIV in straight geometries, the three-dimensional (3D) dynamics of flexible branched structures remains uninvestigated. In this numerical and experimental study, we develop a novel formulation for the accurate computation of in-line and cross-flow VIV of frame structures undergoing large deformation. The finite element approach is used to model arbitrarily complex geometries of branched frame structures. Our formulation allows to model complex geometries with forks or sharp angles. The consistent 3D corotational formulation for frame elements computes the internal, inertial and hydrodynamic forces. A wake-oscillator approach models the near wake dynamics with fluctuating fluid forces on the structure in the in-line and cross-flow directions. The drag and lift coefficients follow distributed Van der Pol oscillators. Moreover, we implement the numerical resolution procedure in the open-source library ONSAS. The present formulation and numerical resolution procedure is validated by solving three examples, including comparisons with an analytical solution, a wake-oscillator, and experimental data from the literature. We also conduct experiments of a flexible and elastic cylinder clamped inside a water tunnel under a constant uniform flow. Amplitudes and power spectral density of the tip transverse displacements are compared with the model prediction. Finally, the proposed formulation is applied on a cylinder with two branches. The simulations demonstrate a multi-frequency response with higher amplitudes of displacements when additional branches are incorporated onto the cylinder, emphasizing the significance of considering VIV in nature and engineering applications for such geometries.

Experimental investigation of flow-induced vibration and flow field characteristics of a flexible triangular cylinder

Flow-induced vibration (FIV) of a flexible cylinder with a triangular cross-section, allowed to oscillate in the cross-flow, inline and torsional direction, is studied experimentally through water tunnel tests. The dynamic response of the cylinder was studied for three different angles of attack ( $0^\circ, 30^\circ, 60^\circ$ ), at reduced velocities of 0.9–16.27, corresponding to Reynolds numbers of 364–3600. At the angle of attack of $0^\circ$ , vortex-induced vibration at low reduced velocity was observed, which transitioned to galloping at higher reduced velocities. At the angles of attack of $30^\circ$ and $60^\circ$ , galloping-type response was observed over the range of the reduced velocities tested. Our results show that the cylinder's torsional oscillation breaks the system's symmetry and affects the structural response at higher reduced velocities regardless of the angle of attack. The FIV response of the flexible triangular cylinder is distinct from that of a rigid flexibly mounted triangular cylinder due to torsional oscillation, spanwise flexibility and the two fixed boundary conditions limiting the amplitude of oscillation. Flow field analysis in the wake of the cylinder was done qualitatively and quantitatively using hydrogen bubble flow visualisation and time-resolved volumetric particle tracking velocimetry techniques, respectively. Our results show the existence of highly three-dimensional vortex structures in the wake of the cylinder. We studied the coupling between the vortex shedding modes in the wake of the cylinder and the structural vibration modes through the spatiotemporal mode analysis using the proper orthogonal decomposition technique to distinguish between different types of the FIV response observed.

Numerical investigations of the effects of spanwise grooves on the suppression of vortex-induced vibration of a flexible cylinder

Numerical investigations of Vortex-induced Vibration (VIV) suppression of a flexible cylinder with spanwise grooves in the uniform flow have been conducted by viv3D-FOAM-SJTU solver, which imports the thick strip model into OpenFOAM. The Reynolds-averaged Navier-Stokes (RANS) method is adopted to calculate hydrodynamic forces at each fluid strip. The vibrations of cylinder are solved through the Euler-Bernoulli bending beam hypothesis and the Finite Element Method (FEM) in two directions. During simulations, four spanwise grooves are arranged equally around the cylinder with an interval of 90° at two configurations. The spanwise groove keeps a constant width of w = 0.2D and a variable groove depth among 0.08D, 0.12D and 0.16D. Specific comparisons on Root Mean Square (RMS) vibration displacements, vibration modal responses, vibration frequency responses and vortex structures are conducted to analyze suppression effects of the spanwise grooves. Numerical studies indicate that the appropriate choose of groove geometry and arrangement can effectively reduce both crossflow and inline VIV responses.

Flow-Induced Vibration of Cantilever Type Elastic Material in Straight Tricylinder

The hydrodynamic performance and wake evaluation results of a cantilever flexible cylindrical triangular array at Re = 9000 and with L/D spacing ratios ranging from 3 to 7 are presented in this paper. The improved delayed separation eddy current simulation (IDDES) SST k-ω turbulence model and tetrahedral mesh are employed to solve the three-dimensional instantaneous flow field. The objective is to find the L/D ratio that the upstream cylinder has the most pronounced effect on the downstream cylinders, to quantify whether a flexible upstream cylinder is more favorable than the rigid upstream cylinder, and to know the flexible cylinder wake distribution. The findings indicate that, at Re = 9000, when the spacing ratio is 3~7 and the spacing ratio L/D is 6, the amplitude of the downstream cylinder is most affected by the wake of the upstream cylinder; the amplitude of downstream cylinders of the rigid upstream cylinder exerted a 1% or 2% greater effect than the flexible cylinder, with vortices predominantly concentrated in the middle and upper parts of the flexible cylinder rather than at its top.