Mode Shape Variation for a Low-Mode Number Flexible Cylinder Subject to Vortex-Induced Vibrations

2014 ◽  
Author(s):  
Ersegun D. Gedikli ◽  
Jason M. Dahl
Keyword(s):  
Natural Frequency ◽  
Mode Shape ◽  
Frequency Ratio ◽  
Cross Flow ◽  
Mode Number ◽  
Rigid Cylinder ◽  
Vortex Induced Vibrations ◽  
The Cross ◽  
The Impact ◽  
Structural Mode

The excitation of two low-mode number, flexible cylinders in uniform-flow is investigated to determine effects of structural mode shape on vortex-induced vibrations. Experiments are performed in a re-circulating flow channel and in a small flow visualization tank using object tracking and digital particle image velocimetry (DPIV) to measure the excitation of the cylinder, to estimate forces acting on the structure, and to observe the wake of the structure under the observed body motions. Previous research has focused on understanding the effect of in-line to cross-flow natural frequency ratio on the excitation of the structure in an attempt to model the excitation of multiple structural modes on long, flexible bodies. The current research investigates the impact of structural mode shape on this relationship by holding the in-line to cross-flow natural frequency constant and attempting to excite a specific structural mode shape. It is found that the combination of an odd mode shape excited in the cross-flow direction with an even mode shape in the in-line direction results in an incompatible synchronization condition, where the dominant forcing frequency in-line may experience a frequency equal to the cross-flow forcing frequency, a condition only observed in rigid cylinder experiments when the natural frequency ratio is less than one. This is consistent with the first mode being excited in both in-line and cross-flow directions, however this leads to an asymmetric wake. The wake is observed using DPIV on a rigid cylinder with forced motions equivalent to the flexible body. A case of mode switching is also observed where the even in-line mode exhibits an excitation at twice the cross-flow frequency; however the spatial mode shape in-line appears similar to the first structural mode shape. It is hypothesized that this situation is possible due to variation in the effective added mass along the length of the cylinder.

Experimental Investigation of Vortex-Induced Vibrations of a Flexibly Mounted Circular Cylinder in Combined Current and Wave Flows

2021 ◽  
Author(s):  
Pierre-Adrien Opinel ◽  
Narakorn Srinil
Keyword(s):  
Experimental Investigation ◽  
Circular Cylinder ◽  
Cross Flow ◽  
Wave Flow ◽  
Regular Wave ◽  
Regular Waves ◽  
Vortex Induced Vibrations ◽  
Flow Frequency ◽  
The Cross ◽  
Wave Flows

Abstract This paper presents the experimental investigation of vortex-induced vibrations (VIV) of a flexibly mounted circular cylinder in combined current and wave flows. The same experimental setup has previously been used in our previous study (OMAE2020-18161) on VIV in regular waves. The system comprises a pendulum-type vertical cylinder mounted on two-dimensional springs with equal stiffness in in-line and cross-flow directions. The mass ratio of the system is close to 3, the aspect ratio of the tested cylinder based on its submerged length is close to 27, and the damping in still water is around 3.4%. Three current velocities are considered in this study, namely 0.21 m/s, 0.29 m/s and 0.37 m/s, in combination with the generated regular waves. The cylinder motion is recorded using targets and two Qualisys cameras, and the water elevation is measured utilizing a wave probe. The covered ranges of Keulegan-Carpenter number KC are [9.6–35.4], [12.8–40.9] and [16.3–47.8], and the corresponding ranges of reduced velocity Vr are [8–16.3], [10.6–18.4] and [14–20.5] for the cases with current velocity of 0.21 m/s, 0.29 m/s and 0.37 m/s, respectively. The cylinder response amplitudes, trajectories and vibration frequencies are extracted from the recorded motion signals. In all cases the cylinder oscillates primarily at the flow frequency in the in-line direction, and the in-line VIV component additionally appears for the intermediate (0.29 m/s) and high (0.37 m/s) current velocities. The cross-flow oscillation frequency is principally at two or three times the flow frequency in the low current case, similar to what is observed in pure regular waves. For higher current velocities, the cross-flow frequency tends to lock-in with the system natural frequency, as in the steady flow case. The inline and cross-flow cylinder response amplitudes of the combined current and regular wave flow cases are eventually compared with the amplitudes from the pure current and pure regular wave flow cases.

