Flow-induced vibrations of a side-by-side arrangement of two flexible circular cylinders

Laboratory experiments with a side-by-side arrangement of two vertical, high aspect ratio (length over diameter) and low mass ratio (mass over mass of displaced fluid) cylinders, pin-jointed at the ends and vibrating at low mode number, were carried out in a free-surface water channel. The dynamic response of the models under two different wake interference situations is presented here. Initially, one of the cylinders was fixed and the other was completely free to move. In a second battery of experiments both cylinders were free to vibrate. A very large parameter space was covered by varying the free-stream flow speeds, the natural frequencies of the system and the separation between the models, allowing the identification of vortex-induced vibrations (VIV) and wake-coupled VIV (WCVIV). Amplitudes, frequencies and phase synchronisation between the models are presented.     

Flow-induced vibration of a flexibly mounted circular cylinder in the proximity of a larger cylinder downstream

A flexibly mounted circular cylinder is placed upstream of a stationary cylinder twice as large. Flow-induced vibration response of the small cylinder is measured with the interfering cylinder placed at 57 relative locations. In most situations, reduced-amplitude vibration or even no vibration is observed. Lock-in resonance remains the dominant vibration behavior, but the reduced velocity of peak lock-in is found to shift to a value higher or lower than the isolated cylinder value, depending on the lateral separation between the two cylinders. When the flexible cylinder is located just in front of the large cylinder, galloping-type vibration of very large amplitude occurs at reduced velocities above 12. Mechanisms of flow-induced vibration are discussed with the aid of flow visualizations. The present study supplements a previous paper reporting amplified vibration of the flexible cylinder with the interfering cylinder placed in various upstream locations.     

Two classes of vibrations of a short circular cylinder

This paper gives a solution of the stationary dynamic problem of elasticity which describes two classes of natural nonaxisymmetric vibrations of a finite circular cylinder. In the particular case of axial symmetry, the resulting solution describes two well-known classes of axisymmetric vibrations: vibrations of the first class become longitudinal-transverse vibrations and vibrations of the second class become torsional vibrations. The existence of two classes of nonaxisymmetric vibrations is due to the boundary conditions at the ends. It is shown that as the length (height) of the cylinder increases, the effect of the boundary conditions at the ends on the frequency spectrum reduces, and the vibration frequencies of the two classes become similar and then identical.     

Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number

Two- and three-dimensional numerical simulations of the flow around two circular cylinders in tandem arrangements are performed. The upstream cylinder is fixed and the downstream cylinder is free to oscillate in the transverse direction, in response to the fluid loads. The Reynolds number is kept constant at 150 for the two-dimensional simulations and at 300 for the three-dimensional simulations, and the reduced velocity is varied by changing the structural stiffness. The in-line centre-to-centre distance is varied from 1.5 to 8.0 diameters, and the results are compared to that of a single isolated flexible cylinder with the same structural characteristics, m^?=2.0 and ζ=0.007. The calculations show that significant changes occur in the dynamic behaviour of the cylinders, when comparing the flow around the tandem arrangements to that around an isolated cylinder: for the tandem arrangements, the lock-in boundaries are wider, the maximum displacement amplitudes are greater and the amplitudes of vibration for high reduced velocities, outside the lock-in, are very significant. The main responsible for these changes appears to be the oscillatory flow in the gap between the cylinders.     

Two-degree-of-freedom vortex-induced vibrations of a circular cylinder at Re=3900

The vortex-induced vibrations of an elastically mounted circular cylinder are investigated on the basis of direct numerical simulations. The body is free to move in the in-line and cross-flow directions. The natural frequencies of the oscillator are the same in both directions. The Reynolds number, based on the free stream velocity and cylinder diameter, is set to 3900 and kept constant in all simulations. The behavior of the coupled flow-structure system is analyzed over a wide range of the reduced velocity (inverse of the natural frequency) encompassing the lock-in range, i.e. where body motion and flow unsteadiness are synchronized. The statistics of the structural responses and forces are in agreement with prior experimental results. Large-amplitude vibrations develop in both directions. The in-line and cross-flow oscillations are close to harmonic; they exhibit a frequency ratio of 2 and a variable phase difference across the lock-in range. Distinct trends are noted in the force-displacement phasing mechanisms in the two directions: a phase difference jump associated with a sign change of the effective added mass and a vibration frequency crossing the natural frequency is observed in the cross-flow direction, while no phase difference jump occurs in the in-line direction. Higher harmonic components arise in the force spectra; their contributions become predominant when the cylinder oscillates close to the natural frequency. The force higher harmonics are found to impact the transfer of energy between the flow and the moving body, in particular, by causing the emergence of new harmonics in the energy transfer spectrum.     

