Passive Suppression Mechanisms in Laminar Vortex-Induced Vibration of a Sprung Cylinder With a Strongly Nonlinear, Dissipative Oscillator

2017 ◽  
Vol 84 (8) ◽  
Author(s):  
Antoine Blanchard ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis
Keyword(s):  
Parameter Space ◽  
Stokes Equations ◽  
Density Ratio ◽  
Cross Flow ◽  
Nonlinear Energy Sink ◽  
Spectral Element ◽  
Body Motion ◽  
Vortex Induced Vibration ◽  
Wake Oscillator ◽  
Viv Suppression

We study cross-flow vortex-induced vibration (VIV) of a linearly sprung circular cylinder equipped with a dissipative oscillator with cubic stiffness nonlinearity, restrained to move in the direction of travel of the cylinder. The dissipative, essentially nonlinear coupling between the cylinder and the oscillator allows for targeted energy transfer (TET) from the former to the latter, whereby the oscillator acts as a nonlinear energy sink (NES) capable of passively suppressing cylinder oscillations. For fixed values of the Reynolds number (Re = 48, slightly above the fixed-cylinder Hopf bifurcation), cylinder-to-fluid density ratio, and dimensionless cylinder spring constant, spectral-element simulations of the Navier–Stokes equations coupled to the rigid-body motion show that different combinations of NES parameters lead to different long-time attractors of the dynamics. We identify four such attractors which do not coexist at any given point in the parameter space, three of which lead to at least partial VIV suppression. We construct a reduced-order model (ROM) of the fluid–structure interaction (FSI) based on a wake oscillator to analytically study those four mechanisms seen in the high-fidelity simulations and determine their respective regions of existence in the parameter space. Asymptotic analysis of the ROM relies on complexification-averaging (CX-A) and slow–fast partition of the transient dynamics and predicts the existence of complete and partial VIV-suppression mechanisms, relaxation cycles, and Hopf and Shilnikov bifurcations. These outcomes are confirmed by numerical integration of the ROM and comparisons with spectral-element simulations of the full system.

Numerical Simulation of Vortex Induced Vibration Using the K-ε Model

2006 ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Gisele H. B. Souza ◽  
Carlos Levi
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Body Motion ◽  
Navier Stokes ◽  
Experimental Investigations ◽  
Real Problem ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration ◽  
Selection Of

Numerical simulations of Vortex Induced Vibration have been failing to duplicate accurately experimental data mostly due to the complexity of the physics involved in the real problem. Therefore, a careful and comprehensive investigation on CFD algorithms is still required to indicate the most suitable numerical scheme to handle such a complicate problem. Grid generation, boundary condition implementation, and coupling between the fluid flow governing equations and body motion equation are known to have strong influence on the qualities of the numerical results. This work presents results obtained from a long-term investigation featuring different CFD methods. The investigations enabled the selection of a very effective algorithm that showed an outstanding agreement between experiment and numerical simulation of the VIV phenomenon. Good agreement is obtained in the entire range of reduced velocity covered by the experimental investigations. The successful algorithm discussed here applies the Beam and Warming implicit scheme to solve the two-dimensional slightly compressible Navier–Stokes equations with the K-ε turbulence model to simulate the turbulent flow at the wake of the cylinder.

Vortex-Induced Vibration of a Sprung Rigid Circular Cylinder Augmented With a Nonlinear Energy Sink

2012 ◽  
Author(s):  
Ravi Kumar R. Tumkur ◽  
Ramon Calderer ◽  
Arif Masud ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Computational Study ◽  
Coupled System ◽  
Nonlinear Energy Sink ◽  
Small Mass ◽  
Limit Cycle Oscillation ◽  
Vortex Induced Vibration ◽  
Energy Sink ◽  
Nonlinear Energy