The Importance of Mode Number on In-Line Amplitude of Vortex-Induced Vibration of Flexible Cylinders

2008 ◽  
Author(s):  
Susan B. Swithenbank ◽  
Carl Martin Larsen
Keyword(s):  
Natural Frequencies ◽  
Flow Direction ◽  
Empirical Relationship ◽  
Cross Flow ◽  
Bending Stiffness ◽  
Mode Number ◽  
Flow Mode ◽  
Physical Parameters ◽  
Complex Data ◽  
The Cross

Most empirical codes for prediction of vortex-induced vibrations (VIV) has so far been limited to cross-flow response. The reason for this is that cross-flow amplitudes are normally larger that in-line amplitudes. Additionally the in-line response is considered to be driven by the cross-flow vibrations. However since the in-line frequency is twice the cross-flow frequency, fatigue damage from in-line vibrations may become as important and even exceed the damage from cross-flow vibrations. A way to predict in-line vibrations is to apply traditional methods that are used for cross-flow VIV and establish an empirical relationship between the cross-flow and in-line response. Previous work suggests that the ratio between the in-line and cross-flow amplitudes depends on the cross-flow mode number, Baarhom et al. (2004), but the empirical basis for this hypothesis is not strong. The motivation for the present work has been to verify or modify this hypothesis by extensive analysis of observed response. The present analysis uses complex data from experiments with wide variations in the physical parameters of the system, including length-to-diameter ratios from 82 to 4236, tension dominated natural frequencies and bending stiffness dominated natural frequencies, sub-critical and critical Reynolds numbers, different damping coefficients, uniform and sheared flows, standing wave and traveling wave vibrations, mode numbers from 1–25th, and different mass ratios. The conclusion from this work is that the cross-flow mode number is not the important parameter, but whether the frequency of vibration in the cross-flow direction is dominated by bending stiffness of tension.

Added Mass of Elastically Mounted Rigid Cylinder in Water Subjected to Vortex-Induced Vibrations

2002 ◽  
Author(s):  
Andre´ L. C. Fujarra ◽  
Celso P. Pesce
Keyword(s):  
Added Mass ◽  
Leaf Spring ◽  
Technical Literature ◽  
Experimental Calibration ◽  
Rigid Cylinder ◽  
Vortex Induced Vibrations ◽  
Mass Coefficient ◽  
Added Mass Coefficient ◽  
The Cross ◽  
Technological Research Institute

Vortex Induced Vibrations (VIV) of elastically mounted rigid cylinders, with low mass-damping parameter values, are strongly dependent on the added mass coefficient. This paper aims to contribute to the technical literature by presenting some results from experiments carried out at University of Sa˜o Paulo – USP and at the Sa˜o Paulo State Technological Research Institute – IPT. A cantilevered rigid cylinder was mounted on an elastic (leaf spring) two-degree-of-freedom device. The device is not only an elastic support, but acts also as a special mechanical transducer to measure accelerations/forces/displacements in the stream-wise (x) and the cross-wise (y) directions. A comprehensive experimental calibration of such a device was carried out, both “in air” and “in water”. The added mass coefficient in the cross-wise direction was indirectly determined from forces and acceleration measurements as a function of the reduced velocity. Results from time-domain and frequency-domain analyses are compared with those obtained by Vikestad et al. (2000) [1].

On the Coupling Between In-Line and Cross-Flow VIV Response

2002 ◽  
Author(s):  
Martin So̸reide
Keyword(s):  
Limit State ◽  
Preliminary Investigation ◽  
Cross Flow ◽  
Design Criterion ◽  
Wave Loads ◽  
Flow Response ◽  
Large Current ◽  
Vortex Induced Vibrations ◽  
The Cross ◽  
Fatigue Limit State

As offshore installations are moving into deeper water, engineers have to face new challenges in design of structures. Risers and free-span pipelines, subjected to heavy wave loads and large current velocities, are important components of these installations. Vortex induced vibrations (VIV) is a well known subject for most offshore engineers. VIV can cause large stresses and fatigue damage of slender marine structures. Hence, large safety factors are applied to the fatigue limit state design criterion (FLS), due to uncertainties regarding VIV. The present paper describes the preliminary investigation into the coupling between in-line and cross-flow VIV response. Most experimental data so far has been concentrated on predicting the cross-flow response. However, in-line displacements can make a valuable contribution. In fact, it has been proved that in-line responses may decrease the cross-flow response significantly when allowing the pipe to oscillate in both directions. The paper is based on a master of science thesis at the Norwegian University of Science and Technology (NTNU).

