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.

Vortex-Induced Vibration of Two Side-by-Side Cylinders With a Small Gap in Uniform Flow

2017 ◽  
Author(s):  
Adnan Munir ◽  
Ming Zhao ◽  
Helen Wu
Keyword(s):  
Stokes Equations ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gap Ratio ◽  
Vortex Induced Vibrations ◽  
Lock In

Vortex-induced vibrations of two elastically mounted and rigidly coupled circular cylinders in side-by-side arrangement in steady flow are investigated numerically. The vibration of the cylinders is limited to the cross-flow direction only. The three-dimensional Navier-Stokes equations are solved using the Petrov-Galerkin Finite element method and the equation of motion is solved using the fourth order Runge Kutta method. It is well known that when the gap between two stationary side-by-side cylinders is very small, the flow between the two cylinders is biased towards one cylinder and the lift force on each cylinder is significantly smaller than that of an isolated single cylinder. The aim of this study is to investigate the effect of a small gap ratio of 0.5 between the two cylinders on the lock-in regime and the amplitude of the vibration of two side-by-side cylinders in a fluid flow. Simulations are carried out for a constant mass ratio of 2, a constant Reynolds number of 1000 and a range of reduced velocities. It is found that in the lock-in range of the reduced velocity, the two cylinders vibrate about their balance position with high amplitudes. Outside the lock-in regime the flow from the gap becomes biased towards one cylinder, which is similar to that from the gap between stationary cylinders.

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.

Numerical Prediction of Flow Fields Around Circular Cylinders: Forced Motion and Dynamic Response Cases

2000 ◽  
Vol 122 (4) ◽  
pp. 703-714 ◽  
Author(s):  
S. Lu ◽  
O¨. F. Turan
Keyword(s):  
Circular Cylinder ◽  
Dynamic Response ◽  
Relative Phase ◽  
Stokes Equations ◽  
Cross Flow ◽  
Structural Equations ◽  
Transverse Oscillation ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equations

At Re=2000, the predicted flow field around a circular cylinder in forced transverse oscillation is verified with experimental results. For coupled torsional and transverse oscillation cases, the numerical results indicate that lock-in depends on the relative phase between torsional and translational oscillations. The dynamic response of an elastically mounted circular cylinder in cross flow, obtained by solving the structural equations simultaneously with the Navier-Stokes equations, is in reasonable agreement with experimental data. The dynamic response results indicate that the change of wake pattern from 2S to 2P with increased frequency ratio, is not always simultaneous with the change in the relative phase between lift force and cylinder displacement. [S0098-2202(00)02003-4]

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.

Direct numerical simulation of oscillatory flow around a circular cylinder at low Keulegan–Carpenter number

2010 ◽  
Vol 666 ◽  
pp. 77-103 ◽  
Author(s):  
HONGWEI AN ◽  
LIANG CHENG ◽  
MING ZHAO
Keyword(s):  
Circular Cylinder ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Empirical Relationship ◽  
Three Dimensional ◽  
Subsequent Development ◽  
Navier Stokes ◽  
Strongly Correlated ◽  
Navier Stokes Equations ◽  
Steady Streaming

The Honji instability is studied using direct numerical simulations of sinusoidal oscillatory flow around a circular cylinder. The three-dimensional Navier–Stokes equations are solved by a finite element method at a relatively small value of the Keulegan–Carpenter number KC. The generation and subsequent development of Honji vortices are discussed over a range of frequency parameters by means of flow visualization. It is found that the spacing between Honji vortices is only weakly dependent on the frequency of oscillation, but is strongly correlated to KC because it is the terms within the governing equation containing KC that dominate the three-dimensional features of the flow. An empirical relationship between KC and the spacing between neighbouring vortices is proposed. The three-dimensional steady streaming structure within the vortices is identified and it is found that at high frequencies the steady streaming is two-dimensional although the instantaneous flow structure is itself fully three-dimensional.

Iterative method for solving fully-coupled fluid solid systems

2010 ◽  
pp. 653-670
Author(s):  
Elisabeth Longatte
Keyword(s):  
Stokes Equations ◽  
Cross Flow ◽  
Elastic Cylinder ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Ale Formulation ◽  
Volume Method ◽  
Fully Coupled ◽  
Solid System

This work is concerned with the modelling of the interaction of a fluid with a rigid or a flexible elastic cylinder in the presence of axial or cross-flow. A partitioned procedure is involved to perform the computation of the fully-coupled fluid solid system. The fluid flow is governed by the incompressible Navier-Stokes equations and modeled by using a fractional step scheme combined with a co-located finite volume method for space discretisation. The motion of the fluid domain is accounted for by a moving mesh strategy through an Arbitrary Lagrangian-Eulerian (ALE) formulation. Solid dyncamics is modeled by a finite element method in the linear elasticity framework and a fixed point method is used for the fluid solid system computation. In the present work two examples are presented to show the method robustness and efficiency.