We study the nonlinear fluid-structure interaction of an elastically supported rigid circular cylinder in a laminar flow. Periodic shedding of counter-rotating vortices from either side of the cylinder results in vortex-induced vibration of the cylinder. We demonstrate the passive suppression of the limit cycle oscillation (LCO) of the cylinder with the use of an essentially nonlinear element, the nonlinear energy sink (NES). The computational study is performed at a Reynolds number (Re) of 100; Re is defined based on the cylinder diameter and inlet velocity. The variational multiscale residual-based stabilized finite-element method is used to compute approximate solutions of the incompressible Navier-Stokes equations. The NES is comprised of a small mass, an essentially nonlinear spring, and a linear damper. With appropriate values for the NES parameters, the coupled system of flow-cylinder-NES exhibits resonant interactions, resulting in targeted energy transfer (TET) from the flow via the cylinder to the NES, where the energy is dissipated by the linear damper. The NES interacts with the fluid via the cylinder by altering the phase relation between the lift force and the cylinder displacement; this brings about significant reduction in the LCO amplitude of the cylinder for several set of values of the NES parameters.

scholarly journals Prediction of Vortex-Induced Vibration Response of Deep Sea Top-Tensioned Riser in Sheared Flow Considering Parametric Excitations

2020 ◽  
Vol 27 (2) ◽  
pp. 48-57
Author(s):  
Guanghai Gao ◽  
Yunjing Cui ◽  
Xingqi Qiu
Keyword(s):  
Prediction Model ◽  
Deep Sea ◽  
Nonlinear Partial Differential Equations ◽  
Solution Process ◽  
Cross Flow ◽  
Vortex Induced Vibration ◽  
Sheared Flow ◽  
Wake Oscillator ◽  
Real Size ◽  
Heave Motion

AbstractIt is widely accepted that vortex-induced vibration (VIV) is a major concern in the design of deep sea top-tensioned risers, especially when the riser is subjected to axial parametric excitations. An improved time domain prediction model was proposed in this paper. The prediction model was based on classical van der Pol wake oscillator models, and the impacts of the riser in-line vibration and vessel heave motion were considered. The finite element, Newmark-β and Newton‒Raphson methods were adopted to solve the coupled nonlinear partial differential equations. The entire numerical solution process was realised by a self-developed program based on MATLAB. Comparisons between the numerical calculation and the published experimental test were conducted in this paper. The in-line and cross-flow VIV responses of a real size top-tensioned riser in linear sheared flow were analysed. The effects of the vessel heave amplitude and frequency on the riser VIV were also studied. The results show that the vibration displacements of the riser are larger than the case without vessel heave motion. The vibration modes and frequencies of the riser are also changed due to the vessel heave motion

Cross-Flow Vortex-Induced Vibration Simulation of Flexible Risers Employing Structural Systems of Different Nonlinearities With a Wake Oscillator

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Shuai Meng ◽  
Xuefeng Wang
Keyword(s):  
Structural Model ◽  
Cross Flow ◽  
Linear Structure ◽  
Structural Systems ◽  
Axial Deformation ◽  
Vortex Induced Vibration ◽  
Wake Oscillator ◽  
Structural Nonlinearities ◽  
Flexible Risers ◽  
Vibration Simulation

To achieve a reliable structural model for vortex-induced vibration (VIV) the prediction of flexible risers, this paper employs structural systems with different geometrical nonlinearities (including a linear structure, a nonlinear one, a coupled cross-flow, and axial nonlinear one) and a classical oscillator to simulate cross-flow VIV. By comparing the experimental and simulation results, it is found that when the drag coefficient is assumed to be a fixed constant along the cylinder (i.e., the damping model is linear function of current velocity), it can affect the vibration amplitude considerably and may alter the dominant modes. When the excited mode of VIV is bending-stiffness dominant, the cross-flow structural nonlinearities can have a profound stiffening effect on vibration response. Although the introduction of axial deformation can reduce this function, the coupled cross-flow and axial nonlinearities still have the effect of decreasing the VIV amplitude.

