Reduced Velocity Vr Research Articles

Fatigue damage characteristics of a flexible cylinder under concomitant excitation of time-varying axial tension and VIV

Flexible cylindrical structures are susceptible to the concomitant excitation of vortex-induced vibration (VIV) and time-varying axial tension in offshore engineering. The structural instability caused by the simultaneous excitation can lead to severe fatigue damage, threatening the safe application of cylindrical structures. In this paper, experimental research was conducted on a long flexible cylinder with an aspect ratio of L/D = 350 to investigate its fatigue characteristics under the concomitant excitation. The reduced velocity Vr ranged from 1.34 to 26.71. The axial tension excitation was characterized by three axial tension amplitude ratios Tv/Tc = 0.1–0.3 (where Tv is the tension amplitude and Tc is the constant tension) and six axial tension frequency ratios fv/f1 = 0.5–4.0 (where fv is the tension frequency and f1 is the fundamental frequency of the cylinder). The S–N curve method and the linear accumulative damage theory were employed to estimate the fatigue damage. The effects of reduced velocity, excitation amplitude and excitation frequency on the fatigue damage characteristics were discussed in terms of the fatigue damage distribution and maximum fatigue damage. The effect of the tension excitation on the fatigue damage is more pronounced at low reduced velocities (Vr ≤ 5.34) when the VIV is not excited, since the axial tension can excite the mode vibration. The fatigue damage area and maximum fatigue damage are significantly enhanced with the increase of the tension amplitude ratio and frequency ratio due to the occurrence of higher-order mode vibrations. The effect of axial tension excitation on the fatigue damage of the cylinder is more pronounced in the in-line (IL) direction than in the cross-flow (CF) direction. However, for a small amplitude ratio (Tv/Tc = 0.1), the tension excitation is only noticeable with a large frequency ratio (fv/f1 = 4.0). On the other hand, as the reduced velocity increases, the VIV of the cylinder is excited and dominates the fatigue characteristics. The accumulative fatigue damage distribution is aggravated with the increase of reduced velocity. The time-varying axial tension has a negligible effect on the fatigue damage distribution features and the maximum fatigue damage values of the cylinder. Nevertheless, under certain circumstances, the axial tension excitation can slightly alleviate the fatigue damage in some regions along the cylinder.

Dual-frequency vortex-induced vibrations of long flexible stepped cylinders

Flexible structures within a non-uniform inflow may undergo complex vortex-induced vibrations (VIV) containing multiple frequencies and vibration modes. Therefore, the critical question arises on whether and how a flexible cylinder's structural response and fluid forces undergoing multi-frequency vibrations resemble or differ from mono-frequency vibrations. Therefore, we experimentally studied the problem of dual-frequency VIV of a stepped flexible cylinder, viz., a large-aspect ratio flexible cylinder consisting of two segments with different diameters and rigid cylinder forced vibration experiments. The results show that the maximum in-line (IL) and cross-flow (CF) displacements and the frequency ratio of the stepped cylinder separated by individual frequency resemble those of a uniform cylinder vibrating in the uniform flow at a single frequency. In addition, it is found that forced vibration results from rigid cylinders undergoing multi-frequency IL and CF motion can improve the prediction of the multi-frequency flexible cylinder VIV, provided the amplitudes and phases, as well as the true reduced velocity Vr for each of the dual frequencies match, especially when Vr∈[4,8].

Spacing effect on the two-degree-of-freedom VIV of two tandem square cylinders

Different spacing cases (L/B = 2–6) are numerically examined to identify the spacing effect on the two-degree-of-freedom vortex-induced vibration (VIV) of two tandem square cylinders at Re = 150. According to the various vibration responses, force characteristics and flow patterns, spacing cases can be divided into three different situations. At a small spacing (L/B = 2, 2.5), the upstream cylinder (UC) has no traditional lock-in region (the frequency ratio fy/fn ≈ 0.95–1.05, and the reduced velocity Vr ≈ 6), and the downstream cylinder (DC) has a narrow lock-in region. However, there is a wide soft-lock-in region (the synchronization region of fy/fn ≈ 0.85) at high reduced velocities (Vr ≈ 9.5–12) for both cylinders. In this region, both cylinders experience large-amplitude transverse vibrations, with the UC exhibiting a higher amplitude. At a moderate spacing (L/B = 3, 4), the UC does not exhibit lock-in or soft-lock-in regions, similar to a single cylinder at the same mass ratio, and the DC exhibits a relatively wide lock-in region (Vr ≈ 5.5–8) instead of a soft-lock-in region. Notably, two amplitude peaks appear within the lock-in region for the DC depending on Vr. At a large spacing (L/B = 5, 6), the amplitude of the DC is typically higher than that of a single cylinder, even within the narrow lock-in region.