On Offset Placement of a Compound Droplet in a Channel Flow

2021 ◽  
Author(s):  
Jagannath Mahato ◽  
Dhananjay Kumar Srivastava ◽  
Dinesh Kumar Chandraker ◽  
Rajaram Lakkaraju
Keyword(s):  
Viscosity Ratio ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Flow Direction ◽  
Navier Stokes ◽  
Volume Of Fluid Method ◽  
Lateral Migration ◽  
Navier Stokes Equations ◽  
Deformation Patterns ◽  
Compound Droplet

Abstract Investigations on flow dynamics of a compound droplet have been carried out in a two-dimensional fully-developed Poiseuille flow by solving the Navier-Stokes equations with the evolution of the droplet using the volume of fluid method with interface compression. The outer droplet undergoes elongation similar to a simple droplet of same size placed under similar ambient condition in the flow direction, but, the inner droplet evolves in compressed form. The compound droplet is varied starting from the centerline towards the walls of the channel. The simulations showed that on applying an offset, asymmetric slipper-like shapes are observed as opposed to symmetric bullet-like shapes through the centerline. Temporal dynamics, deformation patterns, and droplet shell pinch-off mode vary with the offset, with induction of lateral migration. Also, investigations are done on the effect of various parameters like droplet size, Capillary number, and viscosity ratio on the deformation magnitude and lateral migration.

scholarly journals A Stress Mapping Immersed Boundary Method for Viscous Flows

2021 ◽  
Vol 87 (3) ◽  
pp. 1-20
Author(s):  
Karim M. Ali ◽  
Mohamed Madbouli ◽  
Hany M. Hamouda ◽  
Amr Guaily
Keyword(s):  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Cross Flow ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Element Formulation ◽  
Navier Stokes Equations ◽  
Boundary Method ◽  
Background Grid ◽  
Dimensional Simulation

This work introduces an immersed boundary method for two-dimensional simulation of incompressible Navier-Stokes equations. The method uses flow field mapping on the immersed boundary and performs a contour integration to calculate immersed boundary forces. This takes into account the relative location of the immersed boundary inside the background grid elements by using inverse distance weights, and also considers the curvature of the immersed boundary edges. The governing equations of the fluid mechanics are solved using a Galerkin-Least squares finite element formulation. The model is validated against a stationary and a vertically oscillating circular cylinder in a cross flow. The results of the model show acceptable accuracy when compared to experimental and numerical results.

Simulation of Acoustic Streaming in a Resonator

2004 ◽  
Author(s):  
Bakhtier Farouk ◽  
Murat K. Aktas
Keyword(s):  
Flow Field ◽  
Standing Wave ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Flow Patterns ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Streaming Flow

Formation of vortical flow structures in a rectangular enclosure due to acoustic streaming is investigated numerically. The oscillatory flow field in the enclosure is created by the vibration of a vertical side wall of the enclosure. The frequency of the wall vibration is chosen such that a standing wave forms in the enclosure. The interaction of this standing wave with the horizontal solid walls leads to the production of Rayleigh type acoustic streaming flow patterns in the enclosure. All four walls of the enclosure considered are thermally insulated. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to explicitly track the acoustic waves. Numerical solutions are obtained by employing a highly accurate flux corrected transport (FCT) algorithm for the convection terms. A time-splitting technique is used to couple the viscous and diffusion terms of the full Navier-Stokes equations. Non-uniform grid structure is employed in the computations. The simulation of the primary oscillatory flow and the secondary (steady) streaming flows in the enclosure is performed. Streaming flow patterns are obtained by time averaging the primary oscillatory flow velocity distributions. The effect of the amount of wall displacement on the formation of the oscillatory flow field and the streaming structures are studied. Computations indicate that the nonlinearity of the acoustic field increases with increasing amount of the vibration amplitude. The form and the strength of the secondary flow associated with the oscillatory flow field and viscous effects are found to be strongly correlated to the maximum displacement of the vibrating wall. Total number of acoustic streaming cells per wavelength is also determined by the strength and the level of the nonlinearity of the sound field in the resonator.

Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments

2015 ◽  
Vol 767 ◽  
pp. 364-393 ◽  
Author(s):  
P. Lubin ◽  
S. Glockner
Keyword(s):  
Stokes Equations ◽  
Early Stage ◽  
Flow Direction ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Vortex Filaments ◽  
Navier Stokes Equations ◽  
Main Flow Direction

AbstractThe scope of this work is to present and discuss the results obtained from simulating three-dimensional plunging breaking waves by solving the Navier–Stokes equations, in air and water. Recent progress in computational capabilities has allowed us to run fine three-dimensional simulations, giving us the opportunity to study for the first time fine vortex filaments generated during the early stage of the wave breaking phenomenon. To date, no experimental observations have been made in laboratories, and these structures have only been visualised in rare documentary footage (e.g. BBC 2009 South Pacific. Available on YouTube, 7BOhDaJH0m4). These fine coherent structures are three-dimensional streamwise vortical tubes, like vortex filaments, connecting the splash-up and the main tube of air, elongated in the main flow direction. The first part of the paper is devoted to the presentation of the model and numerical methods. The air entrainment occurring when waves break is then carefully described. Thanks to the high resolution of the grid, these fine elongated structures are simulated and explained.

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