Flow-induced vibrations of two circular cylinders in tandem with shear flow at low Reynolds number

The flow-induced vibrations of two elastically mounted circular cylinders subjected to the planar shear flow in tandem arrangement are studied numerically at Re=160. A four-step semi-implicit Characteristic-based split (4-SICBS) finite element method is developed under the framework of the fractional step method to cope with the vortex-induced vibration (VIV) problem. For the computational code verification, two benchmark problems are examined in the laminar region: flow-induced vibration of an elastically mounted cylinder having two degrees of freedom and past two stationary ones in tandem arrangement. Regarding the two-cylinder VIVs in shear flow, the computation is conducted with the cylinder reduced mass M_r=2.5π and the structural damping ratio ξ=0.0. The effects of some key parameters, such as shear rate (k=0.0, 0.05, 0.1), reduced velocity (U_r=3.0–18.0) and spacing ratio (L_x/D=2.5, 3.5, 4.5, 8.0), are demonstrated. It is observed that the shear rate and reduced velocity play an important role in the VIVs of both cylinders at various center-to-center distances. Additionally, in comparison with the single cylinder case, a further study indicated that the gap flow has a significant impact on such a dynamic system, leading it to be more complex. The results show that, the performances of ‘dual-resonant’ are discovered in the shear flow. A valley is formed in transverse oscillation amplitude of DC for each spacing ratio when U_r is about 6.0. For the X–Y trajectories of the circular cylinders, figure-eight, figure-O and oval shape are obtained. Finally, the interactions between cylinders are revealed, together with the wake-induced vibration (WIV) mechanism underlying the oscillation characteristics of both cylinders exposed to shear flow. Besides, the “T+P” wake pattern is discovered herein.     

Three-dimensional computation for flow-induced vibrations of an upstream circular cylinder in two tandem circular cylinders

It is well known from a lot of experimental data that fluid forces acting on two tandem circular cylinders are quite different from those acting on a single circular cylinder. Therefore, we first present numerical results for fluid forces acting on two tandem circular cylinders, which are mounted at various spacings in a smooth flow, and second we present numerical results for flow-induced vibrations of the upstream circular cylinder in the tandem arrangement. The two circular cylinders are arranged at close spacing in a flow field. The upstream circular cylinder is elastically placed by damper-spring systems and moves in both the in-line and cross-flow directions. In such models, each circular cylinder is assumed as a rigid body. On the other hand, we do not introduce a turbulent model such as the Large Eddy Simulation (LES) or Reynolds Averaged Navier-Stokes (RANS) models into the numerical scheme to compute the fluid flow. Our numerical procedure to capture the flow-induced vibration phenomena of the upstream circular cylinder is treated as a fluid-structure interaction problem in which the ideas of weak coupling is taken into consideration.     

Flow-induced vibrations and the Landau equation

The initial and general transient temporal behaviours of flow induced vibrations were studied particularly with regard to the extent with which self-excited, flow-induced vibrations can be described by the Landau equation.Three different cases are studied experimentally, using bodies with generic shape. The first case represents a bluff body: resembling a simplified section of the Tacoma bridge, which has a single torsional degree of freedom. The second case is a two-dimensional airfoil in transonic flow having a heave and a torsional degree of freedom. The third case is an elastic half-wing model, also investigated in transonic flow.It is shown that in all three cases, beyond the critical point and at small initial amplitude the temporal development of the oscillations up to the limit cycle i.e. the envelope of the measured time functions, agrees with the corresponding curve, given by the solution of the Landau equation. For the Tacoma section and the airfoil the same agreement was demonstrated for initial amplitudes much larger than that of the limit cycle. In addition for both last cases the bifurcation behaviour was investigated and the Landau constants were determined. Finally an elementary physical explanation for the instability phenomenon was given.     

