A Model Experiment Investigation on Two Degrees of Freedom VIV of Cylinder

2014 ◽  
Author(s):  
Yunhe Zhai ◽  
Ruxin Song ◽  
Zh. Kang ◽  
Liping Sun ◽  
Peng Li
Keyword(s):  
Degrees Of Freedom ◽  
Cross Flow ◽  
Natural Vibration Frequency ◽  
Mass Ratio ◽  
Response Characteristics ◽  
Line Flow ◽  
Flow Directions ◽  
The Cross ◽  
Spring Constants ◽  
Two Degree Of Freedom

An experimental investigation on vortex-induced vibration (VIV) response characteristics of a rigid cylinder was conducted at the Towing Tank Lab in Harbin Engineering University. The Reynolds Number based on proposed diameter ranged from 6×104 to 2.4×105, with the cross-flow mass ratio my* = 1.127 and the in-line mass ratio mx* = 1.363. In the experiment, the spring constants of the cross-flow and in-line flow directions were regulated to change the natural vibration frequency of the model system. One- and two-degree-of-freedom VIV experiment was respectively carried out to analyze the vibration characteristic and trajectory. It was found that the non-dimension in-line and cross-flow natural frequency ratio fx/fy, is an important parameter which not only affects cross-flow vibration peak but also affects the forms of vibration trajectory except the reduced velocity.

An Experimental Investigation on Cylinder VIV Trajectories Under Different Model Scale

2014 ◽  
Author(s):  
Zh. Kang ◽  
Yunhe Zhai ◽  
Ruxin Song ◽  
Liping Sun
Keyword(s):  
Experimental Investigation ◽  
Vibration Frequency ◽  
Degrees Of Freedom ◽  
Natural Vibration ◽  
Cross Flow ◽  
Small Scale ◽  
Natural Vibration Frequency ◽  
Test Results ◽  
The Cross ◽  
Initial Research

In this paper, model tests were carried out to investigate two degrees of freedom VIV of horizontally-laid cylinders with diameters of 5cm, 11cm, 20cm and length 120cm and compared their vibration trajectories. The test results showed that the in-line and cross-flow vibration frequency of different scale cylinders demonstrate “multi frequency” phenomenon, that is, the in-line vibration frequency is not only twice but also once or four times as much as the cross-flow vibration frequency in some scale, natural frequency and reduced velocity conditions. Also, the cross-flow multi-frequency vibration phenomenon occurred. The trajectory of the vibration cylinder differentiated from the traditional “8” shape accordingly. The vibration trajectory, especially of small-scale cylinder, changed in most conspicuous manner. Through the initial research and analysis, it was found that in addition to in-line and cross-flow natural vibration frequency and the flow velocity, the shape of cylinders was also one of the main causes leading to different vibration trajectory forms.

The Numerical Simulation of Two-Degrees-of-Freedom Vortex-Induced Vibrations of Circular Cylinder with High Mass-Ratio

2013 ◽  
Vol 284-287 ◽  
pp. 557-561
Author(s):  
Jie Li Fan ◽  
Wei Ping Huang
Keyword(s):  
Circular Cylinder ◽  
Drag Force ◽  
Frequency Ratio ◽  
Lift Force ◽  
Degrees Of Freedom ◽  
Cross Flow ◽  
High Mass ◽  
Mass Ratio ◽  
Main Frequency ◽  
Line Amplitude

The two-degrees-of-freedom VIV of the circular cylinder with high mass-ratio is numerically simulated with the software ANSYS/CFX. The VIV characteristic is analyzed in the different conditions (Ur=3, 5, 6, 8, 10). When Ur is 5, 6, 8 and 10, the conclusion which is different from the cylinder with low mass-ratio can be obtained. When Ur is 3, the frequency of in-line VIV is twice of that of cross-flow VIV which is equal to the frequency ratio between drag force and lift force, and the in-line amplitude is much smaller than the cross-flow amplitude. The motion trace is the crescent. When Ur is 5 and 6, the frequency ratio between the drag force and lift force is still 2, but the main frequency of in-line VIV is mainly the same as that of cross-flow VIV and the secondary frequency of in-line VIV is equal to the frequency of the drag force. The in-line amplitude is still very small compared with the cross-flow amplitude. When Ur is up to 8 and 10, the frequency of in-line VIV is the same as the main frequency of cross-flow VIV which is close to the inherent frequency of the cylinder and is different from the frequency of drag force or lift force. But the secondary frequency of cross-flow VIV is equal to the frequency of the lift force. The amplitude ratio of the VIV between in-line and cross-flow direction is about 0.5. When Ur is 5, 6, 8 and 10, the motion trace is mainly the oval.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

Laboratory Experiment of Two-Degree-of-Freedom Vortex-Induced Vibrations of Circular Cylinder in Regular Waves

2020 ◽  
Author(s):  
Pierre-Adrien Opinel ◽  
Narakorn Srinil
Keyword(s):  
Circular Cylinder ◽  
Cross Flow ◽  
Wave Theory ◽  
Degree Of Freedom ◽  
Water Tank ◽  
Regular Waves ◽  
Flow Directions ◽  
Line Cross ◽  
Flow Frequency ◽  
Two Degree Of Freedom

