Interference effect of an upstream larger cylinder on the lock-in vibration of a flexibly mounted circular cylinder

Experiments have been carried out to investigate the flow-induced vibration response of a flexibly mounted circular cylinder located in the vicinity of a larger cylinder and subjected to cross-flow. The interfering larger cylinder was placed upstream and had a diameter twice that of the vibrating cylinder. Complex interaction was observed between the flow over the two cylinders. The vibration responses of the flexible cylinder were classified into different regimes according to the relative positions of the two cylinders. In the-side-by-side arrangement and the tandem or near-tandem arrangement, flow-induced vibrations of the flexible cylinder were greatly suppressed. In the staggered arrangement which covered a large portion of the relative cylinder positions being investigated, vibrations of the smaller cylinder were greatly amplified. The vibration response curves were also largely modified with a broadening of the lock-in resonance range. A shift of the peak reduced velocity for maximum vibration response was also found. Flow visualizations and wake velocity measurements suggested that the modifications of the vibration responses were related to the presence or absence of constant or intermittent flow through the gap region between the two cylinders. The proposed mechanisms of flow interactions and the resulting vibration response characteristics could explain previous observations on flow-induced vibrations of two equal-sized circular cylinders reported in the literature.     

Wake-induced vibrations of an elastically mounted cylinder located downstream of a stationary larger cylinder at low Reynolds numbers

Two-dimensional numerical simulations of flow past two unequal-sized circular cylinders in tandem arrangement are performed at low Reynolds numbers (Re). The upstream larger cylinder is stationary, while the downstream cylinder has both one (transverse-only) and two (transverse and in-line) degrees of freedom (1-dof and 2-dof, respectively). The Re, based on the free stream velocity U_∞ and the downstream cylinder diameter d, varies between 50 and 200 with a wide range of reduced velocities U_r. The diameter of the upstream cylinder is twice that of the downstream cylinder, and the center-to-center spacing is 5.5d. In general, for the 1-dof case, the calculations show that the wake-induced vibrations (WIV) of the downstream cylinder are greatly amplified when compared to the case of a single cylinder or two equal-sized cylinders. The transverse amplitudes build up to a significantly higher level within and beyond the lock-in region, and the U_r associated with the peak amplitude shifts toward a higher value. The dominant wake pattern is 2S mode for Re=50 and 100, while with the increase of Re to 150 and 200, the P+S mode can be clearly observed at some lower U_r. For the 2-dof vibrations, the transverse response characteristics are similar to those presented in the corresponding 1-dof case. The in-line responses are generally much smaller, except for several significant vibrations resulting from in-line resonance. The obvious in-line vibration may induce a C (chaotic) vortex shedding mode for higher Re (Re=200). With regard to the 2-dof motion trajectories, besides the typical figure-eight pattern, several odd patterns such as figure-double eight and single-looped trajectories are also obtained due to the wake interference effect.     

Flow-induced vibrations of a tethered circular cylinder

One of the most basic examples of fluid-structure interaction is provided by a tethered body in a fluid flow. The tendency of a tethered buoy to oscillate when excited by waves is a well-known phenomenon; however, it has only recently been found that a submerged buoy will act in a similar fashion when exposed to a uniform flow at moderate Reynolds numbers, with a transverse peak-to-peak amplitude of approximately two diameters over a wide range of velocities. This paper presents results for the related problem of two-dimensional simulations of the flow past a tethered cylinder. The coupled Navier–Stokes equations and the equations of motion of the cylinder are solved using a spectral-element method. The response of the tethered cylinder system was found to be strongly influenced by the mean layover angle as this parameter determined if the oscillations would be dominated by in-line oscillations, transverse oscillations or a combination of the two. Three branches of oscillation are noted, an in-line branch, a transition branch and a transverse branch. Within the transition branch, the cylinder oscillates at the shedding frequency and modulates the drag force such that the drag signal is dominated by the lift frequency. It is found that the mean amplitude response is greatest at high reduced velocities, i.e., when the cylinder is oscillating predominantly transverse to the fluid flow. Furthermore, the oscillation frequency is synchronized to the vortex shedding frequency of a stationary cylinder, except at very high reduced velocities. Visualizations of the pressure and vorticity in the wake reveal the mechanisms behind the motion of the cylinder.     