Dynamic Response of a Fluid-Conveying Riser Subject to Vortex-Induced Vibration: Integral Transform Solution

2014 ◽  
Author(s):  
Jijun Gu ◽  
Zhenhua Song ◽  
Kang Zhang ◽  
Liguo Su ◽  
Menglan Duan
Keyword(s):  
Differential Equations ◽  
Dynamic Response ◽  
Integral Transform ◽  
Fluid Velocity ◽  
Critical Evaluation ◽  
Cross Flow ◽  
Coupled System ◽  
Vortex Induced Vibration ◽  
Wake Oscillator ◽  
Line Force

Analysis of dynamic response of a fluid-conveying riser is an important aspect in subsea production system. In the present paper, dynamic response of a pinned-pinned riser subject to external fluid force was solved by the generalized integral transform technique (GITT). A nonlinear wake oscillator models was used to represent the cross-flow and in-line force acting on the riser, leading to a coupled system of second-order Partial Differential Equations (PDEs). The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations (ODEs), which was numerically solved by using the Adams-Moulton and Gear method (DIVPAG) developed by the International Mathematics and Statistics Library (IMSL). Numerical results were presented for comparison to those given by the numerical and experimental results, allowing a critical evaluation of the technique performance. The influence of conveying fluid velocity and mean top tension were evaluated to show that they should not be negligible in numerical simulation of Vortex-Induced Vibration of a long flexible riser.

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.

Massively-Parallel Compressible Discontinuous Galerkin Spectral Element LES of Film Cooling

2015 ◽  
Author(s):  
Joshua L. Camp ◽  
Andrew Duggleby
Keyword(s):  
Discontinuous Galerkin ◽  
Film Cooling ◽  
Stokes Equations ◽  
Density Ratio ◽  
Spectral Element ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Blowing Ratio ◽  
Cooling Hole ◽  
Lift Off

There are many gas turbine flows that are subsonic but still at speeds where gas compresses and the assumptions made in a low-Mach formulation are inadequate. In particular, a low-Mach spectral element solver, NEK5000, was used to perform a LES study of a film cooling hole at a blowing ratio and density ratio of 1.0 and 1.5, respectively. Due to a lack of real compressibility effects in the formulation, the simulation over-predicted the velocity in the hole, leading to large coolant lift-off and poorer film cooling performance than expected. Recently, the capabilities of NEK5000 have been extended to solve the compressible Navier-Stokes equations using the discontinuous Galerkin spectral element method (DGSEM). In this paper, details of the new algorithm are given, and results of the new simulation show vast improvements over the low-Mach code and compare well to previous experimental results.

Fully Turbulent Vortex-Induced Vibration on a Cylinder Structure With a Nonlinear Energy Sink Absorber

2019 ◽  
Author(s):  
Dongyang Chen ◽  
Qing Xiao ◽  
Lei Ma ◽  
Weijun Zhu ◽  
Laith K. Abbas ◽  
...  
Keyword(s):  
Coupled System ◽  
Nonlinear Energy Sink ◽  
Vortex Induced Vibration ◽  
Suppression Effect ◽  
Turbulent Vortex ◽  
Fluid Field ◽  
Energy Sink ◽  
Cfd Method ◽  
Viv Suppression ◽  
Nonlinear Energy

Abstract The fully turbulent vortex induced vibration (VIV) suppression of a circular cylinder through a nonlinear energy sink (NES) having linear damping and nonlinear cubic stiffness is investigated numerically. The computational fluid dynamics (CFD) method is carried out to calculate the fluid field, while a fourth-order Runge-Kutta method is used to calculating the nonlinear structure dynamics of flow-cylinder-NES coupled system. The fluid-structure interaction (FSI) model is validated against VIV experimental data for a cylinder in a uniform flow. The simulation results show that placing an NES structure with suitable parameters inside of the cylinder structure achieves a good VIV amplitudes’ suppression effect and narrows the “lock-in” region.

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.

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