Simplified Model for Evaluation of Fatigue From Vortex Induced Vibrations of Marine Risers

2004 ◽  
Author(s):  
Gro Sagli Baarholm ◽  
Carl M. Larsen ◽  
Halvor Lie ◽  
Kim Mo̸rk ◽  
Trond Stokka Meling
Keyword(s):  
Fatigue Damage ◽  
Cross Flow ◽  
Mode Shapes ◽  
Design Stage ◽  
Response Frequency ◽  
Lower Mode ◽  
Marine Risers ◽  
Vortex Induced Vibrations ◽  
Well Yield ◽  
The Cross

This paper presents a novel approach for approximate calculation of the fatigue damage from vortex-induced vibrations (VIV) of marine risers. The method is based on experience from a large number of laboratory tests with models of full-length risers, large-scale tests and also full-scale measurements. The method is intended to provide a conservative result and be used for screening purposes at the early design stage. The model is in particular aimed at predicting fatigue for risers that respond at very high mode orders (above 10), but may as well yield valid results for lower mode numbers. The model will, however, not be adequate for free span pipelines or other structures that normally will respond at first and second mode. The riser will be defined in terms of some key parameters like length, weight, tension, hydrodynamic diameter and stress diameter. A current profile perpendicular to the riser in one plane must be known. The program will apply a simple model for calculation of eigenfrequencies and mode shapes, and these are sorted into in-line (IL) and cross-flow (CF) bins. An effective current velocity and excitation length can be defined from the profile and will be applied to identify the dominating cross-flow response frequency and the total displacement rms value. The dominating in-line response frequency is taken as twice the cross-flow frequency, and inline response rms is taken as a given portion of the cross-flow rms value. A set of contributing modes is defined from an assumed frequency bandwidth that reflects observed bandwidths, but also modal composition for cases with discrete frequency response. A simple mode superposition technique is then used to find the set of modes that gives the identified rms values. Bending stresses will be found directly from the curvature of the mode shapes. Fatigue damage will be found from stress rms values, user defined stress concentration factor and given SN curves. The model has been implemented in a simple computer program and verified by comparing results to measurements. The ambition has not been to obtain an exact match between computed results and observations, but to verify that the model gives reasonable but conservative results in almost all cases. However, an unrealistic over prediction of the fatigue damage is not desired. The results are promising, but the need for more information from measurements and response analyses with programs like VIVANA and SHEAR7 is still obvious.

Dual resonance in vortex-induced vibrations at subcritical and supercritical Reynolds numbers

2010 ◽  
Vol 643 ◽  
pp. 395-424 ◽  
Author(s):  
J. M. DAHL ◽  
F. S. HOVER ◽  
M. S. TRIANTAFYLLOU ◽  
O. H. OAKLEY
Keyword(s):  
Reynolds Number ◽  
Natural Frequency ◽  
Frequency Ratio ◽  
Reynolds Numbers ◽  
Large Reynolds Number ◽  
Resonant Response ◽  
Third Harmonic ◽  
Vortex Induced Vibrations ◽  
Dual Resonance ◽  
Harmonic Components

An experimental study is performed on the vortex induced vibrations of a rigid flexibly mounted circular cylinder placed in a crossflow. The cylinder is allowed to oscillate in combined crossflow and in-line motions, and the ratio of the nominal in-line and transverse natural frequencies is varied systematically. Experiments were conducted on a smooth cylinder at subcritical Reynolds numbers between 15 000 and 60 000 and on a roughened cylinder at supercritical Reynolds numbers between 320 000 and 710 000, with a surface roughness equal to 0.23 % of the cylinder diameter. Strong qualitative and quantitative similarities between the subcritical and supercritical experiments are found, especially when the in-line natural frequency is close to twice the value of the crossflow natural frequency. In both Reynolds number regimes, the test cylinder may exhibit a ‘dual-resonant’ response, resulting in resonant crossflow motion at a frequency fv, near the Strouhal frequency, and resonant in-line motion at 2 fv. This dual resonance is shown to occur over a relatively wide frequency region around the Strouhal frequency, accompanied by stable, highly repeatable figure-eight cylinder orbits, as well as large third-harmonic components of the lift force. Under dual-resonance conditions, both the subcritical and the supercritical response is shown to collapse into a narrow parametric region in which the effective natural-frequency ratio is near the value 2, regardless of the nominal natural-frequency ratio. Some differences are noted in the magnitudes of forces and the cylinder response between the two different Reynolds number regimes, but the dual-resonant response and the resulting force trends are preserved despite the large Reynolds number difference.

