Numerical Study of the Influence of Initial Condition in Vortex Induced Vibration of a Circular Cylinder With Two Degree of Freedom

2011 ◽  
Author(s):  
Bruno C. Ferreira ◽  
Marcelo A. Vitola ◽  
Juan B. V. Wanderley ◽  
Sergio H. Sphaier
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Numerical Study ◽  
Cross Flow ◽  
Degree Of Freedom ◽  
Curvilinear Coordinates ◽  
Initial Condition ◽  
Ocean Engineering ◽  
Vortex Induced Vibration ◽  
Two Degree Of Freedom

The vortex-induced vibration (VIV) is a classical problem in ocean engineering. Intensive research on this field for flow around a circular cylinder has been observed, due to practical application, mainly the design of risers, cables and pipelines with free span. The relevance of this phenomenon is related to the structure failure, consequence of large displacement or fatigue. In the present study the influence of initial condition on the vortex induced vibration (VIV) of a circular cylinder with two degree of freedom is investigated by the numerical solution of the slightly compressible formulation of Reynolds Average Navier-Stokes equations. An upwind and Total Variation Diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates. The k–ε turbulence model is used to simulate the turbulent flow in the wake of the cylinder. Two different initial conditions have been tested, free-stream and continuous reduced velocity increase (using the previous reduced velocity as initial condition for the next value). Results for the phase angle, amplitude, frequency, and lift coefficient are presented. The numerical results have been compared with experimental data of Jauvtis and Williamson [1]. The results indicate that the history of cylinder movement has a important impact in the amplitude oscillation observed in-line and cross-flow, principally in the reduced velocity range associated with the upper branch. Results obtained for the initial and lower branch seems to be independent of the initial condition. Further investigation are necessary to understand the difference observed such as the absence of the jump in the cross-flow oscillation between the initial and upper branch and the absence of in-line oscillation for reduced velocity in the range of 1–4 and the peak of in-line oscillation at reduced velocity 6.0.

Numerical Investigation of Vortex-Induced Vibration of a Circular Cylinder Close to a Plane Boundary

2010 ◽  
Author(s):  
Ming Zhao ◽  
Liang Cheng
Keyword(s):  
Experimental Data ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Degree Of Freedom ◽  
Plane Boundary ◽  
Structural Dynamic ◽  
Vortex Induced Vibration ◽  
Two Degree Of Freedom ◽  
Bounce Back

Two-degree of freedom vortex-induced vibration (VIV) of a circular cylinder close to a plane boundary is investigated numerically. Two-dimensional (2D) Reynolds-Averaged Navier-Stokes Equations (RANS) and structural dynamic equation are solved using a finite element method (FEM). If the cylinder is initially very close to the plane boundary, it will be bounced back after it collides with boundary. It is assumed that the bouncing back only alters the cylinder’s velocity component perpendicular to the boundary. After it is bounced back, the cylinder’s velocity are determined by Uc = Uc′, Vc = −bVc′, where Uc and Vc are the cylinder’s velocity parallel to the boundary and that perpendicular to the boundary respectively, Uc′ and Vc′ are the velocities before cylinder is bounced back, b is the bounce back coefficient which is between 0 and 1. Numerical results of the vibration amplitude and frequency of a one-degree-of-freedom vibration (transverse to flow direction) of a circular cylinder close to a plane boundary are compared with the experimental data by Yang et al. [1]. The overall trends of the variation of the VIV amplitude with the reduced velocity were found to be in agreement with the experimental results. The calculated amplitude is smaller than the measured data. The frequency of the vibration increases with the increase of reduced velocity. The calculated vibrating frequency agrees well with the experimental data. It was found in this study that vortex-induced vibration (VIV) occurs even when the gap between the cylinder and the plane boundary is zero. This contradicts a perception that VIV would not occur for a pipeline close to the seabed with a gap ratio smaller than 0.3, this is because it was understood that vortex shedding would have been suppressed if the gap between the cylinder and the plane boundary is less than about 0.3 times of cylinder diameter for a fixed cylinder. Two-degree-of-freedom VIV of a circular cylinder close to a plane boundary is studied. The XY-trajectories, the frequency and the amplitude of the vibration are studied. The effects of the cylinder-to-boundary gap and the bounce back coefficient on VIV and the link between the vortex shedding mode and the VIV are discussed.

Numerical Investigation of Vortex-Induced Vibration (VIV) of a Circular Cylinder in Oscillatory Flow

2011 ◽  
Author(s):  
Ming Zhao ◽  
Liang Cheng ◽  
Tongming Zhou
Keyword(s):  
Circular Cylinder ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Flow Direction ◽  
Cross Flow ◽  
Frequency Component ◽  
Degree Of Freedom ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration

Vortex-induced vibration (VIV) of a circular cylinder in oscillatory flow is investigated numerically in this study. The incompressible Reynolds-Averaged Navier-Stokes equations governing fluid flow around a circular cylinder are solved using Arbitrary Langrangian-Eulerian (ALE) scheme and Petrov-Galerkin finite element method. The equation of motion is solved for the displacements of the cylinder both in the inline and cross-flow directions. The numerical model is firstly validated against the experimental results of one-degree-of-freedom VIV in cross-flow direction. It is found that both VIV frequency and amplitude vary with reduced velocity for a fixed KC number. In most of the simulated cases the vibration comprises of multiple frequencies of different amplitudes. Each frequency component is multiple times of the frequency of the oscillatory flow. Two-degree-of-freedom VIV is investigated with the same parameters used in the one-degree-of-freedom case. By examining the XY-trajectory of the vibration, it if found that the vibration follows different trajectory for different KC numbers or reduced velocities.

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.

Numerical Investigation of Vortex-Induced Vibration of a Circular Cylinder Close to a Plane Boundary Subject to Oscillatory Flow

2016 ◽  
Author(s):  
Adnan Munir ◽  
Ming Zhao ◽  
Helen Wu
Keyword(s):  
Circular Cylinder ◽  
Oscillatory Flow ◽  
Numerical Study ◽  
Cross Flow ◽  
Navier Stokes ◽  
Plane Boundary ◽  
Vortex Induced Vibration ◽  
Gap Ratio ◽  
Wide Range ◽  
Close Proximity

This paper presents a numerical study of flow around an elastically mounted circular cylinder in close proximity to a plane boundary vibrating in the transverse and inline directions in an oscillatory flow. The Reynolds-Averaged Navier-Stokes (RANS) equations and the SST k-ω turbulent equations are solved using the Arbitrary Langrangian-Eulerian (ALE) scheme and Petrov-Galerkin Finite Element Method for simulating the flow. The equation of motion is solved using the fourth-order Runge-Kutta method to find the displacements of the cylinder in the transverse and inline directions. The numerical model is validated against the previous results of vortex-induced vibration of an isolated circular cylinder in both cross-flow and inline directions. The flow model is further extended to study the vortex-induced vibration of a cylinder near a plane boundary with a very small gap ratio (e/D) of 0.01, with D and e being the diameter and the gap between the cylinder and the plane boundary, respectively. Simulations are carried out for two Keulegan-Carpenter (KC) numbers of 5 and 10 and a wide range of reduced velocities. It is observed that both the KC number and the reduced velocity affect the vibration of the cylinder significantly.

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