Abstract This paper presents new laboratory experiments of two-degree-of-freedom vortex-induced vibration of a flexibly mounted vertical circular cylinder in regular waves. A new experimental model has been developed and tested in the Wind, Wave & Current Tank at Newcastle University. The system mass ratio is close to 3 and the cylinder aspect ratio based on its submerged length is close to 27. The Stokes first-order wave theory is considered to describe the depth-dependent, horizontal velocity amplitude of the wave flow in the circulating water tank. This wave theory is satisfactorily validated by the wave probe measurement. The effects of cylinder stiffness affecting system natural frequencies are also investigated by using a combination of different spring setups in in-line and cross-flow directions. For each set of springs, VIV tests are performed in regular waves, with flow frequency ranging from 0.4 to 1 Hz and amplitude from 0.01 to 0.09 m. The associated Reynolds number at the water surface is in a range of 1.7 × 103–1.5 × 104. The surface Keulegan-Carpenter number (KC) is in the range of 2 < KC < 28 while the surface reduced velocity (Vr) is in the range of 0.5 < Vr < 16 depending on the implemented spring stiffness. Combined in-line/cross-flow oscillations of the cylinder are measured using two non-intrusive Qualisys cameras and the associated data acquisition system. The spring forces are also acquired using four load cells. Results reveal that, depending on KC and Vr, the cylinder primarily oscillates at the flow frequency in the in-line direction and at an integer (mainly 2, 3 and 4) multiple of the flow frequency in the cross-flow direction. Such occurrence of multi frequencies corroborates other experimental and numerical results in the literature. Several peculiar trajectories are observed, including infinity, butterfly, S and V shapes. The present experimental data of vibration amplitudes and oscillation frequencies in in-line/cross-flow directions as well as response patterns provide new results and improved understanding of VIV in oscillatory flows. These will be useful for the development of an industrial tool in predicting offshore structural responses in waves.

On Cross Flow-Induced Vibration of a Flexible Cylinder

2014 ◽  
Author(s):  
H. Cen ◽  
D. S-K. Ting ◽  
R. Carriveau
Keyword(s):  
Reynolds Number ◽  
Degrees Of Freedom ◽  
Cross Flow ◽  
Mass Ratio ◽  
Flexible Cylinder ◽  
Flow Induced Vibration ◽  
Slowing Down ◽  
Mode Vibration ◽  
Inner Diameter ◽  
Multi Mode

An experiment study on the cross flow-induced vibration of a flexible cylinder with two degrees of freedom had been conducted in a towing tank. The test cylinder was a 45 cm long Tygon tubing with outer and inner diameter of 7.9 mm (5/16 in) and 4.8 mm (3/16 in), giving a mass ratio of 0.77 and an aspect ratio of 56. It was towed from rest up to 1.6 m/s before slowing down to rest again over a distance of 1.6 m in still water, covering the range of Reynolds number from 1500 to 13000 and reduced velocity from 4 to 35. Multi-mode vibration and sudden shift between different modes were observed. The vibration amplitude, frequency and mode were quantified. The results obtained during the brief constant towing speed were expressed in term of the corresponding Reynolds number or reduced velocity. These findings were cast with respect to the existing knowledge in the literature.

scholarly journals Fluid nonlinearities effect on wake oscillator model performance

2018 ◽  
Vol 148 ◽  
pp. 04002 ◽  
Author(s):  
Victoria Kurushina ◽  
Ekaterina Pavlovskaia
Keyword(s):  
Structural Damage ◽  
Degrees Of Freedom ◽  
Model Performance ◽  
Cross Flow ◽  
Resonance State ◽  
Oscillator Model ◽  
Mass Ratio ◽  
Wake Oscillator Model ◽  
Wake Oscillator ◽  
Wide Range

Vortex-induced vibrations (VIV) need to be accounted for in the design of marine structures such as risers and umbilicals. If a resonance state of the slender structure develops due to its interaction with the surrounding fluid flow, the consequences can be severe resulting in the accelerated fatigue and structural damage. Wake oscillator models allow to estimate the fluid force acting on the structure without complex and time consuming CFD analysis of the fluid domain. However, contemporary models contain a number of empirical coeffcients which are required to be tuned using experimental data. This is often left for the future work with the opened question on how to calibrate a model for a wide range of cases and find out what is working and is not. The current research is focused on the problem of the best choice of the fluid nonlinearities for the base wake oscillator model [1] in order to improve the accuracy of prediction for the cases with mass ratios around 6.0. The paper investigates six nonlinear damping types for two fluid equations of the base model. The calibration is conducted using the data by Stappenbelt and Lalji [2] for 2 degrees-of-freedom rigid structure for mass ratio 6.54. The conducted analysis shows that predicted in-line and cross-flow displacements are more accurate if modelled separately using different damping types than using only one version of the model. The borders of application for each found option in terms of mass ratio are discussed in this work, and appropriate recommendations are provided.