Effects of a non-linear energy sink (NES) on vortex-induced vibrations of a circular cylinder

We investigate in detail the passive control of vortex-induced vibrations of a freely oscillating circular cylinder using a non-linear energy sink consisting of a secondary system having linear damping and an essential non-linear cubic stiffness. The loads on the cylinder are calculated using a direct numerical simulation of the incompressible flow over the cylinder using a parallel computational fluid dynamics code. A strongly coupled fluid structure control numerical model is used to determine the responses of the cylinder and the sink as well as the flow. We vary the sink parameters (mass and damping) and determine their effects on the response of the coupled system. We find multiple stable responses of the coupled system for different mass ratios and damping coefficient of the sink, depending on the initial conditions.     

Limit-cycle vibrations of a rolling cylinder

An explanation for a violent vibration of a high-speed textile yarn winder is proposed based on the hypothesis that variations in radial compliance around the circumference of the yarn cylinder make the smooth winding process unstable due to parametric excitation. The amplitude of the resulting limit cycle depends on the non-linearity in the radial compliance. An analytical procedure for predicting the limit-cycle amplitude is developed and applied to a specially constructed mechanical model of a yarn winder. The actual response of the mechanical model is accurately predicted when its measured dynamic properties are inserted in the analysis.     

Flow-induced vibration of elastic slender structures in a cylinder wake

Flow-induced vibration of an elastic airfoil due to the wake propagating from an upstream cylinder at a Reynolds number of 10 000 based on cylinder diameter D was investigated. A laser vibrometer was employed to measure the bending and torsional vibration displacements at the mid-span of the airfoil and the cylinder. The dimensionless gap size S/D between the two structures was selected as the governing parameter of the flow-induced vibration problem. It is found that the vibration amplitudes of the elastic airfoil and the vortex shedding frequency of the coupled cylinder–airfoil system are strongly dependent on S/D, due to the different fluid–structure interaction experienced by the airfoil at various S/D. Strong vortex-induced vibration of the airfoil appears to be excited by the organized Karman-vortex-street (KVS) vortices in the cylinder wake for S/D>3 and becomes stabilized for S/D3. However, as a result of the shear-layer-induced vibration at an appropriate frequency, structural resonance is also found to occur even though the airfoil is located in the stabilizing range. The occurrence of structural resonance is further supported by a complementary experiment where the slender structure is an elastic flat plate. This phenomenon indicates that assuming the structures in any fluid–structure interaction problem to be rigid is not appropriate, even though they might appear to be highly stiff. The experimental results were used to validate a numerical model previously developed to estimate the structural responses in complicated fluid–structure interaction problems.     

Flow-induced vibration of a square cylinder without and with interference

This paper presents the results of an investigation on the interference effects of a rigid square cylinder on the transverse vibrations of a spring-mounted square cylinder (test cylinder) exposed to a uniform flow. The interference effects were studied for the tandem, side-by-side and staggered arrangements. Experiments have been carried out for various relative dimensions of the test cylinder and the interfering cylinder; the tests for the staggered arrangements were conducted at several tandem distances between the two. The results indicate that there is a critical combination of relative dimensions and spacing that gives rise to maximum amplitude of vibration. Among the cases studied, tandem arrangement with $L/B=1.25$ and $b/B=0.5$ gives rise to maximum amplitude of vibration with $(a/B{)}_{\max }=0.57$. A tentative explanation is offered for the observed features based on flow-visualization studies conducted as a part of the experimental investigation.     

On the force distribution along the axis of a flexible circular cylinder undergoing multi-mode vortex-induced vibrations

One of the main problems in predicting the response of flexible structures subjected to vortex shedding is that a totally reliable model for the fluid loading does not exist. It is also very difficult to measure the distributed force exerted by the fluid along the length of a marine riser without disturbing the system in some way. The methodology described here uses experimental response data obtained in a test programme undertaken in the Delta Flume in Holland during May 2003, linked to a finite element method model (FEM) of the riser. The length-to-diameter ratio of the model used was around 470, the mass ratio (mass/displaced mass) was 3 and the Reynolds number varied between 2800 and 28 000. By using the response data as the input to the numerical model, the instantaneous distributed in-line and transverse forces acting on a flexible cylinder can be studied.