Two-degree-of-freedom flow-induced vibration suppression of a circular cylinder via externally forced rotational oscillations: comparison of active open-loop and closed-loop control systems

In the current work, both active open-loop and closed-loop control approaches are considered to reduce two-degree-of-freedom vortex-induced vibration (VIV) of a circular-section cylinder, by means of externally imposed rotational oscillations. The open-loop control method utilizes pre-specified rotary oscillations, while the active closed-loop controller computes the proper angular velocity depending on the feedback signal of lift coefficient. The interactions between fluid and structure are realized by utilizing of the moving mesh methodology by means of user-defined function, which incorporated into the central code of computational fluid dynamic solver. According to the numerous set of numerical simulations, three optimum open-loop control systems for appropriate suppression of cylinder vibration are selected. In particular, it is observed that the VIV suppression capability of the closed-loop control strategy in comparison with optimum open-loop systems is more desirable despite the lower level of consuming control effort. Moreover, it is detected the excellent performance of selected closed-loop controller with constant proportional control gain in the entire range of reduced velocities, while the optimum open-loop systems are executable mainly near their corresponding reduced velocities. In particular, the selected closed-loop VIV control system (Kp = 10) is found to suppress the maximum transverse response amplitudes by 99.6%, 99.5%, and 99.3% for reduced velocities Vr = 5, 6, and 7, respectively, while the associated in-line displacement amplitudes decrease by 99.2%, 98.3%, and 96.2%. Also, the closed-loop controller does not require to find the “lock-on” frequency to execute appropriate de-synchronization type action and can effectively shift the C(2S)-mode vortices to the typical von Karman 2S-mode vortex shedding.

Numerical investigation on two degree-of-freedom flow-induced vibration of three tandem cylinders

Numerical simulations of two-degree-of-freedom flow-induced vibration of three elastically mounted tandem cylinders are performed for a low Reynolds number of Re = 150. The spacing ratio L/D is varied from 2 to 5, where L is the center-to-center between the cylinders and D is the cylinder diameter, and the reduced velocity Vr is varied from 3 to 14. The results show a typical vortex-induced vibration response of the upstream cylinder, except for those at L/D=2, where the response amplitudes are about twice those of the single cylinder. Both the midstream and downstream cylinders have large response amplitudes at all the examined spacing ratios. Depending on the flow interferences among three cylinders, the large amplitudes at high reduced velocities are contributed to the gap flow mechanism in the proximity regime and wake-induced vibration mechanism in the co-shedding regime, respectively. The periodic beating phenomenon occurs on both the midstream and downstream cylinders and the range of Vr for beating phenomenon increases with L/D. Depending on the spacing ratios and reduced velocities, six different flow regimes are identified: single bluff body flow, alternating shear layer reattachment flow, deflected gap flow, two parallel vortex streets with co-shedding flow, chaotic wake and 2S wake flow.

Empirical model for Wake Induced Vibrations frequency response of cylinder with low mass ratio

The vortex-induced vibrations (VIV) of two flexible circular cylinders in tandem arrangements were studied using numerical simulations and verified by experimental data. Simulations were conducted for a constant mass ratio of 1.08, the spacing ranges of 6D to 18D, and the reduced velocities of 2.35–6.71. It is shown that the numerical results are in a good agreement with the experimental data of the amplitude and frequency of response. The features of the vibration amplitude, the dominant frequencies, the vortex structures and the fluid force acting on the cylinders are discussed. The results indicate that there is a great difference between the response of the upstream cylinder and that of the downstream cylinder. When the reduced velocity is beyond the critical reduced velocity Vr*, the dominant frequencies of the upstream cylinder and the downstream cylinder are no longer the same. And both the reduced velocity and the spacing of the cylinders have a great influence on the wake-induced vibrations (WIV) responses of the downstream cylinder. Considering these influences, an empirical model for WIV frequency response of the downstream cylinder with a low mass ratio was proposed and verified.