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.     

On the stability of a flexibly mounted rotating cylinder partially filled with liquid

Summary An investigation is made into the unstable behaviour of a rotor which is flexibly mounted with some damping and which is forced to rotate around its axis of symmetry with a constant angular velocity. The rotor is assumed to be partially filled with an ideal liquid. Assuming relative liquid motion in two dimensions a perturbation theory leads to an algebraic equation of the fourth degree from which information can be derived about unstable regions and the effect of the combined action of dissipative and gyroscopic forces.     

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 interference between a stationary cylinder and an elastically mounted cylinder arranged in proximity

The flow interference between two circular cylinders, one stationary and the other free to oscillate in the transverse direction, are studied numerically at Re=150. The incompressible Navier–Stokes equation in two space dimensions, an assumption that is expected to be valid at the considered Re, is solved by the characteristic-based-split (CBS) finite element method using the T4/C3 MINI triangular element. The center-to-center spacing between the two cylinders is fixed at 4D, where D is the cylinder diameter. The angle of incident flow, α, with respect to the line through the two cylinder centers, varies within the range from α=0° to 90°. For the elastically mounted cylinder, the reduced mass considered is M_r=2.0; the structural damping coefficient is assigned to be zero, which encourages high amplitude oscillations. For each α, the computations are conducted for a wide range of reduced velocities, U_r. The flow interference is examined by scrutinizing (i) the frequency characteristics of the vortex shedding and oscillation; (ii) the dynamic response of the oscillating cylinder, including the amplitude of displacement, the drag and lift force characteristics and the phase relationship between the lift and the displacement series; and (iii) the flow response in terms of the instantaneous vorticity field. It was found that the flow interference type is significantly affected by the angle of the incident flow. As the cylinder is oscillated outside of the region of the wake behind the stationary cylinder (α≥30°), it behaves similarly to its isolated counterpart. In contrast, if the cylinder is partially or entirely submerged within the upstream wake (α<30°), then both the flow and body responses are substantially modified due to the vigorous interaction between the upstream wake and the oscillating cylinder; the response therefore belongs to the wake-induced regime. The U_r range associated with the higher amplitude response is significantly shifted toward a higher U_r. The maximum vibration amplitude builds up to a significantly higher level, even increasing the U_r far beyond the resonance regime. In general, the wake flow associated with the wake-induced vibration (WIV) regime appears to be more unperiodic than does that corresponding to the vortex-induced oscillation regime. It is also revealed that both the vortex-cylinder and the shear layer-cylinder interaction mechanisms are responsible for the characteristics of the responses of oscillating cylinder. The larger momentum required for the higher oscillation amplitude is obtained from the duration of the energy transfer from the fluid to the cylinder, which is ascribed to the phase lag between the lift force and the cylinder displacement.     

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.     

Three-dimensional numerical simulation of vortex-induced vibration of an elastically mounted rigid circular cylinder in steady current

Vortex-induced vibration (VIV) of an elastically mounted rigid circular cylinder in steady current is investigated by solving the three-dimensional Navier–Stokes equations. The cylinder is allowed to vibrate only in the cross-flow direction. The aim of this study is to investigate the variation of the vortex shedding flow in the axial direction of the cylinder and to study the transition of the flow from two-dimensional (2D) to three-dimensional (3D) for VIV of a cylinder. Simulations are carried out for a constant mass ratio of 2, the Reynolds numbers ranging from 150 to 1000 and the reduced velocities ranging from 2 to 12. The three-dimensionality of the flow is found to be the strongest in the upper branch of the VIV response and weakest in the initial branch. The 2S and 2P vortex shedding modes are found to coexist along the cylinder span in the upper branch, leading to strong variations of the lift coefficient in the axial direction of the cylinder. The difference between the flow transition from 2D to 3D in the VIV lock-in regime and that in the wake of a stationary cylinder is identified. The transition mode B found in the wake of a stationary cylinder is also found in the wake of a vibrating cylinder. The critical Reynolds number for flow transition from 2D to 3D of a cylinder undergoing cross-flow VIV at a reduced velocity of 6 is found to be greater than that for a stationary cylinder. For a constant reduced velocity of 6, the wake flow changes from 2D to 3D as the Reynolds number is increased from 250 to 300. Some 2D numerical simulations are performed and it is found that the 2D Navier–Stokes (NS) equations are not able to predict the VIV in the turbulent flow regime, while the 2D Reynolds-averaged Navier–Stokes (RANS) equations improve the results.     