scholarly journals Vortex-induced vibrations of a cylinder in planar shear flow

2017 ◽  
Vol 825 ◽  
pp. 353-384 ◽  
Author(s):  
Simon Gsell ◽  
Rémi Bourguet ◽  
Marianna Braza
Keyword(s):  
Steady Flow ◽  
Cross Flow ◽  
The Body ◽  
Body Motion ◽  
Inflow Velocity ◽  
Asymmetric Pattern ◽  
Planar Shear ◽  
The Cross ◽  
The Impact ◽  
Body Case

The system composed of a circular cylinder, either fixed or elastically mounted, and immersed in a current linearly sheared in the cross-flow direction, is investigated via numerical simulations. The impact of the shear and associated symmetry breaking are explored over wide ranges of values of the shear parameter (non-dimensional inflow velocity gradient, $\unicode[STIX]{x1D6FD}\in [0,0.4]$) and reduced velocity (inverse of the non-dimensional natural frequency of the oscillator, $U^{\ast }\in [2,14]$), at Reynolds number $Re=100$; $\unicode[STIX]{x1D6FD}$, $U^{\ast }$ and $Re$ are based on the inflow velocity at the centre of the body and on its diameter. In the absence of large-amplitude vibrations and in the fixed body case, three successive regimes are identified. Two unsteady flow regimes develop for $\unicode[STIX]{x1D6FD}\in [0,0.2]$ (regime L) and $\unicode[STIX]{x1D6FD}\in [0.2,0.3]$ (regime H). They differ by the relative influence of the shear, which is found to be limited in regime L. In contrast, the shear leads to a major reconfiguration of the wake (e.g. asymmetric pattern, lower vortex shedding frequency, synchronized oscillation of the saddle point) and a substantial alteration of the fluid forcing in regime H. A steady flow regime (S), characterized by a triangular wake pattern, is uncovered for $\unicode[STIX]{x1D6FD}>0.3$. Free vibrations of large amplitudes arise in a region of the parameter space that encompasses the entire range of $\unicode[STIX]{x1D6FD}$ and a range of $U^{\ast }$ that widens as $\unicode[STIX]{x1D6FD}$ increases; therefore vibrations appear beyond the limit of steady flow in the fixed body case ($\unicode[STIX]{x1D6FD}=0.3$). Three distinct regimes of the flow–structure system are encountered in this region. In all regimes, body motion and flow unsteadiness are synchronized (lock-in condition). For $\unicode[STIX]{x1D6FD}\in [0,0.2]$, in regime VL, the system behaviour remains close to that observed in uniform current. The main impact of the shear concerns the amplification of the in-line response and the transition from figure-eight to ellipsoidal orbits. For $\unicode[STIX]{x1D6FD}\in [0.2,0.4]$, the system exhibits two well-defined regimes: VH1 and VH2 in the lower and higher ranges of $U^{\ast }$, respectively. Even if the wake patterns, close to the asymmetric pattern observed in regime H, are comparable in both regimes, the properties of the vibrations and fluid forces clearly depart. The responses differ by their spectral contents, i.e. sinusoidal versus multi-harmonic, and their amplitudes are much larger in regime VH1, where the in-line responses reach $2$ diameters ($0.03$ diameters in uniform flow) and the cross-flow responses $1.3$ diameters. Aperiodic, intermittent oscillations are found to occur in the transition region between regimes VH1 and VH2; it appears that wake–body synchronization persists in this case.

Comparison of Calculated In-Line Vortex Induced Vibrations to Model Tests

2012 ◽  
Author(s):  
Elizabeth Passano ◽  
Carl M. Larsen ◽  
Halvor Lie
Keyword(s):  
Cross Flow ◽  
Added Mass ◽  
Model Tests ◽  
The Finite Element Method ◽  
Response Frequency ◽  
Flow Response ◽  
Vortex Induced Vibrations ◽  
Flow Directions ◽  
The Cross ◽  
Semi Empirical