Experimental identification of the fluid-elastic coupling forces on a flexible tube within a rigid square bundle subjected to single-phase cross-flow

The importance of fluid-elastic coupling forces in tube bundle vibrations is well documented and can hardly be over-emphasized, in view of their damaging potential. Even when adequate tube supports are provided to suppress fluid-elastic instabilities, the flow-coupling forces still affect the dynamical tube responses and remain a significant issue, in particular concerning the vibro-impact motions of tubes assembled using clearance supports. Therefore, the need remains for more advanced models of fluid-elastic coupling, as well as for experimental flow-coupling coefficients to feed and validate such models. In this work, we report an extensive series of experiments performed at CEA-Saclay leading to the identification of stiffness and damping fluid-elastic coefficients, for a 3×5 square tube bundle (D = 30 mm, P/D = 1.5) subjected to single-phase transverse flow, in a water test-loop. The bundle is rigid, except for the central tube which is mounted on a flexible suspension (two parallel steel blades) allowing for translation motions of the tube in the lift direction. The system is thus single-degree of freedom, allowing fluid-elastic instability to arise through a negative damping mechanism. The flow-coupling stiffness and damping coefficients, Kf(Vr) and Cf(Vr), are experimentally identified as functions of the reduced velocity Vr. The maximum value of the Reynolds number ranged from 105 to 2.16 105 (based on the maximum pitch velocity), according to the tested configuration. Identification is achieved on the basis of changes in tube vibration frequency and reduced damping as a function of flow velocity, assuming a constant fluid added mass. In the present experiments, coefficient identification is performed well beyond the instability boundary, by using active control, thereafter allowing exploration of a significant range of flow velocity. The modal frequency and the modal mass of the system are respectively modified by changing the tube suspension stiffness, and/or by adding a mass to the system. We can thus assert how the fluid-elastic coefficients change, for this configuration, with these two system parameters, all other parameters being kept constant. The results obtained from the configurations tested suggest that formulations for coefficient reduction may be improved, in order to better collapse the identified data.

Numerical investigation on vortex-induced vibrations of four circular cylinders in a square configuration

This paper presents a numerical study of two-degree-of-freedom vortex-induced vibration of four elastically mounted circular cylinders in a square arrangement at a low Reynolds number of Re = 150 and mass ratio of 2.0. The incident angle α is ranged from 0° to 45° and the reduced velocity Vr is ranged from 3 to 14. The effects of incident angle and reduced velocity on the dynamic responses and wake flow patterns behind four cylinders are investigated. The results show that the incident angle has a significant effect on the vibration amplitudes and force coefficients of four cylinders, especially for the downstream cylinders, where the maximum vibration amplitudes and force coefficients are occurred mostly on the downstream cylinder. With increasing of the incident angle α, the orbital trajectory for each cylinder becomes irregular and complicated, especially at high reduced velocities Vr ≥ 8, corresponding to multiple oscillation frequencies. Moreover, the wake flow patterns behind four cylinders are modified significantly with variations of incident angles, accompanied by different vortex shedding modes.

Effect of Vortex Induced Vibration on a Paired-Column Semisubmersible Platform

This paper describes a numerical study of the effect of vortex induced movement (VIM) on the hull of a paired-column semisubmersible (pc-semi) platform in relation to the column geometric properties. A computational fluid dynamics (CFD) analysis was carried out and vortex shedding was observed. The response of the square and rectangular columns hull configuration was investigated using ANSYS AQWA and the maximum amplitude was observed to be almost the same for both geometry, but it occurred at different range of reduced velocity Vr. The effect of surface wave and flow incidence angle were investigated for extreme and regular weather conditions, and it was found that VIM occurred at 2 ≤ Vr ≤ 12.

Experimental Investigation of Added Mass Coefficient with a Free-Oscillating Circular Cylinder

The shell and circular cylinder heat exchanger are widely used for various devices, such as kettle reboilers, feed water heaters, steam generator, evaporator in power, generation and so on. In late years, taking measures for an anti-vibration of the heat exchanger, it begins to be important problem to investigate flow induced vibration. The added mass is one of the essential parameters about flow induced vibration. Though the added mass coefficient is same as the displaced mass in the conventional understanding, recent study with the forced oscillation experiments revealed the added mass coefficient varies depending on the reduced velocity Vr. In this study, the added mass coefficients of the circular cylinder oscillation were measured by free oscillation experiments in a water channel. The frequency of circular cylinder oscillation and the flow oscillation around the circular cylinder were measured simultaneously with DynamicPIV, no intrusive to the flow and high spatial and time resolved, measurement techniques. The result showed the added mass coefficient varies depending on the reduced velocity Vr in free oscillation also.