Flow-induced vibration of curved cylinder arrays subject to loose support

In this paper, an improved model is developed aimed at analyzing the fluidelastic vibration of a single flexible curved tube which is surrounded by rigid cylinders and subjected to cross-flow and loose support. Based on the previous model, the axial extension of the curved tube described by von Karman nonlinearity has been accounted for in the current research. Simulations are performed to explore the effect of quasi-steady fluid force model and velocity-limited friction model on the post-instability behavior. Numerical results show that the out-of-plane response is confined to a limit cycle by the von Karman nonlinearity and the in-plane vibration is induced by the out-of-plane vibration through the nonlinear coupling. When the loose support comes into play, the nonlinear impact forces become dominate. The results are presented; comparisons are made to analyze the parameters influencing the fretting-wear damage, such as normal work rate, contact ratio and impact force level.     

Numerical investigation on vortex-induced vibration of an elastically mounted circular cylinder at low Reynolds number using the fictitious domain method

A direct numerical simulation of two-dimensional (2D) flow past an elastically mounted circular cylinder at low Reynolds number using the fictitious domain method had been undertaken. The cylinder motion was modelled by a two degree-of-freedom mass–spring–damper system. The computing code was verified against a benchmark problem in which flow past a stationary circular cylinder is simulated. Then, analyses of vortex-induced vibration (VIV) responses, drag and lift forces and the phase and vortex structures were carried out. Results show that the cylinder's non-dimensional cross-flow response amplitude reaches its summit of 0.572 in the ‘lock-in’ regime. The ‘2S’, instead of the ‘2P’, vortex shedding mode is dominated in the ‘lower’ branch for this 2D low-Re VIV. A secondary oscillation is observed in the lift force when ‘lock-in’ occurs. It is shown that this secondary component changes the phase, offset the energy input by the primary component and thus reduces the cylinder responses. Effects of the Skop–Griffin parameter on cylinder responses were also investigated.     

Interaction of circular cylinder wake with a short asymmetrically located downstream plate

This study reveals the interaction patterns of separated shear layers from a circular cylinder with a short downstream plate and their reflection on the frequency and the formation length of the vortices from the cylinder as a function of plate location relative to the cylinder. The effect of horizontal (G/D) and vertical (Z/D) distances between the cylinder and the plate on the near wake is studied via Digital Particle Image Velocimetry (DPIV) in a water channel for Reynolds numbers of 200, 400 and 750, based on the cylinder diameter D. It is shown that the interaction of wake with the plate of length D can be categorized depending on the horizontal and the vertical distances between the cylinder and the plate. For the vertical distance range of Z/D ≤ 0.7, there is a critical horizontal spacing before which the shear layers from the cylinder are inhibited to form vortices in front of the plate. Resulting elongated recirculation region between the plate and the cylinder suggests modification of the absolutely unstable near wake of free circular cylinder in favor of convective instability. Z/D = 0.9 provides a passage from Z/D ≤ 0.7 to ≥1.1 and is associated with a dominant effect on the near-wake characteristics of interaction of shear layers from the cylinder with those from the downstream plate. For Z/D ≥ 1.1, there is again, yet a smaller critical horizontal spacing after which vortices interact with decreased downstream plate interference. In this vertical separation distance range, a gap flow between the plate and the cylinder plays a determining role on the formation length and St number of vortices for small horizontal spacing values.     