The purpose of the present paper is to compare vortex-induced vibrations (VIV) in both in-line and cross-flow directions calculated by a semi-empirical computer program to experimental data. The experiments used are the Bearman and Chaplin experiments in which a model of a tensioned riser is partly exposed to current and partly in still water. The VIVANA program is a semi-empirical frequency domain program based on the finite element method. The program was developed by MARINTEK and the Norwegian University of Science and Technology (NTNU) to predict cross-flow response due to VIV. The fluid-structure interaction in VIVANA is described using added mass, excitation and damping coefficients. Later, curves for excitation, added mass and damping for pure in-line VIV response were added. These curves are valid for low current levels, before the onset of cross-flow VIV response. Recently, calculation of response from simultaneous cross-flow and in-line excitation has been included in VIVANA. The in-line response frequency is fixed at twice the cross-flow response frequency and the in-line added mass is adjusted so that this frequency becomes an eigenfrequency. A set of curves based on forces measured during combined cross-flow and inline motions are used. At present, the in-line excitation curves are not dependent on the cross-flow response amplitude. In the paper, in-line and cross-flow response predicted by VIVANA will be compared to the Bearman and Chaplin model tests. The choice of added mass and excitation coefficients will be discussed.

scholarly journals Experimental Investigation of Two-Degree-of-Freedom VIV of Circular Cylinder With Low Equivalent Mass and Variable Natural Frequency Ratio

2013 ◽  
Author(s):  
Narakorn Srinil ◽  
Hossein Zanganeh ◽  
Alexander Day
Keyword(s):  
Experimental Investigation ◽  
Numerical Model ◽  
Circular Cylinder ◽  
Natural Frequency ◽  
Frequency Ratio ◽  
Cross Flow ◽  
Number Range ◽  
Numerical Predictions ◽  
Equivalent Mass ◽  
Wake Oscillators

This paper presents an experimental investigation and validation of numerical prediction model for a 2-DOF VIV of a flexibly mounted circular cylinder by also accounting for the effect of geometrically nonlinear displacement coupling. A mechanical spring-cylinder system, achieving a low equivalent mass ratio in both in-line and cross-flow directions, is tested in a water towing tank and subject to a uniform steady flow in a sub-critical Reynolds number range of about 2000–50000. A generalized numerical model is based on double Duffing-van der Pol (structure-wake) oscillators which can capture the structural geometrical coupling and fluid-structure interaction effects through system cubic and quadratic nonlinearities. Experimental results are compared with numerical predictions in terms of response amplitudes, lock-in ranges and time-varying trajectories of cross-flow/in-line motions. Some good qualitative and quantitative agreements are found which encourage the use of the proposed numerical model subject to calibration and tuning of empirical coefficients. Various features of figure-of-eight orbital motions due to dual resonances are observed experimentally as well as numerically, depending on the natural frequency ratio of the oscillating cylinder.

Simulation of Flow Induced Vibrations of Tube Bundle in Cross Flow

2001 ◽  
Vol 17 (3) ◽  
pp. 139-147
Author(s):  
Tsun-Kuo Lin ◽  
Ming-Huei Yu
Keyword(s):  
Flow Field ◽  
Natural Frequency ◽  
Stokes Equations ◽  
Tube Bundle ◽  
Cross Flow ◽  
Calculated Data ◽  
Major Axis ◽  
Damping Factor ◽  
Inlet Velocity ◽  
The Cross

ABSTRACTThe flow-induced vibration of tubes in a rotated triangular array subject to cross flow is simulated numerically. In the study, the flow field around the tube bundle is computed by solving the continuity and Navier-Stokes equations with assumption of constant fluid properties, and the kε-model for turbulent Reynolds stress. With the flow field known, the fluid forces on the tube surfaces can be calculated, and then the displacement of each tube due to the fluid force can be evaluated. Iteration is needed to obtain the dynamic response of the tube structure in the fluid flow. The parameters in the study are inlet velocity of the cross flow and properties of the tube bundle including natural frequency, damping factor, and mass. Based on the tube response, the critical flow conditions of tube vibration are determined for varying mass damping. Once tube vibrations occur, it is shown that the vibrations of the tubes in the second and fourth tube rows are significant as compared to other tubes. The orbits of the tube vibration look like an ellipse with major axis in the cross-stream direction, implying large lift force on the tubes. The dominant frequency in the spectrum of lift coefficients of the tubes is the same as the natural frequency, and the corresponding amplitude is increased with increasing the inlet velocity. The calculated data predicted for the critical reduced velocity agrees well with the data by Kassera and Strohmeier [17].

Sign in / Sign up

Export Citation Format

Share Document