Numerical Experiment of Flow Around a Two-Dimensional Self-Oscillating Circular Cylinder with Whirling Limitation by a Vortex Method with Boundary Layer Calculation

In this study, a numerical experiment of flow around a self-oscillating circular cylinder with whirling limitation was performed using the boundary element method combined with the vortex method. The flow feature of vortex shedding and the characteristics of vibration due to the fluid force were simulated about various initial setting position of circular cylinder at the Reynolds number Re=1×105, the mass ratio M=5.15, the damping factor C=0.0 and the reduced velocities Vr=1.8 and Vr=2.4. As a result of calculation, in the case of coaxial setting, the flow feature and the characteristics of cylinder vibration due to the fluid force were as same as a result of self-oscillating case, however, in the case of not coaxial setting, the frequency of cylinder's motion was changed and the flow features were changed from the twin type vortex shedding pattern to the Karman type vortex shedding pattern. It was shown that the characteristic of cylinder vibration frequency depended on both of the distance and the direction between the circular cylinder and the wall of pit.

The Vibration Response of a Cantilevered Rectangular Cylinder in Cross-Flow Oscillation

It is well known that a large-amplitude oscillation called galloping @1–3# is generated, in addition to Karman vortex excitation, for rectangular cylinders supported perpendicularly to a uniform flow when the slenderness b/d is in the range of 0.6 to 2.8 ~d5height, b5streamwise length of the rectangular cross-section!. The basic aerodynamic excitation mechanism of the cross-flow galloping of a rectangular cylinder is explained by the quasisteady nonlinear aerodynamic theory developed by Parkinson et al. @4#. In this theory, the relative attack angle plays an important role in the excitation mechanism of galloping. Also, as was shown by Deniz and Staubli @5#, the attack angle of a fixed rectangular cylinder strongly affects the vortex shedding frequency and lift. Although the mechanism of pure cross-flow oscillation for a circular and rectangular cylinder is becoming clear, as seen in the recent paper @6#, a slight difference in support conditions may affect strongly the oscillation behavior. The specific aim of this

Numerical Experiment of Flow around a Self-Oscillating Circular Cylinder by a Vortex Method Combined with Boundary Layer Calculation. (The Flow Features and the Motion of Circular Cylinder in the Initial Stage of Self-Oscillation)

In this study, the flow features of vortex shedding from a self-oscillating circular cylinder and the characteristics of fluid force were examined using a vortex method simulation combined with boundary layer calculation in a uniform flow at high Reynolds number in order to investigate validity and applicability to the analysis of the flow-induced vibration problems. The calculations were performed for the parameters of the mass ratio M (=1.78, 5.15), the damping factor C (=0.0, 0.0153) and the reduced velocity Vr (=1.38-4.13) at the Reynolds number Re=1×105 based on the uniform flow velocity U and the cylinder diameter D. As a result of the calculations, two typical patterns of vortex shedding were observed, one of which is symmetric twin vortex shedding and the other is antisymmetric twin vortex shedding. It was confirmed that the calculated flow patterns and the free-oscillation motions of the cylinder, were in reasonable agreement with experimental results. The relationship between the fluid force and the resultant cylinder's displacement was investigated.

Experimental Study on the Avoidance and Suppression Criteria for the Vortex-Induced Vibration of a Cantilever Cylinder

Experimental validation of the design guideline to prevent the failure of a thermometer well by vortex-induced vibration is presented, clarifying the effect of structure damping on displacement amplitudes of a cantilever cylinder. The available experimental data in piping are limited to those with small damping in water flow, because of the difficulty in increasing structure damping of the cantilever cylinders in experiments. In the present experiment, high-viscosity oil within cylinders is used to control their structure damping. Resulting values of reduced damping Cn are 0.49, 0.96, 1.23, 1.98, and 2.22. The tip displacements of the cylinder induced by vortex vibration were measured in the range of reduced velocity Vr from 0.7 to 5 (Reynolds number is 7.8×104 at Vr=1). Cylinders with reduced damping 0.49 and 0.96 showed vortex-induced vibration in the flow direction in the Vr>1 region. However, in cases of reduced damping of 1.23, 1.98, and 2.22, the vibration was suppressed to less than 1 percent diameter. It is confirmed that the criteria of “Vr<3.3 and Cn>1.2” for the prevention of vortex-induced vibration is reasonably applicable to a cantilever cylinder in a water flow pipe.

