Response Analysis of a Circular Cylinder Undergoing Vortex Induced Vibrations Along Two Degrees of Freedom in the Presence of Noise

2017 ◽  
Author(s):  
M. S. Aswathy ◽  
Sunetra Sarkar
Keyword(s):  
Circular Cylinder ◽  
Degrees Of Freedom ◽  
Nonlinear Dynamical System ◽  
Real Life ◽  
Stochastic Modelling ◽  
Response Analysis ◽  
Mean Flow ◽  
Time Step ◽  
Two Degrees Of Freedom ◽  
Vortex Induced Vibrations

In this study, we perform uncertainty quantification of a nonlinear dynamical system consisting of a circular cylinder undergoing free vibrations with two degrees-of-freedom in the presence of a fluctuating flow-field. Most of the studies in Vortex Induced Vibrations till now are conducted in a deterministic environment. Real life situations involving VIV are subjected to high amount of uncertainties, with the main culprit being the randomness in the incoming flow. Studies involving modelling of the flow with a prescribed set of parameters, represents only an idealistic situation and hence is not sufficient for a complete understanding of the associated dynamics. In this context, we make an attempt to characterise the flow by doing a stochastic modelling on the same. In the current study, we have mathematically modelled the noise through a uniform distribution. These fluctuations are superimposed on a mean flow at every time step. We use a Duffing Van der Pol combined system to model the structure and flow oscillators. It is observed that stochastic modelling brings noticeable changes in the structural responses both quantitatively and qualitatively. The influence of the fluctuations on both the transverse and inline oscillations have been studied. One of the most important changes in the response of the structure is in its amplitude. Noise amplifies the maximum amplitude attained both for transverse and inline oscillations. Further, additional qualitative types of responses are visible in the presence of noise which were absent in the deterministic environment. One such behaviour the ‘intermittent’ response which occurs during the transition from higher to lower amplitudes in the lock-in region. Intermittency is observed both for transverse and inline oscillations. It has been seen that the system undergoes stochastic Phenomenological bifurcations, which have been characterised by the probability density functions of both the transverse and inline responses.

The Numerical Research of Two-Degrees-of-Freedom Vortex-Induced Vibrations of Circular Cylinders

2012 ◽  
Vol 204-208 ◽  
pp. 4598-4601
Author(s):  
Jie Li Fan ◽  
Wei Ping Huang
Keyword(s):  
Degrees Of Freedom ◽  
Amplitude Ratio ◽  
Flow Direction ◽  
Cross Flow ◽  
Circular Cylinders ◽  
Two Degrees Of Freedom ◽  
Line Frequency ◽  
Ansys Cfx ◽  
Vortex Induced Vibrations ◽  
Lock In

The two-degrees-of-freedom of vortex-induced vibration of circular cylinders is numerically simulated with the software ANSYS/CFX. The VIV characteristic, in the two different conditions (A/D=0.07 and A/D=1.0), is analyzed. When A/D is around 0.07, the amplitude ratio of the cylinder’s VIV between in-line and cross-flow direction in the lock-in is lower than that in the lock-out. The in-line frequency is twice of that in cross-flow direction in the lock-out, but in the lock-in, it is the same as that in cross-flow direction and the same as that of lift force. When A/D is around 1.0, the amplitude ratio of the VIV between in-line and cross-flow in the lock-in is obviously larger than that in the lock-out. Both in the lock-in and in the lock-out, the in-line frequency is twice of that in cross-flow direction.

On the Efficiency of Some Recently Developed Integration Algorithms for Offshore Problems

1983 ◽  
Vol 105 (1) ◽  
pp. 73-77 ◽  
Author(s):  
T. K. Datta ◽  
A. M. Sood
Keyword(s):  
Degrees Of Freedom ◽  
Large Time ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Response Analysis ◽  
Time Step ◽  
Beam Elements ◽  
Integration Schemes ◽  
Large Time Step ◽  
Integration Algorithms

The efficiency of some recently developed integration schemes, namely, Hilber’s ∝-method, collocation schemes and large time step integration schemes developed by Argyris, is evaluated by applying them to the response analysis of an idealized offshore tower. The tower is fixed at the base, having an additional mass at the top. For the analysis the tower has been modeled as an assemblage of 2-D beam elements. The dynamic degrees of freedom at each node are taken as those corresponding to the rotational and sway degrees of freedom. Using the normal mode theory the equations of motion have been decoupled except for the generalized loading vector which appear nonlinearly coupled, thus requiring iterative solution at every time step. The results of the study show that the large time step integration schemes developed by Argyris are more efficient than other integration methods considered here.