Implementation of active control on flexibly mounted pipe exposed to vortex induced vibration using rotating rod

This paper presents the experimental works on the active control implementation of a flexibly mounted cylinder exhibiting vortex induced vibration phenomena. The dynamic response of the system was initially studied by fixing single and double passive control rods to the main cylinder. It was found that the fixed control rod could not suppress the vibration for both cases. In fact, the vibration was amplified as compared with the bare cylinder response. By retaining the same position, an active open loop control strategy was introduced to the vibrating system by rotating the single control rod in clockwise and counter clockwise directions. The results indicated that the counter clockwise direction has suppressed the vibration up to 29.81 dB. Further investigation was made by studying the performance of the control rod at several speeds in a single reduced speed of 4.29. It was found that the maximum attenuation level of 19.56 dB was attained based on 1676 RPM of control rod rotating speed. In addition, an overview of attenuation level trends at both varying control speed and reduced speed were presented in this study. Through the experimental implementation of control strategies conducted in this research, it was found that the active control strategy has performed well as suppression strategy at ineffective fixed control rod position.     

Simulation of transverse self-oscillations for a free circular cylinder mounted with a narrow gap in a plane channel

The experimentally observed self-oscillations of a cylinder mounted with a narrow gap in a plane channel are simulated. The added masses of the cylinder are calculated in the framework of ideal fluid theory by a generalized image method. In order to describe the self-oscillations in a real fluid, some dissipative factors and an impulsive impact force exerted on the cylinder are introduced.     

Vortex-induced vibration of a circular cylinder with nonlinear stiffness: prediction using forced vibration data

Nonlinear Dynamics - Vortex-induced vibration (VIV) systems with stiffness nonlinearity have received increasing attention because the stiffness nonlinearity can broaden the effective flow velocity...     

Numerical investigation of two-degree-of-freedom vortex-induced vibration of a circular cylinder in oscillatory flow

Two-degree-of-freedom (2dof) vortex-induced vibration (VIV) of a circular cylinder in oscillatory flow is investigated numerically. The direction of the oscillatory flow is perpendicular to the spanwise direction of the circular cylinder. Simulations are carried out for the Keulegan–Carpenter (KC) numbers of 10, 20 and 40 and the Reynolds numbers ranging from 308 to 9240. The ratio of the Reynolds number to the reduced velocity is 308. At KC=10, the amplitude of the primary frequency component is much larger than those of other frequency components. Most vibrations for KC=20 and 40 have multiple frequencies. The primary frequency of the response in the cross-flow direction decreases with the increasing reduced velocity, except when the reduced velocity is very small. Because the calculated primary frequencies of the response in the cross-flow direction are multiple of the oscillatory flow frequency in most of the calculated cases, the responses are classified into single-frequency mode, double-frequency mode, triple frequency mode, etc. If the reduced velocity is in the range where the VIV is transiting from one mode to another, the vibration is very irregular.For each KC number the range of the reduced velocity can be divided into a cross-flow-in-phase regime (low V_r), where the response and the hydrodynamic force in the cross-flow direction synchronize, and a cross-flow-anti-phase regime (high V_r), where the response and the hydrodynamic force in the cross-flow direction are in anti-phase with each other. The boundary values of V_r between the cross-flow-in-phase and the cross-flow-anti-phase regimes are 7, 9 and 11 for KC=10, 20 and 40, respectively. For KC=20, another cross-flow-anti-phase regime is found between 15≤V_r≤19. Similarly the in-line-in-phase and the in-line-anti-phase regimes are also identified for the response in the in-line direction. It is found that the boundary value of V_r between the in-line-in-phase and the in-line-anti-phase regimes is greater than that in the cross-flow direction. They are 14 and 26 for KC=10 and 20, respectively. Maximum amplitude occurs at the boundary value of the reduced velocity between in-phase regime and anti-phase regime in both the x- and the y-directions.