Flow-Induced Vibration of Bluff Bodies. Vortex-Induced Vibration of a Cantilever Circular Cylinder in Super-Critical Reynolds Number Flow and Its Suppression by Structure Damping.

Experimental validation of the design criteria for preventing the failure of a thermometer well by vortex-induced vibration is presented, clarifying the effects of Reynolds number and structure damping. An existing avoidance criterion for the vortex-induced vibration in the flow direction, which is given in terms of the reduced velocity Vr as Vr<1.0, has been developed based on the experimental data mainly in the sub-critical range. The applicability of this criterion in the super-critical range is examined in this paper based on the results of experiments performed in the Reynolds number region from 7.8×104 up to 1.1×106 at Vr=1.0. On the other hand, an existing suppression criterion of vortex-induced vibration in the flow direction is given in terms of the reduced damping Cn as Cn>1.2 (or 2.5) under the condition of Vr<3.3 in design guidelines. This criterion, however, has been proposed based on very limited available data The appropriateness of the suppression criterion is also examined in this paper based on the results of experiments in realistic thermometer well conditions, i.e. cantilever cylinders with varied structure damping in a pipe water flow. As a result, it becomes clear that Vr<1.0 is applicable in the super-critical range up to 1.1×106 and that the criteria of Vr<3.3 and Cn>1.2 are reasonably applicable to a cantilever cylinder in a pipe water flow.

AMPLIFICATION OF FLUID FORCES ACTING ON A VORTEX-EXCITED CIRCULAR CYLINDER VIBRATING IN STEADY FLOW

This study describes experimental investigations into the non-linear vortex-excited vibration of a circular cylinder in steady and uniform flow in open chanel with emphasis being placed on the amplification of fluid forces caused by the fluid-structure interaction. The dynamic transverse responses of a spring supported circular cylinder were investigated in the range of reduced velocity Vr=4 to 10 for several values of reduced damping Ksa. The value Ksa of deduced damping was adjusted by using a electromagnetic damper. Hydrodynamic forces, drag and lift, acting on the vortex-excited circular cylinder freely vibrating in uniform flow were measured by using a load cellinstalled in the test cylinder and a load cell supporting the test cylinder. The variation of amplification of the hydrodynamic forces acting on the vortex-excited vibrating cylinder in comparison with the hydrodynamic forces acting on the cylinder stationary mounted at the reduced velocities Vr and amplitudes of transverse vibration of cylinder were evaluated quantitatively.

In-line Oscillation of a Circular Structure

Aeroelastic instability of a circular cylinder was experimentally studied by free-oscillation tests in a wind tunnel. For an in-line oscillation in the subcritical regime of Reynolds number, detailed data of response amplitude of a cylinder have been obtained in a wide range of Scruton number (values of a mass-damping parameter), 0.80-2.82 by free-oscillation tests of two-dimensional cylinder spring-mounted to oscillate as a rigid cylinder, There are certified to be two excitation regions; one within a range of reduced velocities Vr between roughly 1.4 and 2.4, and the other above Vr=2.6. It is found that aeroelastic characteristics of two unstable regions are quite different; i.e., the response amplitude are very sensitive to the Scanlan number in the first unstable region, while those of the second region are rather insensitive. Also a fixed splitter plate with the longitudinal length of 8d (d: a cylinder diameter) was mounted behind a cylinder to eliminate the vortex shedding of alternate vortices from the cylinder, after Aguirre's experiments, and the results were compared with those without a splitterplate.

Vortex-induced motions of a tethered sphere

Abstract Despite the practical significance of studying the vibrations of a tethered sphere in a steady fluid flow, there are almost no laboratory investigations of such a problem, and it was previously unknown whether such a system would tend to oscillate or not. The present work demonstrates that a tethered sphere will oscillate vigorously, at a peak-to-peak amplitude of about two diameters, over a large range of velocities. The RMS amplitude of these oscillations is found to be independent of the tether length when plotted against the reduced velocity VR = U/fnD. However, the saturation value of the RMS is found to vary with the mass ratio. Also interesting is the observed oscillation frequency, at low mass ratios, which does not correspond to either the natural frequency nor the sphere vortex shedding frequency (in the absence of vibrations). The observed large amplitude oscillations also induce an increase in drag and tether angle of the order of 100% The above results suggest that oscillations are highly significant to predictions of sphere response in a steady flow, and should not be neglected.