POD Analysis of the Wake Development of a Pivoted Circular Cylinder Undergoing Vortex Induced Vibrations

2017 ◽  
Author(s):  
E. Marble ◽  
C. Morton ◽  
S. Yarusevych
Keyword(s):  
Circular Cylinder ◽  
Degrees Of Freedom ◽  
Structural Response ◽  
Cylinder Wake ◽  
Time Resolved ◽  
Vortex Induced Vibrations ◽  
Image Velocimetry ◽  
Pod Analysis ◽  
Component Particle ◽  
Proper Orthogonal

Vortex Induced Vibrations (VIV) of a pivoted circular cylinder with two degrees of freedom are investigated experimentally, focusing on quantifying the wake topology. Experiments are performed in a water tunnel for a pivoted cylinder with a fixed mass ratio of 10.8, moment of inertia ratio of 87.0–109.5, and a diameter-based Reynolds number of 3100. The reduced velocity was varied from 4.42 to 9.05 by varying the natural frequency of the structure. Velocity measurements were performed via time-resolved, two-component Particle Image Velocimetry (PIV), synchronized with cylinder displacement measurements. Time and phase-averaging are employed to analyze the wake development and relate it to the structural response. Proper Orthogonal Decomposition (POD) is utilized to gain insight into the development of coherent structures in the cylinder wake. The observed shedding patterns agree well with the Morse & Williamson [1] shedding map except for the cases at the boundary between 2P and non-synchronized shedding. The results show that the cylinder follows an elliptical trajectory with equal frequency of oscillation in streamwise and transverse directions. For the 2P regime, the tilt and direction of trajectory affect the formation and development of vortices in the wake. This results in a distinct asymmetry about the wake centerline in time-averaged statistics.

Two Degrees of Freedom Vortex-Induced Vibration Responses With Zero Mass and Damping at Low Reynolds Number

2013 ◽  
Author(s):  
Kintak Raymond Yu ◽  
Alexander Hay ◽  
Dominique Pelletier ◽  
Simon Corbeil-Létourneau ◽  
Shahin Ghasemi ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Parameter Space ◽  
Degrees Of Freedom ◽  
Low Reynolds Number ◽  
Mass Ratio ◽  
Vortex Induced Vibration ◽  
Two Degrees Of Freedom ◽  
Zero Mass ◽  
Vortex Induced Vibrations ◽  
Low Reynolds

Vortex-induced vibration is an important phenomenon for offshore engineering. For applications like the piping in the deep water oil exploration projects, the mass ratios can be of order of one [1]. Hence, there is a practical need to understand the effects of low mass ratio on vortex-induced vibrations to enhance design safety. The main purpose of this study is to numerically explore the two degrees of freedom (transverse and streamwise) responses of vortex-induced vibrations of a cylinder at low Reynolds number for the limiting case of zero mass ratio and zero damping. We aim to characterize the responses. In particular, we focus on determining the maximum amplitude values. It is a continuation from the work of Etienne and Pelletier who studied such behaviors at very low Reynolds number (Re < 50) [2]. We investigate the responses in the following parameter space: Reynolds number (75 ≤ Re ≤ 175), reduced velocity (5.0 ≤ Ur ≤ 11.0) and mass ratio (m* = {0, 0.1, 1}) with a fully coupled fluid-structure interaction numerical model based on the finite element method. Our results are generally in accordance with those from previous works for the displacement trajectories, force phase diagram, and the trends in frequency response and oscillation amplitude. The maximum transverse amplitude is found to be around 0.9 in the studied parameter space. In particular, with zero mass ratio, the maximum transverse amplitude starts to occur at values of reduced velocity higher than 6.5 for Reynolds number larger than 150. This is in contrast to the results of Etienne and Pelletier [2] who found that the maximum transverse amplitude always occurs at the reduced velocity of 6.5 for Reynolds number less than 50. Furthermore, with zero mass ratio, the maximum transverse amplitude increases when the Reynolds number increases. This behavior differs from what was suggested by Williamson and Govardhan [3] for a cylinder oscillating only in the transverse direction at Reynolds numbers in the range of 85 to 200. They found that the Reynolds number has no influence on the maximum transverse amplitude. We do not notice any response branching in this parameter space. However, the results in the present work clearly consist of two distinct characteristics. This indicates that the investigated mass ratio values encompass the critical mass ratio; whose value is estimated to be around 0.1 to 0.2.