Simultaneous Wake- and Vortex-Induced Vibrations of a Cylinder With Two Degrees of Freedom in Each Direction

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
J. R. Chaplin ◽  
W. M. J. Batten
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Elastic System ◽  
Cross Flow ◽  
Structural Response ◽  
Flow Induced Vibration ◽  
Vortex Induced Vibrations ◽  
Complicated Process ◽  
The Subject ◽  
Flow Directions

The flow-induced vibration of one cylinder in the wake of another is the subject of continuing interest in connection with interactions between vertical tension risers in deep water. When one riser is downstream of another, it is likely to be subject to wake-induced and vortex-induced excitations at different frequencies simultaneously. Both are complex mechanisms, and it is reasonable to assume that they interact. To begin to understand this complicated process, it is desirable that any modeling should incorporate some features of a multidegree-of-freedom structural response. With this aim, this paper describes experiments in which one cylinder was free to undergo simultaneous wake- and vortex-induced vibrations downstream of a similar but stationary cylinder in a steady flow. The downstream cylinder was mounted on an elastic system that had two natural frequencies in both the in-line and cross-flow directions. Mass ratios were almost the same in all four modes. Measurements are presented of simultaneous wake- and vortex-induced vibrations for cylinder separations of 5 and 10 diameters in the in-line direction, and up to 4 diameters transversely. At a reduced velocity of 83 (based on the cylinder's lower submerged natural frequency) and a separation of 5 diameters, excursions of wake-induced vibrations peaked at almost 5 diameters, when the downstream cylinder was near the edge of the upstream cylinder's wake.

Phenomenological Modelling of Cylinder VIV With Contributions From Oscillatory Flows

2018 ◽  
Author(s):  
Pierre-Adrien Opinel ◽  
Narakorn Srinil
Keyword(s):  
Flow Direction ◽  
Cross Flow ◽  
Single Frequency ◽  
Oscillatory Flows ◽  
Response Characteristics ◽  
Frequency Responses ◽  
The Cross ◽  
Wake Oscillators ◽  
Primary Frequency ◽  
Empirical Coefficients

This paper presents a numerical phenomenological model for a two-degree-of-freedom VIV of a flexibly mounted circular rigid cylinder subject to sinusoidal oscillatory flows. This prediction model is based on the use of double Duffing-van der Pol (structure-wake) oscillators which capture the structural geometrical coupling and fluid-solid interaction effects through system cubic-quadratic nonlinearities. Empirical coefficients are calibrated based on computational fluid dynamics results in the literature for the Keulegan-Carpenter numbers (KC) of 10, 20 and 40, satisfying a reasonable correspondence in amplitude and frequency responses. For KC = 10, the cross-flow vibrations present a single-frequency response. For KC = 20 and 40, cross-flow vibrations have multi-frequency responses. The primary frequency of the response in the cross-flow direction decreases with increasing reduced velocity, except for small values of the reduced velocities. In all KC cases, the in-line vibrations exhibit mostly a single frequency. Overall, parametric studies capture the dependence of response characteristics on the KC, reduced velocity, mass ratio, frequency ratios and empirical coefficients.

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.

Experimental Investigations of the Efficiency of Round-Sectioned Helical Strakes in Suppressing Vortex Induced Vibrations

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Raed K. Lubbad ◽  
Sveinung Løset ◽  
Geir Moe
Keyword(s):  
Flow Direction ◽  
Cross Flow ◽  
Experimental Investigations ◽  
Outer Diameter ◽  
Reference Case ◽  
Test Cylinder ◽  
Vortex Induced Vibrations ◽  
Helical Strakes ◽  
Flow Directions ◽  
The Cross

Vortex induced vibrations (VIVs) may cause a large amount of damage to deep water risers. Helical strakes are used as a mitigating measure to suppress these vibrations. The purpose of this paper is to verify the efficiency of round-sectioned helical strakes in suppressing VIV. It is believed that round-sectioned helical strakes can be more readily mounted on risers for intervention and maintenance compared with sharp-edged strakes that may have to be welded onto the risers. Systematic experimental investigations including 28 configurations of round-sectioned helical strakes were tested in an attempt to find the most suitable strake configuration. The experiments were performed in a steady flow flume with an elastically mounted rigid circular cylinder of 500 mm in length and 50 mm in outer diameter. The test cylinder was spring-supported in both the inline and cross-flow directions. The measurements were limited to mapping the displacement of the cylinder. First, the cylinder was tested without strakes as a reference case. The best configuration among the tested round-sectioned helical strake configurations was found to reduce the amplitude of oscillation relative to the bare cylinder case by 96% in the cross-flow direction and by 97% in the inline direction. The main features of this configuration are the number of starts (3), the pitch (5D), and the diameter of the strake (0.15D), where D is the outer diameter of the test cylinder. Additionally, this paper investigates the effects of varying pitch, the effects of surface roughness, and the effects of the ratio between the cross-flow and inline natural frequencies of the test rig on the efficiency of the suggested configuration of round-sectioned helical strakes.

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