Vortex-induced vibrations of a circular cylinder at low Reynolds numbers

2007 ◽  
Vol 594 ◽  
pp. 463-491 ◽  
Author(s):  
T. K. PRASANTH ◽  
S. MITTAL
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Two Dimensions ◽  
Element Formulation ◽  
Transverse Displacement ◽  
Mean Flow ◽  
Phase Jump ◽  
Vortex Induced Vibrations

Results are presented for a numerical simulation of vortex-induced vibrations of a circular cylinder of low non-dimensional mass (m* = 10) in the laminar flow regime (60 < Re < 200). The natural structural frequency of the oscillator, fN, matches the vortex shedding frequency for a stationary cylinder at Re = 100. This corresponds to fND2/ν = 16.6, where D is the diameter of the cylinder and ν the coefficient of viscosity of the fluid. A stabilized space–time finite element formulation is utilized to solve the incompressible flow equations in primitive variables form in two dimensions. Unlike at high Re, where the cylinder response is known to be associated with three branches, at low Re only two branches are identified: ‘initial’ and ‘lower’. For a blockage of 2.5% and less the onset of synchronization, in the lower Re range, is accompanied by an intermittent switching between two modes with vortex shedding occurring at different frequencies. With higher blockage the jump from the initial to lower branch is hysteretic. Results from free vibrations are compared to the data from experiments for forced vibrations reported earlier. Excellent agreement is observed for the critical amplitude required for the onset of synchronization. The comparison brings out the possibility of hysteresis in forced vibrations. The phase difference between the lift force and transverse displacement shows a jump of almost 180° at, approximately, the middle of the synchronization region. This jump is not hysteretic and it is not associated with any radical change in the vortex shedding pattern. Instead, it is caused by changes in the location and value of the maximum suction on the lower and upper surface of the cylinder. This is observed clearly by comparing the time-averaged flow for a vibrating cylinder for different Re. While the mean flow for Re beyond the phase jump is similar to that for a stationary cylinder, it is associated with a pair of counter-rotating vortices in the near wake for Re prior to the phase jump. The phase jump appears to be one of the mechanisms of the oscillator to self-limit its vibration amplitude.

scholarly journals Nonlinear Bearing Effects on Rotor Dynamic Analysis

1982 ◽  
Author(s):  
R. Colsher ◽  
I. Anwar ◽  
V. Obeid
Keyword(s):  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Nonlinear Effects ◽  
Fluid Film ◽  
Response Analysis ◽  
Time Step ◽  
Tilting Pad ◽  
Rotor Support ◽  
Rotor Dynamic ◽  
Large Rotor

Nonlinear effects due to fluid film bearings become significant when vibratory amplitudes are large. To include these effects in rotor dynamic analysis requires conducting time-transient response analysis, where the fluid film forces are estimated at each time step. The present paper describes an approach where a unique treatment of bearing forces results in an efficient computational scheme for performing time transient analysis. The method developed is applicable to a flexible-rotor system with multi-degrees of freedom. A study conducted on a canned annulus motor pump using tilting pad bearings for the rotor support is described in this paper. The results showed severe loading at the bearings due to the canned annulus forces. Nonlinear effects due to the bearings were found only at large rotor unbalance loads.

Transient Response of Inductrack Systems for Maglev Transport: Part I—A New Transient Model

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Ruiyang Wang ◽  
Bingen Yang
Keyword(s):  
Transient Response ◽  
Degrees Of Freedom ◽  
Permanent Magnets ◽  
Magnetic Interaction ◽  
Response Analysis ◽  
Governing Equations ◽  
Interaction Forces ◽  
Transient Model ◽  
Two Degrees Of Freedom ◽  
Halbach Arrays

Abstract As a new strategy for magnetic levitation, Inductrack systems with Halbach arrays of permanent magnets have been applied to Maglev trains and intensively researched in various projects. In an Inductrack system, the magnetic interaction forces are coupled with the motion of a moving vehicle carrying Halbach arrays, which in many situations results in complicated transient behaviors of the system. In this two-part paper, a new transient model of two degrees-of-freedom for Inductrack systems is proposed. The highlight of this work is that the transient model is developed based on the fundamental principle of physics, without the assumption of steady-state quantities and averaged magnetic forces and with the finite dimensions of Halbach arrays in consideration. In Part I, the transient model is derived through the establishment of a set of nonlinear integro-differential governing equations, and the magnetic interaction forces in the Inductrack system are determined in analytical form. In Part II, the solution of the governing equations, model validation with the previous results in the literature, and transient response analysis via numerical simulation is presented. Although only two degrees-of-freedom have been considered, the approach of modeling and analysis presented in this paper can be extended to general cases of multi-degrees-of-freedom.

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